arXiv subjects

D. Rainer

Publications and source records attributed to D. Rainer.

At least 19 recordsLinked to original sources

arXiv2024

Impurity States in D-wave Superconductors

The structure of the order parameter and the excitation spectrum are investigated for isolated impurities in d-wave superconductors. Atomic scale impurities, or defects, scatter quasiparticles and lead to local suppression (pair-breaking) near the impurity. The pair-breaking effect arises from the formation of quasiparticle states bound to the impurity. The corresponding reduction in spectral weight in the pair condensate is responsible for pair-breaking. The formation of the bound state is due to multiple Andreev scattering by the combined effects of potential scattering, which leads to changes in momentum of the scattered quasiparticle, and the anisotropy of the d-wave order on the Fermi surface. The spectral weight of the bound state decays exponentially away from the impurity on a length scale $\xi_{*}=\hbar v_f/ \sqrt{|\Delta({\bf p}_f)|^2-\varepsilon_{*}^2}$, where $\varepsilon_{*}$ is the energy of the impurity state. The continuum spectrum exhibits Tomasch oscillations due to the interference between Andreev reflected particle- and hole-like quasiparticles.

cond-mat.supr-con↗

arXiv2024

Fermi-Liquid Theory of Non-S-Wave Superconductivity

These lectures present the Fermi-liquid theory of superconductivity, which is applicable to a broad range of systems that are candidates for non-s wave pairing, {\it e.g.} the heavy fermions, organic metals and the CuO superconductors. Ginzburg-Landau (GL) theory provides an important link between experimental properties of non-s wave superconductors and the more general Fermi-liquid theory. The multiple superconducting phases of UPt$_3$ provide an ideal example of the role that is played by the GL theory for non-s wave superconductors. The difference between non-s wave superconductivity and conventional anisotropic superconductivity is illustrated here by the unique effects that impurities are predicted to have on the properties of non-s wave superconductors.

cond-mat.supr-con↗

arXiv2018

Strong Coupling Theory of Superconductivity

The electronic properties of correlated metals with a strong electron-phonon coupling may be understood in terms of a combination of Landau's Fermi-liquid theory and the strong-coupling theory of Migdal and Eliashberg. In these lecture notes we discuss the microscopic foundations of this phenomenological Fermi-liquid model of correlated, strong-coupling metals. We formulate the basic equations of the model, which are quasiclassical transport equations that describe both equilibrium and non-equilibrium phenomena for the normal and superconducting states of a metal. Our emphasis is on superconductors close to equilibrium, for which we derive the general linear response theory. As an application we calculate the dynamical conductivity of strong-coupling superconductors.

cond-mat.supr-con↗

arXiv2003

Nonlinear magnetic field dependence of the conductance in d-wave NIS tunnel junctions

The ab-plane NIS-tunnelling conductance in d-wave superconductors shows a zero-bias conductance peak which is predicted to split in a magnetic field. In a pure d-wave superconductor the splitting is linear for fields small on the scale of the thermodynamic critical field. The field dependence is shown to be nonlinear, even at low fields, in the vicinity of a surface phase transition into a local time-reversal symmetry breaking state. The field evolution of the conductance is sensitive to temperature, doping, and the symmetry of the sub-dominant pairing channel.

cond-mat.supr-con↗

arXiv2001

Magnetic Susceptibility of the Balian-Werthamer Phase of 3He in Aerogel

The equilibrium superfluid phase of 3He impregnated into high-porosity silica aerogels appears to be a non-equal-spin-pairing state in zero field at all pressures, which is generally assumed to be the Balian-Werthamer (BW) phase modified by the depairing effects of the aerogel structure. The nuclear magnetic susceptibility played a key role in identifying the B-phase of pure 3He with the BW state. We report theoretical calculations of the nuclear magnetic susceptibility for the BW model of superfluid 3He in aerogel within the framework of the Fermi-liquid theory of superfluid 3He. Scattering of quasiparticles by the aerogel, in addition to Fermi-liquid exchange corrections, leads to substantial changes in the susceptibility of the BW phase. The increase in the magnetic susceptibility of 3He-aerogel compared to pure 3He-B is related to the polarizability of the gapless excitations and the impurity-induced local field. The limited data that is available is in rough agreement with theoretical predictions. Future measurements could prove important for a more definitive identification of the ordered phase, as well as for refining the theoretical model for the effects of disorder and scattering on the properties of superfluid 3He.

cond-mat↗

arXiv2001

Vortex Core Structure and Dynamics in Layered Superconductors

We investigate the equilibrium and nonequilibrium properties of the core region of vortices in layered superconductors. We discuss the electronic structure of singly and doubly quantized vortices for both s-wave and d-wave pairing symmetry. We consider the intermediate clean regime, where the vortex-core bound states are broadened into resonances with a width comparable to or larger than the quantized energy level spacing, and calculate the response of a vortex core to an {\em a.c.} electromagnetic field for vortices that are pinned to a metallic defect. We concentrate on the case where the vortex motion is nonstationary and can be treated by linear response theory. The response of the order parameter, impurity self energy, induced fields and currents are obtained by a self-consistent calculation of the distribution functions and the excitation spectrum. We then obtain the dynamical conductivity, spatially resolved in the region of the core, for external frequencies in the range, $0.1Δ< \hbarω\lsim 3Δ$. We also calculate the dynamically induced charge distribution in the vicinity of the core. This charge density is related to the nonequilibrium response of the bound states and collective mode, and dominates the electromagnetic response of the vortex core.

cond-mat.supr-con↗

arXiv2000

Anisotropic conductivity of Nd_{1.85}Ce_{0.15}CuO_{4-δ} films at submillimeter wavelengths

The anisotropic conductivity of thin Nd$_{1.85}$Ce$_{0.15}$CuO$_{4-δ}$ films was measured in the frequency range 8 cm$^{-1}<ν<$ 40 cm$^{-1}$ and for temperatures 4 K $<T<300$ K. A tilted sample geometry allowed to extract both, in-plane and c-axis properties. The in-plane quasiparticle scattering rate remains unchanged as the sample becomes superconducting. The temperature dependence of the in-plane conductivity is reasonably well described using the Born limit for a d-wave superconductor. Below $T_{{\rm C}%}$ the c-axis dielectric constant $ε_{1c}$ changes sign at the screened c-axis plasma frequency. The temperature dependence of the c-axis conductivity closely follows the linear in T behavior within the plane.

cond-mat.supr-con↗

arXiv1999

Interplay of Fulde-Ferrell-Larkin-Ovchinnikov and Vortex states in two-dimensional Superconductors

Clean superconductors with weakly coupled conducting planes have been suggested as promising candidates for observing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We consider here a layered superconductor in a magnetic field of arbitrary orientation with respect to the conducting plane. In this case there is competition of spin-pair-breaking and orbital-pair-breaking effects. In previous work, phase boundaries characterized by Landau quantum numbers n > 0 have been predicted. Here, we calculate the actual structure of the stable states below Hc2 by minimizing the free energy. We find several new order parameter structures differing from both the traditional Abrikosov and FFLO solutions. Some interesting unsolved questions appear in the limit of large n.

cond-mat.supr-con↗

arXiv1999

Effects of Strong Magnetic Fields on Pairing Fluctuations in High Temperature Superconductors

We present the theory for the effects of superconducting pairing fluctuations on the nuclear spin-lattice relaxation rate, 1/T_1, and the NMR Knight shift for layered superconductors in high magnetic fields. These results can be used to clarify the origin of the pseudogap in high-T_c cuprates, which has been attributed to spin fluctuations as well as pairing fluctuations. We present theoretical results for s-wave and d-wave pairing fluctuations and show that recent experiments in optimally doped YBa_2Cu_3O_{7-d} are described by d-wave pairing fluctuations. In addition, we show that the orthorhombic distortion in YBa_2Cu_3O_{7-d} accounts for an experimentally observed discrepancy between 1/T_1 obtained by NQR and NMR at low field. We propose an NMR experiment to distinguish a fluctuating s-wave order parameter from a fluctuating strongly anisotropic order parameter, which may be applied to the system Nd_{2-x}Ce_xCuO_{4-d} and possibly other layered superconductors.

cond-mat.supr-con↗

arXiv1998

Electromagnetic Response of a Vortex in Layered Superconductors

We calculate the response of a vortex core in a layered superconductor to {\em ac} electromagnetic fields with frequencies $\omega\lsim 2\Delta/\hbar$. In this frequency range the response is dominated by order parameter collective modes which are coupled to the vortex-core bound states of Caroli, de Gennes and Matricon. Our calculations show that a vortex core has a more complex and richer dynamics than predicted by previous theories. The {\em ac} field drives an oscillating, nearly homogeneous supercurrent in the direction of the electric field, superimposed with a dissipative current flow which has a dipolar spatial structure. The order parameter response at low frequencies is an approximately rigid collective motion of the vortex structure perpendicular to the external field. This structure becomes strongly deformed at frequencies of order $\omega\gsim 0.5 \Delta /\hbar $. Coupling of the vortex-core bound states to collective modes of the order parameter at low frequencies leads to substantial enhancement of the dissipation near the vortex-center well above that of the normal-state.

cond-mat.supr-con↗

arXiv1997

Andreev Bound States, Surfaces and Subdominant Pairing in High Tc Superconductors

A characteristic feature of the BCS theory of superconductivity is the quantum-mechanical coherence of particle and hole states. Direct observation of particle-hole coherence in unusual superconducting materials is a strong indication of traditional superconductivity. We use the Fermi liquid theory of superconductivity to study the implications of particle-hole coherence on properties of d-wave superconductors near surfaces. Typical surface phenomena are the suppression of the superconducting order parameter, surface bound states associated with Andreev reflection, anomalous screening currents, and spontaneous breaking of time-reversal symmetry. We review these phenomena and present new results for the effects of surface roughness.

cond-mat.supr-con↗

arXiv1997

Tunneling into Current-Carrying Surface States of High T$_c$ Superconductors

Theoretical results for the ab-plane tunneling conductance in the d-wave model for high Tc superconductors are presented. The d-wave model predicts surface bound states below the maximum gap. A sub-dominant order parameter, stabilized by the surface, leads to a splitting of the zero-bias conductance peak (ZBCP) in zero external field and to spontaneous surface currents. In a magnetic field screening currents shift the quasiparticle bound state spectrum and lead to a voltage splitting of the ZBCP that is linear in H at low fields, and saturates at a pairbreaking critical field of order 3 Tesla. Comparisons with recent experimental results on Cu/YBCO junctions are presented.

cond-mat.supr-con↗

arXiv1996

Unconventional Pairing in Heavy Fermion Metals

The Fermi-liquid theory of superconductivity is applicable to a broad range of systems that are candidates for unconventional pairing. Fundamental differences between unconventional and conventional anisotropic superconductors are illustrated by the unique effects that impurities have on the low-temperature transport properties of unconventional superconductors. For special classes of unconventional superconductors the low-temperature transport coefficients are {\it universal}, i.e. independent of the impurity concentration and scattering phase shift. The existence of a universal limit depends on the symmetry of the order parameter and is achieved at low temperatures $k_B T \ll \gamma \ll \Delta_0$, where $\gamma$ is the bandwidth of the impurity induced Andreev bound states. In the case of UPt$_3$ thermal conductivity measurements favor an $E_{1g}$ or $E_{2u}$ ground state. Measurements at ultra-low temperatures should distinguish different pairing states.

cond-mat.supr-con↗

arXiv1996

The Current Carried by Bound States of a Superconducting Vortex

We investigate the spectrum of quasiparticle excitations in the core of isolated pancake vortices in clean layered superconductors. Analysis of the spectral current density shows that both the circular current around the vortex center as well as any transport current through the vortex core is carried by localized states bound to the core by Andreev scattering. Hence the physical properties of the core are governed in clean high-$κ$ superconductors (e.g. the cuprate superconductors) by the Andreev bound states, and not by normal electrons as it is the case for traditional (dirty) high-$κ$ superconductors.

cond-mat↗

arXiv1995

Thermodynamics of a d-wave Superconductor Near a Surface

We study the properties of an anisotropically paired superconductor in the presence of a specularly reflecting surface. The bulk stable phase of the superconducting order parameter is taken to have $d_{x^2-y^2}$ symmetry. Contributions by order parameter components of different symmetries vanish in the bulk, but may enter in the vicinity of a wall. We calculate the self-consistent order parameter and surface free energy within the quasiclassical formulation of superconductivity. We discuss, in particular, the dependence of these quantities on the degree of order parameter mixing and the surface to lattice orientation. Knowledge of the thermodynamically stable order parameter near a surface is a necessary precondition for calculating measurable surface properties which we present in a companion paper.

cond-mat↗

arXiv1995

The Effect of Surfaces on the Tunneling Density of States of an Anisotropically Paired Superconductor

We present calculations of the tunneling density of states in an anisotropically paired superconductor for two different sample geometries: a semi-infinite system with a single specular wall, and a slab of finite thickness and infinite lateral extent. In both cases we are interested in the effects of surface pair breaking on the tunneling spectrum. We take the stable bulk phase to be of $d_{x^2-y^2}$ symmetry. Our calculations are performed within two different band structure environments: an isotropic cylindrical Fermi surface with a bulk order parameter of the form $Δ\sim k_x^2-k_y^2$, and a nontrivial tight-binding Fermi surface with the order parameter structure coming from an anti-ferromagnetic spin-fluctuation model. In each case we find additional structures in the energy spectrum coming from the surface layer. These structures are sensitive to the orientation of the surface with respect to the crystal lattice, and have their origins in the detailed form of the momentum and spatial dependence of the order parameter. By means of tunneling spectroscopy, one can obtain information on both the anisotropy of the energy gap, $|Δ(\p)|$, as well as on the phase of the order parameter, $Δ(\p) = |Δ(\p)|e^{iφ(\p)}$.

cond-mat↗

arXiv1995

Infrared Conductivity in Layered $d$-wave Superconductors

We calculate the infrared conductivity of a stack of coupled, two-dimensional superconducting planes within the Fermi liquid theory of superconductivity. We include the effects of random scattering processes and show that the presence of even a small concentration of resonant impurities, in a $d$-wave superconductor, has an important effect on both the in-plane and $c$-axis transport properties, which could serve as signatures for $d$-wave pairing.

cond-mat↗

arXiv1995

Optical absorption in the strong coupling limit of Eliashberg theory

We calculate the optical conductivity of superconductors in the strong-coupling limit. In this anomalous limit the typical energy scale is set by the coupling energy, and other energy scales such as the energy of the bosons mediating the attraction are negligibly small. We find a universal frequency dependence of the optical absorption which is dominated by bound states and differs significantly from the weak coupling results. A comparison with absorption spectra of superconductors with enhanced electron-phonon coupling shows that typical features of the strong-coupling limit are already present at intermediate coupling.

cond-mat↗