Dissertations / Theses on the topic 'D-wave superconductor'

We studied the local single-particle tunneling characteristics [as observed with scanning tunnel microscopy (STM)] for N D and S D tunneling, where N is a normal metal, S is a s-wave superconductor, and D is a d-wave superconductor with a {100} | {110} grain boundary. The tunneling Hamiltonian method was used. The self-consistent order parameter is first determined using the quasiclassical Green'sfunction method, and then the tunneling characteristics at various distances from the interface, reectivity of the interface, and temperature are studied. For N D tunneling, a zero-bias conductance peak (ZBCP) occurs near the interface with diminishing magnitude away from it. For S D tunneling, the ZBCP splits to exhibit the gap of the s-wave low-Tc superconducting tunneling tip and there is a range of negative conductance just outside the peaks when the tunneling point is near the grain boundary. The results are compared with those obtained by using a constant order parameter in each grain.

One of the challenges facing condensed matter physics nowadays is to understand the electronic structure of high temperature superconductors. This dissertation compiles our contribution to the experimental information concerning this subject. Tunneling conductance spectroscopy a technique capable of probing the electronic density of states in hybrid structures was used to study the current and spin transport properties across junctions between metallic counterelectrodes and Bi2Sr2CaCu2O8- (BSCCO) crystals. Since in these structures the transport is mediated by transmission channels depending on superconductive characteristics, the energy resolved density of states is a signature of the mechanism of superconductivity. For instance, one can observe the superconductive energy gap and the behavior of subgap bound states due to phase sensitive Andreev reflections at the junction interface. In particular, tunneling spectroscopy makes possible the observation of the LOFF state characterized by the coexistence of superconductivity and magnetism. Cuprates like BSCCO are highly anisotropic materials and their superconductivity is almost two dimensional, being confined in the CuO2 planes. Therefore, our junctions combine monocrystals of underdoped samples of BSCCO with various thin film counterelectrodes normal metal (Ag), conventional superconductor (Pb) and ferromagnetic metal (Fe) deposited perpendicular onto the cuprate ab-plane (CuO2 plane). We performed measurements on Ag/BSCCO junctions for two current injection directions into the same crystal. We observed that, near the 110 crystal surface, the conductance spectra show a high zero bias peak (ZBCP) which is a manifestation of zero energy Andreev bound states due to an anisotropic superconductive order parameter. Near the 100 surface, the ZBCP is largely suppressed. This is consistent with a predominantly 2 2 x y d - -wave pairing symmetry. In some cases, the ZBCP splits or decreases in amplitude at low temperatures. This is consistent with the existence of a subdominant s-wave (or xy d ) resulting in a mixed d is + state which breaks time reversal symmetry (BTRS). Since we observe this phenomenon in the underdoped case, we do not confirm the possibility of a quantum critical point close to the optimal doping. Our Pb/BSCCO spectra contradict the theory explaining the BTRS by proximity effect. The Fe/BSCCO junctions measure the effect of spin polarization. We explain the recorded 4-peak asymmetric structure by the combined effect of a spin independent BTRS state and a spin filtering exchange energy in the barrier responsible for a large ZBCP splitting. The LOFF state was observed in the proximity region induced on the ferromagnetic side of multilayered-Fe/Ag/BSCCO structures. As expected for the LOFF order parameter, the spectra develops coherent damped oscillations with the Fe layer thickness probing different regions. The magnitude and sign of the oscillation depends on the energy. The conductances at energy zero or equal to the superconductive gap are modulated in antiphase proving that the order parameters takes successively positive and negative values. Changing the junction orientation with 4 p , results in an opposite behavior for the same distance. The maximal amplitudes in one direction is replaced by minima, showing that, besides space, the LOFF state modulation depends on the phase of the high temperature order parameter inducing the proximity

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2002.
Includes bibliographical references (p. 120-124).
Experiments have now established that the order parameter (gap) in the high-Tc cuprate superconductors exhibits d-wave symmetry, vanishing at four nodal points on the Fermi surface. Near each of these four gap nodes, quasiparticles are easily excited and behave more like massless relativistic particles than electrons in a metal. In this thesis, we study the transport properties of these nodal quasiparticles, providing theoretical interpretations for the results of low temperature thermal and (microwave) electrical transport experiments in the cuprates. We begin by considering the very low temperature regime in which transport is dominated by quasiparticles induced by the very presence of impurities. This is known as the universal limit because prior calculations indicate that the transport coefficients obtain universal (scattering-independent) values. We improve upon prior results by including the contribution of vertex corrections and find that while the electrical conductivity obtains a scattering-dependent correction, the thermal and spin conductivity maintain their universal values.
(cont.) We then focus on the microwave electrical conductivity and consider the slightly higher temperature regime where quasiparticles are excited thermally. Since measurements in detwinned samples yield results that are inconsistent with simple models of impurity scattering, we hypothesize that line defects, remnant from the process of removing twin boundaries, may provide an additional scattering mechanism. We calculate the self-energy and microwave conductivity due to line defect scattering and obtain results that agree well with experiment. Finally, we turn on a magnetic field and consider thermal transport in the mixed (vortex) state. In the weak-field regime, the thermal conductivity tensor can be expressed in terms of the cross section for quasiparticle scattering from a single vortex. We calculate this cross section and thereby obtain both the longitudinal thermal conductivity and the thermal Hall conductivity in surprisingly good qualitative agreement with the measured data. The transparent nature of our calculation allows us to obtain a physical understanding of the features seen in experiments.
by Adam Craig Durst.
Ph.D.

Comprendre les propriétés des composés à électrons fortement corrélés nouvellement découverts est un important défi à la fois pour des raisons fondamentales et un impact industriel à long terme. Une activité expérimentale sur les métaux et supraconducteurs à électrons lourds a mis en évidence des effets qui se démarquent clairement de notre compréhension actuelle. Le but de cette thèse est de modéliser les effets de spin spéciaux qui ont été observés en réponse à un champ magnétique dans le supraconducteur CeCoIn(5). Elle est composée de deux parties. Dans un premier temps nous avons à faire à la distribution anormale du champ magnétique local dans le réseau de vortex révélé par les expériences de diffraction de neutrons à petits angles et rotation de spin muonique. Sur la base de a théorie de Ginzburg-Landau avec prise en compte de l'effet de spin, nous analysons l'inhomogénéité du champ local dans le réseau de vortex et calculons des expressions pour les facteurs de forme en diffraction neutronique et la largeur de raie statique en rotation de spin muonique. Nous montrons que les données expérimentales anormales sont le résultat de supercourants générés par le spin circulant autour du cœur du vortex et donnent une augmentation de l'inhomogénéité du champ sur une distance de l'ordre de la longueur de corrélation du supraconducteur à partir de l'axe du vortex. L'importance de l'effet est contrôlée par une seule quantité (le paramètre de Maki) qui permet la détermination de propriétés physiques du système à partir de données expérimentales. La seconde partie traite d'une transition d'onde de densité de spin presque commensurable dans un supraconducteur non-conventionnel. Elle est motivée par l'observation du confinement d'un ordre d'onde de densité de spin dans la phase supraconductrice de CeCoIn(5) dans un champ magnétique. Dans le cadre de la formulation spin-fermion nous proposons un mécanisme pour la transition de l'état fondamental qui consiste du ralentissement du mode collectif de fluctuation de densité de spin induit par le champ (exciton de spin) vers un ordre statique. Cela représente un scénario par lequel la transition vers l'ordre de spin est reliée intrinsèquement au supraconducteur
Understanding the properties of newly discovered strongly correlated electron compounds is a considerable challenge for both fundamental matters and long-term industrial impact. Experimental activity on heavy electron metals and superconductors has lead to highlighting effects that depart from current knowledge. The thesis is aimed at modelling effects that have been observed in response to magnetic field in the heavy electron superconductor CeCoIn$_5$. This consists of two parts. In the first time we deal with the vortex lattice state anomalous local magnetic field space variations as highlighted by small angle neutron scattering and muon spin rotation experiment. On the basis of the Ginzburg-Landau theory with account of spin effect, we analyse the local field inhomogeneity in the vortex lattice and derive expressions for the neutron scattering form factors and muon spin rotation static linewidth. The anomalous experimental data are shown to be result of spin driven supercurrents which circulate around the vortex cores and lead to an increase with external field in the internal field inhomogeneity on a distance of the order of the superconducting coherence length from the vortex axis. The importance of the effect is controlled by a single quantity (the Maki parameter). The second part is on nearly commensurate spin density wave transition in a quasi two-dimensional superconductor. It is motivated by observation of the confinement of spin density wave ordering inside the superconducting state of CeCoIn$_5$ in magnetic field. In the frame of the spin-fermion formulation we propose a mechanism for the ground state transition consisting in the field-induced slowing down of a collective spin density fluctuation mode (spin-exciton) to static ordering. This represents a scenario by which the transition to spin ordering is intrinsically related to superconductivity

This thesis is about unconventional superconductors out of equilibrium. More precisely, it summarizes our theoretical efforts in addressing a few questions related to the real-time evolution in models displaying unconventional superconductivity. Apart from the purely theoretical interest, the motivation for these studies comes from the recent achievement in the field of ultrafast time-resolved spectroscopy on correlated materials, such as the high-temperature copper-oxide superconductors. The task of describing such systems in nonequilibrium is a very difficult one. In this thesis we attack the problem from two different points of view: • the anisotropic unconventional d-wave symmetry, • the strong electron-electron correlations. The thesis is organized as follows: The first part introduces the basic concepts which lay at the foundation of the work presented in the other two parts. In Chapter 1, the concept of unconventional superconductivity is briefly introduced. This mainly includes the high-temperature copper-oxide superconductors and their phenomenology: d-wave symmetry of the super- conducting gap and strong electron-electron interaction. Chapter 2 is devoted to a review of the recent experimental advances in the field of ultrafast spectroscopy of high temperature superconductors and correlated materials, with a particular focus on time- and angle- resolved photoemission spectroscopy. Finally, Chapter 3 is a short review of some works in the field of cold-atom Fermi gases. In the second part we address the physics of the d-wave superconductor after a sudden excitation. First, in Chapter 4 we introduce in some detail a model of mean-field superconductor with a d-wave symmetry. The principal feature of this model is the anisotropy of the gap and the nodal lines along which the gap vanishes. The results concerning the dynamics of the gap after a “quantum quench” are exposed in Chapter 5 where we compare our model to the s-wave superconductor. This comparison allows to identify the consequences of the unconventional symmetry. In Chapter 6 we discuss the spectral features of the transient nonequilibrium state of the d-wave superconductor. This is particularly important to move a first step towards photoemission experiments. In the third part we concentrate on the attractive Hubbard model as a prototype of strongly correlated superconductor. In Chapter 8 we discuss the superconducting state at equilibrium with the use of dynamical mean-field theory. In Chapter 9 we discuss the extension of this technique to systems out of equilibrium. In particular it is described the implementation in the superconducting phase. At the end of the thesis two appendices give some details of the calculations.

The present thesis is devoted to the investigation of novel superconductors by phase-sensitive terahertz transmission and infrared to ultraviolet spectroscopy. In particular, a nominally undoped Pr2CuO4 superconducting thin film, an FeTe0.5Se0.5 thin film, and a LiFeAs single crystal have been investigated. The emphasis is on the low-frequency part of the optical spectrum (i.e., the terahertz and infrared spectrum), as the goal of the study was to shed light on the size and symmetry of the superconducting gaps and also to determine the temperature dependences as well as the absolute values of the penetration depth, which are key input parameters for models applicable for new superconductors. In addition, niobium has been investigated as a reference, so as to see what is expected from conventional superconductors and to clarify the electrodynamics of niobium. A superconducting Nb thin film with Tc of 8.04 K has been investigated by backward wave oscillator-based (BWO-based) and time-domain terahertz (TDT) spectrometers in the frequency range between 4 and 100 cm−1 for temperatures ranging from 2 to 10 K. From these measurements an energy gap of 22.50 cm−1 = 2.79 meV = 4.02kBTc have been determined. The optical conductivity below Tc could nicely be described by calculations according to the Eliashberg theory, with the electron-phonon interaction evaluated from tunneling measurements. Absolute values of the penetration depth have been calculated from phase-sensitive terahertz measurements. The zero-temperature limit of at T = 0 is found to be 115 ± 5 nm. From this value, a London penetration depth of 43 ± 2 nm has been obtained. The overall temperature dependence of the penetration depth follows a behavior typical for conventional s-wave superconductors. A superconducting Pr2CuO4 film with T0 structure and Tc of 27 K has been investigated by use of optical methods in a wide frequency (5 – 55000 cm−1) and temperature (2 – 300 K) range. A Drude-like peak centered at zero frequency is observed in the optical conductivity below 150 K, above which it shifts to finite frequencies. The detailed analysis of the low-frequency conductivity reveals that the Drude peak and a far-infrared (FIR) peak centered at about 300 cm−1 persist at all temperatures. The FIR spectral weight is found to grow at the expense of the Drude spectral weight with increasing temperature. Absolute values of the penetration depth have been obtained from temperature and frequency-dependent measurements. The zero-temperature limit of is estimated to be 1600 ± 100 nm. The overall temperature dependence of follows a behaviour typical for cuprate superconductors. However, a closer look at the penetration depth at T 12 K reveals a flattening in the temperature dependence. A superconducting FeTe0.5Se0.5 thin film with Tc = 19 K has been investigated using a combination of BWO and TDT spectroscopy in the frequency range 4 - 80 cm−1 and between 3 and 150 K. From such measurements, a superconducting energy gap of 30 cm−1, representing a coupling strength = 2.27, is observed. Further, the penetration depth has been derived from the temperature dependence of the imaginary part of complex conductivity with the penetration depth = 530 ± 10 nm at lowest measured temperature. The temperature-dependent normalized superfluid density, just as is the case with most iron-based superconductors, could nicely be described by the so-called two-gap gamma model. Finally, a superconducting LiFeAs single crystal with Tc = 18 K has been investigated by optical spectroscopy in the frequency range 15 - 55000 cm−1 between 5 and 300 K. From these measurements, no clear signature of the superconducting energy-gap opening could be identified in spite of the spectral weight been suppressed in the infrared frequency regime below Tc. This indicates that LiFeAs single crystal is in a clean limit. With the aid of the Ferrell-Glover-Tinkham (FGT) sum rule, an absolute penetration depth of 215 nm has been calculated from the missing area at 5 K.

碩士
國立中山大學
物理學系
87
Very recently quasiparticles in d-wave vortex state have attracted much attention. To explore this issue, magnetic field dependence of the low-temperature specific heat (LTSH) of La-1.78Sr0.22Cu1-xNixO4 is desirable to provide information about the quasiparticle electronic states of cuprates in vortex state with the presence of impurities. We found that the magnetic dependence of linear-T coefficient g of Ni-doped samples varies as Hln(1/H) rather than H1/2, consistent with the most recent theoretical approach including impurity scattering of dirty d-wave scenario. Furthermore, our results are compared with the recently proposed scaling theory.

The physics of strongly correlated electron systems is among the central problems of condensed matter physics. One of the outstanding problems in this category is that of the high-Tc superconductivity obtained by doping of insulating parent materials like some layered copper oxides. Since its discovery in 1986, this unconventional class of superconductors has motivated extensive experimental and theoretical studies. In the context of hole doped cuprates, most of the theories have focused on d-wave superconductivity, which is characterized by the presence of nodes in its gap structure. However, recent experiments suggest that underdoped cuprates can support node-less superconductivity. In a similar vein, while early experiments on cuprates had found that these materials don’t break time reversal symmetry, recent improved experiments reveal clear signatures of microscopic time reversal symmetry breaking in underdoped cuprates, manifesting in a non-zero Polar Kerr Effect (PKE) signal. In this thesis we aim to elucidate a mechanism to account for some of the important aspects of the above mentioned experiments, within the slave-particle formulation of the widely used t-J model. We show that in the presence of strong correlations, a d-wave superconductor (d-SC) on a 2D square lattice is generically susceptible to large fluctuations of its internal phase mode. Within a large-N extension of the t-J model, these fluctuations, at zero temperature, reduce the mean field d-wave pairing scale substantially in the underdoped region. This is in contrast with the experimentally observed pseudogap scale which increases almost linearly with underdoping, and hence, suggests that the physics of the cuprate pseudogap may not solely be attributable to preformed d-wave pairs. This may also help in understanding recent ARPES and STM experiments on cuprates which do report two distinct single particle gaps in the system. Furthermore, we present a fluctuation-consistent theory of the t-J model at zero temperature wherein we find that the inclusion of the quantum fluctuations leads to a d-SC to (d + is)-SC transition at a doping of ∼ 0.12 holes per unit cell, as one moves from the overdoped to the underdoped region. The qualitative behaviour of the d-SC pairing scale on the overdoped side is similar to that obtained in the large-N theory described before. The similarity and differences of these results with respect to other theories of the t-J model like those using cluster extensions of DMFT are discussed. We also describe how these results can help in understanding the phenomenology of underdoped cuprates. One of the important messages that come out of our study is that competing non-superconducting orders may not be essential to explain the fragility of the d-SC in the underdoped region. Rather, they might be arising opportunistically when the d-SC becomes unstable to its internal phase mode fluctuations, and makes a transition to the (d + is)-SC. Overdoped cuprate superconductors are also quite unusual, and, contrary to the general belief, have a small superfluid stiffness. The stiffness has also been shown to have peculiar dependence on temperature. We perform the relevant finite temperature calculations within the t-J model, and indeed, find that the superfluid stiffness thus obtained can, qualitatively, explain the unusual features of overdoped cuprates. We have also found that the Van Hove singularity in the electronic density of states seems to be one of the important factors behind the unusual nature of the superfluid stiffness in overdoped cuprates. Overall, this thesis brings forth some notable and interesting possibilities in understanding the physics of cuprate superconductors. An idea that stands out is that underdoped cuprates may have a prominent presence of (d + is) pairing. This will have important implications for the competing or intertwined order scenario proposed for underdoped cuprates, where typically a d-SC is assumed to be competing (intertwined) with other orders. The physics of moderately overdoped and underdoped cuprates at finite temperatures will also have to be revisited to incorporate the effect of soft internal phase mode fluctuations more carefully.

碩士
國立臺灣大學
物理研究所
99
We study the d-wave (spin two) superconductors through its dual gravitational description using AdS/CFT duality with finite temperature. To give the anisotropic nature of spectral function, we introduce the Majorana coupling in the neutral blackhole metric without back reaction. We find that the spectral function is indeed anisotropically gapped. At low temperature or strong Majorana coupling, the spectral function shrinks to four nodal points. At high temperature or weak Majorana coupling, the spectral function is partially gapped and generates fermi arc. Also we consider the effect of the dirac mass and there is a phase difference between the condensate fields, that is the d+id scenario. The dirac mass term will cause the spectral function to shrink or to expand with respect to the origin in the momentum space. In the d+id scenario, we find the s-wave and d-wave mixing in the spectral function.

博士
國立交通大學
電子物理系
87
The Ginzburg-Landau theory has successfully predicted many interesting properties of $d$-wave superconductors near $T_c$. Most of the theories proposed so far assumed the order parameter with purely $d_{x^2-y^2}$-wave symmetry or mixed $s$+$d$ symmetry. Within the context of the relevant phenomenological and microscopical Ginzburg-Landau theory, this thesis is concerned with studies of the magnetic properties for a $d$-wave superconductor. Underlain by the Ginzburg-Landau theory of a $d$-wave superconductor with mass anisotropy $\lambda = m_x/m_y$, we have derived the non-zero, subsidiary order parameter induced by an external current. The amplitude of induced $s$-component depends on the amplitude and direction of the current. The extreme values appear in some specific conditions. Unlike the isotropic case, we find that the current density is not parallel to the wave vector any more except $M_a = 1$. The single vortex structure is derived in the presence of applied magnetic field. According to our results, the winding number of the $s$-wave does not change regardless of the vector potential. The generic London equation for a $d_{x^2-y^2}$-wave superconductor with mass anisotropy is expressed. By neglecting higher order terms, this work analyzes the magnetic-field distribution with and without a vortex. The interaction force between two parallel vortices is derived as well. Our results further reveal the presence of a torque between vortices irrespective of $s$- or $d$-wave order parameter, which is expected to vanish for isotropic cases. This implies that a torque between vortices due to mass anisotropy can change the lattice structure. A $d_{x^2-y^2}$ superconductor is modeled as the superconducting layers in the $a$-$b$ plane, whose coupling in the $c$-direction is approximated by the effective mass, within the Ginzburg-Landau theory. In this work, this model is applied to the system where the coherence length along the $c$-direction is greater than the layer spacing. Based on our model, we calculate the upper critical field in a magnetic field lying in $a$-$c$ plane and tilted by an angle from the $c$-axis. According to our results, the curvature of $H_{c2}(T)$ is upward, and the slope $-dH_{c2}(T)/dT$ depends on the angle between the c-axis and the external field. It is worthwhile to note that the ratio of the $c$-direction parameter related to the effective mass to the $a$-$b$ plane parameter connected with the effective mass can make enormous influence $H_{c2}$. As this ratio decreases, $H_{c2}$ becomes increasing. We also find that there is no admixture of $s$-wave component in the critical regime and believe that the upward curvature of the $H_{c2}(T)$ is illuminated as the characteristic property of a $d$-wave superconductor. In the context of the time-dependent Ginzburg-Landau theory for a $d_{x^2-y^2}$-wave superconductor, we investigate the energy theorem that demonstrates that the rate of increase of the total free energy plus the rate of dissipation equals the inflow of energy current. In addition, we derive an equation of motion for a single vortex $(h \ll H_{c2})$ in the presence of an applied transport current. Our results indicate that the imaginary parts of the relaxation times for $s$- and $d$-wave order parameters can change a sign of the Hall effect. We also find that the change of the parameters in the Ginzburg-Landau free energy functional, due to the nonmagnetic impurities, can affect the anomalous Hall effect. The tangent of Hall angle is investigated and found that the negative part of the tangent of Hall angle is essentially due to the imaginary parts of the relaxation time.

碩士
國立清華大學
物理學系
88
Metal-insulator transition in the Gd-doped (R1-yGdy)1.85Ce0.15CuO4-d systems occurred around y ~ 0.65 for R = Nd and y ~ 0.1 for R = Eu with a simultaneous structural transition from the tetragonal T￠-phase (space group I4/mmm) to an orthorhombic O￠-phase (Acam, ao ￡ bo ~O2 at). The structural change is due to the lattice mismatch between (R,Gd,Ce)2O2 layer and CuO2 layer which results with an oxygen distortion in the perfect square CuO2 plane. The phase diagram indicates that the superconductivity can only occur in the metallic T￠-phase cuprates where the metallic state is controlled by a delicate balance between oxygen reduction and structural stability. The oxygen distortion lowers the crystal symmetry from T￠-phase to O￠-phase (space group: Acam) at room temperature. The Cu2+ weak ferromagnetic weak-ferromagnetic/canted-antiferromagnetic (WF/CAF) order observed in the insulating region is the direct result of non-180° a(Cu-O-Cu) canting angle of the O￠-phase. In order to confirm the pairing state of the high temperature electron superconductor Pr1.85Ce0.15CuO4-d was chosen for further study. The temperature dependence of the in-plane magnetic penetration depth lab(T) of magnetically aligned powders of crystalline Pr1.85Ce0.15CuO4-d is reported. The temperature dependence of lab(T)- lab(0) shows a power law component but not all exponential decay indicative there are nodes on the Fermi surface. The result implies that the order parameter of high Tc electron superconductors should not be totally s-wave but a little d-wave symmetry.