arXiv subjects

Sankar Das Sarma

Publications and source records attributed to Sankar Das Sarma.

At least 127 records · Page 7Linked to original sources

arXiv2022

Proximity-induced superconductivity generated by thin films: Effects of Fermi surface mismatch and disorder in the superconductor

We investigate the effects of disorder characterising a superconducting thin film on the proximity-induced superconductivity generated by the film (in, e.g., a semiconductor) based on the exact numerical analysis of a three-dimensional microscopic model. To make the problem numerically tractable, we use a recursive Green's function method in combination with a patching approach that exploits the short-range nature of the interface Green's function in the presence of disorder. As a result of the Fermi surface mismatch between the superconductor (SC) and the semiconductor (SM) in combination with the confinement-induced quantization of the transverse SC modes, the proximity effect induced by a clean SC film is typically one to three orders of magnitude smaller that the corresponding quantity for a bulk SC and exhibits huge thickness-dependent variations. The presence of disorder has competing effects: on the one hand it enhances the proximity-induced superconductivity and suppresses its strong thickness dependence, on the other hand it generates proximity-induced effective disorder in the SM. The effect of proximity-induced disorder on the topological superconducting phase and the associated Majorana modes is studied nonperturbatively.

cond-mat.supr-con↗

arXiv2022

Weak quantization of non-interacting topological Anderson insulator

We study the transition between the two-dimensional topological insulator (TI) featuring quantized edge conductance and the trivial Anderson insulator (AI) induced by strong disorder. We discover a distinct scaling behavior of TI near the phase transition where the longitudinal conductance approaches the quantized value by a power law with system size, instead of an exponential law in clean TI. This region is thus called the weak quantization topological insulator (WQTI). By using the self-consistent Born approximation, we associate the emergence of the weak quantization with the imaginary part of the effective self-energy acquiring a finite value at strong disorder. We use our analytical theory, supported by direct numerical simulations, to study the effect of disorder range on the topological Anderson insulator. Interestingly, while this phase is quite generic for uncorrelated or short-range disorder, it is strongly suppressed by long-range disorder, perhaps explaining why it has never been seen in solid state systems.

cond-mat.mes-hall↗

arXiv2022

Random matrix theory for the robustness, quantization, and end-to-end correlation of zero-bias conductance peaks in a class D ensemble

We develop a general theory to study strong random quenched disorder effects in systems of experimental relevance in the search for Majorana zero modes (MZM) in topological superconductors. Using the random matrix theory in a class D ensemble, we simulate the transport properties of random quantum dots by attaching leads, and calculating the differential conductance in the $S$ matrix formalism. To add the concept of the length to the random system so that disordered Majorana nanowires can be simulated by the random matrix theory, we generalize the model of a single quantum dot to a chain of quantum dots by analogy with the superconductor-semiconductor (SC-SM) nanowire Majorana platform. We first define a new concept, the robustness of zero-bias conductance peaks (ZBCPs), in terms of an effective random Hamiltonian considering the self-energy of leads. We then study the joint distribution for the robustness and ZBCPs, and find a strong correlation that the ZBCP with stronger robustness is also prone to carry a larger conductance peak near $2e^2/h$. This trend is more prominent in shorter chains than in longer chains. This is consistent with experimentally observed ZBCPs associated with disorder-induced trivial Andreev bound states (the so-called ugly ZBCPs). Finally, we study the end-to-end correlation of the disorder-induced ZBCPs from two leads by calculating the normalized mutual information, which estimates the degrees of the correlation arising from the trivial ZBCPs. Our work provides an estimate of several important metrics used in SC-SM experiments to determine the nature of ZBCPs, including the robustness, quantization, and end-to-end correlation of the trivial ZBCPs. Therefore, in order to claim any evidence for MZMs, one must establish the observed ZBCPs to have considerable statistical significance well beyond what we find in this work to exist for the trivial peaks.

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

Thermal melting of a quantum electron solid in the presence of strong disorder: Anderson versus Wigner

We consider temperature-induced melting of a Wigner solid in one dimensional (1D) and two dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged impurities in the system. The system simulates semiconductor-based 2D electron layers where Wigner crystallization is often claimed to be observed experimentally. Using exact diagonalization and utilizing the inverse participation ratio as well as conductance to distinguish between the localized insulating solid phase and the extended metallic liquid phase, we find that the effective melting temperature may be strongly enhanced by disorder since the disordered crystal typically could be in a localized glassy state incorporating the combined nonperturbative physics of both Anderson localization and Wigner crystallization. This disorder-induced enhancement of the melting temperature may explain why experiments often manage to observe insulating disorder-pinned Wigner solids in spite of the experimental temperature being decisively far above the theoretical melting temperature of the pristine Wigner crystal phase in many cases.

cond-mat.dis-nn↗

arXiv2022

Topological Phases in AB-Stacked MoTe$_2$/WSe$_2$: $\mathbb{Z}_2$ Topological Insulators, Chern Insulators, and Topological Charge Density Waves

We present a theory on the quantum phase diagram of AB-stacked MoTe$_2$/WSe$_2$ using a self-consistent Hartree-Fock calculation performed in the plane-wave basis, motivated by the observation of topological states in this system. At filling factor $ν=2$ (two holes per moiré unit cell), Coulomb interaction can stabilize a $\mathbb{Z}_2$ topological insulator by opening a charge gap. At $ν=1$, the interaction induces three classes of competing states, spin density wave states, an in-plane ferromagnetic state, and a valley polarized state, which undergo first-order phase transitions tuned by an out-of-plane displacement field. The valley polarized state becomes a Chern insulator for certain displacement fields. Moreover, we predict a topological charge density wave forming a honeycomb lattice with ferromagnetism at $ν=2/3$. Future directions on this versatile system hosting a rich set of quantum phases are discussed.

cond-mat.str-el↗

arXiv2022

Strange metallicity of moiré twisted bilayer graphene

Recent measurements in several different laboratories report the observation of an approximately linear-in-temperature resistivity with a large twist-angle-dependent slope (or temperature coefficient) in moiré twisted bilayer graphene (tBLG) down to a few K and sometimes to much lower temperatures. In this note, we theoretically discuss this `strange metal' linear-in-temperature transport behavior from the perspective of resistive scattering by acoustic phonons, emphasizing the aspects of the transport data, which are and which are not consistent with the phonon scattering mechanism. Extensive theoretical comparison with a new experiment [A. Jaoui et al., Nature Physics 18, 633 (2022)] is the central new aspect of this work.

cond-mat.mes-hall↗

arXiv2022

Hydrodynamics, viscous electron fluid, and Wiedeman-Franz law in 2D semiconductors

Considering theoretically the transition between hydrodynamic and ballistic regimes in 2D semiconductors, we show that electrons in high-mobility 2D GaAs are by far the best system for the direct observation of collective hydrodynamic effects even in bulk transport properties independent of complicated transport features in narrow constrictions and small systems where Gurzhi phenomena are typically studied experimentally. We predict a strong hydrodynamics-induced generic violation of the Wiedeman-Franz law in bulk 2D GaAs systems for mobilities as modest as $10^6 \mathrm{cm}^2/Vs$ and densities $1$-$5\times10^{11} \mathrm{cm}^{-2}$ in the temperature range of $T=1$-$40K$.

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

Anderson localization crossover in 2D Si systems: The past and the present

Using Ioffe-Regel-Mott (IRM) criterion for strong localization crossover in disordered doped 2D electron systems, we theoretically study the relationships among the three key experimentally determined localization quantities: critical density ($n_\mathrm{c}$), critical resistance ($ρ_\mathrm{c}$), and sample quality defined by the effective impurity density (as experimentally diagnosed by the sample mobility, $μ_\mathrm{m}$, at densities much higher than critical densities). Our results unify experimental results for 2D metal-insulator transitions (MIT) in Si systems over a 50-year period (1970-2020), showing that $n_\mathrm{c}$ ($ρ_\mathrm{c}$) decrease (increase) with increasing sample quality, explaining why the early experiments in the 1970s, using low-quality samples ($μ_\mathrm{m} \sim 10^3 \mathrm{cm}^2/Vs$) reported strong localization crossover at $n_c \sim 10^{12} \mathrm{cm}^{-2}$ with $ρ_c \sim 10^3Ω$ whereas recent experiments (after 1995), using high-quality samples ($μ_\mathrm{m} >10^4 \mathrm{cm}^2/Vs$), report $n_c \sim 10^{11} \mathrm{cm}^{-2}$ with $ρ_c>10^4Ω$. Our theory establishes the 2D MIT to be primarily a screened Coulomb disorder-driven strong localization crossover phenomenon, which happens at different sample-dependent critical density and critical resistance, thus unifying Si 2D MIT phenomena over a 50-year period.

cond-mat.dis-nn↗

arXiv2022

Temperature dependent resistivity in the doped two dimensional metallic phase of mTMD bilayers

Two recent experiments from Cornell and Columbia have reported insulator-to-metal transitions in two-dimensional (2D) moiré transition metal dichalcogenides (mTMD) induced by doping around half-filling, where the system is a Mott insulator. In the current work, we consider the temperature dependent resistivity of this metallic phase in the doped situation away from half-filling, arguing that it arises from the strongly temperature dependent 2D Friedel oscillations (i.e. finite momentum screening) associated with random quenched charged impurities, leading to the observed strongly increasing linear-in-$T$ resistivity in the metallic phase. Our theory appears to account for the temperature-dependent metallic resistivity for doping around half-filling of the effective moiré TMD band, showing that temperature-dependent screened Coulomb disorder is an essential ingredient of doped 2D mTMD physics.

cond-mat.mes-hall↗

arXiv2022

Disorder induced 2D metal-insulator transition in moiré transition metal dichalcogenide multilayers

We develop a minimal theory for the recently observed metal-insulator transition (MIT) in two-dimensional (2D) moiré multilayer transition metal dichalcogenides (mTMD) using Coulomb disorder in the environment as the underlying mechanism. In particular, carrier scattering by random charged impurities leads to an effective 2D MIT approximately controlled by the Ioffe-Regel criterion, which is qualitatively consistent with the experiments. We find the necessary disorder to be around $5$-$10\times10^{10}$cm$^{-2}$ random charged impurities in order to quantitatively explain much, but not all, of the observed MIT phenomenology as reported by two different experimental groups. Our estimate is consistent with the known disorder content in TMDs.

cond-mat.mes-hall↗

arXiv2022

On-demand large-conductance in trivial zero-bias tunneling peaks in Majorana nanowires

Motivated by recent experiments that report the almost-generic large-conductance peaks without very extensive fine-tuning, we propose an alternative mechanism through direct theoretical simulations that can explain the large zero-bias conductance peaks being generated on-demand in the nontopological regime in Majorana nanowires by satisfying the following three sufficient conditions: (i) strong potential disorder in the bulk of the nanowire, suppressing the topological regime; (ii) strong suppression of the disorder near the nanowire ends connecting to the tunneling leads, perhaps because of screening by the metallic leads and gates; and (iii) low tunnel barrier strength leading to large tunneling amplitude. The third condition is typically achieved experimentally by fine-tuning the tunnel barrier and the first condition is generic in all existing nanowires by virtue of considerable sample disorder induced by unintentional random quenched charged impurities. The second condition is likely to apply to many samples since the disorder potential would be typically screened more strongly at the wire ends because of the large metallic tunnel pads used experimentally. We show that the resultant tunneling conductance manifests large trivial zero-bias peaks almost on demand, and such peaks could be $\sim 2e^2/h$, when appropriately fine-tuned by the tunnel barrier strength and the temperature, as reported experimentally. Our work not only solves the mystery in recent experiments that the observations of the large zero-bias conductance peaks are generic by proposing a theoretically possible mechanism but also explains why these hypothesized conditions are naturally satisfied in experiments.

cond-mat.mes-hall↗

arXiv2022

Euler Obstructed Cooper Pairing: Nodal Superconductivity and Hinge Majorana Zero Modes

Since the proposal of monopole Cooper pairing in [Phys. Rev. Lett. 120, 067003 (2018)], considerable research efforts have been dedicated to the study of Cooper pairing order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces in 3D systems. In the current work, we generalize the topologically obstructed pairings between Chern states (like the monopole Cooper pairing) by proposing Euler obstructed Cooper pairing in 3D systems. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterized by nonzero Euler numbers; such Fermi surfaces can exist in 3D PT-protected spinless-Dirac/nodal-line semimetals with negligible spin-orbit coupling, where PT is the space-time inversion symmetry. An Euler obstructed pairing channel must have pairing nodes on the pairing-relevant Fermi surfaces, and the total winding number of the pairing nodes is determined by the sum or difference of the Euler numbers on the Fermi surfaces. In particular, we find that when the normal state is time-reversal invariant and the pairing is weak, a sufficiently-dominant Euler obstructed pairing channel with zero total momentum leads to nodal superconductivity. If the Fermi surface splitting is small, the resultant nodal superconductor hosts hinge Majorana zero modes. The possible dominance of the Euler obstructed pairing channel near the superconducting transition and the robustness of the hinge Majorana zero modes against disorder are explicitly demonstrated using effective or tight-binding models. Our work presents the first class of higher-order nodal superconductivity originating from the topologically obstructed Cooper pairing.

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↗

arXiv2022

Euler Obstructed Cooper Pairing in Twisted Bilayer Graphene: Nematic Nodal Superconductivity and Bounded Superfluid Weight

Magic-angle twisted bilayer graphene (MATBG) hosts normal-state nearly-flat bands with nonzero Euler numbers and shows superconductivity. In this work, we study the effects of the nontrivial normal-state band topology on the intervalley $C_{2z}\mathcal{T}$-invariant mean-field Cooper pairing order parameter in MATBG. We show that the pairing order parameter can always be split into a trivial channel and an Euler obstructed channel in all gauges for the normal-state basis, generalizing the previously-studied channel splitting in the Chern gauge. The nonzero normal-state Euler numbers require the pairing gap function of the Euler obstructed channel to have zeros, while the trivial channel can have a nonvanishing pairing gap function. When the pairing is spontaneously nematic, we find that a sufficiently-dominant Euler obstructed channel with two zeros typically leads to nodal superconductivity. Under the approximation of exactly-flat bands, we find that the mean-field zero-temperature superfluid weight is generally bounded from below, no matter whether the Euler obstructed channel is dominant or not, generalizing the previously-derived bound for the uniform s-wave pairing. We numerically verify these statements for pairings derived from a local attractive interaction. Our work suggests that Euler obstructed Cooper pairing may play an essential role in the superconducting MATBG.

cond-mat.supr-con↗

arXiv2022

Density-dependent two-dimensional optimal mobility in ultra-high-quality semiconductor quantum wells

We calculate using the Boltzmann transport theory the density dependent mobility of two-dimensional (2D) electrons in GaAs, SiGe and AlAs quantum wells as well as of 2D holes in GaAs quantum wells. The goal is to precisely understand the recently reported breakthrough in achieving a record 2D mobility for electrons confined in a GaAs quantum well. Comparing our theory with the experimentally reported electron mobility in GaAs quantum wells, we conclude that the mobility is limited by unintentional background random charged impurities at an unprecedented low concentration of $\sim10^{13} \mathrm{cm}^{-3}$. We find that this same low level of background disorder should lead to 2D GaAs hole and 2D AlAs electron mobilities of $\sim10^7 \mathrm{cm}^2/Vs$ and $\sim4\times10^7 \mathrm{cm}^2/Vs$, respectively, which are much higher theoretical limits than the currently achieved experimental values in these systems. We therefore conclude that the current GaAs hole and AlAs electron systems are much dirtier than the state of the arts 2D GaAs electron systems. We present theoretical results for 2D mobility as a function of density, effective mass, quantum well width, and valley degeneracy, comparing with experimental data.

cond-mat.mes-hall↗