Electromagnetic properties of viscous charged fluids

We provide a general theoretical framework to describe the electromagnetic properties of viscous charged fluids, consisting for example of electrons in certain solids or plasmas. We confirm that finite viscosity leads to multiple modes of evanescent electromagnetic waves at a given frequency, one of which is characterized by a negative index of refraction, as previously discussed in a simplified model by one of the authors. In particular we explain how optical spectroscopy can be used to probe the viscosity. We concentrate on the impact of this on the coefficients of refraction and reflection at the sample-vacuum interface. Analytical expressions are obtained relating the viscosity parameter to the reflection and transmission coefficients of light. We demonstrate that finite viscosity has the effect to decrease the reflectivity of a metallic surface, while the electromagnetic field penetrates more deeply. While on a phenomenological level there are similarities to the anomalous skin effect, the model presented here requires no particular assumptions regarding the corpuscular nature of the charge liquid. A striking consequence of the branching phenomenon into two degenerate modes is the occurrence in a half-infinite sample of oscillations of the electromagnetic field intensity as a function of distance from the interface.Comment: 12 pages, 5 figure

A theory of the strain-dependent critical field in Nb3Sn, based on anharmonic phonon generation

We propose a theory to explain the strain dependence of the critical properties in A15 superconductors. Starting from the strong-coupling formula for the critical temperature, and assuming that the strain sensitivity stems mostly from the electron-phonon alpha^2F function, we link the strain dependence of the critical properties to a widening of alpha^2F. This widening is attributed to the nonlinear generation of phonons, which takes place in the anharmonic deformation potential induced by the strain. Based on the theory of sum- and difference-frequency wave generation in nonlinear media, we obtain an explicit connection between the widening of alpha^2F and the anharmonic energy. The resulting model is fit to experimental datasets for Nb3Sn, and the anharmonic energy extracted from the fits is compared with first-principles calculations.Comment: 10 pages, 3 figure

Correlation between phase stiffness and condensation energy across the non-Fermi to Fermi-liquid crossover in the Yukawa-Sachdev-Ye-Kitaev model on a lattice

We construct and analyze a lattice generalization of the Yukawa-Sachdev-Ye-Kitaev model, where spinful fermions experience on-site, random, all-to-all interactions with an Einstein bosonic mode, and random intersite coherent hopping. We obtain the exact self-consistent numerical solution of the model at mean-field level, and analytical approximations, for all values of fermion-boson coupling and hopping, under the spin-singlet ansatz and at particle-hole symmetry, both in the normal and superconducting states, thus tracing the entire phase diagram. In the normal state, the competition between hopping and coupling leads to crossovers between Fermi-liquid and non-Fermi liquid states, as reflected by the fermionic and bosonic spectral functions and the normal-state entropy. We calculate the finite phase stiffness of the superconducting state through the equilibrium electromagnetic response. Furthermore, we study the critical temperature $T_c$, as well as the spectral functions, the quasiparticle weight, the gap, and the condensation energy in the superconducting state. At weak coupling, we retrieve a disordered generalization of Bardeen-Cooper-Schrieffer theory. At strong coupling, asymptotically $T_c$ saturates but the stiffness decreases, which suggests strong superconducting fluctuations. $T_c$ is maximum in the single-dot limit, while the stiffness peaks exactly at the crossover between non-Fermi liquid and Fermi-liquid phases. We discover that the quasiparticle weight, the stiffness, and the condensation energy, are all correlated as a function of coupling, reminiscent of the correlations observed in high-temperature cuprate superconductors.Comment: 53 pages, 22 figures; companion paper: arXiv:2302.1313

BCS to incoherent superconductivity crossovers in the Yukawa-SYK model on a lattice

We provide a quantitative and controlled analysis of the phase diagram of the the Yukawa-SYK model on a lattice, in the normal and superconducting states. We analyze the entire crossover from BCS/weak-coupling to Eliashberg/strong coupling superconductivity, as a function of fermion-boson interaction strength and hopping parameter. Cooper pairs of sharp Fermi-liquid quasiparticles at weak coupling evolve into pairing of fully incoherent fermions in the non-Fermi liquid regime. The crossovers leave observable traces in the critical temperature, the zero-temperature and zero-energy gap, the entropy, and the phase stiffness.Comment: 7 pages, 4 figures; companion paper: arXiv:2302.1313

Quantum discontinuity fixed point and renormalization group flow of the Sachdev-Ye-Kitaev model

We determine the global renormalization group (RG) flow of the Sachdev-Ye-Kitaev (SYK) model. From a controlled truncation of the infinite hierarchy of the exact functional RG flow equations, we identify several fixed points. Apart from a stable fixed point, associated with the celebrated non-Fermi liquid state of the model, we find another stable fixed point related to an integer-valence state. These stable fixed points are separated by a discontinuity fixed point with one relevant direction, describing a quantum first-order transition. Most notably, the fermionic spectrum continues to be quantum critical even at the discontinuity fixed point. This rules out a description of the transition in terms of a local effective Ising variable as is established for classical transitions. We propose an entangled quantum state at phase coexistence as a possible physical origin of this critical behavior

Kinetic theory of the nonlocal electrodynamic response in anisotropic metals: Skin effect in 2D systems

The electrodynamic response of ultrapure materials at low temperatures becomes spatially nonlocal. This nonlocality gives rise to phenomena such as hydrodynamic flow in transport and the anomalous skin effect in optics. In systems characterized by an anisotropic electronic dispersion, the nonlocal dynamics becomes dependent on the relative orientation of the sample with respect to the applied field, in ways that go beyond the usual, homogeneous response. Such orientational dependence should manifest itself not only in transport experiments, as recently observed, but also in optical spectroscopy. In this paper, we develop a kinetic theory for the distribution function and the transverse conductivity of two- and three-dimensional Fermi systems with anisotropic electronic dispersion. By expanding the collision integral into the eigenbasis of a collision operator, we include momentum-relaxing scattering as well as momentum-conserving collisions. We examine the isotropic 2D case as a reference, as well as anisotropic hexagonal and square Fermi-surface shapes. We apply our theory to the quantitative calculation of the skin depth and the surface impedance, in all regimes of skin effect. We find qualitative differences between the frequency dependence of the impedance in isotropic and anisotropic systems. Such differences are shown to persist even for more complex 2D Fermi surfaces, including the “supercircle” geometry and an experimental parametrization for PdCoO$_2$, which deviate from an ideal polygonal shape. We study the orientational dependence of skin effect due to Fermi-surface anisotropy, thus providing guidance for the experimental study of nonlocal optical effects