arXiv subjects

Sankar Das Sarma

Publications and source records attributed to Sankar Das Sarma.

At least 109 records · Page 6Linked to original sources

arXiv2023

Statistics of noninteracting many-body fermionic states: The question of a many-body mobility edge

In this work, we study the statistics of a generic noninteracting many-body fermionic system whose single-particle counterpart has a single-particle mobility edge (SPME). We first prove that the spectrum and the extensive conserved quantities follow the multivariate normal distribution with a vanishing standard deviation $\sim O(1/\sqrt L)$ in the thermodynamic limit, regardless of SPME. Consequently, the theorem rules out an infinite-temperature or high-temperature many-body mobility edge (MBME) for generic noninteracting fermionic systems. Further, we also prove that the spectrum of a fermionic many-body system with short-range interactions is qualitatively similar to that of a noninteracting many-body system up to the third-order moment. These results partially explain why neither short-range [1] nor long-range interacting systems exhibit an infinite-temperature MBME.

cond-mat.dis-nn↗

arXiv2023

Interaction-enhanced many body localization in a generalized Aubry-Andre model

We study the many-body localization (MBL) transition in a generalized Aubry-Andre model (also known as the GPD model) introduced in Phys. Rev. Lett. 114, 146601 (2015). In contrast to MBL in other disordered or quasiperiodic models, the interaction seems to unexpectedly enhance MBL in the GPD model in some parameter ranges. To understand this counter-intuitive result, we demonstrate that the highest-energy single-particle band in the GPD model is unstable against even infinitesimal disorder, which leads to this surprising MBL phenomenon in the interacting model. We develop a mean-field theory description to understand the coupling between extended and localized states, which we validate using extensive exact diagonalization and DMRG-X numerical results.

cond-mat.dis-nn↗

arXiv2023

Density-tuned effective metal-insulator transitions in 2D semiconductor layers: Anderson localization or Wigner crystallization

Electrons (or holes) confined in 2D semiconductor layers have served as model systems for studying disorder and interaction effects for almost 50 years. In particular, strong disorder drives the metallic 2D carriers into a strongly localized Anderson insulator (AI) at low densities whereas pristine 2D electrons in the presence of no (or little) disorder should solidify into a Wigner crystal at low carrier densities. Since the disorder in 2D semiconductors is mostly Coulomb disorder arising from random charged impurities, the applicable physics is complex as the carriers interact with each other as well as with the random charged impurities through the same long-range Coulomb coupling. By critically theoretically analyzing the experimental transport data in depth using a realistic transport theory to calculate the low-temperature 2D resistivity as a function of carrier density in 11 different experimental samples covering 9 different materials, we establish, utilizing the Ioffe-Regel-Mott criterion for strong localization, a direct connection between the critical localization density for the 2D metal-insulator transition (MIT) and the sample mobility deep into the metallic state, which for clean samples could lead to a localization density low enough to make the transition appear to be a Wigner crystallization. We believe that the insulating phase is always an effective Coulomb disorder-induced localized AI, which may have short-range WC-like correlations at low carrier densities. Our theoretically calculated disorder-driven critical MIT density agrees with experimental findings in all 2D samples, even for the ultra-clean samples. In particular, the extrapolated critical density for the 2D MIT seems to vanish when the high-density mobility goes to infinity, indicating that transport probes a disorder-localized insulating ground state independent of how low the carrier density might be.

cond-mat.mes-hall↗

arXiv2023

The kinetic theory of ultra-subsonic fermion systems and applications to flat band magic angle twisted bilayer graphene

The only kinematically-allowed phonon-scattering events for bands of subsonic fermions ($v_F < v_p$) are interband transitions, leading to different low-$T$ transport physics than in the typical supersonic case. We apply a kinetic theory of phonon-limited transport to a generic two-band system of subsonic fermions, deriving formulae for relaxation times and resistivity that are accurate in the limit of close bands and small $v_F/v_p$. We predict regimes of $ρ\propto T$, $ρ\propto T^2$, and perfect conductivity. Our theory predicts linear-in-$T$ resistivity down to a crossover temperature that is suppressed from its supersonic analogue by a factor of $v_F/v_p$, offering a new explanation for low-$T$ "strange metal" behavior observed in flat band systems.

cond-mat.mes-hall↗

arXiv2023

Anderson localization in doped semiconductors

We theoretically consider the problem of doping induced insulator to metal transition in bulk semiconductors by obtaining the transition density as a function of compensation, assuming that the transition is an Anderson localization transition controlled by the Ioffe-Regel-Mott (IRM) criterion. We calculate the mean free path, on the highly doped metallic side, arising from carrier scattering by the ionized dopants, which we model as quenched random charged impurities. The Coulomb disorder of the charged dopants is screened by the carriers themselves, leading to an integral equation for localization, defined by the density-dependent mean free path being equal to the inverse of the Fermi wave number, as dictated by the IRM criterion. Solving this integral equation approximately analytically and exactly numerically, we provide detailed results for the localization critical density for the doping induced metal-insulator transition.

cond-mat.dis-nn↗

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↗

arXiv2023

Realizable time crystal of four silicon quantum dot qubits

We demonstrate that exciting possible realizations of quantum Floquet matter are within reach for modern silicon spin qubits based in quantum dots, most notably the discrete time crystal (DTC). This is significant given that spin qubits have fallen behind other qubit architectures in terms of size and control. However, silicon spin qubits are especially well suited to this task as the charge noise that usually foils gate operations can now be leveraged as an asset in this time-crystal realization. We illustrate differences between prethermal phenomena and true time-crystalline spatiotemporal order. We demonstrate that even for a spin chain of four qubits, rich regime structures can be established by observing signatures of the discrete time crystal and the Floquet symmetry-protected topological regime both distinct from the thermal regime. We also analyze the persistence of these signatures at longer chain lengths, showing that the DTC lifetime grows exponentially with the system length and that these signatures may even be detectable for chains as small as three qubits. We also discuss the effects of longer pulse durations and the effectiveness of pulse sequences for converting the exchange interaction to an Ising model. Our theoretical predictions are well suited for immediate experimental implementations using currently existing quantum dot spin qubit systems.

quant-ph↗

arXiv2023

Dissipative prethermal discrete time crystal

An ergodic system subjected to an external periodic drive will be generically heated to infinite temperature. However, if the applied frequency is larger than the typical energy scale of the local Hamiltonian, this heating stops during a prethermal period that extends exponentially with the frequency. During this prethermal period, the system may manifest an emergent symmetry that, if spontaneously broken, will produce sub-harmonic oscillation of the discrete time crystal (DTC). We study the role of dissipation on the survival time of the prethermal DTC. On one hand, a bath coupling increases the prethermal period by slowing down the accumulation of errors that eventually destroy prethermalization. On the other hand, the spontaneous symmetry breaking is destabilized by interaction with environment. The result of this competition is a non-monotonic variation, i.e. the survival time of the prethermal DTC first increases and then decreases as the environment coupling gets stronger.

cond-mat.mes-hall↗

arXiv2023

Apparent Kondo effect in Moiré TMD bilayers: Heavy fermions or disorder?

A recent work by Zhao et al. [1] reports the realization of a synthetic Kondo lattice in a gate-tunable Moiré TMD bilayer system. The observation of a Kondo lattice is supported by a plateau (or dip, depending on filling) in the temperature dependence of the resistivity $ρ(T)$ around $T^*\sim 40~$K, which is interpreted as the Kondo temperature scale, and an apparent enhancement of carrier mass extracted from the low-temperature resistivity data, indicating the emergence of `heavy fermions'. The latter observation is crucially based on the assumption that the primary resistive scattering mechanism is Umklapp electron-electron scattering in the underlying Fermi liquid. In this work, we analyze the experimental data under the assumption that the primary resistive scattering mechanism is not electron-electron scattering, but Coulomb scattering by random quenched charged impurities and phonon scattering. We show that a combination of impurity and phonon scattering is a plausible alternative explanation for the observed resistivity that can describe the key features of the experimental data, even if no Kondo lattice has formed, indicating that further theoretical and experimental work is needed to conclusively verify the formation of a Kondo lattice in Ref. [1]. [1] W. Zhao, B. Shen, Z. Tao, Z. Han, K. Kang, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, arXiv:2211.00263 (2022).

cond-mat.mes-hall↗

arXiv2023

Wiedemann-Franz law in graphene

We analyze a well-known experimental work [J. Crossno et al., Science 351, 1058 (2016)] which reported on the failure of the Wiedemann-Franz law in graphene at $T\sim 10$-$100\,\mathrm{K}$, attributing this failure to the non-Fermi liquid nature of the Dirac fluid associated with undoped intrinsic graphene. In spite of serious theoretical efforts, the reported observations remain unexplained. Our detailed quantitative analysis based on Fermi liquid considerations, which apply to extrinsic doped graphene, establishes that one possible explanation for the reported observations is the opening of a gap at the Dirac point, induced perhaps by the boron nitride substrate. We suggest that more experiments are necessary to resolve the issue, and we believe that the experiment may not actually have anything to do with Dirac fluid hydrodynamics, but relates to finite-temperature low-density bipolar diffusive transport by electrons and holes in the presence of short- and long-range disorder, and phonons.

cond-mat.mes-hall↗

arXiv2023

Majorana nanowires, Kitaev chains, and spin models

Motivated by the fact that the idealized Kitaev chain toy model and the experimental semiconductor-superconductor Majorana nanowire can both host the Majorana zero modes, we theoretically investigate the question to what extent the two models are equivalent or similar, using the perspective of the corresponding dual spin models for both. We start with the duality between the Kitaev chain and the transverse-field XY spin model through the Jordan-Wigner transformation with the goal of establishing the connection between the Kitaev chain and the nanowire. By applying the Jordan-Wigner transformation to the nanowire, we find that the corresponding bosonic spin model is a generalized spin cluster model, containing 3-spin and 4-spin terms, with staggered couplings. By projecting out the upper band of the bare semiconductor with higher energy, we obtain an effective low-energy spinless system from the spinful nanowire system deep in the topological regime. Finally, we establish the connection between the Kitaev chain and Majorana nanowire by showing that the spinless Kitaev chain can be viewed as the first-order approximation of the spinful Majorana nanowire deep in the topological regime.

cond-mat.mes-hall↗

arXiv2023

Phonon-limited resistivity of multilayer graphene systems

We calculate the theoretical contribution to the doping and temperature ($T$) dependence of electrical resistivity due to scattering by acoustic phonons in Bernal bilayer graphene (BBG) and rhombohedral trilayer graphene (RTG). We focus on the role of nontrivial geometric features of the detailed, anisotropic $k\cdot p$ band structures of these systems - e.g. Van Hove singularities, Lifshitz transitions, Fermi surface anisotropy, and band curvature near the gap - whose effects on transport have not yet been systematically studied. We find that these geometric features strongly influence the temperature and doping dependencies of the resistivity. In particular, the band geometry leads to a nonlinear $T$-dependence in the high-$T$ equipartition regime, complicating the usual $T^4$ to $T$ Bloch-Grüneisen crossover. Our focus on BBG and RTG is motivated by recent experiments in these systems that have discovered several exotic low-$T$ superconductivity proximate to complicated hierarchies of isospin-polarized phases. These interaction-driven phases are intimately related to the geometric features of the band structures, highlighting the importance of understanding the influence of band geometry on transport. While resolving the effects of the anisotropic band geometry on the scattering times requires nontrivial numerical solution, our approach is rooted in intuitive Boltzmann theory. We compare our results with recent experiment and discuss how our predictions can be used to elucidate the relative importance of various scattering mechanisms in these systems.

cond-mat.mes-hall↗

arXiv2023

Certain exact many-body results for Hubbard model ground states testable in small quantum dot arrays

We present several interesting phenomena related to flatband ferromagnetism in the Hubbard model. The first is a mathematical theorem stating certain conditions under which a flatband ferromagnetic must necessarily be degenerate with a nonferromagnetic state. This theorem is generally applicable and geometry-independent, but holds only for a small number of holes in an otherwise filled band. The second phenomenon is a peculiar example where the intuition fails that particles prefer to doubly occupy low-energy states before filling higher-energy states. Lastly, we show a pattern of ferromagnetism which appears in small pentagonal and hexagonal plaquettes at filling factors of roughly 3/10 and 1/4. These examples require only a small number of lattice sites, and may be observable in quantum dot arrays currently available as laboratory spin qubit arrays.

cond-mat.mes-hall↗

arXiv2023

Avalanche stability transition in interacting quasiperiodic systems

Coupling a 1D quasiperiodic interacting system to a Markovian bath, we study the avalanche instability of the many body localized phase numerically, finding that many body localization (MBL) is more stable in pseudorandom quasiperiodic systems than the corresponding randomly disordered systems for a disorder strength $W>8$, potentially up to arbitrarily large system sizes. We support our conclusion by additionally developing real space RG arguments, and provide a detailed comparison between quasiperiodic and random MBL from the avalanche instability perspective, concluding that the two belong to different universality classes.

cond-mat.dis-nn↗

arXiv2022

Collective modes in interacting two-dimensional tomographic Fermi liquids

We develop an analytically solvable model for interacting two-dimensional Fermi liquids with separate collisional relaxation rates for parity-odd and parity-even Fermi surface deformations. Such a disparity of collisional lifetimes exists whenever scattering is restricted to inversion-symmetric Fermi surfaces, and should thus be a generic feature of two-dimensional Fermi liquids. It implies an additional unanticipated "tomographic" transport regime (in between the standard collisionless and hydrodynamic regimes) in which even-parity modes are overdamped while odd-parity modes are collisionless. We derive expressions for both the longitudinal and the transverse conductivity and discuss the collective mode spectrum along the collisionless-tomographic-hydrodynamic crossover. Longitudinal modes cross over from zero sound in the collisionless regime to hydrodynamic first sound in the tomographic and hydrodynamic regime, where odd-parity damping appears as a subleading correction to the lifetime. In charged Fermi liquids with long-range Coulomb coupling, these modes reduce to plasmons with a strongly suppressed odd-parity correction to the damping. The transverse response, by contrast, has a specific tomographic transport regime with two imaginary odd-parity modes, one of which requires a finite repulsive interaction, distinct from both the shear sound in the collisionless regime and an overdamped diffusive current mode in the hydrodynamic limit. Our work demonstrates that there are deep many-body aspects of interacting Fermi liquids, which are often thought to be well understood theoretically, remaining unexplored.

cond-mat.mes-hall↗

arXiv2022

Enhanced superconductivity through virtual tunneling in Bernal bilayer graphene coupled to WSe$_2$

Motivated by a recent experiment [arXiv:2205.05087], we investigate a possible mechanism that enhances superconductivity in hole-doped Bernal bilayer graphene due to a proximate WSe$_2$ monolayer. We show that the virtual tunneling between WSe$_2$ and Bernal bilayer graphene, which is known to induce Ising spin-orbit coupling, can generate an additional attraction between two holes, providing a potential explanation for enhancing superconductivity in Bernal bilayer graphene. Using microscopic interlayer tunneling, we derive the Ising spin-orbit coupling and the effective attraction as functions of the twist angle between Bernal bilayer graphene and the WSe$_2$ monolayer. Our theory provides an intuitive and physical explanation for the intertwined relation between Ising spin-orbit coupling and superconductivity enhancement, which should motivate future studies.

cond-mat.supr-con↗

arXiv2022

Planckian properties of 2D semiconductor systems

We describe and discuss the low-temperature resistivity (and the temperature-dependent inelastic scattering rate) of several different doped 2D semiconductor systems from the perspective of the Planckian hypothesis asserting that $\hbar/τ=k_\mathrm{B}T$ provides a scattering bound, where $τ$ is the appropriate relaxation time. The regime of transport considered here is well-below the Bloch-Gruneisen regime so that phonon scattering is negligible. The temperature-dependent part of the resistivity is almost linear-in-$T$ down to arbitrarily low temperatures, with the linearity arising from an interplay between screening and disorder, connected with carrier scattering from impurity-induced Friedel oscillations. The temperature dependence disappears if the Coulomb interaction between electrons is suppressed. The temperature coefficient of the resistivity is enhanced at lower densities, enabling a detailed study of the Planckian behavior both as a function of the materials system and carrier density. Although the precise Planckian bound never holds, we find somewhat surprisingly that the bound seems to apply approximately with the scattering rate never exceeding $k_\mathrm{B} T$ by more than an order of magnitude either in the experiment or in the theory. In addition, we calculate the temperature-dependent electron-electron inelastic scattering rate by obtaining the temperature-dependent self-energy arising from Coulomb interaction, also finding it to obey the Planckian bound within an order of magnitude at all densities and temperatures. We introduce the concept of a generalized Planckian bound where $\hbar/τ$ is bounded by $αk_\mathrm{B} T$ with $α\sim 10$ or so in the super-Planckian regime with the strict Planckian bound of $α$=1 being a nongeneric finetuned situation.

cond-mat.mes-hall↗

arXiv2022

In search of Majorana

Majorana particles are the same as their antiparticle, and their analogues in condensed matter may be a platform for quantum computing. We describe the search for these modes in semiconductor heterostructures and how disorder is a limiting factor.

cond-mat.mes-hall↗