arXiv subjects

Catherine Kallin

Publications and source records attributed to Catherine Kallin.

At least 19 recordsLinked to original sources

arXiv2023

Anomalous quasiparticle lifetime in geometric quantum critical metals

Metals can undergo geometric quantum phase transitions where the local curvature of the Fermi surface changes sign without a change in symmetry or topology. At the inflection points on the Fermi surface, the local curvature vanishes, leading to an anomalous dynamics of quasiparticles. In this paper, we study geometric quantum critical metals that support inflection points in two dimensions, and show that the decay rate of quasiparticles goes as $E^{\alpha}$ with $1<\alpha<2$ as a function of quasiparticle energy $E$ at the inflection points.

cond-mat.str-el↗

arXiv2022

Higher angular momentum pairing states in Sr$_2$RuO$_4$ in the presence of longer-range interactions

The superconducting symmetry of Sr$_2$RuO$_4$ remains a puzzle. Time-reversal symmetry breaking $d_{x^2-y^2} + ig_{xy(x^2-y^2)}$ pairing has been proposed for reconciling multiple key experiments. However, its stability remains unclear. In this work, we theoretically study the superconducting instabilities in Sr$_2$RuO$_4$, including the effects of spin-orbit coupling (SOC), in the presence of both local and longer-range interactions within a random phase approximation. We show that the inclusion of second nearest neighbor repulsions, together with non-local SOC in the $B_{2g}$ channel or orbital-anisotropy of the non-local interactions, can have a significant impact on the stability of both $d_{x^2-y^2}$- and $g$-wave pairing channels. We analyze the properties, such as Knight shift and spontaneous edge current, of the realized $d_{x^2-y^2} + ig$, $s^{\prime}+id_{xy}$ and mixed helical pairings in different parameter spaces and find that the $d_{x^2-y^2} + ig$ solution is in better agreement with the experimental data.

cond-mat.supr-con↗

arXiv2021

Probing time reversal symmetry breaking topological superconductivity in twisted double layer copper oxides with polar Kerr effect

Recent theoretical work predicted emergence of chiral topological superconducting phase with spontaneously broken time reversal symmetry in a twisted bilayer composed of two high-$T_c$ cuprate monolayers, such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. Here we identify large intrinsic Hall response that can be probed through the polar Kerr effect measurement as a convenient signature of the $\mathcal{T}$-broken phase. Our modelling predicts the Kerr angle $θ_K$ to be in the range of 10-100 $μ$rad, which is a factor of $10^3-10^4$ times larger than what is expected for the leading chiral supercondutor candidate Sr$_2$RuO$_4$. In addition we show that the optical Hall conductivity $σ_H(ω)$ can be used to distinguish between the topological $d_{x^2-y^2}\pm id_{xy}$ phase and the $d_{x^2-y^2}\pm is$ phase which is also expected to be present in the phase diagram but is topologically trivial.

cond-mat.supr-con↗

arXiv2020

Spin-orbit coupling and spin-triplet pairing symmetry in $\mathrm{Sr_2 Ru O_4}$

Spin-orbit coupling (SOC) plays a crucial role in determining the spin structure of an odd parity psedospin-triplet Cooper pairing state. Here, we present a thorough study of how SOC lifts the degeneracy among different p-wave pseudospin-triplet pairing states in a widely used microscopic model for $\mathrm{Sr_2 Ru O_4}$, combining a Ginzburg-Landau (GL) free energy expansion, a symmetry analysis of the model, and numerical weak-coupling renormalization group (RG) and random phase approximation (RPA) calculations. These analyses are then used to critically re-examine previous numerical results on the stability of chiral p-wave pairing. The symmetry analysis can serve as a guide for future studies, especially numerical calculations, on the pairing instability in $\mathrm{Sr_2 Ru O_4}$ and can be useful for studying other multi-band spin-triplet superconductors where SOC plays an important role.

cond-mat.supr-con↗

arXiv2018

Effects of deep superconducting gap minima and disorder on residual thermal transport in $\mathrm{Sr_2 Ru O_4}$

Recent thermal conductivity measurements on $\mathrm{Sr_2 Ru O_4}$ [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)] were interpreted as favoring a pairing gap function with vertical line nodes while conflicting with chiral $p$-wave pairing. Motivated by this work we study the effects of deep superconducting gap minima on impurity induced quasiparticle thermal transport in chiral $p$-wave models of $\mathrm{Sr_2 Ru O_4}$. Combining a self-consistent T-matrix analysis and self-consistent Bogoliubov-de-Gennes calculations, we show that the dependence of the residual thermal conductivity on the normal state impurity scattering rate can be quite similar to the $d$-wave pairing state that was shown to fit the thermal conductivity measurements, provided the normal state impurity scattering rate is large compared with the deep gap minima. Consequently, thermal conductivity measurements on $\mathrm{Sr_2RuO_4}$ can be reconciled with a chiral $p$-wave pairing state with deep gap minima. However, the data impose serious constraints on such models and these constraints are examined in the context of several different chiral $p$-wave models.

cond-mat.supr-con↗

arXiv2018

Spontaneous Edge Current in Higher Chirality Superconductors

The effects of finite temperature, Meissner screening and surface roughness on the spontaneous edge current for higher chirality quasi-two dimensional superconductors are studied in the continuum limit using the quasiclassical Eilenberger equations. We find that the total spontaneous current is non-zero at finite temperature $T$ and maximized near $T=T_c/2$, where $T_c$ is the transition temperature, although it vanishes at $T=0$. In the presence of surface roughness, we observe a surface current inversion in the chiral $d$-wave case that can be understood in terms of a disorder induced $s$-wave pairing component in the rough surface regime. This conclusion is supported by a Ginzburg-Landau analysis. However, this current inversion is non-universal beyond the continuum limit as demonstrated by self-consistent lattice Bogoliubov-de Gennes calculations.

cond-mat.supr-con↗

arXiv2017

Intrinsic ac anomalous Hall effect of nonsymmorphic chiral superconductors with an application to $\mathrm{UPt_3}$

We identify an intrinsic mechanism of the anomalous Hall effect for non-symmorphic chiral superconductors. This mechanism relies on both a nontrivial multi-band chiral superconducting order parameter, which is a mixture of pairings of even and odd angular momentum channels, and a complex normal state inter-sublattice hopping, both of which are consequences of the nonsymmorphic group symmetry of the underlying lattice. We apply this mechanism to the putative chiral superconducting phase of the heavy-fermion superconductor $\mathrm{UPt_3}$ and calculate the anomalous ac Hall conductivity in a simplified two-band model. From the ac Hall conductivity and optical data we estimate the polar Kerr rotation angle and compare it to the measured results for $\mathrm{UPt_3}$ [E. R. Schemm \textit{et al.}, Science \textbf{345},190(2014)].

cond-mat.supr-con↗

arXiv2016

Leggett modes and multi-band superconductivity in Sr2RuO4

Sr$_2$RuO$_4$ is a prototypical multi-band superconductor with three bands crossing the Fermi level. These bands exhibit distinct dimensional characteristics, with one quasi-2D $γ$-band and two quasi-1D $α$- and $β$-bands. This leads to the expectation that the superconductivity on the $γ$-band may be only weakly Josephson-coupled to that on the other two bands. Based on an explicit microscopic weak coupling calculation appropriate for Sr$_2$RuO$_4$, we study the collective Leggett modes associated with the relative phase oscillations between the bands and show that a relatively soft Leggett mode exists due to the comparatively weaker inter-band Josephson coupling. These calculations also provide insight into why the superconducting gap magnitudes may be comparable on all three bands, despite the noticeable differences between the $γ$ and $α, β$ bands. The analyses can be readily applied to other multi-band superconductors.

cond-mat.supr-con↗

arXiv2016

Chiral Superconductors

Chiral superconductivity is a striking quantum phenomenon in which an unconventional superconductor spontaneously develops an angular momentum and lowers its free energy by eliminating nodes in the gap. It is a topologically non-trivial state and, as such, exhibits distinctive topological modes at surfaces and defects. In this paper we discuss the current theory and experimental results on chiral superconductors, focusing on two of the best-studied systems, Sr2RuO4, which is thought to be a chiral triplet p-wave superconductor, and UPt3, which has two low-temperature superconducting phases (in zero magnetic field), the lower of which is believed to be chiral triplet f-wave. Other systems that may exhibit chiral superconductivity are also discussed. Key signatures of chiral superconductivity are surface currents and chiral Majorana modes, Majorana states in vortex cores, and the possibility of half-flux quantum vortices in the case of triplet pairing. Experimental evidence for chiral superconductivity from muSR, NMR, strain, polar Kerr effect and Josephson tunneling experiments are discussed.

cond-mat.supr-con↗

arXiv2015

Renormalization group analysis on a neck-narrowing Lifshitz transition in the presence of weak short-range interactions in two dimensions

We study a system of weakly interacting electrons described by the energy dispersion $ξ(\mathbf{k}) = k_x^2 - k_y^2 - μ$ in two dimensions within a renormalization group approach. This energy dispersion exhibits a neck-narrowing Lifshitz transition at the critical chemical potential $μ_c=0$ where a van Hove singularity develops. Implementing a systematic renormalization group analysis of this system has long been hampered by the appearance of nonlocal terms in the Wilsonian effective action. We demonstrate that non-locality at the critical point is intrinsic, and the locality of the effective action can be maintained only away from the critical point. We also point out that it is crucial to introduce a large momentum cutoff to keep locality even away from the critical point. Based on a local renormalization group scheme employed near the critical point, we show that, as the energy scale $E$ is lowered, an attractive four-fermion interaction grows as $\log^2 E$ for $E > μ$, whereas it retains the usual BCS growth, $-\log E$, for $E < μ$. Starting away from the critical point, this fast growth of the pairing interaction suggests that the system becomes unstable toward a superconducting state well before the critical point is reached.

cond-mat.str-el↗

arXiv2015

Locally gauge-invariant spin response of $^3$He-$B$ films with Majorana surface states

A locally gauge-invariant theory of the spin response of a thin film of $^3$He-$B$ film is given that describes fluctuation effects arising from the coupled dynamics of the superconducting order parameter (the collective mode) and in-gap Majorana surface states. In contrast to a mean-field calculation of the spin response, which predicts a nonzero imaginary longitudinal spin susceptibility at frequencies inside the bulk gap due to absorption from the Majorana states, our gauge-invariant theory shows that this response is strongly suppressed above the collective mode frequency and vanishes if dipole-dipole interactions are neglected. In the presence of dipole-dipole interactions, in sufficiently thin films, and at ultra-low temperatures, the Majorana states lead to a distinctive magnetic-field- and temperature-dependent damping of the collective mode, a feature that may be observable in longitudinal NMR experiments.

cond-mat.supr-con↗

arXiv2014

Vanishing edge currents in non-$p$-wave topological chiral superconductors

The edge currents of two dimensional topological chiral superconductors with nonzero Cooper pair angular momentum---e.g., chiral $p$-, $d$-, and $f$-wave superconductivity---are studied. Bogoliubov-de Gennes and Ginzburg--Landau calculations are used to show that in the continuum limit, \emph{only} chiral $p$-wave states have a nonzero edge current. Outside this limit, when lattice effects become important, edge currents in non-$p$-wave superconductors are comparatively smaller, but can be nonzero. Using Ginzburg--Landau theory, a simple criterion is derived for when edge currents vanish for non-$p$-wave chiral superconductivity on a lattice. The implications of our results for putative chiral superconductors such as Sr2RuO4 and UPt3 are discussed.

cond-mat.supr-con↗

arXiv2014

Non-topological nature of the edge current in a chiral p-wave superconductor

The edges of time reversal symmetry breaking topological superconductors support chiral Majorana bound states as well as spontaneous charge currents. The Majorana modes are a robust, topological property, but the charge currents are non-topological--and therefore sensitive to microscopic details--even if we neglect Meissner screening. We give insight into the non-topological nature of edge currents in chiral p-wave superconductors using a variety of theoretical techniques, including lattice Bogoliubov-de Gennes equations, the quasiclassical approximation, and the gradient expansion, and describe those special cases where edge currents do have a topological character. While edge currents are not quantized, they are generically large, but can be substantially reduced for a sufficiently anisotropic gap function, a scenario of possible relevance for the putative chiral p-wave superconductor Sr$_2$RuO$_4$.

cond-mat.supr-con↗

arXiv2014

Suppression of spontaneous currents in Sr$_2$RuO$_4$ by surface disorder

A major challenge to the chiral $p$-wave hypothesis for the pairing symmetry of the unconventional superconductor Sr$_2$RuO$_4$ is the null result of sensitive scanning magnetometry experiments designed to detect the expected spontaneous charge currents. Motivated by junction tunneling conductance measurements which indicate the quenching of superconductivity at the surfaces of even high-purity samples, we examine the spontaneous currents in a chiral $p$-wave superconductor near a normal metal / superconductor interface using the lattice Bogoliubov-de Gennes equations and Ginzburg-Landau theory, and find that the edge current is suppressed by more than an order of magnitude compared to previous estimates. These calculations demonstrate that interface details can have a quantitatively meaningful effect on the expectations for magnetometry experiments.

cond-mat.supr-con↗

arXiv2013

Anomalous Hall conductivity of clean Sr2RuO4 at finite temperatures

Building on previous work, we calculate the temperature- and frequency-dependent {\it anomalous} Hall conductivity for the putative multiband chiral superconductor $\Sr$ using a simple microscopic two-orbital model without impurities. A Hall effect arises in this system without the application of an external magnetic field due to the time-reversal-symmetry breaking chiral superconducting state. The anomalous Hall conductivity is nonzero only when there is more than one superconducting order parameter, involving inter- as well as intra-band Cooper pairing. We find that such a multiband superconducting state gives rise to a distinctive resonance in the frequency-dependence of the Hall conductivity at a frequency close to the inter-orbital hopping energy scale that describes hopping between Ru $d_{xz}$ and $d_{yz}$ orbitals. The detection of this feature, robust to temperature and impurity effects in the superconducting phase, would thus constitute compelling evidence in favour of a multiband origin of superconductivity in $\Sr$, with strong superconductivity on the $α$ and $β$ bands. The temperature dependence of the Hall conductivity and Kerr rotation angle are studied within this model at the one-loop approximation.

cond-mat.supr-con↗

arXiv2012

Chiral P-Wave Order in Sr_2RuO_4

Shortly after the discovery in 1994 of superconductivity in Sr2RuO4, it was proposed on theoretical grounds that the superconducting state may have chiral p-wave symmetry analogous to the A phase of superfluid He-3. Substantial experimental evidence has since accumulated in favor of this pairing symmetry, including several interesting recent results related to broken time reversal symmetry and vortices with half of the usual superconducting flux quantum. Great interest surrounds the possibility of chiral p-wave order in Sr2RuO4, since this state may exhibit topological order analogous to that of a quantum Hall state, and can support such exotic physics as Majorana fermions and non-Abelian winding statistics, which have been proposed as one route to a quantum computer. However, serious discrepancies remain in trying to connect the experimental results to theoretical predictions for chiral p-wave order. In this paper, I review a broad range of experiments on Sr2RuO4 that are sensitive to p-wave pairing, triplet superconductivity and time-reversal symmetry breaking and compare these experiments to each other and to theoretical predictions. In this context, the evidence for triplet pairing is strong, although some puzzles remain. The "smoking gun" experimental results for chiral p-wave, those which directly look for evidence of broken time-reversal symmetry in the superconducting state of Sr2RuO4, are most perplexing when the results are compared to each other and to theoretical predictions. Consequently, the case for chiral p-wave in Sr2RuO4 remains unresolved, suggesting the need to consider either significant modifications to the standard chiral p-wave models or possible alternative pairing symmetries. Recent ideas along these lines are discussed.

cond-mat.supr-con↗

arXiv2012

Quantum Oscillations in a $π$-Striped Superconductor

Within Bogoliubov-de Gennes theory, a semiclassical approximation is used to study quantum oscillations and to determine the Fermi surface area associated with these oscillations in a model of a $π$-striped superconductor, where the d-wave superconducting order parameter oscillates spatially with period 8 and zero average value. This system has a non-zero density of particle-hole states at the Fermi energy, which form Landau-like levels in the presence of a magnetic field, B. The Fermi surface is reconstructed via Andreev-Bragg scattering, and the semiclassical motion is along these Fermi surface sections as well as between them via magnetic breakdown. Within the approximation, oscillations periodic in 1/B are found in both the positions and widths of the lowest Landau levels. The area corresponding to these quantum oscillations for intermediate pairing interaction strength is similar to that reported for experimental measurements in the cuprates. A comparison is made of this theory to data for quantum oscillations in the specific heat measured by Riggs et al.

cond-mat.supr-con↗

arXiv2012

Intrinsic Hall effect in a multiband chiral superconductor in the absence of an external magnetic field

We identify an intrinsic Hall effect in multiband chiral superconductors in the absence of a magnetic field (i.e., an anomalous Hall effect). This effect arises from interband transitions involving time-reversal symmetry-breaking chiral Cooper pairs. We discuss the implications of this effect for the putative chiral p-wave superconductor, Sr2RuO4, and show that it can contribute significantly to Kerr rotation experiments. Since the magnitude of the effect depends on the structure of the order parameter across the bands, this result may be used to distinguish between different models proposed for the superconducting state of Sr2RuO4.

cond-mat.supr-con↗