arXiv subjects

J. A. Sauls

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

At least 19 recordsLinked to original sources

arXiv2026

Excitation of Collective Modes in a Chiral Superfluid by Thermal Quench

Based on time-dependent Ginzburg-Landau field theory we show that rapid cooling through the second-order phase transition into superfluid $^3$He-A excites collective modes of newly formed chiral domains, in addition to topological defects that are formed via the Kibble-Zurek mechanism. Simulations of temperature quenches in the presence of Gaussian space-time white noise generate a highly excited inhomogeneous condensate. Large-scale simulations exhibit a complex network of domain walls and vortices. We report results for the excitation of bosonic collective modes by thermal noise as well as nonequilibrium temperature quenches, followed by coarsening dynamics tracked in terms of the Fourier components of the order parameter amplitudes. For thermal states, the spectrum of bosonic excitations is defined by a power spectral density (PSD) for each mode, which is sensitive to the Langevin damping. For weak damping the PSD onsets sharply at the frequency corresponding to the mass of the bosonic mode, then decays as $1/ω$. We also track the dynamics of the order parameter following a temperature quench. We report results for the scaling exponents of Kibble-Zurek freeze-out time and correlation length as a function of quench rate for several damping rates. The dynamical exponent $z$ is shown to transition smoothly from $z=1$ to $z=2$ as the damping is increased, while the correlation length exponent, $ν\approx 1/2$, is independent of damping.

cond-mat.supr-con↗

arXiv2026

Generation of Quantum Turbulence by Neutrino Cooling in Neutron Stars

The interior crust and much of the liquid core of neutron stars is believed to be a quantum liquid mixture of neutron and proton superfluids and a relativistic electron liquid. Quantized vortices in the neutron superfluid and quantized flux lines in the proton superconductor are topological defects of these hadronic condensates. I consider the formation of the superfluid state in young neutron stars under non-equilibrium conditions imposed by the neutrino cooling rate. The nonequilibrium phase transition implies that the onset of superfluidity is accompanied by the generation of quantized vortices based on the mechanism envisioned by Kibble in the context cosmic string formation in an evolutionary models of an expanding universe, and further developed by Zurek for nonequilibrium phase transitions in quantum liquids such as $^4$He. I discuss the Kibble-Zurek mechanism (KZM) and scaling relations for topological defect formation starting from the Cooper pair fluctuation propagator for temperatures approaching $T_c$. I then calculate the predicted vortex densities based on Urca and modified Urca cooling mechanisms in the cores of neutron stars for several models of the superfluid gap and transition temperature of the interior neutron superfluid. In all cases studied the KZM leads to a large density of topological defects in the condensate phase, which in 3D form a random network of vortex lines and loops, i.e. the generation of quantum turbulence.

astro-ph.HE↗

arXiv2026

Microwave Response of Superconductors with Paramagnetic Impurities

We develop theoretical methods to predict the effects of paramagnetic impurities on the microwave response of conventional spin-singlet superconductors. Our focus is on superconducting devices and resonators with low concentrations of impurities and exchange interactions with conduction electrons. We connect the sub-gap quasiparticle spectrum generated by pair-breaking to the frequency and temperature dependence of the conductivity for superconductors operating at microwave frequencies. We report theoretical results for superconducting device performance -- dissipation, quality factor and frequency shift anomalies -- based on self-consistent calculations of the current response and penetraion of the electromagnetic field at the vacuum-superconducting interface. Key results include the prediction of a non-monotonic anomaly in the low-frequency superfluid fraction and penetration depth at very low temperatures related to the sub-gap quasiparticle spectrum. Dissipation of microwave power is predicted from intra- and inter- impurity band transitions at GHz frequencies at low temperatures, including a physical mechanism responsible for residual resistance. We predict anomalies in the resonant frequency, $f(T)$, and quality factor, $Q(T)$, of high-Q SRF cavities operating in the GHz range at low-temperatures that are sensitive to non-magnetic and paramagnetic impurity disorder.

cond-mat.supr-con↗

arXiv2025

Trapping and Tunneling of Hydrogen, Deuterium and Oxygen in Niobium

We investigate isolated O-H and O-D pairs trapped in BCC Nb using a machine-learning interatomic potential (MLIP) trained to density-functional theory (DFT). The MLIP enables large-supercell analysis and identification of trapping sites within BCC Nb, as well as efficient mapping of three-dimensional (3D) potential-energy surfaces. In addition to the pair of tetrahedral``face'' sites previously identified based on DFT, we identify a lower-energy pair of ``edge'' trapping sites and confirm the stability of H and D at these trapping sites with DFT. We solve the Schrödinger equation for H and D in the 3D potential that surrounds the trapping sites. Solutions based on the static-lattice limit yield tunnel splittings in the range $J/h \in\{3-100\}$ GHz for both trapping sites.

cond-mat.other↗

arXiv2025

Kibble-Zurek Dynamics & Statistics of Topological Defects in Chiral Superfluid $^3$He Films

In equilibrium, confined films of superfluid $^3$He-A have the chiral axis, $\hat{\ell}$, locked normal to the surface of the film. There are two degenerate ground states $\hat{\ell}\;||\pm\hat{z}$. However, for a temperature quench, i.e. cool down through the phase transition at a finite rate, causally disconnected regions of order parameter fluctuations develop and evolve into an inhomogeneous ordered phase that hosts both domain walls between time-reversed chiral phases as well as vortices with winding numbers $p\in\mathbb{Z}$. We present simulations based on a time-dependent generalization of Ginzburg-Landau theory for strong-coupling $^3$He that reveal both types of topological defects to be present following the temperature quench. Results for the dynamics of vortices interacting with anti-vortices as well as domain walls are presented. The vortex number density as a function of quench rate agrees well with the scaling predicted by Kibble and Zurek. We also present results for the number distribution and compare with other theoretical models for full counting statistics of the topological defect density. Finally, we present results for an asymmetry in the post-freeze-out populations of inequivalent vortex core structures that are characteristic of a chiral superfluid.

cond-mat.supr-con↗

arXiv2025

The Frequency Shift and Q of Disordered Superconducting RF Cavities

Niobium superconducting radio-frequency (SRF) cavities for high energy accelerator applications have been greatly improved in terms of the quality factor $Q$ by techniques such as Nitrogen doping. However, the mechanisms leading improvement in $Q$ are still not fully understood. Quite recently the SRF group at Fermilab measured anomalies in the frequency shift of N-doped SRF Niobium cavities near the transition temperature. Here we report our theoretical analysis of these results based on the microscopic theory of superconductivity that incorporates anisotropy of the superconducting gap and inhomogeneous disorder in the screening region of the SRF cavities. We are able to account for frequency shift anomalies very close to $T_c$ of the order of fractions of a kHz. Our results for the frequency shift and Q are in good agreement with the experimental data reported for all four N-doped Nb SRF cavities by Bafia et al. We also compare our theory with an earlier report of on a Nb sample measured at 60 GHz. We also show that the quality factor calculated theoretically has a peak of upper convexity with the largest $Q$ at intermediate levels of disorder. For strong disorder, i.e. the dirty limit, pair breaking in the presence of disorder and screening currents limits the $Q$.

cond-mat.supr-con↗

arXiv2025

Theory of Two-level Tunneling Systems in Superconductors

We develop a field theory formulation for the interaction of an ensemble of two-level tunneling systems (TLS) with the electronic states of a superconductor. Predictions for the impact of two-level tunneling systems on superconductivity are presented, including $T_c$ and spectrum of quasiparticle states for conventional BCS superconductors. We show that non-magnetic TLS impurities in conventional s-wave superconductors can act as pair-breaking or pair-enhancing defects depending on the level population of the distribution of TLS impurities. We present calculations of the enhancement of superconductivity, both $T_c$ and the order parameter, for TLS defects in thermal equilibrium with the electrons and lattice. The scattering of quasiparticles by TLS impurities leads to sub-gap states below the bulk excitation gap, $Δ$, as well as resonances in the continuum above $Δ$. The energies and spectral weights of these states depend on the distribution of tunnel splittings, while the spectral weights are particularly sensitive to the level occupation of the TLS impurities. Under microwave excitation, or decoupling from the thermal bath, a nonequilibrium level population of the TLS distribution generates subgap quasiparticle states near the Fermi level which contribute to dissipation and thus degrade the performance of superconducting devices at low temperatures.

cond-mat.supr-con↗

arXiv2025

Hydrogen and Deuterium Tunneling in Niobium

We use density functional methods to identify the atomic configurations of H and D atoms trapped by O impurities and embedded in bulk Nb. We calculate the double-well potential for O-H and O-D impurities, wave functions, and tunnel splittings for H and D atoms. Our results are in agreement with those obtained from analysis of heat capacity and neutron scattering measurements on Nb with low concentrations of O-H and O-D.

cond-mat.mtrl-sci↗

arXiv2024

Photon Frequency Conversion in High-$Q$ Superconducting Resonators: Axion Electrodynamics, QED & Nonlinear Meissner Radiation

High-Q superconducting resonators have been proposed and developed as detectors of light-by-light scattering mediated by the hypothesized axion or virtual electron-positron pairs in quantum electrodynamics - the Euler-Heisenberg (EH) interaction. Photon frequency and mode conversion is central to the scheme for detecting such rare events. Superconducting resonators are nonlinear devices. The Meissner screening currents that confine the electromagnetic fields to the vacuum region of a superconducting RF cavity are nonlinear functions of the EM field at the vacuum-superconducting interface, and as a result can generate source currents and frequency conversion of microwave photons in the cavity. In this report we consider photon frequency and mode conversion in superconducting resonators with high quality factors from Meissner currents in single and dual cavity setups proposed for axion and QED searches based on light-by-light scattering. In a single cavity with two pump modes photon frequency conversion by the Meissner screening current dominates photon generation by the EH interaction for cavities with $Q \lesssim 10^{12}$. The Meissner currents also generate background photons that limits the operation of the resonator for axion detection in three-mode, single cavity setups. We also consider the leakage of photons from pump modes into the signal mode for both axion and EH mediated light-by-light scattering. Photon frequency conversion by the EH interaction can compete with Meissner and leakage radiation in \emph{ultra-high-Q} cavities that are beyond current state of the art. Meissner radiation and leakage backgrounds can be suppressed in dual cavity setups with appropriate choices for pump and spectator modes, as well as the single-cavity setup proposed for heterodyne detection of galactic axion dark matter.

hep-ph↗

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 $ξ_{*}=\hbar v_f/ \sqrt{|Δ({\bf p}_f)|^2-\varepsilon_{*}^2}$, 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↗

arXiv2024

Fermi-Liquid Theory for Unconventional Superconductors

Fermi liquid theory is used to generate the Ginzburg-Landau free energy functionals for unconventional superconductors belonging to various representations. The parameters defining the GL functional depend on Fermi surface anisotropy, impurity scattering and the symmetry class of the pairing interaction. As applications I consider the basic models for the superconducting phases of UPt$_3$. Two predictions of Fermi liquid theory for the two-dimensional representations of the hexagonal symmetry group are (i) the zero-field equilibrium state exhibits spontaneously broken time-reversal symmetry, and (ii) the gradient energies for the different 2D representations, although described by a similar GL functionals, are particularly sensitive to the orbital symmetry of the pairing state and Fermi surface anisotropy.

cond-mat.supr-con↗

arXiv2024

Anomalous Hall Effects in Chiral Superconductors

We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E$_1$ and E$_2$ representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and -- as we highlight -- the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the winding number, $ν$, of the chiral order parameter via Andreev scattering that transfers angular momentum from the chiral condensate to excitations that scatter off the random potential. For heat transport in a chiral superconductor with isotropic impurity scattering, i.e., point-like impurities, a transverse heat current is obtained for $ν=\pm 1$, but vanishes for $|ν|>1$. This is not a universal result. For finite-size impurities with radii of order or greater than the Fermi wavelength, $R\ge\hbar/p_f$, the thermal Hall conductivity is finite for chiral order with $|ν|\ge2$, and determined by a specific Fermi-surface average of the differential cross-section for electron-impurity scattering. Our results also provide quantitative formulae for analyzing and interpreting thermal transport measurements for superconductors predicted to exhibit broken time-reversal and mirror symmetries.

cond-mat.supr-con↗

arXiv2024

A-B transition in superfluid $^3$He and cosmological phase transitions

First order phase transitions in the very early universe are a prediction of many extensions of the Standard Model of particle physics and could provide the departure from equilibrium needed for a dynamical explanation of the baryon asymmetry of the Universe. They could also produce gravitational waves of a frequency observable by future space-based detectors such as the Laser Interferometer Space Antenna (LISA). All calculations of the gravitational wave power spectrum rely on a relativistic version of the classical nucleation theory of Cahn-Hilliard and Langer, due to Coleman and Linde. The high purity and precise control of pressure and temperature achievable in the laboratory made the first-order A to B transition of superfluid $^3$He an ideal for test of classical nucleation theory. As Leggett and others have noted the theory fails dramatically. The lifetime of the metastable A phase is measurable, typically of order minutes to hours, far faster than classical nucleation theory predicts. If the nucleation of B phase from the supercooled A phase is due to a new, rapid intrinsic mechanism that would have implications for first-order cosmological phase transitions as well as predictions for gravitational wave (GW) production in the early universe. Here we discuss studies of the AB phase transition dynamics in $^3$He, both experimental and theoretical, and show how the computational technology for cosmological phase transition can be used to simulate the dynamics of the A-B transition, support the experimental investigations of the A-B transition in the QUEST-DMC collaboration with the goal of identifying and quantifying the mechanism(s) responsible for nucleation of stable phases in ultra-pure metastable quantum phases.

cond-mat.supr-con↗

arXiv2023

Weyl Fermions and Broken Symmetry Phases of Laterally Confined $^3$He Films

Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D) $^3$He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum, $L_z = (N/2) \hbar$, for $N/2$ Cooper pairs. The power law suppression of the angular momentum, $L_z(T) \simeq (N/2)\,\hbar\,[1 - \frac{2}{3}(πT/Δ)^2 ]$ for $0 \le T \ll T_c$, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid $^3$He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at $D_{c2} \sim 16 ξ_0$. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length $D\rightarrow D_{c_2}$. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ``polar phase'' at $D_{c1} \sim 9ξ_0$, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

cond-mat.supr-con↗

arXiv2023

Effects of anisotropy and disorder on the superconducting properties of Niobium

We report results for the superconducting transition temperature and anisotropic energy gap for pure Niobium based on Eliashberg's equations and electron and phonon band structures computed from density functional theory. The electronic band structure is used to construct the Fermi surface and calculate the Fermi velocity at each point on the Fermi surface.The phonon bands are in excellent agreement with inelastic neutron scattering data. The corresponding phonon density of states and electron-phonon coupling define the electron-phonon spectral function, $α^2F({\bf p},{\bf p}';ω)$, and the corresponding electron-phonon pairing interaction, which is the basis for computing the superconducting properties. The electron-phonon spectral function is good agreement with existing tunneling spectroscopy data except for the spectral weight of the longitudinal phonon peak at $\hbarω_{\text{LO}}=23\,\mbox{meV}$. We obtain an electron-phonon coupling constant of $λ=1.057$, renormalized Coulomb interaction, $μ^{\star}=0.218$ and transition temperature $T_c=9.33\,\mbox{K}$. The corresponding strong-coupling gap at $T=0$ is modestly enhanced, $Δ_0=1.55\,\mbox{meV}$, compared to the weak-coupling BCS value $Δ_0^{\text{wc}}=1.78\,k_{\mbox{b}}\,T_c= 1.43\,\mbox{meV}$. The superconducting gap function exhibits substantial anisotropy on the Fermi surface. We analyze the distribution of gap anisotropy and compute the suppression of the superconducting transition temperature using a self-consistent T-matrix theory for quasiparticle-impurity scattering to describe Niobium doped with non-magnetic impurities. We compare these results with experimental results on Niobium SRF cavities doped with Nitrogen impurities.

cond-mat.supr-con↗

arXiv2023

The Heat Capacity of $^3$He-B in Silica Aerogel

The thermodynamic potential for superfluid $^3$He-B embedded in a homogeneously distributed random potential is calculated from a quasiclassical reduction of the Luttinger-Ward functional to leading order in $k_{\mbox{$\tiny B$}} T_c/E_f$. The resulting functional provides an extension of the Ginzburg-Landau free energy functional to all temperatures $0<T\le T_c$. Theoretical predictions based on this functional for the heat capacity of superfluid $^3$He-B embedded in homogeneous, isotropic silica aerogel are in good agreement with experimental reports for superfluid $^3$He-B infused into 98.2% porous silica aerogel over the pressure range $p=11 - 29\,\mbox{bar}$. The analysis supports a conclusion that superfluid $^3$He-B infused into high-porosity silica aerogels is a gapless superfluid at all pressures.

cond-mat.supr-con↗

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↗