arXiv subjects

J. A. Sauls

Publications and source records attributed to J. A. Sauls.

At least 37 records · Page 2Linked to original sources

arXiv2023

Electromagnetic Response of Disordered Superconducting Cavities

We present results for the resonant frequency shift and quality factor of disordered Nb SRF cavities driven out of equilibrium by the resonant microwave field. The theory is based on the nonequilibrium theory of superconductivity for the current response to the electromagnetic field at the vacuum-metal interface. We are able to accurately predict the observed frequency shifts with a precision of order several Hz over the full temperature range $0 < T \le T_c$, including the negative frequency shift anomalies that are observed very near $T_c$. The origin of these anomalies is shown to be the competition between the normal metal skin depth and the London penetration depth which diverges as $T\rightarrow T_c^-$. An analytic approximation to the full current response, valid for $|T-T_c|\ll T_c$, accounts for the negative frequency shift near $T_c$. The non-monotonic dependence of the quality factor on the quasiparticle scattering rate is related to the pair-breaking effect of disorder on the superfluid fraction, and thus the London penetration depth.

cond-mat.supr-con↗

arXiv2022

Disorder Induced Anomalous Thermal Hall Effect in Chiral Phases of Superfluid $^3$He

NMR experiments on liquid $^3$He infused into uniaxially anisotropic silica aerogels show the stabilisation of two equal-spin-pairing chiral phases on cooling from the normal phase. The alignment of the chiral axis relative to the anisotropy axis for these phases is predicted to depend upon temperature. A chiral A-like phase is also stabilized when $^3$He is confined to a slab of thickness $D\sim ξ$, the superfluid coherence length. For both types of confinement, scattering of quasiparticles by the random potential - aerogel or surface - is pair breaking and generates a sub-gap density of quasiparticle states. The random field also conspires with the chiral order parameter to generate skew scattering of quasiparticles in the plane normal to the chiral axis. This scattering mechanism leads to anomalous thermal Hall transport for nonequilibrium quasiparticles driven by a thermal gradient. We report theoretical results for the anomalous thermal Hall conductivity for theoretical models for chiral phases of $^3$He in both anisotropic aerogel and slabs. The anomalous thermal Hall effect (ATHE) provides an important tool to identify signatures of broken time-reversal and mirror symmetries and topology in chiral superconductors/superfluids.

cond-mat.supr-con↗

arXiv2022

Electromagnetic Response of Superconducting RF Cavities

Recently reported anomalies in frequency shift of order $δf\sim 0.1 -10\,\mbox{kHz}$ for Niobium SRF cavities in a narrow temperature region near $T_c\simeq 9\,\mbox{K}$ are sensitive to the surface preparation and Nitrogen doping. We developed methods for calculating the surface current response of Nb SRF cavities, as well as the resonant frequency shift and quality factor, as functions of temperature, frequency and disorder based on the Keldysh formulation of the theory for nonequilibrium superconductivity coupled with Maxwell's theory and boundary conditions for the response functions and electromagnetic field. We show that the anomaly is sensitive to impurity disorder. Our results for the anomaly in the frequency shift are in good agreement with experimental results for Nb with an anisotropic gap on the Fermi surface and inhomogeneous non-magnetic disorder. We also show that the quality factor as a function of the impurity scattering rate is maximum for in SRF cavities with intermediate disorder, $\hbar/τΔ\sim{\cal O}(1)$ with the maximum $Q$ decreasing with increasing frequency.

cond-mat.supr-con↗

arXiv2022

On the Excitations of a Balian-Werthamer Superconductor

My contribution to this collection of articles in honor of David Lee and John Reppy on their 90th birthdays is a reflection on the remarkable phenomenology of the excitation spectra of superfluid $^3$He, in particular the B-phase which was identified by NMR and acoustic spectroscopy as Balian-Werthamer state shown in 1963 to be the ground state of a spin-triplet, p-wave superconductor within weak-coupling BCS theory. The superfluid phases of $^3$He provide paradigms for electronic superconductors with broken space-time symmetries and non-trivial ground-state topology. Indeed broken spin- and orbital rotation symmetries lead to a rich spectrum of collective modes of the order parameter that can be detected using NMR, acoustic and microwave spectroscopies. The topology of the BW state implies its low-temperature, low-energy transport properties are dominated by gapless Majorana modes confined on boundaries or interfaces. Given the central role the BW state played I discuss the acoustic and electromagnetic signatures of the BW state, the latter being relevant if an electronic analog of superfluid $^3$He-B is realized.

cond-mat.supr-con↗

arXiv2022

Majorana fermions as quanta of a superfluid vacuum

This short article on a thermodynamic signature of Majorana fermions confined on the surface of a 3D topological superfluid in the presence of a moving condensate was circulated to a limited audience in Fall 2013. Since recent experiments are looking at possible signatures of a gas of Majorana excitations confined in two dimensions on the surface of superfluid $^3$He-B it seems timely to post this earlier perspective to arXiv.

cond-mat.supr-con↗

arXiv2022

Theory of Disordered Superconductors with Applications to Nonlinear Current Response

I present a review of the theory and basic equations for charge transport in superconducting alloys starting from the Keldysh formulation of the quasiclassical transport equations developed by Eilenberger, Larkin and Ovchinnikov and Eliashberg. This formulation is the natural extension of Landau's theory of normal Fermi liquids to the superconducting state of strongly correlated metals. For dirty metals the transport equations reduce to equations for charge diffusion, with the current response given by the Drude conductivity at low temperatures. The extension of the diffusion equation for the charge and current response of a strongly disordered normal metal to the superconducting state yields Usadel's equations for the non-equilibrium quasiclassical Keldysh propagator. The conditions for the applicability of the Usadel equations are discussed, the pair-breaking effect of disorder on the current response, including the nonlinear current response to an EM field in the dirty limit, $τ\ll \hbar/Δ$, are reported. The same nonlinearity is shown to lead to source currents for photon generation and nonlinear Kerr rotation driven by the nonlinear response to excitation of the superconductor by a multi-mode EM field. The potential relevance of the nonlinear source currents to SRF cavities as detectors of axion-like dark matter candidates is briefly discussed.

cond-mat.supr-con↗

arXiv2021

Anomalous Thermal Hall Effect in Chiral Phases of $^3$He-Aerogel

We report theoretical results for heat transport by quasiparticle excitations in superfluid $^3$He infused into silica aerogel engineered with uniaxial anisotropy. For this system two distinct equal spin pairing (ESP) superfluid phases have been reported based on NMR spectroscopy. Theoretical analysis predicts the first ESP state to be the chiral A phase with chiral axis aligned along the strain axis, and the lower temperature phase to be a polar-distorted chiral phase with random transverse fluctuations in the orientation of the chiral axis. We report calculations of heat transport for the high temperature chiral phase, including an anomalous (zero field) thermal Hall current originating from branch conversion scattering of Bogoliubov quasiparticles by the chiral order parameter induced by potential scattering by the silica aerogel. Observation of an anomalous thermal Hall current would provide a direct signature of the underlying chirality and topology of the superfluid phase of $^3$He in "stretched" silica aerogels.

cond-mat.supr-con↗

arXiv2021

Pairing Fluctuation Corrections to the Kinetic Theory of Liquid $^3\mathrm{He}$

Liquid $^3\mathrm{He}$ is a Fermi liquid that undergoes a BCS-type phase transition to a spin-triplet superfluid, making it valuable for understanding interacting fermions. When the temperature approaches the transition temperature $T_{\mathrm{c}}$ from above, physical properties can be modified by Cooper pair fluctuations, leading to deviations from the predictions of Fermi liquid theory. We use nonequilibrium Green's function theory to study the role of pair fluctuations on quasiparticle transport. The Boltzmann-Landau kinetic equation, which describes the transport properties of Fermi liquids, acquires corrections from the interaction of quasiparticles with pair fluctuations. As an application, we study the effects of pair fluctuations on the propagation of zero sound in liquid $^3\mathrm{He}$. We calculate the temperature-dependent correction to the zero sound velocity due to pair fluctuations, and compare the result with existing experimental data.

cond-mat.supr-con↗

arXiv2021

Pair Fluctuation Effects on Quasiparticle Transport in Fermi Systems

The leading corrections to Fermi liquid theory for non-equilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. We formulate the corrections to the Landau-Boltzmann transport equation starting from Keldysh's field theory for non-equilibrium, strongly interacting Fermions. The theory is applicable to quasiparticle transport in conventional and unconventional superconductors, dense nuclear matter and the low temperature phases of liquid $^3$He. Validation of the theory is provided by our analysis, and quantitative agreement between theory and experiment, of the excess attenuation of zero sound in liquid $^3$He near the superfluid transition. We propose an additional experimental test of the theory based on the effects of a Zeeman field on the spectrum of pairing fluctuations for the Cooper instability in spin-triplet superfluids.

cond-mat.supr-con↗

arXiv2021

Effects of Incipient Pairing on Non-equilibrium Quasiparticle Transport in Fermi Liquids

The low temperature properties of a wide range of many-fermion systems are well understood within the framework of Landau's theory of Fermi liquids. The low-energy physics of these systems is governed by interacting fermionic quasiparticles with momenta and energies near a Fermi surface in momentum space. Nonequilibrium properties are described by a kinetic equation for the distribution function for quasiparticles proposed by Landau. Quasiparticle interactions with other quasiparticles, phonons or impurities lead to internal forces acting on a distribution of nonequilibrium quasiparticles, as well as collision processes that ultimately limit the transport of mass, heat, charge and magnetization, as well as limit the coherence times of quasiparticles. For Fermi liquids that are close to a second order phase transition, e.g. Fermi liquids that undergo a superfluid transition, \emph{incipient} Cooper pairs - long-lived fluctuations of the ordered phase - provide a new channel for scattering quasiparticles, as well as corrections to internal forces acting on the distribution of nonequilibrium quasiparticles. We develop the theory of quasiparticle transport for Fermi liquids in the vicinity of a BCS-type superfluid transition starting from Keldysh's field theory for non-equilibrium, strongly interacting fermions. The leading corrections to Fermi liquid theory for non-equilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. Our theory is applicable to quasiparticle transport in superconductors, nuclear matter and the low temperature phases of liquid $^3$He. As an implementation of the theory we calculate the pairing fluctuation corrections to the attenuation of zero sound in liquid $^3$He near the superfluid transition and demonstrate quantitative agreement with experimental results.

cond-mat.supr-con↗

arXiv2021

The AB transition in Superfluid 3He

The discovery of superfluidity in 3He in 1971, published in 1972, [1, 2] has influenced a wide range of investigations that extend well beyond fermionic superfluids, including electronic quantum ma- terials, ultra-cold gases and degenerate neutron matter. Observation of thermodynamic transitions from the 3He Fermi liquid to two other liquid phases, A and B-phases, along the melting curve of liquid and solid 3He, discovered by Osheroff, Richardson, and Lee, were the very first indications of 3He superfluidity leading to their Nobel prize in 1996. This is a brief retrospective specifically focused on the AB transition.

cond-mat.supr-con↗

arXiv2021

Half-Quantum Vortices in Nematic and Chiral Phases of $^3$He

We report theoretical results for the stability of half-quantum vortices (HQVs) in the superfluid phases of $^3$He confined in highly anisotropic Nafen aerogel. Superfluidity of $^3$He confined in Nafen is the realization of a "nematic superfluid" with Cooper pairs condensed into a single p-wave orbital aligned along the anisotropy axis of the Nafen aerogel. In addition to the nematic phase, we predict a second "chiral" phase that onsets at a lower transition temperature. This chiral phase spontaneously breaks time-reversal symmetry and is a topological superfluid. Both superfluid phases are equal-spin pairing condensates that host arrays of HQVs as equilibrium states of rotating superfluid $^3$He. We present results for the structure of HQVs, including magnetic and topological signatures of HQVs in both the nematic and chiral phases of $^3$He-Nafen.

cond-mat.supr-con↗

arXiv2020

Impurity-Induced Anomalous Thermal Hall Effect in Chiral Superconductors

Chiral superconductors exhibit novel transport properties that depend on the topology of the order parameter, topology of the Fermi surface, the spectrum of bulk and edge Fermionic excitations, and the structure of the impurity potential. In the case of electronic heat transport, impurities induce an anomalous (zero-field) thermal Hall conductivity that is easily orders of magnitude larger than the quantized edge contribution. The effect originates from branch-conversion scattering of Bogoliubov quasiparticles by the chiral order parameter, induced by potential scattering. The former transfers angular momentum between the condensate and the excitations that transport heat. The anomalous thermal Hall conductivity is shown to depend to the structure of the electron-impurity potential, as well as the winding number, $ν$, of the chiral order parameter, $Δ(p)=|Δ(p)|\,e^{iνϕ_{p}}$. The results provide quantitative formulae for interpreting heat transport experiments seeking to identify broken T and P symmetries, as well as the topology of the order parameter for chiral superconductors.

cond-mat.supr-con↗

arXiv2020

The Vortex Phase Diagram of Rotating Superfluid $^3$He-B

We present the first theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid $^3$He-B. Based on a strong-coupling extension of the Ginzburg-Landau theory that accounts for the relative stability of the bulk A and B phases of $^3$He at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid $^3$He-B. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of $H=284\,\mbox{G}$ parallel to the rotation axis, $\vec{H}\parallel\vecΩ$, are reported, as well as the supercooling transition line, $T^{*}_ {v} (p,H)$. In zero field the vortex phases of $^3$He-B are separated by a first-order phase transition line $T_ {v} (p)$ that terminates on the bulk critical line $T_{c}(p)$ at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly-quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and $β$ phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, $T^{*}_ {v} (p,H)$, below which it is globally unstable to an array of D-core vortices. For $H\gtrsim 60\,\mbox{G}$ external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating $^3$He-B, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating $^3$He-B.

cond-mat.supr-con↗

arXiv2020

Superfluidity in Disordered Neutron Stars Crusts

Nonequilibrium conditions imposed by neutrino cooling through the liquid-solid transition lead to disorder in the solid crust of neutron stars. Disorder reduces the superfluid fraction, $ρ_s/ρ$, at densities above that of neutron drip, $ρ_d \approx 4\times 10^{11}\,g/cm^3$. For an amorphous solid crust the suppression of $ρ_s$ is small, except in the highest density regions of the crust. In contrast to the strong reduction in neutron conduction predicted for coherent Bragg scattering in a crystalline crust, the disordered solid crust supports sufficient neutron superfluid density to account for pulsar glitches.

astro-ph.HE↗

arXiv2019

Chiral Higgs Mode in Nematic Superconductors

Nematic superconductivity with spontaneously broken rotation symmetry has recently been reported in doped topological insulators, $M_x$Bi$_2$Se$_3$ ($M$=Cu, Sr, Nb). Here we show that the electromagnetic (EM) response of these compounds provides a spectroscopy for bosonic excitations that reflect the pairing channel and the broken symmetries of the ground state. Using quasiclassical Keldysh theory, we find two characteristic bosonic modes in nematic superconductors: the nematicity mode and the chiral Higgs mode. The former corresponds to the vibrations of the nematic order parameter associated with broken crystal symmetry, while the latter represents the excitation of chiral Cooper pairs. The chiral Higgs mode softens at a critical doping, signaling a dynamical instability of the nematic state towards a new chiral ground state with broken time reversal and mirror symmetry. Evolution of the bosonic spectrum is directly captured by EM power absorption spectra. We also discuss contributions to the bosonic spectrum from sub-dominant pairing channels to the EM response.

cond-mat.supr-con↗

arXiv2019

Circuit quantization in the presence of time-dependent external flux

Circuit quantization links a physical circuit to its corresponding quantum Hamiltonian. The standard quantization procedure generally assumes any external magnetic flux to be static. Time dependence naturally arises, however, when flux is modulated or when flux noise is considered. In this case, application of the existing quantization procedure can lead to inconsistencies. To resolve these, we generalize circuit quantization to incorporate time-dependent external flux.

quant-ph↗

arXiv2018

The Order Parameter for the Superconducting Phases of UPt$_3$

I review the principal theories that have been proposed for the superconducting phases of UPt$_3$. The detailed H-T phase diagram places constraints on any theory for the multiple superconducting phases. I comment on the limitations of the models proposed so far for the superconducting phases of UPt$_3$. I also find that a theory in which the order parameter belongs to an orbital 2D representation coupled to a SBF is a viable model for the phases of UPt$_3$, based on the existing body of experimental data. Specifically, I show that (1) the existing phase diagram (including an apparent tetracritical point for all field orientations), (2) the anisotropy of the upper critical field over the full temperature range, (3) the correlation between superconductivity and basal plane antiferromagnetism and (4) low-temperature power laws in the transport and thermodynamic properties can be explained qualitatively, and in many respects quantitatively, by an odd-parity, E$_{2u}$ order parameter with a pair spin projection of zero along the ${\bf c}$-axis. The coupling of an AFM moment to the superconducting order parameter acts as a symmetry breaking field (SBF) which is responsible for the apparent tetracritical point, in addition to the zero-field double transition. The results presented here for the E$_{2u}$ representation are based on an analysis of the material parameters calculated within BCS theory for the 2D representations, and a refinement of the SBF model of Hess, et al. [J. Phys. Condens. Matter, 1, 8135 (1989)]. I also discuss possible experiments to test the symmetry of the order parameter.

cond-mat.supr-con↗