Journal articles: 'Dirac nodal lines'

1

Fu, B. B., C. J. Yi, T. T. Zhang, M. Caputo, J. Z. Ma, X. Gao, B. Q. Lv, et al. "Dirac nodal surfaces and nodal lines in ZrSiS." Science Advances 5, no. 5 (May 2019): eaau6459. http://dx.doi.org/10.1126/sciadv.aau6459.

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Topological semimetals are characterized by symmetry-protected band crossings, which can be preserved in different dimensions in momentum space, forming zero-dimensional nodal points, one-dimensional nodal lines, or even two-dimensional nodal surfaces. Materials harboring nodal points and nodal lines have been experimentally verified, whereas experimental evidence of nodal surfaces is still lacking. Here, using angle-resolved photoemission spectroscopy (ARPES), we reveal the coexistence of Dirac nodal surfaces and nodal lines in the bulk electronic structures of ZrSiS. As compared with previous ARPES studies on ZrSiS, we obtained pure bulk states, which enable us to extract unambiguously intrinsic information of the bulk nodal surfaces and nodal lines. Our results show that the nodal lines are the only feature near the Fermi level and constitute the whole Fermi surfaces. We not only prove that the low-energy quasiparticles in ZrSiS are contributed entirely by Dirac fermions but also experimentally realize the nodal surface in topological semimetals.

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Shao, Yinming, Zhiyuan Sun, Ying Wang, Chenchao Xu, Raman Sankar, Alexander J. Breindel, Chao Cao, et al. "Optical signatures of Dirac nodal lines in NbAs2." Proceedings of the National Academy of Sciences 116, no. 4 (December 17, 2018): 1168–73. http://dx.doi.org/10.1073/pnas.1809631115.

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Using polarized optical and magneto-optical spectroscopy, we have demonstrated universal aspects of electrodynamics associated with Dirac nodal lines that are found in several classes of unconventional intermetallic compounds. We investigated anisotropic electrodynamics of NbAs2 where the spin-orbit coupling (SOC) triggers energy gaps along the nodal lines. These gaps manifest as sharp steps in the optical conductivity spectra σ1(ω). This behavior is followed by the linear power-law scaling of σ1(ω) at higher frequencies, consistent with our theoretical analysis for dispersive Dirac nodal lines. Magneto-optics data affirm the dominant role of nodal lines in the electrodynamics of NbAs2.

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Zhou, Biao, Shoji Ishibashi, Tatsuru Ishii, Takahiko Sekine, Ryosuke Takehara, Kazuya Miyagawa, Kazushi Kanoda, Eiji Nishibori, and Akiko Kobayashi. "Single-component molecular conductor [Pt(dmdt)2]—a three-dimensional ambient-pressure molecular Dirac electron system." Chemical Communications 55, no. 23 (2019): 3327–30. http://dx.doi.org/10.1039/c9cc00218a.

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Zou, Z. C., P. Zhou, Z. S. Ma, and L. Z. Sun. "Strong anisotropic nodal lines in the TiBe family." Physical Chemistry Chemical Physics 21, no. 16 (2019): 8402–7. http://dx.doi.org/10.1039/c9cp00508k.

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5

Zhang, Honghong, Yuee Xie, Zhongwei Zhang, Chengyong Zhong, Yafei Li, Zhongfang Chen, and Yuanping Chen. "Dirac Nodal Lines and Tilted Semi-Dirac Cones Coexisting in a Striped Boron Sheet." Journal of Physical Chemistry Letters 8, no. 8 (April 3, 2017): 1707–13. http://dx.doi.org/10.1021/acs.jpclett.7b00452.

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Araki, Yasufumi, Jin Watanabe, and Kentaro Nomura. "Nodal Lines and Boundary Modes in Topological Dirac Semimetals with Magnetism." Journal of the Physical Society of Japan 90, no. 9 (September 15, 2021): 094702. http://dx.doi.org/10.7566/jpsj.90.094702.

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7

Cheng, Zhengwang, Zhilong Hu, Shaojian Li, Xinguo Ma, Zhifeng Liu, Mei Wang, Jing He, et al. "Searching for a promising topological Dirac nodal-line semimetal by angle resolved photoemission spectroscopy." New Journal of Physics 23, no. 12 (December 1, 2021): 123026. http://dx.doi.org/10.1088/1367-2630/ac3d51.

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Abstract Topological semimetals, in which conduction and valence bands cross each other at either discrete points or along a closed loop with symmetry protected in the momentum space, exhibited great potential in applications of optical devices as well as heterogeneous catalysts or antiferromagnetic spintronics, especially when the crossing points/lines matches Fermi level (E F). It is intriguing to find the ‘ideal’ topological semimetal material, in which has a band structure with Dirac band-crossing located at E F without intersected by other extraneous bands. Here, by using angle resolved photoemission spectroscopy, we investigate the band structure of the so-called ‘square-net’ topological material ZrGeS. The Brillouin zone (BZ) mapping shows the Fermi surface of ZrGeS is composed by a diamond-shaped nodal line loop at the center of BZ and small electron-like Fermi pockets around X point. The Dirac nodal line band-crossing located right at E F, and shows clearly the linear Dirac band dispersions within a large energy range >1.5 eV below E F, without intersected with other bands. The obtained Fermi velocities and effective masses along Γ–X, Γ–M and M–X high symmetry directions were 4.5–5.9 eV Å and 0–0.50 m e, revealing an anisotropic electronic property. Our results suggest that ZrGeS, as a promising topological nodal line semimetal, could provide a promising platform to investigate the Dirac-fermions related physics and the applications of topological devising.

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Rosmus, Marcin, Natalia Olszowska, Zbigniew Bukowski, Paweł Starowicz, Przemysław Piekarz, and Andrzej Ptok. "Electronic Band Structure and Surface States in Dirac Semimetal LaAgSb2." Materials 15, no. 20 (October 14, 2022): 7168. http://dx.doi.org/10.3390/ma15207168.

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LaAgSb2 is a Dirac semimetal showing charge density wave (CDW) order. Previous angle-resolved photoemission spectroscopy (ARPES) results suggest the existence of the Dirac-cone-like structure in the vicinity of the Fermi level along the Γ–M direction. This paper is devoted to a complex analysis of the electronic band structure of LaAgSb2 by means of ARPES and theoretical studies within the ab initio method as well as tight binding model formulation. To investigate the possible surface states, we performed the direct DFT slab calculation and the surface Green function calculation for the (001) surface. The appearance of the surface states, which depends strongly on the surface, points to the conclusion that LaSb termination is realized in the cleaved crystals. Moreover, the surface states predicted by our calculations at the Γ and X points are found by ARPES. Nodal lines, which exist along the X–R and M–A paths due to crystal symmetry, are also observed experimentally. The calculations reveal other nodal lines, which originate from the vanishing of spin–orbit splitting and are located at the X–M–A–R plane at the Brillouin zone boundary. In addition, we analyze the band structure along the Γ–M path to verify whether Dirac surface states can be expected. Their appearance in this region is not confirmed.

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9

Wu, Rongting, Ze‐Bin Wu, and Ivan Božović. "2D Mg‐Cu Intermetallic Compounds with Nontrivial Band Topology and Dirac Nodal Lines." Advanced Electronic Materials 8, no. 3 (December 23, 2021): 2100927. http://dx.doi.org/10.1002/aelm.202100927.

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10

Sun, Yi, Licheng Wang, Xiaoyan Li, Xiaojing Yao, Xiaokang Xu, Tianxia Guo, Ailei He, Bing Wang, Yongjun Liu, and Xiuyun Zhang. "TM₂B₃ monolayers: Intrinsic anti-ferromagnetism and Dirac nodal line semimetal." Applied Physics Letters 121, no. 18 (October 31, 2022): 183103. http://dx.doi.org/10.1063/5.0113408.

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Searching for two-dimensional materials combining both magnetic order and topological order is of great significance for quantum devices and spintronic devices. Here, a class of two-dimensional transition metal borides, TM2B3 (TM = Ti–Ni), with high stability and stable antiferromagnetic (AFM) orders was predicted by using the first-principles method. The result shows that they possess large magnetic anisotropy energy and high critical temperature. Interestingly, Mn2B3 monolayer is confirmed to be AFM Dirac node line semimetal with several Dirac points near the Fermi level. Detailed analysis of the irreducible representations shows that the nodal lines are protected by the horizontal mirror symmetry Mz. Our findings provide an excellent platform for exploring topological and magnetic materials ready for the next generation of spintronic devices.

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11

Kato, Reizo, and Yoshikazu Suzumura. "A Tight-binding Model of an Ambient-pressure Molecular Dirac Electron System with Open Nodal Lines." Journal of the Physical Society of Japan 89, no. 4 (April 15, 2020): 044713. http://dx.doi.org/10.7566/jpsj.89.044713.

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12

Piéchon, Frédéric, and Yoshikazu Suzumura. "Inversion Symmetry and Wave-Function Nodal Lines of Dirac Electrons in Organic Conductor α-(BEDT-TTF)2I3." Journal of the Physical Society of Japan 82, no. 12 (December 15, 2013): 123703. http://dx.doi.org/10.7566/jpsj.82.123703.

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13

Wang, Jianhua, Hongkuan Yuan, Ying Liu, Gang Zhang, and Xiaotian Wang. "Degenerate line modes in the surface and bulk phonon spectra of orthorhombic NaMgF₃ perovskite." Applied Physics Letters 121, no. 19 (November 7, 2022): 192201. http://dx.doi.org/10.1063/5.0126759.

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Degenerate bulk-line phonon modes have been widely reported in various crystal system types; however, degenerate surface-line phonon modes have only been reported in monoclinic crystal systems, such as SnIP with space group [Formula: see text] (No. 13). Herein, we propose that degenerate surface-line phonon modes can also emerge in solids with orthorhombic structures. Based on first-principle calculations and symmetry analysis, we propose that orthorhombic NaMgF3 fluoroperovskite with space group Pnma (No. 62) is a material candidate with degenerate line states in both the bulk phonon mode and the (010) surface phonon mode. We discovered four closed nodal loops (two type-I and two hybrid-type) on the ky = 0 plane in the bulk phonon mode, all of which coexisted with Dirac points on the Z–U and X–U paths. Moreover, we discovered symmetry-projected doubly degenerate nodal lines along the [Formula: see text] surface path in the (010) surface phonon mode. The proposed degenerate surface-line phonons in NaMgF3 is quite clean and protected by symmetries, which will aid future experimental detection.

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14

Palumbo, Giandomenico. "Topological phase transitions with zero indirect band gaps." Journal of Physics: Condensed Matter 36, no. 26 (April 4, 2024): 26LT01. http://dx.doi.org/10.1088/1361-648x/ad3872.

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Abstract Topological phase transitions in band models are usually associated to the gap closing between the highest valance band and the lowest conduction band, which can give rise to different types of nodal structures, such as Dirac/Weyl points, lines and surfaces. In this work, we show the existence of a different kind of topological phase transitions in one-dimensional systems, which are instead characterized by the presence of a robust zero indirect gap, which occurs when the top of the valence band coincides with the bottom of the conduction band in energy but not in momentum. More specifically, we consider an one-dimensional model on a trimer chain that is protected by both particle–hole and chiral-inversion symmetries. At the critical point, the system supports a Dirac-like point. After introducing a deforming parameter that breaks both inversion and chiral symmetries but preserves their combination, we observe the emergence of a zero indirect band gap, which results to be related to the persymmetry of our Hamiltonian. Importantly, the zero indirect gap holds for a range of values of the deforming parameter. We finally discuss the implementation of the deforming parameter in our tight-binding model through time-periodic (Floquet) driving.

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15

Keles, Ahmet, and Erhai Zhao. "Weyl nodes in periodic structures of superconductors and spin-active materials." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2125 (June 20, 2018): 20150151. http://dx.doi.org/10.1098/rsta.2015.0151.

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Motivated by recent progress in epitaxial growth of proximity structures of s -wave superconductors (S) and spin-active materials (M), in this paper we show that certain periodic structures of S and M can behave effectively as superconductors with pairs of point nodes, near which the low-energy excitations are Weyl fermions. A simple model, where M is described by a Kronig–Penney potential with both spin–orbit coupling and exchange field, is proposed and solved to obtain the phase diagram of the nodal structure, the spin texture of the Weyl fermions, as well as the zero-energy surface states in the form of open Fermi lines (Fermi arcs). As a second example, a lattice model with alternating layers of S and magnetic Z 2 topological insulators is solved. The calculated spectrum confirms previous predictions of Weyl nodes based on the tunnelling Hamiltonian of Dirac electrons. Our results provide further evidence that periodic structures of S and M are well suited for engineering gapless topological superconductors. This article is part of the theme issue ‘Andreev bound states’.

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16

Bhattacharyya, A., P. P. Ferreira, K. Panda, S. H. Masunaga, L. R. de Faria, L. E. Correa, F. B. Santos, et al. "Electron–phonon superconductivity in C-doped topological nodal-line semimetal Zr₅Pt₃: a muon spin rotation and relaxation (μSR) study." Journal of Physics: Condensed Matter 34, no. 3 (November 2, 2021): 035602. http://dx.doi.org/10.1088/1361-648x/ac2bc7.

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Abstract In the present work, we demonstrate that C-doped Zr5Pt3 is an electron–phonon superconductor (with critical temperature T C = 3.8 K) with a nonsymmorphic topological Dirac nodal-line semimetal state, which we report here for the first time. The superconducting properties of Zr5Pt3C0.5 have been investigated by means of magnetization, resistivity, specific heat, and muon spin rotation and relaxation (μSR) measurements. We find that at low temperatures, the depolarization rate is almost constant and it can be well described by a single-band s‐wave model with a superconducting gap of 2Δ(0)/k B T C = 3.84, somewhat higher than the value of BCS theory. From the transverse field μSR analysis, we estimate the London penetration depth λ L = 469 nm, superconducting carrier density n s = 1.83 × 1026 m−3, and effective mass m* = 1.428m e. The zero field μSR confirms the absence of any spontaneous magnetic field in the superconducting ground state. In order to gain additional insights into the electronic ground state of C-doped Zr5Pt3, we also performed first-principles calculations within the framework of density functional theory (DFT). The observed homogenous electronic character of the Fermi surface as well as the mutual decrease of T C and density of states at the Fermi level are consistent with the experimental findings of this study. However, the band structure reveals the presence of robust, gapless fourfold-degenerate nodal lines protected by 63 screw rotations and glide mirror planes. Therefore, Zr5Pt3 represents a novel, unprecedented condensed matter system to investigate the intricate interplay between superconductivity and topology.

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17

Zhang, T. X., A. L. Coughlin, Chi-Ken Lu, J. J. Heremans, and S. X. Zhang. "Recent progress on topological semimetal IrO₂: electronic structures, synthesis, and transport properties." Journal of Physics: Condensed Matter 36, no. 27 (April 10, 2024): 273001. http://dx.doi.org/10.1088/1361-648x/ad3603.

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Abstract 5d transition metal oxides, such as iridates, have attracted significant interest in condensed matter physics throughout the past decade owing to their fascinating physical properties that arise from intrinsically strong spin-orbit coupling (SOC) and its interplay with other interactions of comparable energy scales. Among the rich family of iridates, iridium dioxide (IrO2), a simple binary compound long known as a promising catalyst for water splitting, has recently been demonstrated to possess novel topological states and exotic transport properties. The strong SOC and the nonsymmorphic symmetry that IrO2 possesses introduce symmetry-protected Dirac nodal lines (DNLs) within its band structure as well as a large spin Hall effect in the transport. Here, we review recent advances pertaining to the study of this unique SOC oxide, with an emphasis on the understanding of the topological electronic structures, syntheses of high crystalline quality nanostructures, and experimental measurements of its fundamental transport properties. In particular, the theoretical origin of the presence of the fourfold degenerate DNLs in band structure and its implications in the angle-resolved photoemission spectroscopy measurement and in the spin Hall effect are discussed. We further introduce a variety of synthesis techniques to achieve IrO2 nanostructures, such as epitaxial thin films and single crystalline nanowires, with the goal of understanding the roles that each key parameter plays in the growth process. Finally, we review the electrical, spin, and thermal transport studies. The transport properties under variable temperatures and magnetic fields reveal themselves to be uniquely sensitive and modifiable by strain, dimensionality (bulk, thin film, nanowire), quantum confinement, film texture, and disorder. The sensitivity, stemming from the competing energy scales of SOC, disorder, and other interactions, enables the creation of a variety of intriguing quantum states of matter.

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18

Zhang, Tiantian, T. Yilmaz, E. Vescovo, H. X. Li, R. G. Moore, H. N. Lee, H. Miao, S. Murakami, and M. A. McGuire. "Endless Dirac nodal lines in kagome-metal Ni3In2S2." npj Computational Materials 8, no. 1 (July 19, 2022). http://dx.doi.org/10.1038/s41524-022-00838-z.

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AbstractTopological semimetals are a frontier of quantum materials. In multiband electronic systems, topological band crossings can form closed curves, known as nodal lines. In the presence of spin–orbit coupling and/or symmetry-breaking operations, topological nodal lines can break into Dirac/Weyl nodes and give rise to interesting transport properties, such as the chiral anomaly and giant anomalous Hall effect. Recently, the time-reversal symmetry-breaking induced Weyl fermions are observed in a kagome-metal Co3Sn2S2, triggering interests in nodal-line excitations in multiband kagome systems. Here, using first-principles calculations and symmetry-based indicator theories, we find six endless nodal lines along the stacking direction of kagome layers and two nodal rings in the kagome plane in nonmagnetic Ni3In2S2. The linear dipsersive electronic structure, confirmed by angle-resolved photoemission spectroscopy, induces large magnetoresistance up to 2000% at 9 T. Our results establish a diverse topological landscape of multiband kagome metals.

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19

Scheie, A., Pontus Laurell, P. A. McClarty, G. E. Granroth, M. B. Stone, R. Moessner, and S. E. Nagler. "Dirac Magnons, Nodal Lines, and Nodal Plane in Elemental Gadolinium." Physical Review Letters 128, no. 9 (March 2, 2022). http://dx.doi.org/10.1103/physrevlett.128.097201.

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20

Santos-Cottin, David, Michele Casula, Luca de' Medici, F. Le Mardelé, J. Wyzula, M. Orlita, Yannick Klein, Andrea Gauzzi, Ana Akrap, and R. P. S. M. Lobo. "Optical conductivity signatures of open Dirac nodal lines." Physical Review B 104, no. 20 (November 29, 2021). http://dx.doi.org/10.1103/physrevb.104.l201115.

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21

fernandez, hector, Rafael González-Hernández, Jose Paez, D. M. Hoat, Noboru Takeuchi Tan, Jonathan Guerrero-Sanchez, and Eduardo Pérez-Tijerina. "Two-dimensional antiferromagnetic nodal-line semimetal and spin Hall eﬀect in MnC4." Journal of Physics: Condensed Matter, January 3, 2024. http://dx.doi.org/10.1088/1361-648x/ad1a7a.

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Abstract Nodal-line semimetals, characterized by Dirac-like crossings along one dimensional k-space lines, represent a unique class of topological materials. In this study, we investigate the intriguing properties of room-temperature antiferromagnetic MnC4 and its nodal-line features both with and without spin-orbit coupling (SOC). In the absence of SOC, we identify a doubly degenerate Dirac-nodal line, robustly protected by a combination of time-reversal, mirror, and partial-translation symmetries. Remarkably, this nodal line withstands various external perturbations, including isotropic and anisotropic strain, and torsional deformations, due to the ionic-like bonding between Mn atoms and C clusters. With the inclusion of SOC, we observe a distinctive quasi-Dirac-nodal line that emerges due to the interplay between antiferromagnetism and SOC-induced spin-rotation symmetry breaking. Finally, we observed a robust spin Hall conductivity that aligns with the energy range where the quasi-nodal line appears. This study presents a compelling example of a robust symmetry-protected Dirac-nodal line antiferromagnetic monolayer, which has potential for applications in next-generation spintronic devices.

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22

Hao, Zhanyang, Yongqing Cai, Yixuan Liu, Yuan Wang, Xuelei Sui, Xiao-Ming Ma, Zecheng Shen, et al. "Dirac nodal lines and nodal loops in the topological kagome superconductor CsV3Sb5." Physical Review B 106, no. 8 (August 2, 2022). http://dx.doi.org/10.1103/physrevb.106.l081101.

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23

An, Gijeong, Yoonseok Hwang, Yunjae Kim, Changmo Kang, Yoonah Chung, Minsu Kim, Seyeong Cha, et al. "Double Dirac nodal lines enforced by multiple nonsymmorphic symmetries." Physical Review B 109, no. 15 (April 16, 2024). http://dx.doi.org/10.1103/physrevb.109.155146.

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24

Min, Hong-Guk, Churlhi Lyi, Moon Jip Park, and Youngkuk Kim. "Hosohedral nodal-line superconductivity in hexagonal ABC Dirac semimetals." Communications Physics 7, no. 1 (January 5, 2024). http://dx.doi.org/10.1038/s42005-023-01501-9.

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AbstractThe recently identified hexagonal non-polar phase of KZnBi, an archetypal topological semimetal, has been found to cohost superconductivity on the surface. We propose that KZnBi can realize an unconventional topological superconductor featuring the hosohedral formation of nodal lines and Bogoliubov Fermi surface emerging under a magnetic field. Our density functional theory (DFT)-based low-energy model shows that the nonsymmorphic band degeneracy of the Dirac bands generically triggers topological nodal line superconductivity fostered by inter-band Coulomb interaction. In particular, the nodal lines of the gap resemble a hexagonal hosohedron with the Schläfli symbol of {2, 6}. Remarkably, the holohedral nodal line superconductor defines the topological phase boundary of the Bogoliubov Fermi surface in the limit where time-reversal symmetry is restored. Our results demonstrate that line nodes readily inflate to the Bogoliubov Fermi surface under an external magnetic field. We provide an experimentally verifiable explanation for the observed superconductivity and suggest a feasible platform for observing topological superconductivity in the hexagonal ABC ternary systems class.

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25

Flores-Calderón, Rafael, Leonardo Medel Onofre, and Alberto Martin-Ruiz. "Electrochemical transport in Dirac nodal-line semimetals." Europhysics Letters, June 14, 2023. http://dx.doi.org/10.1209/0295-5075/acde5e.

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Abstract Nodal-line semimetals are topological phases where the conduction and the valence bands cross each other along one-dimensional lines in the Brillouin zone, which are symmetry protected by either spatial symmetries or time-reversal symmetry. In particular, nodal lines protected by the combined $\mathcal{PT}$ symmetry exhibits the parity anomaly of 2D Dirac fermions. In this Letter, we study the electrochemical transport in a $\mathcal{PT}$-symmetric Dirac nodal line semimetals by using the semiclassical Boltzmann equation approach. We derive a general formula for the topological current that includes both the Berry curvature and the orbital magnetic moment. We first evaluate the electrochemical current by introducing a small $\mathcal{PT}$-breaking mass term (which could be induced by inversion-breaking uniaxial strain, pressure, or an external electric field) and apply it to the hexagonal pnictide CaAgP. The electrochemical current vanishes in the zero-mass limit. Introducing a tilting term that does not spoil $\mathcal{PT}$ symmetry that protects the nodal ring, we obtain a finite electrochemical current in the zero-mass limit, which can be regarded as a direct consequence of the parity anomaly. We show that the parity anomaly induced electrochemical transport is also present at nonzero temperatures.

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26

Cameau, Mathis, Natalia Olszowska, Marcin Rosmus, Mathieu G. Silly, Tristan Cren, Axel Malécot, Pascal David, and Marie D'angelo. "Synthesis and characterisation of Cu₂Ge, a new two-dimensional Dirac nodal line semimetal." 2D Materials, May 3, 2024. http://dx.doi.org/10.1088/2053-1583/ad471e.

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Abstract Dirac nodal line semimetals are a novel class of topological materials in which the valence and conduction bands touch along lines in the reciprocal space, with linear dispersion. These materials attract a growing attention, but the experimental realizations for two-dimensional systems are sparse. We report here the first experimental realization of a two-dimensional hexagonal monolayerCu2Ge, grown by evaporation of Ge on a Cu(111) substrate. Through a combination of LEED, XPS and ARPES measurements, we show that the surface presents all characteristics expected from calculations for a free-standing Cu2Ge monolayer. More specifically, the preservation of the two concentric nodal lines around the Γ point indicates weak interactions between the Cu2Ge surface and its Cu(111) substrate, making it an ideal system for the study of Dirac nodal line materials.

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27

Park, Haedong, Wenlong Gao, Xiao Zhang, and Sang Soon Oh. "Nodal lines in momentum space: topological invariants and recent realizations in photonic and other systems." Nanophotonics, February 2, 2022. http://dx.doi.org/10.1515/nanoph-2021-0692.

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Abstract Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely accurate measurements of the Hall conductivity. Recently, new topological effects occurring at Dirac/Weyl points have been better understood and demonstrated using artificial materials such as photonic and phononic crystals, metamaterials and electrical circuits. In comparison, the topological properties of nodal lines, which are one-dimensional degeneracies in momentum space, remain less explored. Here, we explain the theoretical concept of topological nodal lines and review recent and ongoing progress using artificial materials. The review includes recent demonstrations of non-Abelian topological charges of nodal lines in momentum space and examples of nodal lines realized in photonic and other systems. Finally, we will address the challenges involved in both experimental demonstration and theoretical understanding of topological nodal lines.

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28

Zyuzin, Alexander A., and Pascal Simon. "Disorder-induced exceptional points and nodal lines in Dirac superconductors." Physical Review B 99, no. 16 (April 29, 2019). http://dx.doi.org/10.1103/physrevb.99.165145.

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29

Nelson, J. N., J. P. Ruf, Y. Lee, C. Zeledon, J. K. Kawasaki, S. Moser, C. Jozwiak, et al. "Dirac nodal lines protected against spin-orbit interaction in IrO2." Physical Review Materials 3, no. 6 (June 18, 2019). http://dx.doi.org/10.1103/physrevmaterials.3.064205.

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30

Hu, Mengying, Ye Zhang, Xi Jiang, Tong Qiao, Qiang Wang, Shining Zhu, Meng Xiao, and Hui Liu. "Double-bowl state in photonic Dirac nodal line semimetal." Light: Science & Applications 10, no. 1 (August 20, 2021). http://dx.doi.org/10.1038/s41377-021-00614-6.

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AbstractThe past decade has seen a proliferation of topological materials for both insulators and semimetals in electronic systems and classical waves. Topological semimetals exhibit topologically protected band degeneracies, such as nodal points and nodal lines. Dirac nodal line semimetals (DNLS), which own four-fold line degeneracy, have drawn particular attention. DNLSs have been studied in electronic systems but there is no photonic DNLS. Here in this work, we provide a new mechanism, which is unique for photonic systems to investigate a stringent photonic DNLS. When truncated, the photonic DNLS exhibits double-bowl states (DBS), which comprise two sets of perpendicularly polarized surface states. In sharp contrast to nondegenerate surface states in other photonic systems, here the two sets of surface states are almost degenerate over the whole-spectrum range. The DBS and the bulk Dirac nodal ring (DNR) dispersion along the relevant directions, are experimentally resolved.

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Chang, Yu, Xin Wang, Sanggyun Na, and Weiwei Zhang. "Computational Simulation of the Electronic State Transition in the Ternary Hexagonal Compound BaAgBi." Frontiers in Chemistry 9 (November 11, 2021). http://dx.doi.org/10.3389/fchem.2021.796323.

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Topological properties in metals or semimetals have sparked tremendous scientific interest in quantum chemistry because of their exotic surface state behavior. The current research focus is still on discovering ideal topological metal material candidates. We propose a ternary compound with a hexagonal crystal structure, BaAgBi, which was discovered to exhibit two Weyl nodal ring states around the Fermi energy level without the spin–orbit coupling (SOC) effect using theoretical calculations. When the SOC effect is considered, the topological phases transform into two Dirac nodal line states, and their locations also shift from the Weyl nodal rings. The surface states of both the Weyl nodal ring and Dirac nodal lines were calculated on the (001) surface projection using a tight-binding Hamiltonian, and clear drumhead states were observed, with large spatial distribution areas and wide energy variation ranges. These topological features in BaAgBi can be very beneficial for experimental detection, inspiring further experimental investigation.

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32

Liu, Jian-Wei, Fu-Long Shi, Ke Shen, Xiao-Dong Chen, Ke Chen, Wen-Jie Chen, and Jian-Wen Dong. "Antichiral surface states in time-reversal-invariant photonic semimetals." Nature Communications 14, no. 1 (April 11, 2023). http://dx.doi.org/10.1038/s41467-023-37670-y.

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AbstractBesides chiral edge states, the hallmark of quantum Hall insulators, antichiral edge states can exhibit unidirectional transport behavior but in topological semimetals. Although such edge states provide more flexibility for molding the flow of light, their realization usually suffers from time-reversal breaking. In this study, we propose the realization of antichiral surface states in a time-reversal-invariant manner and demonstrate our idea with a three-dimensional (3D) photonic metacrystal. Our system is a photonic semimetal possessing two asymmetrically dispersed Dirac nodal lines. Via dimension reduction, the nodal lines are rendered a pair of offset Dirac points. By introducing synthetic gauge flux, each two-dimensional (2D) subsystem with nonzero kz is analogous to a modified Haldane model, yielding a kz-dependent antichiral surface transport. Through microwave experiments, the bulk dispersion with asymmetric nodal lines and associated twisted ribbon surface states are demonstrated in our 3D time-reversal-invariant system. Although our idea is demonstrated in a photonic system, we propose a general approach to realize antichiral edge states in time-reversal-invariant systems. This approach can be easily extended to systems beyond photonics and may pave the way for further applications of antichiral transport.

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33

Xie, Ying-Ming, Xue-Jian Gao, Xiao Yan Xu, Cheng-Ping Zhang, Jin-Xin Hu, Jason Z. Gao, and K. T. Law. "Kramers nodal line metals." Nature Communications 12, no. 1 (May 24, 2021). http://dx.doi.org/10.1038/s41467-021-22903-9.

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AbstractRecently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.

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34

Damljanović, Vladimir. "Movable but unavoidable nodal lines through high-symmetry points in two-dimensional materials." Progress of Theoretical and Experimental Physics, April 14, 2023. http://dx.doi.org/10.1093/ptep/ptad050.

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Abstract In two-dimensional materials electronic band contacts often give non-trivial contribution to materials topological properties. Besides band contacts at high-symmetry points (HSP) in the Brillouin zone (BZ), like those in graphene, there are nodal lines which form various patterns in the reciprocal space. In this paper we have found all movable nodal lines, whose shape depends on the model, that pass through HSPs in the presence of time-reversal symmetry. Cases with and without spin-orbit coupling are included by studying all eighty layer groups and their double extensions. Eight single and six double groups, including three symmorphic, necessarily host Dirac and Weyl nodal lines that extend through the whole BZ, respectively. Our research might be of interest in designing new materials with interesting physical properties.

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35

Mo, Shi-Cong, Xin-Yue Qiu, Guang-Ye Li, Feng Ning, Zile Wang, Fang Lin, and Shi-Zhang Chen. "Coexistence of Multiple Dirac Nodal Points and Nodal Lines in Two-dimensional Carbon Nanotube Arrays." Materials Today Communications, November 2023, 107590. http://dx.doi.org/10.1016/j.mtcomm.2023.107590.

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36

He, Junwei, and Zhirong Liu. "Dirac cones in bipartite square–octagon lattice: A theoretical approach." Journal of Chemical Physics 159, no. 4 (July 28, 2023). http://dx.doi.org/10.1063/5.0160658.

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Dirac cones are difficult to achieve in a square lattice with full symmetry. Here, we have theoretically investigated a bipartite tetragonal lattice composed of tetragons and octagons using both Tight-Binding (TB) model and density functional theory (DFT) calculations. The TB model predicts that the system exhibits nodal line semi-metallic properties when the on-site energies of all atoms are identical. When the on-site energies differ, the formation of an elliptical Dirac cone is predicted. Its physical properties (anisotropy, tilting, merging, and emerging) can be regulated by the hopping energies. An exact analytical formula is derived to determine the position of the Dirac point by the TB parameters, and a criterion for the existence of Dirac cones is obtained. The “divide-and-coupling” method is applied to understand the origin of the Dirac cone, which involves dividing the bands into several groups and examining the couplings among inter-groups and intra-groups. Various practical systems computed by DFT methods, e.g., t-BN, t-Si, 4,12,2-graphyne, and t-SiC, are also examined, and they all possess nodal lines or Dirac cones as predicted by the TB model. The results provide theoretical foundation for designing novel Dirac materials with tetragonal symmetry.

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Gao, Hongli, Weizhen Meng, Lirong Wang, and Jinxiang Deng. "Multiple-symmetry-protected lantern-like nodal walls in lithium-rich compound LiRuO2." Frontiers in Physics 10 (December 14, 2022). http://dx.doi.org/10.3389/fphy.2022.1081708.

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Topological semimetals have attracted wide attention due to their potential applications, such as electronic devices and electrocatalysis. Herein, based on the first-principles calculations and symmetry analysis, we first report that ternary compound pnnm-type LiRuO2 is a typical lantern-like nodal wall semimetal. Specifically, without considering spin-orbit coupling (SOC), one-dimensional (1D) two-fold degenerate bands on the ki = ±π (i = x, y) planes form the two-dimensional (2D) topological state (namely, nodal surface) under the constraint of multiple symmetry operations. In addition, the symmetry-enforced nodal network is formed on the kz = ±π planes. Finally, these nodal networks and nodal surfaces are coupled together to form lantern-like nodal walls. Remarkably, these topological states are protected by multiple symmetries, namely, nonsymmorphic two-fold screw-rotational symmetry [S2i (i = x, y)], time-reversal symmetry (T), inversion symmetry (I), glide plane symmetry (σz), and two-fold rotational symmetry (C2x/y). In addition, we further discuss the effect of spin-orbit coupling on the lantern-like nodal walls. We find that even if LiRuO2 contains S2z and T symmetries, these nodal surfaces and nodal networks are still broken. Then, due to the existence of I and T symmetries, Dirac nodal lines and Dirac points are formed in the low-energy region. Therefore, our work indicates that LiRuO2 is an excellent material platform for researching multiple topological states.

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Xiao, Shaozhu, Wen-He Jiao, Yu Lin, Qi Jiang, Xiufu Yang, Yunpeng He, Zhicheng Jiang, et al. "Dirac nodal lines in the quasi-one-dimensional ternary telluride TaPtTe5." Physical Review B 105, no. 19 (May 27, 2022). http://dx.doi.org/10.1103/physrevb.105.195145.

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Hao, Zhanyang, Weizhao Chen, Yuan Wang, Jiayu Li, Xiao-Ming Ma, Yu-Jie Hao, Ruie Lu, et al. "Multiple Dirac nodal lines in an in-plane anisotropic semimetal TaNiTe5." Physical Review B 104, no. 11 (September 27, 2021). http://dx.doi.org/10.1103/physrevb.104.115158.

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40

Cai, Yongqing, Jianfeng Wang, Yuan Wang, Zhanyang Hao, Yixuan Liu, Liang Zhou, Xuelei Sui, et al. "Type‐II Dirac Nodal Lines in a Double‐Kagome‐Layered Semimetal." Advanced Electronic Materials, April 28, 2023. http://dx.doi.org/10.1002/aelm.202300212.

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41

Damljanovic, Vladimir, and Nataša Lazić. "Electronic structures near unmovable nodal points and lines in two-dimensional materials." Journal of Physics A: Mathematical and Theoretical, April 21, 2023. http://dx.doi.org/10.1088/1751-8121/accf51.

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Abstract Unmovable nodal points (UNP) and lines (UNL) are band crossings whose positions in the Brillouin zone are unaltered by symmetry preserving perturbations. Not only positions but also the band structure in their vicinity are determined by the little group of wave vectors and its irreducible (co)representations. In this paper, we give the full set of electronic dispersions near all UNPs and UNLs in non-magnetic quasi two-dimensional (2D) materials, both with and without spin-orbit coupling (SOC). Analysis of all layer gray single and double groups gives nineteen different quasiparticles, the great majority of which are unavoidable for a 2D material that belongs to a certain layer group. This includes Weyl and Dirac nodal lines, dispersions with quadratic or cubic splitting, anisotropic Weyl and Dirac cones, whose orientation can be varied by \emph{e.g.}, strain \emph{etc}. We indicated quasiparticles that are robust to SOC. For convenience, our results are concisely presented graphically - as a map, not in a tabular, encyclopedia form. They may be of use as checkpoints and/or for fitting experimentally (via \emph{e.g.}, ARPES) and numerically obtained electronic band structures data, as well as for deeper theoretical investigations.

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42

Sun, Yan, Yang Zhang, Chao-Xing Liu, Claudia Felser, and Binghai Yan. "Dirac nodal lines and induced spin Hall effect in metallic rutile oxides." Physical Review B 95, no. 23 (June 2, 2017). http://dx.doi.org/10.1103/physrevb.95.235104.

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43

Hirayama, Motoaki, Ryo Okugawa, Takashi Miyake, and Shuichi Murakami. "Topological Dirac nodal lines and surface charges in fcc alkaline earth metals." Nature Communications 8, no. 1 (January 11, 2017). http://dx.doi.org/10.1038/ncomms14022.

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Fumega, Adolfo O., Victor Pardo, and A. Cortijo. "Increasing the number of topological nodal lines in semimetals via uniaxial pressure." Scientific Reports 11, no. 1 (May 19, 2021). http://dx.doi.org/10.1038/s41598-021-90165-y.

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AbstractThe application of pressure has been demonstrated to induce intriguing phase transitions in topological nodal-line semimetals. In this work we analyze how uniaxial pressure affects the topological character of BaSn$$_2$$ 2 , a Dirac nodal-line semimetal in the absence of spin-orbit coupling. Using calculations based on the density functional theory and a model tight-binding Hamiltonian, we find the emergence of a second nodal line for pressures higher than 4 GPa. We examine the topological features of both phases demonstrating that a nontrivial character is present in both of them. Thus, providing evidence of a topological-to-topological phase transition in which the number of topological nodal lines increases. The orbital overlap increase between Ba $$d_{xz}$$ d xz and $$d_{yz}$$ d yz orbitals and Sn $$p_z$$ p z orbitals and the preservation of crystal symmetries are found to be responsible for the advent of this transition. Furthermore, we pave the way to experimentally test this kind of transition by obtaining a topological relation between the zero-energy modes that arise in each phase when a magnetic field is applied.

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45

Sahoo, Biswajit, Alex Frano, and Eric E. Fullerton. "Efficient charge to spin conversion in iridium oxide thin films." Applied Physics Letters 123, no. 3 (July 17, 2023). http://dx.doi.org/10.1063/5.0153329.

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Many 5d transition metal oxides have a unique electronic structure, where the density of states near the Fermi level is dominated by only 5d electrons with strong spin–orbit coupling. IrO2, a Dirac nodal line semi-metal, is the simplest of these oxides. The presence of 5d electrons and gap opening of Dirac nodal lines via strong spin–orbit coupling allows for the hybridization of the 5d electrons of the oxide with the itinerant d electrons of a ferromagnet, while simultaneously increasing the intrinsic spin Hall effect. We report large charge-to-spin conversion in thin films of this material using spin-torque ferromagnetic resonance experiments. By independently performing line shape analysis and linewidth modulation experiments, we conclusively determine the spin Hall angle of optimized IrO2 films to be ∼8 times larger than that of Pt.

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46

Herrera, Miguel A. J., and Dario Bercioux. "Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice." Communications Physics 6, no. 1 (March 8, 2023). http://dx.doi.org/10.1038/s42005-023-01156-6.

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AbstractNon-symmorphic symmetries protect Dirac nodal lines and cones in lattice systems. Here, we investigate the spectral properties of a two-dimensional lattice belonging to a non-symmorphic group. Specifically, we look at the herringbone lattice, characterized by two sets of glide symmetries applied in two orthogonal directions. We describe the system using a nearest-neighbor tight-binding model containing horizontal and vertical hopping terms. We find two nonequivalent Dirac cones inside the first Brillouin zone along a high-symmetry path. We tune these Dirac cones’ positions by breaking the lattice symmetries using on-site potentials. These Dirac cones can merge into a semi-Dirac cone or unfold along a high-symmetry path. Finally, we perturb the system by applying a dimerization of the hopping terms. We report a flow of Dirac cones inside the first Brillouin zone describing quasi-hyperbolic curves. We present an implementation in terms of CO atoms placed on the top of a Cu(111) surface.

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47

Jovic, Vedran, Roland J. Koch, Swarup K. Panda, Helmuth Berger, Philippe Bugnon, Arnaud Magrez, Kevin E. Smith, et al. "Dirac nodal lines and flat-band surface state in the functional oxide RuO2." Physical Review B 98, no. 24 (December 3, 2018). http://dx.doi.org/10.1103/physrevb.98.241101.

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48

Yuan, Danwen, Changming Yue, Yuefang Hu, and Wei Zhang. "Nontrivial topological phases in ternary borides M₂XB₂ (M = W, Mo; X = Co, Ni)." Chinese Physics Letters, February 28, 2024. http://dx.doi.org/10.1088/0256-307x/41/3/037304.

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Abstract The nontrivial band topologies protected by certain symmetries have attracted significant interest in condensed matter physics. The discoveries of nontrivial topological phases in real materials provide a series of archetype materials to further explore the topological physics. Ternary borides M2XB2 (M = W, Mo; X = Co, Ni) have been widely investigated as the wear-resistant and high-hardness materials. In this work, based on first-principles calculations, we find the nontrivial topological properties in these materials. Taking W2NiB2 as an example, this material shows the nodal line semimetal state in absence of spin-orbit coupling. Two types of nodal lines appear near the Fermi level simultaneously. One is protected by the combined space-inversion and time-reversal symmetry, and the other one is by the mirror symmetry. Part of these two types nodal lines form nodal chains. When spin-orbit coupling is included, these nodal lines are fully gapped and the system becomes a strong topological insulator with nontrivial Z2 index (1; 000). Our calculations demonstrate that a nontrivial spin-momentum locked surface Dirac cone appears on the ($\overline 1$10) surface. We also find that other isostructural ternary borides Mo2NiB2, Mo2CoB2 and W2CoB2 possess similar topological band structures. Therefore, our work not only enriches the understanding of band topology for ternary borides, but also lays the foundation for the further study of topological phases manipulation and potential spintronic applications in realistic materials.

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Xiong, Zhongfei, Ruo-Yang Zhang, Rui Yu, C. T. Chan, and Yuntian Chen. "Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals." Light: Science & Applications 9, no. 1 (October 19, 2020). http://dx.doi.org/10.1038/s41377-020-00382-9.

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Abstract It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups. We discover that in an AB-layer-stacked photonic crystal composed of anisotropic dielectrics, the unique photonic band connectivity leads to a new kind of symmetry-enforced triply degenerate points at the nexuses of two nodal rings and a Kramers-like nodal line. The emergence and intersection of the line nodes are guaranteed by a generalized 1/4-period screw rotation symmetry of Maxwell’s equations. The bands with a constant kz and iso-frequency surfaces near a nexus point both disperse as a spin-1 Dirac-like cone, giving rise to exotic transport features of light at the nexus point. We show that spin-1 conical diffraction occurs at the nexus point, which can be used to manipulate the charges of optical vortices. Our work reveals that Maxwell’s equations can have hidden symmetries induced by the fractional periodicity of the material tensor components and hence paves the way to finding novel topological nodal structures unique to photonic systems.

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Hou, Wenjie, Jian Liu, Xi Zuo, Jian Xu, Xueying Zhang, Desheng Liu, Mingwen Zhao, Zhen-Gang Zhu, Hong-Gang Luo, and Weisheng Zhao. "Prediction of crossing nodal-lines and large intrinsic spin Hall conductivity in topological Dirac semimetal Ta3As family." npj Computational Materials 7, no. 1 (March 5, 2021). http://dx.doi.org/10.1038/s41524-021-00504-w.

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AbstractTopological insulators (TIs) are considered as ideal platforms for generating large spin Hall conductivity (SHC), however, the bulk carrier problem, which is unavoidable in TIs, hinders their practical applications. Recently, topological semimetals (TSMs) have been proposed to achieve large SHC to replace TIs. However, the ideal TSM candidates with large SHC are still lacking. In terms of first-principles calculations, we predict that Ta3As family compounds exhibit complex crossing nodal-lines (CNL) properties in absence of the spin-orbit coupling (SOC). However, they transfer to Dirac TSMs under the influence of strong SOC, and present large SHC around Fermi level in particular. Remarkably, the SHC value of Ta3Y (Y = As, Sb, Bi) is around 1500–1700 $$(\hbar /e)({\mathrm{{\Omega}}} \cdot {\mathrm{cm}})^{ - 1}$$ ( ħ / e ) ( Ω ⋅ cm ) − 1 , which is comparable to noble metal Pt and much larger than TIs, Weyl TSMs, and 4d/5d transition metals. Our work not only suggests a kind of TSM family with interesting Dirac CNL around Fermi level, but also paves the way for searching large intrinsic SHC materials in complex CNL TSM systems.

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Journal articles on the topic 'Dirac nodal lines'

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