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Artículos de revistas sobre el tema "Mott materials"

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Autor: Grafiati

Publicado: 7 de julio de 2024

Última modificación: 7 de julio de 2024

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1

Kiffner, Martin, Jonathan Coulthard, Frank Schlawin, Arzhang Ardavan y Dieter Jaksch. "Mott polaritons in cavity-coupled quantum materials". New Journal of Physics 21, n.º 7 (31 de julio de 2019): 073066. http://dx.doi.org/10.1088/1367-2630/ab31c7.

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2

Furukawa, Tetsuya, Kazuya Miyagawa, Hiromi Taniguchi, Reizo Kato y Kazushi Kanoda. "Quantum criticality of Mott transition in organic materials". Nature Physics 11, n.º 3 (9 de febrero de 2015): 221–24. http://dx.doi.org/10.1038/nphys3235.

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3

Feng, Dong-Lai. "Mott physics — one of main themes in quantum materials". Acta Physica Sinica 72, n.º 23 (2023): 237101. http://dx.doi.org/10.7498/aps.72.20231508.

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<sec>The competition and cooperation between the itinerancy behavior and localization behavior of electrons in correlated quantum materials, known as Mott physics, is the physical mechanism behind the diverse states of many quantum materials. This article reviews the manifestation of Mott physics in various quantum materials and establishes it as one of the main themes of quantum materials. Finding and understanding its ever-changing ways of manifestation is one of the central tasks of experimental research on condensed matter physics.</sec><sec>Specifically, the filling-control route of Mott transition is illustrated by exampling the surface K-dosed Sr<sub>2</sub>IrO<sub>4</sub>, which exhibits d-wave gap, pseudogap behavior in underdoped regime, and phase separation with inhomogeneous electronic state distribution. All of these show strong resemblances to the doped cuprate superconductors, another prototypical filling-control type of Mott transition case. On the other hand, the bandwidth-control route of Mott transition could be found in NiS<sub>2–<i>x</i></sub>Se<sub><i>x</i></sub>, where its bandwidth continuously decreases with Se concentration decreasing, until it becomes an insulator. In addition, the essence of various ways of doping in iron-based superconductors is to change their bandwidths. The superconductivity shows up at intermediate bandwidth with moderate correlations, and it diminishes when the bandwidth is large and the electron correlations are weak. For heavily electron-doped iron-selenides, there is even a Mott insulator phase with strong correlations.</sec><sec>For carbon based materials, the phase transition between the antiferromagnetic insulator and superconducting state of A15 Cs<sub>3</sub>C<sub>60</sub> as the volume of fullerene anions decreases could be understood in terms of a bandwidth-control Mott transition; the insulator-superconductor transition discovered in electrically gated twisted-angle bilayer graphene could be understood as a filling-control Mott transition.</sec><sec>For f electron systems, the interplay between itinerancy and localization dominates the heavy fermion behavior and their ground states. The behaviors of the f electrons are demonstrated by using the angle-resolved photoemission data of CeCoIn<sub>5</sub>, whose f electron band becomes more coherent with temperature decreasing, and the c-f hybridization is thus enhanced and the band mass of conduction band continuously increases. The c-f hybridization behaviors of CeCoIn<sub>5,</sub> CeIrIn<sub>5</sub>, and CeRhIn<sub>5</sub> are compared with each other, and the differences in hybridization strength put their ground states into different regimes of the Doniach phase diagram. Similarly, the Skutterudites 4f<sup>2</sup> Kondo lattice system PrOs<sub>4</sub>Sb<sub>12</sub> and its sibling 4f<sup>1</sup> system CeOs<sub>4</sub>Sb<sub>12</sub> also have different ground states due to a slight difference in their c-f hybridization strengths.</sec>

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4

Wang, Yue, Kyung-Mun Kang, Minjae Kim, Hong-Sub Lee, Rainer Waser, Dirk Wouters, Regina Dittmann, J. Joshua Yang y Hyung-Ho Park. "Mott-transition-based RRAM". Materials Today 28 (septiembre de 2019): 63–80. http://dx.doi.org/10.1016/j.mattod.2019.06.006.

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5

Inoue, Isao H. y Marcelo J. Rozenberg. "Taming the Mott Transition for a Novel Mott Transistor". Advanced Functional Materials 18, n.º 16 (22 de agosto de 2008): 2289–92. http://dx.doi.org/10.1002/adfm.200800558.

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6

Gavrichkov, Vladimir A. "A simple metal–insulator criterion for the doped Mott–Hubbard materials". Solid State Communications 208 (abril de 2015): 11–14. http://dx.doi.org/10.1016/j.ssc.2015.02.014.

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7

Tan, Yuting, Vladimir Dobrosavljević y Louk Rademaker. "How to Recognize the Universal Aspects of Mott Criticality?" Crystals 12, n.º 7 (30 de junio de 2022): 932. http://dx.doi.org/10.3390/cryst12070932.

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In this paper we critically discuss several examples of two-dimensional electronic systems displaying interaction-driven metal-insulator transitions of the Mott (or Wigner–Mott) type, including dilute two-dimension electron gases (2DEG) in semiconductors, Mott organic materials, as well as the recently discovered transition-metal dichalcogenide (TMD) moiré bilayers. Remarkably similar behavior is found in all these systems, which is starting to paint a robust picture of Mott criticality. Most notable, on the metallic side a resistivity maximum is observed whose temperature scale vanishes at the transition. We compare the available experimental data on these systems to three existing theoretical scenarios: spinon theory, Dynamical Mean Field Theory (DMFT) and percolation theory. We show that the DMFT and percolation pictures for Mott criticality can be distinguished by studying the origins of the resistivity maxima using an analysis of the dielectric response.

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8

Brandow, Baird. "The physics of Mott electron localization". Journal of Alloys and Compounds 181, n.º 1-2 (abril de 1992): 377–96. http://dx.doi.org/10.1016/0925-8388(92)90334-6.

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9

LaGasse, Samuel W., Prathamesh Dhakras, Kenji Watanabe, Takashi Taniguchi y Ji Ung Lee. "Schottky-Mott Limit: Gate-Tunable Graphene-WSe2 Heterojunctions at the Schottky-Mott Limit (Adv. Mater. 24/2019)". Advanced Materials 31, n.º 24 (junio de 2019): 1970169. http://dx.doi.org/10.1002/adma.201970169.

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10

H�fner, S. "Mott insulation in transition metal compounds". Zeitschrift f�r Physik B Condensed Matter 61, n.º 2 (junio de 1985): 135–38. http://dx.doi.org/10.1007/bf01307767.

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11

Cuono, Giuseppe y Carmine Autieri. "Mott Insulator Ca2RuO4 under External Electric Field". Materials 15, n.º 19 (26 de septiembre de 2022): 6657. http://dx.doi.org/10.3390/ma15196657.

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We have investigated the structural, electronic and magnetic properties of the Mott insulator Ca2RuO4 under the application of a static external electric field in two regimes: bulk systems at small fields and thin films at large electric fields. Ca2RuO4 presents S- and L-Pbca phases with short and long c lattice constants and with large and small band gaps, respectively. Using density functional perturbation theory, we have calculated the Born effective charges as response functions. Once we break the inversion symmetry by off-centering the Ru atoms, we calculate the piezoelectric properties of the system that suggest an elongation of the system under an electric field. Finally, we investigated a four-unit cell slab in larger electric fields, and we found insulator–metal transitions induced by the electric field. By looking at the local density of states, we have found that the gap gets closed on surface layers while the rest of the sample is insulating. Correlated to the electric-field-driven gap closure, there is an increase in the lattice constant c. Regarding the magnetic properties, we have identified two phase transitions in the magnetic moments with one surface that gets completely demagnetized at the largest field investigated. In all cases, the static electric field increases the lattice constant c and reduces the band gap of Ca2RuO4, playing a role in the competition between the L-phase and the S-phase.

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12

Porai-Koshits, E. A. "Recipient of the 1988 Mott Award". Journal of Non-Crystalline Solids 111, n.º 1 (septiembre de 1989): v. http://dx.doi.org/10.1016/0022-3093(89)90413-4.

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13

Eric Spear, Walter y Robert A. Weeks. "Recipient of the 1989 Mott award". Journal of Non-Crystalline Solids 124, n.º 2-3 (octubre de 1990): i. http://dx.doi.org/10.1016/0022-3093(90)90250-p.

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14

Lashley, J. C., K. Gofryk, B. Mihaila, J. L. Smith y E. K. H. Salje. "Thermal avalanches near a Mott transition". Journal of Physics: Condensed Matter 26, n.º 3 (18 de diciembre de 2013): 035701. http://dx.doi.org/10.1088/0953-8984/26/3/035701.

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15

Huda, Muhammad N., Mowafak M. Al-Jassim y John A. Turner. "Mott insulators: An early selection criterion for materials for photoelectrochemical H2 production". Journal of Renewable and Sustainable Energy 3, n.º 5 (septiembre de 2011): 053101. http://dx.doi.org/10.1063/1.3637367.

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16

Pesin, Dmytro y Leon Balents. "Mott physics and band topology in materials with strong spin–orbit interaction". Nature Physics 6, n.º 5 (21 de marzo de 2010): 376–81. http://dx.doi.org/10.1038/nphys1606.

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17

Scheiderer, Philipp, Matthias Schmitt, Judith Gabel, Michael Zapf, Martin Stübinger, Philipp Schütz, Lenart Dudy et al. "Tailoring Materials for Mottronics: Excess Oxygen Doping of a Prototypical Mott Insulator". Advanced Materials 30, n.º 25 (7 de mayo de 2018): 1706708. http://dx.doi.org/10.1002/adma.201706708.

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18

Pollak, Michael. "Electrons in Anderson–Mott insulators". European Physical Journal Special Topics 227, n.º 15-16 (28 de enero de 2019): 2221–40. http://dx.doi.org/10.1140/epjst/e2018-800055-9.

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19

Nichols, Matthew A., Lawrence W. Cheuk, Melih Okan, Thomas R. Hartke, Enrique Mendez, T. Senthil, Ehsan Khatami, Hao Zhang y Martin W. Zwierlein. "Spin transport in a Mott insulator of ultracold fermions". Science 363, n.º 6425 (6 de diciembre de 2018): 383–87. http://dx.doi.org/10.1126/science.aat4387.

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Strongly correlated materials are expected to feature unconventional transport properties, such that charge, spin, and heat conduction are potentially independent probes of the dynamics. In contrast to charge transport, the measurement of spin transport in such materials is highly challenging. We observed spin conduction and diffusion in a system of ultracold fermionic atoms that realizes the half-filled Fermi-Hubbard model. For strong interactions, spin diffusion is driven by super-exchange and doublon-hole–assisted tunneling, and strongly violates the quantum limit of charge diffusion. The technique developed in this work can be extended to finite doping, which can shed light on the complex interplay between spin and charge in the Hubbard model.

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20

Rajbhandari, A., K. Manandhar y R. R. Pradhananga. "Mott-Schottky Analysis of Laboratory Prepared Ag2S-AgI Membrane Electrode". Journal of Nepal Chemical Society 28 (23 de mayo de 2013): 89–93. http://dx.doi.org/10.3126/jncs.v28i0.8113.

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Mott-Schottky analysis has been carried out to study the semiconducting behavior of Ag2S-AgI material, which is used as membrane material in iodide ion sensors. Polycrystalline Ag2S-AgI materials with mixing ratios 1:1wasprepared by co-precipitation method and Mott-Schottky analysis was carried out. The impedance was recorded using a Solartron 1280 Schlumberger frequency response analyzer at 5 KHz and 10 mV perturbing signal. A straight line with a positive slope is observed between + 0.2 V to -0.2 V (SSE) indicating n-type semiconductor behavior of polycrystalline Ag2S-AgI membrane. The donor concentration ND was calculated from the slope using dielectric constant of Ag2S-AgI. The values obtained are ~ 6 orders of magnitude lower than in metals. This is an important implication for the charge and potential distribution at the semiconductor/electrolyte interface. The Mott Schottky analysis hasshown that the present materials are n-type semiconductors with donor defect concentration of 7.4x1017/cm3. DOI: http://dx.doi.org/10.3126/jncs.v28i0.8113 Journal of Nepal Chemical Society Vol. 28, 2011 Page: 89-93 Uploaded Date: May 24, 2013

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21

Zheng, Ming y Pengfei Guan. "Coupled straintronic–optoelectronic effect in Mott oxide films". Nanoscale 14, n.º 14 (2022): 5545–50. http://dx.doi.org/10.1039/d2nr01099b.

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22

Marianetti, C. A., G. Kotliar y G. Ceder. "A first-order Mott transition in LixCoO2". Nature Materials 3, n.º 9 (22 de agosto de 2004): 627–31. http://dx.doi.org/10.1038/nmat1178.

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23

Manuel, L. O., C. J. Gazza, A. E. Feiguin y A. E. Trumper. "The spectral function for Mott insulating surfaces". Journal of Physics: Condensed Matter 15, n.º 17 (22 de abril de 2003): 2435–40. http://dx.doi.org/10.1088/0953-8984/15/17/301.

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24

Casado, J. M., J. H. Harding y G. J. Hyland. "Small-polaron hopping in Mott-insulating UO2". Journal of Physics: Condensed Matter 6, n.º 25 (20 de junio de 1994): 4685–98. http://dx.doi.org/10.1088/0953-8984/6/25/007.

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25

Stefanovich, G., A. Pergament y D. Stefanovich. "Electrical switching and Mott transition in VO2". Journal of Physics: Condensed Matter 12, n.º 41 (26 de septiembre de 2000): 8837–45. http://dx.doi.org/10.1088/0953-8984/12/41/310.

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26

Logan, David E., Martin R. Galpin y Jonathan Mannouch. "Mott transitions in the periodic Anderson model". Journal of Physics: Condensed Matter 28, n.º 45 (12 de septiembre de 2016): 455601. http://dx.doi.org/10.1088/0953-8984/28/45/455601.

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27

Logan, David E. y Martin R. Galpin. "Mott insulators and the doping-induced Mott transition within DMFT: exact results for the one-band Hubbard model". Journal of Physics: Condensed Matter 28, n.º 2 (11 de diciembre de 2015): 025601. http://dx.doi.org/10.1088/0953-8984/28/2/025601.

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28

Ciorciaro, L., T. Smoleński, I. Morera, N. Kiper, S. Hiestand, M. Kroner, Y. Zhang et al. "Kinetic magnetism in triangular moiré materials". Nature 623, n.º 7987 (15 de noviembre de 2023): 509–13. http://dx.doi.org/10.1038/s41586-023-06633-0.

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AbstractMagnetic properties of materials ranging from conventional ferromagnetic metals to strongly correlated materials such as cuprates originate from Coulomb exchange interactions. The existence of alternate mechanisms for magnetism that could naturally facilitate electrical control has been discussed theoretically1–7, but an experimental demonstration8 in an extended system has been missing. Here we investigate MoSe2/WS2 van der Waals heterostructures in the vicinity of Mott insulator states of electrons forming a frustrated triangular lattice and observe direct evidence of magnetic correlations originating from a kinetic mechanism. By directly measuring electronic magnetization through the strength of the polarization-selective attractive polaron resonance9,10, we find that when the Mott state is electron-doped, the system exhibits ferromagnetic correlations in agreement with the Nagaoka mechanism.

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29

Belitz, D. y T. R. Kirkpatrick. "Order parameter description of the Anderson-Mott transition". Zeitschrift f�r Physik B Condensed Matter 98, n.º 4 (diciembre de 1995): 513–26. http://dx.doi.org/10.1007/bf01320853.

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30

Brazovskii, S., P. Monceau y F. Nad. "The ferroelectric Mott-Hubbard phase in organic conductors". Synthetic Metals 137, n.º 1-3 (abril de 2003): 1331–33. http://dx.doi.org/10.1016/s0379-6779(02)01076-7.

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31

Kawasugi, Yoshitaka, Kazuhiro Seki, Satoshi Tajima, Jiang Pu, Taishi Takenobu, Seiji Yunoki, Hiroshi M. Yamamoto y Reizo Kato. "Two-dimensional ground-state mapping of a Mott-Hubbard system in a flexible field-effect device". Science Advances 5, n.º 5 (mayo de 2019): eaav7282. http://dx.doi.org/10.1126/sciadv.aav7282.

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A Mott insulator sometimes induces unconventional superconductivity in its neighbors when doped and/or pressurized. Because the phase diagram should be strongly related to the microscopic mechanism of the superconductivity, it is important to obtain the global phase diagram surrounding the Mott insulating state. However, the parameter available for controlling the ground state of most Mott insulating materials is one-dimensional owing to technical limitations. Here, we present a two-dimensional ground-state mapping for a Mott insulator using an organic field-effect device by simultaneously tuning the bandwidth and bandfilling. The observed phase diagram showed many unexpected features such as an abrupt first-order superconducting transition under electron doping, a recurrent insulating phase in the heavily electron-doped region, and a nearly constant superconducting transition temperature in a wide parameter range. These results are expected to contribute toward elucidating one of the standard solutions for the Mott-Hubbard model.

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32

Ioffe, L. B. y A. J. Millis. "D-wave superconductivity in doped Mott insulators". Journal of Physics and Chemistry of Solids 63, n.º 12 (diciembre de 2002): 2259–68. http://dx.doi.org/10.1016/s0022-3697(02)00254-8.

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33

Grzybowski, Przemysław R. y Ravindra W. Chhajlany. "Hubbard-I approach to the Mott transition". physica status solidi (b) 249, n.º 11 (6 de agosto de 2012): 2231–38. http://dx.doi.org/10.1002/pssb.201248194.

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34

Hansmann, P., A. Toschi, G. Sangiovanni, T. Saha-Dasgupta, S. Lupi, M. Marsi y K. Held. "Mott-Hubbard transition in V2 O3 revisited". physica status solidi (b) 250, n.º 7 (20 de marzo de 2013): 1251–64. http://dx.doi.org/10.1002/pssb.201248476.

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35

Baskaran, Ganapathy. "Impurity band Mott insulators: a new route to highTcsuperconductivity". Science and Technology of Advanced Materials 9, n.º 4 (diciembre de 2008): 044104. http://dx.doi.org/10.1088/1468-6996/9/4/044104.

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36

Martelo, L. M., M. Dzierzawa, L. Siffert y D. Baeriswyl. "Mott-Hubbard transition and antiferromagnetism on the honeycomb lattice". Zeitschrift für Physik B Condensed Matter 103, n.º 2 (junio de 1996): 335–38. http://dx.doi.org/10.1007/s002570050384.

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37

Pustogow, A., M. Bories, A. Löhle, R. Rösslhuber, E. Zhukova, B. Gorshunov, S. Tomić et al. "Quantum spin liquids unveil the genuine Mott state". Nature Materials 17, n.º 9 (6 de agosto de 2018): 773–77. http://dx.doi.org/10.1038/s41563-018-0140-3.

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38

Sipos, B., A. F. Kusmartseva, A. Akrap, H. Berger, L. Forró y E. Tutiš. "From Mott state to superconductivity in 1T-TaS2". Nature Materials 7, n.º 12 (9 de noviembre de 2008): 960–65. http://dx.doi.org/10.1038/nmat2318.

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39

NAYAK, CHETAN y FRANK WILCZEK. "POSSIBLE ELECTRONIC STRUCTURE OF DOMAIN WALLS IN MOTT INSULATORS". International Journal of Modern Physics B 10, n.º 17 (30 de julio de 1996): 2125–36. http://dx.doi.org/10.1142/s0217979296000970.

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We discuss the quantum numbers of domain walls of minimal length induced by doping Mott insulators, carefully distinguishing between holon and hole walls. We define a minimal wall hypothesis that uniquely correlates the observed spatial structure with the doping level for the low-temperature commensurate insulating state of La 2−x Ba x CuO 4 and related materials at x = ⅛. We remark that interesting walls can be supported not only by conventional antiferromagnetic but also by orbital antiferromagnetic (staggered flux phase, d-density) bulk order. We speculate on the validity of the minimal wall hypothesis more generally, and argue that it plausibly explains several of the most striking anomalous features of the cuprate high-temperature superconductors.

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40

Craco, L., M. S. Laad y E. Müller-Hartmann. "Metallizing the Mott insulator TiOCl by electron doping". Journal of Physics: Condensed Matter 18, n.º 48 (17 de noviembre de 2006): 10943–53. http://dx.doi.org/10.1088/0953-8984/18/48/021.

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41

Saket, Abhinav y Rajarshi Tiwari. "Orbital Mott transition in two dimensional pyrochlore lattice". Journal of Physics: Condensed Matter 32, n.º 25 (30 de marzo de 2020): 255601. http://dx.doi.org/10.1088/1361-648x/ab7a4b.

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42

Suzuki, Yuta, Seiji Shibasaki, Yoshihiro Kubozono y Takashi Kambe. "Antiferromagnetic resonance in the Mott insulator fcc-Cs3C60". Journal of Physics: Condensed Matter 25, n.º 36 (8 de agosto de 2013): 366001. http://dx.doi.org/10.1088/0953-8984/25/36/366001.

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43

Janotti, A., L. Bjaalie, B. Himmetoglu y C. G. Van de Walle. "Band alignment at band-insulator/Mott-insulator interfaces". physica status solidi (RRL) - Rapid Research Letters 8, n.º 6 (14 de mayo de 2014): 577–82. http://dx.doi.org/10.1002/pssr.201409088.

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44

Mitra, Sanchali y Santanu Mahapatra. "Schottky–Mott limit in graphene inserted 2D semiconductor–metal interfaces". Journal of Applied Physics 132, n.º 14 (14 de octubre de 2022): 145301. http://dx.doi.org/10.1063/5.0106620.

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The insertion of a graphene (or h-BN) layer in a two-dimensional (2D) MoS2–metal interface to de-pin the Fermi level has been a common strategy in experiments. Recently, however, the 2D material space has expanded much beyond transition metal dichalcogenides, and it is not clear if the same strategy will work for other materials. Here, we select a family of twelve emerging, commercially available 2D semiconductors with the work function range of 3.8–6.1 eV and study their interfaces with metals in the presence and absence of the graphene buffer layer. Using the density functional theory, we show that the graphene buffer layer preserves the ideal Schottky–Mott rule to a great extent when the interfaces are made with Ag and Ti. However, the h-BN buffer layer does not yield a similar performance since its electrons are not as localized as graphene. It is further observed that even graphene is not very effective in preserving the ideal Schottky–Mott rule while interfacing with high work function metals (Au, Pd, and Pt). The quantum chemical insights presented in this paper could aid in the design of high-performance electronic devices with low contact resistance based on newly developed 2D materials.

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45

Grimes, Robin W. y C. Richard A. Catlow. "Modeling Localized Defects in Ionic Materials Using Mott-Littleton and Embedded Quantum Cluster Methodology". Journal of the American Ceramic Society 73, n.º 11 (noviembre de 1990): 3251–56. http://dx.doi.org/10.1111/j.1151-2916.1990.tb06446.x.

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46

Ho, Chang-Ming, V. N. Muthukumar, Masao Ogata y P. W. Anderson. "Nature of Spin Excitations in Two-Dimensional Mott Insulators: Undoped Cuprates and Other Materials". Physical Review Letters 86, n.º 8 (19 de febrero de 2001): 1626–29. http://dx.doi.org/10.1103/physrevlett.86.1626.

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47

Shore, K. Alan. "Electronic Processes in Non-crystalline Materials (Second Edition), by N.F. Mott and E.A. Davis". Contemporary Physics 55, n.º 4 (25 de junio de 2014): 337. http://dx.doi.org/10.1080/00107514.2014.933254.

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48

Nagaosa, N., T. K. Lee, C. M. Ho, T. Tohyama y S. Maekawa. "Theory of slightly doped Mott insulator". Physica C: Superconductivity 388-389 (mayo de 2003): 15–18. http://dx.doi.org/10.1016/s0921-4534(02)02604-7.

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49

Kohno, Masanori, Xiao Hu y Masashi Tachiki. "Charge dynamics in doped Mott insulators". Physica C: Superconductivity 412-414 (octubre de 2004): 82–85. http://dx.doi.org/10.1016/j.physc.2003.11.077.

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van Loon, Erik G. C. P., Malte Schüler, Daniel Springer, Giorgio Sangiovanni, Jan M. Tomczak y Tim O. Wehling. "Coulomb engineering of two-dimensional Mott materials". npj 2D Materials and Applications 7, n.º 1 (6 de julio de 2023). http://dx.doi.org/10.1038/s41699-023-00408-x.

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AbstractTwo-dimensional materials can be strongly influenced by their surroundings. A dielectric environment screens and reduces the Coulomb interaction between electrons in the two-dimensional material. Since in Mott materials the Coulomb interaction is responsible for the insulating state, manipulating the dielectric screening provides direct control over Mottness. Our many-body calculations reveal the spectroscopic fingerprints of such Coulomb engineering: we demonstrate eV-scale changes to the position of the Hubbard bands and show a Coulomb engineered insulator-to-metal transition. Based on our proof-of-principle calculations, we discuss the (feasible) conditions under which our scenario of Coulomb engineering of Mott materials can be realized experimentally.

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