arXiv subjects

Jay D. Sau

Publications and source records attributed to Jay D. Sau.

At least 37 records · Page 2Linked to original sources

arXiv2024

Theory of anomalous Hall effect from screened vortex charge in a phase disordered superconductor

Motivated by recent experiments showing evidence for chiral superconductivity in an anomalous Hall phase of tetralayer graphene, we study the relation between the normal state anomalous Hall conductivity and that in the phase disordered state above the critical temperature of the superconductor. By a numerical calculation of superconductivity in an anomalous Hall metal, we find that a difference in vortex and antivortex charge is determined by the Fermi surface Berry phase. Combining this with the vortex dynamics in a back-ground supercurrent leads to a Hall response in the phase disordered state of the superconductor that is close to the normal state anomalous Hall response. However, using a gauge-invariant superconducting response framework, we find that while vortex charge is screened by interactions, the screening charge, after a time-delay, reappears in the longitudinal current. Thus, the dc Hall conductivity in this phase, instead of matching the screened vortex charge, matches the ac Hall conductance in the superconducting and normal phase, which are similar.

cond-mat.supr-con↗

arXiv2024

Germanium-based hybrid semiconductor-superconductor topological quantum computing platforms: Disorder effects

It was recently suggested that proximitized gate-defined Ge hole nanowires could serve as an alternative materials platform for the realization of topological Majorana zero modes (MZMs). Here, we theoretically study the expected experimental signatures of Ge-based MZMs in tunneling conductance measurements, taking into account that unintentional random disorder is unavoidably present in realistic devices. Explicitly, we present numerically calculated local and nonlocal tunneling conductance spectra (as functions of bias voltage and magnetic field) for two different wire lengths, two different disorder models, two different parent superconductors (Al and NbTiN), and various disorder strengths, which we relate to an estimated lower bound for the disorder strength in Ge-based hybrid devices that we extract from the experimentally reported hole mobilities in current state-of-the-art two-dimensional Ge hole gases. We find that even if the actual disorder strength in the Ge-based hybrid device exceeds this theoretical lower bound by an order of magnitude, the system is still in the weak disorder regime, where the topological superconductivity is intact and the local conductance spectra manifest clear end-to-end correlated zero-bias peaks if and only if the system hosts topological end MZMs. This shows that, despite the relatively small pristine topological gaps ($\sim\,$a few tens of $μ$eV), Ge-based hybrid devices are a promising alternative platform for Majorana experiments due to the extremely high materials quality, which leads to an increased gap-to-disorder ratio and, therefore, to less ambiguity in the experimental tunneling conductance data compared to InAs-based devices.

cond-mat.mes-hall↗

arXiv2024

Comparing numerical methods for hydrodynamics in a one-dimensional lattice spin model

In ergodic quantum spin chains, locally conserved quantities such as energy or particle number generically evolve according to hydrodynamic equations as they relax to equilibrium. We investigate the complexity of simulating hydrodynamics at infinite temperature with multiple methods: time evolving block decimation (TEBD), TEBD with density matrix truncation (DMT), the recursion method with a universal operator growth hypothesis (R-UOG), and operator-size truncated (OST) dynamics. Density matrix truncation and the OST dynamics give consistent dynamical correlations to $t=60/J$ and diffusion coefficients agreeing within 1%. TEBD only converges for $t\lesssim 20$, but still produces diffusion coefficients accurate within 1%. The universal operator growth hypothesis fails to converge and only matches other methods on short times. We see no evidence of long-time tails in either DMT or OST calculations of the current-current correlator, although we cannot rule out that they appear at longer times. We do observe power-law corrections to the energy density correlator. At finite wavelength, we observe a crossover from purely diffusive, overdamped decay of the energy density, to underdamped oscillatory behavior similar to that of cold atom experiments. We dub this behavior "hot band second sound" and offer a microscopically-motivated toy model.

cond-mat.str-el↗

arXiv2024

Eliashberg theory for dynamical screening in bilayer exciton condensation

We study the effect of dynamical screening of interactions on the transition temperatures ($T_c$) of exciton condensation in a symmetric bilayer of quadratically dispersing electrons and holes by solving the linearized Eliashberg equations for the anomalous interlayer Green's functions. We find that $T_c$ is finite for the range of density and layer separations studied, decaying exponentially with interlayer separation. $T_c$ is suppressed well below that predicted by a Hartree Fock mean field theory with unscreened Coulomb interaction, but is above the estimates from the statically screened Coulomb interaction. Furthermore, using a diagrammatic framework, we show that the system is always an exciton condensate at zero temperature but $T_c$ is exponentially small for large interlayer separation.

cond-mat.str-el↗

arXiv2024

Machine Learning the Disorder Landscape of Majorana Nanowires

We develop a practical machine learning approach to determine the disorder landscape of Majorana nanowires by using training of the conductance matrix and inverting the conductance data in order to obtain the disorder details in the system. The inversion carried out through machine learning using different disorder parametrizations turns out to be unique in the sense that any input tunnel conductance as a function of chemical potential and Zeeman energy can indeed be inverted to provide the correct disorder landscape. Our work opens up a qualitatively new direction of directly determining the topological invariant and the Majorana wave-function structure corresponding to a transport profile of a device using simulations that quantitatively match the specific conductance profile. In addition, this also opens up the possibility for optimizing Majorana systems by figuring out the (generally unknown) underlying disorder only through the conductance data. An accurate estimate of the applicable spin-orbit coupling in the system can also be obtained within the same scheme.

cond-mat.mes-hall↗

arXiv2024

Topologically protected emergent Fermi surface in an Abrikosov vortex lattice

We show that a three-dimensional (3D) fully gapped type-II superconductor can feature emergent in-gap Fermi surfaces of Caroli-de Gennes Matricon (CdGM) quasiparticles in the presence of an Abrikosov vortex lattice. In particular, these CdGM Fermi surfaces manifest in the emergent 3D band structure enabled by the intervortex tunneling physics, and their stability is guaranteed by a $\mathbb{Z}_2$ topological index. By developing an effective analytical theory, we find that each vortex line carrying a 1D nodal dispersion is a sufficient condition for the vortex lattice to form CdGM Fermi surfaces. Following this prediction, in-gap CdGM Fermi surfaces are numerically confirmed in a microscopic vortex-lattice simulation of a superconducting Dirac semimetal with an $s$-wave spin-singlet pairing, which is directly applicable to a large class of type-II superconductors such as LiFeAs. Remarkably, the CdGM Fermi surfaces persist even when the normal state is deformed to a doped insulator of trivial band topology. Our work establishes the vortex lattice as a new experimentally feasible control knob for emergent topological phenomena in conventional superconductors.

cond-mat.supr-con↗

arXiv2024

Majorana zero modes in gate-defined germanium hole nanowires

We theoretically study gate-defined one-dimensional channels in planar Ge hole gases as a potential platform for non-Abelian Majorana zero modes. We model the valence band holes in the Ge channel by adding appropriate confinement potentials to the 3D Luttinger-Kohn Hamiltonian, additionally taking into account a magnetic field applied parallel to the channel, an out-of-plane electric field, as well as the effect of compressive strain in the parent quantum well. Assuming that the Ge channel is proximitized by an $s$-wave superconductor (such as, e.g., Al) we calculate the topological phase diagrams for different channel geometries, showing that sufficiently narrow Ge hole channels can indeed enter a topological superconducting phase with Majorana zero modes at the channel ends. We estimate the size of the topological gap and its dependence on various system parameters such as channel width, strain, and the applied out-of-plane electric field, allowing us to critically discuss under which conditions Ge hole channels may manifest Majorana zero modes. Since ultra-clean Ge quantum wells with hole mobilities exceeding one million and mean-free paths on the order of many microns already exist, gate-defined Ge hole channels may be able to overcome some of the problems caused by the presence of substantial disorder in more conventional Majorana platforms.

cond-mat.mes-hall↗

arXiv2024

Constrained motions and slow dynamics in one-dimensional bosons with double-well dispersion

We demonstrate slow dynamics and constrained motion of domain walls in one-dimensional (1D) interacting bosons with double-well dispersion. In the symmetry-broken regime, the domain-wall motion is ``fractonlike'' -- a single domain wall cannot move freely, while two nearby domain walls can move collectively. Consequently, we find an Ohmic-like linear response and a vanishing superfluid stiffness, which are atypical for a Bose condensate in a 1D translation invariant closed quantum system. Near Lifshitz quantum critical point, we obtain superfluid stiffness $ρ_s\sim T$ and sound velocity $v_s\sim T^{1/2}$, showing similar unconventional low-temperature slow dynamics to the symmetry-broken regime. Particularly, the superfluid stiffness suggests an order by disorder effect as $ρ_s$ increases with temperature. Our results pave the way for studying fractons in ultracold atom experiments.

cond-mat.quant-gas↗

arXiv2023

Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors

We propose a general theoretical framework for both constructing and diagnosing inversion-protected higher-order topological superconductors using Kitaev building blocks, a higher-dimensional generalization of Kitaev's one-dimensional Majorana model. For a given crystalline symmetry, the Kitaev building blocks serve as a complete basis to construct all possible Kitaev superconductors that satisfy the symmetry requirements. We derive a simple yet powerful Majorana counting rule that can unambiguously diagnose the existence of higher-order topology for all Kitaev superconductors. We expect this real-space diagnosis to work for general two-dimensional higher-order topological superconductors within this symmetry class. As proof of concept, we have identified two inequivalent stacking strategies using the Kitaev building blocks, based on which we have constructed minimal tight-binding models with symmetry-protecetd Majorana corner modes. Moreover, we have successfully applied our diagnosis to comprehend the Majorana corner physcis in a superconductor model with a fragile Wannier obstruction, confirming the validity of our theory beyond the Kitaev limit. Our work paves the way for interpreting higher-order topological superconductivity from the real-space perspective.

cond-mat.supr-con↗

arXiv2023

Fusion protocol for Majorana modes in coupled quantum dots

In a recent breakthrough experiment [Nature (London) 614, 445 (2023)], signatures of Majorana zero modes have been observed in tunnel spectroscopy for a minimal Kitaev chain constructed from coupled quantum dots. However, as Ising anyons, Majoranas' most fundamental property of non-Abelian statistics is yet to be detected. Moreover, the minimal Kitaev chain is qualitatively different from topological superconductors in that it supports Majoranas only at a sweet spot. Therefore, it is not obvious whether non-Abelian characteristics such as braiding and fusion can be demonstrated in this platform with a reasonable level of robustness. In this work, we theoretically propose a protocol for detecting the Majorana fusion rules in an artificial Kitaev chain consisting of four quantum dots. In contrast with the previous proposals for semiconductor-superconductor hybrid nanowire platforms, here we do not rely on mesoscopic superconducting islands, which are difficult to implement in quantum dot chains. To show the robustness of the fusion protocol, we discuss the effects of three types of realistic imperfections on the fusion outcomes, e.g., diabatic errors, dephasing errors, and calibration errors. We also propose a fermion parity readout scheme using quantum capacitance. Our work will shed light on future experiments on detecting the non-Abelian properties of Majorana modes in a quantum dot chain.

cond-mat.mes-hall↗

arXiv2023

Symmetric, off-diagonal, resistance from rotational symmetry breaking in graphene-WSe$_2$ heterostructure: prediction for a large magic angle in a Moire system

We show that any two-dimensional system with a non-zero \textit{symmetric} off-diagonal component of the resistance matrix, $R_{xy}=R_{yx} \neq 0$, must have the in-plane rotational symmetry broken down to $C_2$. Such a resistance response is Ohmic, and is different from the Hall response which is the \textit{anti-symmetric} part of the resistance tensor, $R_{xy}=-R_{yx}$, is rotationally symmetric in the 2D plane, and requires broken time-reversal symmetry. We show how a minute amount of strain due to lattice mismatch - less than $1 \%$ - can produce a vastly exaggerated symmetric off-diagonal response - $\frac{R_{xy}}{R_{xx}} \sim 20\%$ - because of the momentum matching constraints in a Moire system. Our results help explain an important new transport experiment on graphene-WSe$_2$ heterostructures, as well as are relevant for other experimental systems with rotational symmetry breaking, such as nematic systems and Kagome charge density waves. Additionally, our work predicts an example of a `magic' angle, $θ\sim 27^0$, in a Moire system which is a significant fraction of $π$. Our prediction that the anomalous resistance anisotropy occurs at a large value of magic angle, in contrast to known examples of magic angle transport anomalies that are small fractions of $π$, can be experimentally tested in graphene-WSe$_2$ heterostructures.

cond-mat.mes-hall↗

arXiv2023

Half unit cell shift defect induced helical states in Fe-based chalcogenide superconductors

Recent scanning tunneling spectroscopy along crystalline domain-walls associated with a half unit cell shift have revealed sub-gap density of states that are expected to arise from helical Majorana modes. Such propagating Majorana modes have been proposed to exist on the surface state of topological materials similar to FeTe$_{\text{1-x}}$Se$_\text{x}$ (FTS) along line defects where the superconducting order parameter (OP) is phase shifted by $π$. Here we show that such a $π$ shift in theOP across the half unit-cell shift domain-wall can occur in quite conventional tight-binding models of superconducting FTS as a result of the $s_{\pm}$ pairing symmetry across $Γ$ and M pockets of FTS. The resultant inter-pocket transmission between $Γ$ and M pockets is found to be typically larger than the intra-pocket transmissions. We confirm these conclusions with a calculation based on the Bogoliubov-de-Gennes (BdG) formalism which shows that a $π$-shift across the domain-wall is favored for a large range of model parameters for FTS. We discuss parameter regimes where this mechanism might explain the STS experiments as well as propose to test this explanation by searching for evidence of large inter-pocket scattering.

cond-mat.supr-con↗

arXiv2023

Spectral properties, topological patches, and effective phase diagrams of finite disordered Majorana nanowires

We consider theoretically the physics of bulk topological superconductivity accompanied by boundary non-Abelian Majorana zero modes in semiconductor-superconductor (SM-SC) hybrid systems consisting of finite wires in the presence of correlated disorder arising from random charged impurities. We find the system to manifest a highly complex behavior due to the subtle interplay between finite wire length and finite disorder, leading to copious low-energy in-gap states throughout the wire and considerably complicating the interpretation of tunneling spectroscopic transport measurements used extensively to search for Majorana modes. The presence of disorder-induced low-energy states may lead to the non-existence of end Majorana zero modes even when tunneling spectroscopy manifests zero bias conductance peaks in local tunneling and signatures of bulk gap closing/reopening in the nonlocal transport. In short wires within the intermediate disorder regime, apparent topology may manifest in small ranges ("patches") of parameter values, which may or may not survive the long wire limit depending on various details. Because of the dominance of disorder-induced in-gap states, the system may even occasionally have an appropriate topological invariant without manifesting isolated end Majorana zero modes. We discuss our findings in the context of a recent breakthrough experiment from Microsoft reporting the simultaneous observations of zero bias conductance peaks in local tunneling and gap opening in nonlocal transport within small patches of parameter space. Based on our analysis, we believe that the disorder strength to SC gap ratio must decrease further for the definitive realization of non-Abelian Majorana zero modes in SM-SC devices.

cond-mat.mes-hall↗

arXiv2022

Quality factor for zero-bias conductance peaks in Majorana nanowire

Despite recent experimental progress towards observing large zero-bias conductance peaks (ZBCPs) as signatures of Majorana modes, confusion remains about whether Majorana modes have been observed. This is in part due to the theoretical prediction of fine-tuned trivial (i.e., non-topological) zero-bias peaks that occur because of uncontrolled quantum dots or disorder potentials. While many aspects of the topological phase can be somewhat fine-tuned because the topological phase space is often small, the quantized height of the ZBCP associated with a Majorana mode is known to be robust at sufficiently low temperatures even as the tunnel barrier is pinched off to vanishingly small normal-state conductance. The key shortcoming of the existing experimental works is an acute lack of stability of the putative Majorana mode features, indicating the probable absence of a topological phase, and the current paper suggests specific experimentally accessible measures for a careful quantitative analysis of the measured ZBCP stability. In this paper, we study how the counter-intuitive robustness of the ZBCP height to the tunnel barrier strength can be used to distinguish Majorana modes from non-topological ZBCPs. To this end, we introduce a dimensionless quality factor $F$ to quantify the robustness of the ZBCP height based on the range of normal-state (i.e. above-gap) conductance (which depends crucially on the tunnel barrier height) over which the ZBCP height remains within a pre-specified range of quantization. By computing this quality factor $F$ together with the topological characteristics for a wide range of models and parameters, we find that Majoranas are significantly more robust (i.e., have a higher value of $F$) compared with non-topological ZBCPs in the ideal low-temperature limit. Even at a temperature as high as the experimentally used $20$ mK, we find that we can set a threshold value of $F\sim 2.5$ (for $ε=0.1$) so that ZBCPs associated with a quality factor $F>2.5$ are likely topological and $F\ll 2.5$ are topologically trivial. More precisely, the value of $F$ is operationally related to the degree of separation of the Majorana modes in the system, although $F$ uses only the experimentally measured tunnel conductance properties. Finally, we discuss how the quality factor $F$ measured in a transport setup can help estimate the quality of topological qubits made from Majorana modes. In particular, we show that if the induced gap can be enhanced somehow beyond the currently available $\sim 30$ $μ$eV in InAs/Al samples, large (small) values of $F$ could easily distinguish between stable topological (unstable trivial) ZBCPs with the quantum dot induced quasi-Majorana bound states occasionally behaving similar to topological Majorana modes in short wires.

cond-mat.mes-hall↗

arXiv2022

Disorder Suppression in Topological Semiconductor-Superconductor Junctions

Disorder in a proximitizing bulk superconductor can scatter quasiparticles in a putative topological superconductor and eventually destroy the topological superconducting state. We use a scattering approach and a random-matrix calculation to estimate the disorder scattering time in a topological Josephson junction. We find that the disorder scattering rate from the bulk of the superconductor, even in the strong coupling limit, is suppressed in the ratio of Fermi momenta between the semiconductor and superconductor. This suppression of disorder scattering is accompanied by near perfect Andreev reflection at such semiconductor/superconductor interfaces, which can be used as a signature of such clean proximity effect. We also find that these results can be understood by a semiclassical estimate of scattering. We discuss limits in other systems such as the semiconductor nanowire where disorder scattering is suppressed according to similar classical estimates.

cond-mat.mes-hall↗

arXiv2022

Acoustic-phonon-mediated superconductivity in moiréless graphene multilayers

We investigate the competition between acoustic-phonon-mediated superconductivity and the long-range Coulomb interaction in moiréless graphene multilayers, specifically, Bernal bilayer graphene, rhombohedral trilayer graphene, and ABCA-stacked tetralayer graphene. In these graphene multilayers, the acoustic phonons can realize, through electron-phonon coupling, both spin-singlet and spin-triplet pairings, and the intra-sublattice pairings ($s$-wave spin-singlet and $f$-wave spin-triplet) are the dominant channels. Our theory naturally explains the distinct recent experimental findings in Bernal bilayer graphene and rhombohedral trilayer graphene, and we further predict existence of superconductivity in ABCA tetralayer graphene arising from electron-phonon interactions. In particular, we demonstrate that the acoustic-phonon-mediated superconductivity prevails over a wide range of doping in rhombohedral trilayer graphene and ABCA tetralayer graphene while superconductivity exists only in a narrow range of doping near the Van Hove singularity in Bernal bilayer graphene. Key features of our theory are the inclusion of realistic band structures with the appropriate Van Hove singularities and Coulomb repulsion effects (the so-called "$μ^*$ effect") opposing the phonon-induced superconducting pairing. We also discuss how intervalley scatterings can suppress the spin-triplet spin-polarized superconductivity. Our work provides detailed prediction based on electron-acoustic-phonon-interaction-induced graphene superconductivity, which should be investigated in future experiments.

cond-mat.supr-con↗

arXiv2022

Acoustic-phonon-mediated superconductivity in Bernal bilayer graphene

We present a systematic theory of acoustic-phonon-mediated superconductivity, which incorporates Coulomb repulsion, explaining the recent experiment in Bernal bilayer graphene under a large displacement field. The acoustic-phonon mechanism predicts that $s$-wave spin-singlet and $f$-wave spin-triplet pairings are degenerate and dominant. Assuming a spin-polarized valley-unpolarized normal state, we obtain $f$-wave spin-triplet superconductivity with a $T_c\sim 20$ mK near $n_e=-0.6\times 10^{12}$ cm$^{-2}$ for hole doping, in approximate agreement with the experiment. We further predict the existence of superconductivity for larger doping in both electron-doped and hole-doped regimes. Our results indicate that the observed spin-triplet superconductivity in Bernal bilayer graphene arises from acoustic phonons.

cond-mat.supr-con↗

arXiv2021

Correlation-induced triplet pairing superconductivity in graphene-based moiré systems

Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlation-induced spin-fermion model on a honeycomb lattice. We find that the $f$-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and non-topological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced. Our results apply qualitatively for the triplet-pairing superconductivity in graphene-based moiré systems, which is fundamentally distinct from triplet superconductivity in $^3$He and ferromagnetic superconductors.

cond-mat.supr-con↗