arXiv subjects

Rufus Boyack

Publications and source records attributed to Rufus Boyack.

At least 19 recordsLinked to original sources

arXiv2026

Universal Theory of Incoherent Metals

Numerous unconventional superconductors such as cuprates, heavy-fermions, and twisted-bilayer graphene exhibit incoherent metallic transport above the superconducting critical temperature. This phenomenon cannot be described with Fermi-liquid theory and has presented a significant theoretical challenge to overcome. We utilize the two-dimensional Yukawa-SYK model of fermions with spatially random coupling to quantum-critical bosons to study transport in a manner which is non-perturbative in the coupling strength. Our work provides a microscopic model of quantum-critical incoherent metals and their concomitant properties, including a non-Boltzmann transport formula between resistivity and quasi-particle lifetime, violation of the Mott-Ioffe-Regel resistivity bound, and violation of the Kovtun-Son-Starinets shear viscosity to entropy density bound.

cond-mat.str-el↗

arXiv2026

Electrodynamic Signatures of Bogoliubov Fermi Surfaces in Moir\'e Graphene

Understanding the superfluid stiffness $D_s$ is a central problem in flat-band superconductivity. It is often interpreted together with spectroscopic probes such as tunneling, since both ultimately reflect the same superconducting quasiparticles. Their relationship is nevertheless complicated in flat bands, where quantum-geometric contributions to $D_s$ must be included. The situation in moir\'e graphene is particularly complex: tunneling experiments in some cases reveal an evolution between V- and U-shaped spectra together with a quite universal finite zero-bias conductance (ZBC). These two phenomena along with others have been argued to suggest the presence of a Bogoliubov Fermi surface (BFS), often generated by finite-momentum pair-density-wave (PDW) superconductivity. In this paper we calculate the superfluid stiffness in the presence of such a PDW. Virtual interband processes provide the familiar positive geometric contribution that gives phase rigidity to the flat-band condensate, allowing superconductivity to survive even in the presence of a BFS. At the same time, the multiband PDW pair structure enables the gapless BFS quasiparticles to respond to a phase gradient despite the negligible ordinary flat-band velocity. Their resulting counterflow reduces the stiffness even at zero temperature. As an experimentally accessible consequence, we predict a correlated evolution of the residual ZBC and the low-temperature stiffness: enhanced zero-bias spectral weight should accompany reduced phase rigidity. Observation of this correlation would support the presence of a BFS and indicate that the residual zero-energy states are intrinsic.

cond-mat.supr-con↗

arXiv2025

Physical constraints on effective non-Hermitian systems

Interacting and open quantum systems can be formulated in terms of an effective non-Hermitian Hamiltonian (NHH), however, there are important constraints that must be satisfied by the effective action and the associated Green's functions. One common approach to many-body non-Hermitian (NH) systems is to incorporate the anti-Hermitian part of the Hamiltonian directly in the Matsubara Green's function. Here, we show that such an approach is incompatible with the standard framework for systems with interactions. Furthermore, we furnish a consistent physical description for such systems by determining their distinction from conventional interacting physics, and find that they are described by pseudo-Hermitian quantum mechanics. Furthermore, we characterize the zero-temperature distribution functions within several frameworks for NH systems. As an application of our results, we consider the electromagnetic response of a NH quasiparticle Hamiltonian based on the (1+1)-dimensional NH Dirac model subject to various physical descriptions.

quant-ph↗

arXiv2025

Anomalous Superfluid Density in Pair-Density-Wave Superconductors

Pair-density-wave (PDW) states are a long-sought-after phase of quantum materials, with the potential to unravel the mysteries of high-$T_c$ cuprates and other strongly correlated superconductors. Yet, surprisingly, a key signature of stable superconductivity, namely the positivity of the superfluid density, $n_s(T)$, has not yet been demonstrated. Here, we address this central issue by calculating $n_s(T)$ for a generic model two-dimensional PDW superconductor. We uncover a surprisingly large region of intrinsic instability, associated with negative $n_s(T)$, revealing that a significant portion of the parameter space thought to be physical cannot support a pure PDW order. In the remaining stable regime, we predict two striking and observable fingerprints: a small longitudinal superfluid response and an unusual temperature dependence for $n_s(T)$. These generally model-independent, as well as experimentally relevant findings suggest that the fragility of the superfluid density poses a significant problem for the formation of stable, finite temperature PDW superconductivity.

cond-mat.supr-con↗

arXiv2025

Upper bound on $T_c$ in a strongly coupled electron-boson superconductor

Migdal-Eliashberg theory of boson-mediated superconductivity contains a $\sqrt{\lambda}$ divergence in the critical temperature $T_c$ for strong electron-boson coupling $\lambda$. In the conventional Migdal-Eliashberg theory, the strong-coupling regime can be accessed only in the limit that $\lambda_E = \lambda \, \omega_D/\varepsilon_F\ll1$, where $\omega_D$ is the Debye frequency and $\varepsilon_F$ is the Fermi energy. Here we go beyond this restriction in the context of the two-dimensional Yukawa-SYK (Y-SYK) model, which is solvable for arbitrary values of $\lambda_E$. We find that $T_c\approx 0.18 \,\omega_D \sqrt{\lambda}$ for large $\lambda$, provided $\lambda_E$ remains small, and crosses over to a universal value of $T_c \approx 0.04\, \varepsilon_F$ for large $\lambda_E$. The saturation of $T_c$ is due to a self-consistent account of the boson dynamics for large $\lambda_E$ and remains valid provided the vertex corrections are negligible. Depending on the value of $\lambda$, this self-consistent approach leads to pairing that describes multiple classes of quantum critical electronic systems. These results demonstrate how the $\sqrt{\lambda}$ growth of $T_c$ in Migdal-Eliashberg theory saturates to a universal value independent of $\lambda$ and $\omega_D$, providing an upper bound on the critical temperature at strong electron-boson coupling.

cond-mat.str-el↗

arXiv2024

The Higgs-Amplitude mode in the optical conductivity in the presence of a supercurrent: Gauge-invariant formulation with disorder

Observing the ``Higgs" or amplitude mode in superconductors has been a central challenge in condensed matter physics. Moreover, arriving at a theoretical understanding of this mode and how it is accessible in, say, conductivity experiments presents an additional challenge as here one needs to satisfy gauge invariance in the presence of disorder. In this paper, we characterize the Higgs contribution within a fully gauge-invariant treatment of the linear optical conductivity, $\sigma(\omega)$, for a disordered superconductor carrying a uniform supercurrent. As a consequence of gauge invariance, there are two distinct charge conservation laws underlying the linear electromagnetic response with two associated sets of $f$-sum rules. An interesting finding from the Higgs-related sum rule is that the imaginary part of $\sigma(\omega)$ yields an anisotropic, \textit{negative} $1/\omega$ contribution in the THz regime. This is relevant to device applications and appears to be consistent with recent experiments. The work presented here emphasizes how difficult it is to disentangle the neutral amplitude mode contributions from those of the charged quasi-particles and we demonstrate why this is the case.

cond-mat.supr-con↗

arXiv2024

Universal scaling relations in electron-phonon superconductors

We study linear scaling relations in electron-phonon superconductors. By combining numerical and analytical techniques, we find linear Homes scaling relations between the zero-temperature superfluid density and the normal-state dc conductivity. This phenomenon arises via either a large impurity scattering rate or inelastic scattering of electrons and Einstein phonons at large electron-phonon coupling. Thus, our Letter shows that Homes scaling is more universal than either cuprate or BCS-like physics and is, instead, a fundamental result in a wide class of superconductors.

cond-mat.supr-con↗

arXiv2023

Conformal field theories in a magnetic field

We study the properties of 2+1d conformal field theories (CFTs) in a background magnetic field. Using generalized particle-vortex duality, we argue that in many cases of interest the theory becomes gapped, which allows us to make a number of predictions for the magnetic response, background monopole operators, and more. Explicit calculations at large N for Wilson-Fisher and Gross-Neveu CFTs support our claim, and yield the spectrum of background (defect) monopole operators. Finally, we point out that other possibilities exist: certain CFTs can become metallic in a magnetic field. Such a scenario occurs for a Dirac fermion coupled to a Chern-Simons gauge field, where a non-Fermi liquid is argued to emerge.

hep-th↗

arXiv2023

Test for BCS-BEC Crossover in the Cuprate Superconductors

In this paper we address the question of whether high-temperature superconductors have anything in common with BCS-BEC crossover theory. Towards this goal, we present a proposal and related predictions which provide a concrete test for the applicability of this theoretical framework. These predictions characterize the behavior of the Ginzburg-Landau coherence length, $\xi_0^{\text{coh}}$, near the transition temperature $T_{\text{c}}$, and across the entire superconducting $T_{\text{c}}$ dome in the phase diagram. That we are lacking a systematic characterization of $\xi_0^{\text{coh}}$ in the entire class of cuprate superconductors is perhaps surprising, as it is one of the most fundamental properties of any superconductor. This paper is written to motivate further experiments and, thus, address this shortcoming. Here we show how measurements of $\xi_0^{\text{coh}}$ contain direct indications for whether or not the cuprates are associated with BCS-BEC crossover and, if so, where within the crossover spectrum a particular superconductor lies.

cond-mat.supr-con↗

arXiv2023

Electrical conductivity and nuclear magnetic resonance relaxation rate of Eliashberg superconductors in the weak-coupling limit

Electrical conductivity is an important transport response in superconductors, enabling clear signatures of dynamical interactions to be observed. Of primary interest in this paper is to study characteristics of the electron-phonon interaction in weak-coupling Eliashberg theory (Eth), and to note the distinctions with Bardeen-Cooper-Schrieffer (BCS) theory. Recent analysis of weak-coupling Eth has shown that while there are modifications from the BCS results, certain dimensionless ratios are in agreement. Here we show that the conductivities in BCS theory and Eth fundamentally differ, with the latter having an imaginary gap component that damps a divergence. We focus on the dirty limit, and for both BCS theory and Eth we derive expressions for the low-frequency limit of the real conductivity. For Eth specifically, there are two limits to consider, depending on the relative size of the frequency and the imaginary part of the gap. In the case of identically zero frequency, we derive an analytical expression for the nuclear magnetic resonance relaxation rate. Our analysis of the conductivity complements the previous study of the Meissner response and provides a thorough understanding of weak-coupling Eth.

cond-mat.supr-con↗

arXiv2022

When Superconductivity Crosses Over: From BCS to BEC

New developments in superconductivity, particularly through unexpected and often astonishing forms of superconducting materials, continue to excite the community and stimulate theory. It is now becoming clear that there are two distinct platforms for superconductivity: natural and synthetic materials. The study of these artificial materials has greatly expanded in the last decade or so, with the discoveries of new forms of superfluidity in artificial heterostructures and the exploitation of proximitization. Natural superconductors continue to surprise through the Fe-based pnictides and chalcogenides, and nickelates as well as others. It is the goal of this review to present this two-pronged investigation into superconductors, with a focus on those that we have come to understand belong somewhere between the Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) regimes. We characterize in detail the nature of this "crossover" superconductivity, which is to be distinguished from crossover superfluidity in atomic Fermi gases. In the process, we address the multiple ways of promoting a system out of the BCS and into the BCS-BEC crossover regime within the context of concrete experimental realizations. These involve natural materials, such as organic conductors, as well as artificial, mostly two-dimensional materials, such as magic-angle twisted bilayer and trilayer graphene, or gate-controlled devices, as well as one-layer and interfacial superconducting films. This work should be viewed as a celebration of BCS theory by showing that even though this theory was initially implemented with the special case of weak correlations in mind, it can in a very natural way be extended to treat the case of these more exotic strongly correlated superconductors.

cond-mat.supr-con↗

arXiv2022

Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids

Monopole operators are studied in a large family of quantum critical points between Dirac and topological quantum spin liquids (QSLs): chiral and Z$_{2}$ QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED$_{3}$-GN), while for the transitions to Z$_{2}$ QSLs it is a superconducting pairing term with general spin/valley structure (generalized QED$_{3}$-Z$_{2}$GN). Using the state-operator correspondence, we obtain monopole scaling dimensions to sub-leading order in 1/N. For monopoles with a minimal topological charge q=1/2, the scaling dimension is 2N*0.26510 at leading-order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the simplest Z$_{2}$ case (the expression is also given for a general pairing term). Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins. The analogous result in QED$_{3}$ is also obtained and we find a sub-leading contribution of -0.038138(5), which differs slightly from the value first obtained in the literature. The scaling dimension of a QED$_{3}$-GN monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between QED$_{3}$-GN with 2N=2 flavors and the CP$^{1}$ model. Additionally, non-minimally charged monopoles on both sides of the duality have similar scaling dimensions. By studying the large-q asymptotics of the scaling dimensions in QED$_{3}$, QED$_{3}$-GN, and QED$_{3}$-Z$_{2}$GN we verify that the constant O(q$^{0}$) coefficient precisely matches the universal non-perturbative prediction for CFTs with a global U(1) symmetry.

cond-mat.str-el↗

arXiv2022

Heat-bath approach to anomalous thermal transport: effects of inelastic scattering

We present results for the entire set of anomalous charge and heat transport coefficients for metallic systems in the presence of a finite-temperature heat bath. In realistic physical systems this necessitates the inclusion of inelastic dissipation mechanisms; relatively little is known theoretically about their effects on anomalous transport. Here we demonstrate how these dissipative processes are strongly intertwined with Berry-curvature physics. Our calculations are made possible by the introduction of a Caldeira-Leggett reservoir which allows us to avoid the sometimes-problematic device of the pseudogravitational potential. Using our formulas, we focus on the finite-temperature behavior of the important anomalous Wiedemann-Franz ratio. Despite previous expectations, this ratio is found to be non-universal as it can exhibit either an upturn or a downturn as temperature increases away from zero. We emphasize that this derives from a \textit{competition} between Berry curvatures having different signs in different regions of the Brillouin zone. We point to experimental support for these observations and for the behavior of an alternative ratio involving a thermoelectric response which, by contrast, appears to be more universal at low temperatures. Our work paves the way for future theory and experiment, demonstrating how inelastic scattering at non-zero temperature affects the behavior of all anomalous transport coefficients.

cond-mat.mes-hall↗

arXiv2022

Triangular pair density wave in confined superfluid $^3$He

Recent advances in experiment and theory suggest that superfluid $^3$He under planar confinement may form a pair density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wavevectors, of possibly square or hexagonal symmetry. In this Letter, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landau's theory of the liquid-solid transition. A soft-mode instability at finite wavevector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wavevectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice.

cond-mat.supr-con↗

arXiv2021

The bound-state solutions of the one-dimensional pseudoharmonic oscillator

We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $α$. The singular form of this potential has doubly-degenerate bound states for $-1/4\leqα<0$ and $α>0$; since the potential is symmetric, these consist of even and odd-parity states. In addition we consider a regularized form of this potential with a constant cutoff near the origin. For this regularized potential, there are also even and odd-parity eigenfunctions for $α\geq-1/4$. For attractive potentials within the range $-1/4\leqα<0$, there is an even-parity ground state with increasingly negative energy and a probability density that approaches a Dirac delta function as the cutoff parameter becomes zero. These properties are analogous to a similar ground state present in the regularized one-dimensional hydrogen atom. We solve this problem both analytically and numerically, and show how the regularized excited states approach their unregularized counterparts.

quant-ph↗

arXiv2021

Summation of certain trigonometric series with logarithmic coefficients

The sums of three trigonometric series with logarithmic coefficients are derived by extending an approach first utilized by Lerch. By applying Frullani's theorem to two of these series, two non-trivial integrals involving hyperbolic functions are evaluated in terms of the digamma function.

math.CA↗

arXiv2021

Unified approach to electrical and thermal transport in high-$T_c$ superconductors

In this paper we present a consolidated equation for all low-field transport coefficients, based on a reservoir approach developed for non-interacting quasiparticles. This formalism allows us to treat the two distinct types of charged (fermionic and bosonic) quasiparticles that can be simultaneously present, as for example in superconductors. Indeed, in the underdoped cuprate superconductors these two types of carriers result in two onset temperatures with distinct features in transport: $T^*$, where the fermions first experience an excitation (pseudo)gap, and $T_c$, where bosonic conduction processes are dominant and often divergent. This provides the central goal of this paper, which is to address the challenges in thermoelectric transport that stem from having two characteristic temperatures as well as two types of charge carriers whose contributions can in some instances enhance each other and in others compete. We show how essential features of the cuprates (their bad-metal character and the presence of Fermi arcs) provide an explanation for the classic pseudogap onset signatures at $T^*$ in the longitudinal resistivity, $ρ_{xx}$. Based on the fits to the temperature-dependent $ρ_{xx}$, we present the implications for all of the other thermoelectric transport properties.

cond-mat.supr-con↗

arXiv2021

Quantum phase transitions in Dirac fermion systems

A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention has been paid in recent years to two-dimensional (2D) materials in which itinerant fermions acquire a pseudo-relativistic Dirac dispersion, such as graphene, topological insulator surfaces, and certain spin liquids. This article reviews the phenomenology and theoretical description of quantum phase transitions in systems of 2D Dirac fermions.

cond-mat.str-el↗