arXiv subjects

Sankar Das Sarma

Publications and source records attributed to Sankar Das Sarma.

At least 163 records · Page 9Linked to original sources

arXiv2021

Exact analytical treatment of multiqubit noisy dynamics in exchange-coupled semiconductor spin qubits

Charge noise remains the primary obstacle to the development of quantum information technologies with semiconductor spin qubits. We use an exact analytical calculation to determine the effects of quasistatic charge noise on a ring of three equally spaced exchange-coupled quantum dots. We calculate the disorder-averaged return probability from a specific initial state, and use it to determine the coherence time T2* and show that it depends only on the disorder strength and not the mean interaction strength. We also use a perturbative approach to investigate other arrangements of three or four qubits, finding that the return probability contains multiple oscillation frequencies. These oscillations decay in a Gaussian manner, determined by differences in energy levels of the Hamiltonian. We give quantitative values for gate times resulting in several target fidelities. We find that the decoherence time decreases with increasing number of qubits. Our work provides useful analytical insight into the charge noise dynamics of coupled spin qubits.

cond-mat.mes-hall↗

arXiv2021

Hydrodynamic sound and plasmons in three dimensions

In a recent paper by Lucas and Das Sarma [Physical Review B 97, 115449 (2018)], a solvable model of collective modes in 2D metals was considered in the hydrodynamic regime. In the current work, we generalize the hydrodynamic theory to 3D metals for which the calculation of sound modes in a strongly-coupled quantum Coulomb plasma can be made explicit. The specific theoretical question of interest is how the usual linearly dispersing hydrodynamic sound mode relates to the well-known gapped 3D plasmon collective mode in the presence of long-range Coulomb interaction. We show analytically that both the zero sound in the collisionless regime and the first sound in the hydrodynamic region become massive in 3D, acquiring a finite gap because of the long-range Coulomb interaction, while their damping rates become quadratic in momentum. We also discuss other types of long-range potential, where the dispersion of sound modes is modified accordingly. The general result is that the leading order hydrodynamic sound mode is always given by the leading-order plasmon frequency in the presence of long-range Coulomb interaction, but the next-to-leading-order dispersion corrections differ in hydrodynamic and colllisionless regimes.

cond-mat.str-el↗

arXiv2021

Charge impurity effects in hybrid Majorana nanowires

We address an outstanding problem that represents a critical roadblock in the development of the Majorana-based topological qubit using semiconductor-superconductor hybrid structures: the quantitative characterization of disorder effects generated by the unintentional presence of charge impurities within the hybrid device. Given that disorder can have far-reaching consequences for the Majorana physics, but is intrinsically difficult to probe experimentally in a hybrid structure, providing a quantitative theoretical description of disorder effects becomes essential. To accomplish this task, we develop a microscopic theory that (i) provides a quantitative characterization of the effective potential generated by a charge impurity embedded inside a semiconductor wire proximity-coupled to a superconductor layer by solving self-consistently the associated three-dimensional Schrödinger-Poisson problem, (ii) describes the low-energy physics of the hybrid structure in the presence of s-wave superconductivity, spin-orbit coupling, Zeeman splitting, and disorder arising from multiple charge impurities by using the results of (i) within a standard free fermion approach, and (iii) links the microscopic results to experimentally observable features by generating tunneling differential conductance maps as function of the control parameters (e.g., Zeeman field and chemical potential). We find that charge impurities lead to serious complications regarding the realization and observation of Majorana zero modes, which have direct implications for the development of Majorana-based qubits. More importantly, our work provides a clear direction regarding what needs to be done for progress in the field, including specific materials quality and semiconductor purity targets that must be achieved to create a topological qubit.

cond-mat.mes-hall↗

arXiv2020

Time-reversal-invariant $C_2$-symmetric higher-order topological superconductors

We propose a minimal lattice model for two-dimensional class DIII superconductors with $C_2$-protected higher-order topology. While this class of superconductors cannot be topologically characterized by symmetry eigenvalues at high symmetry momenta, we propose a simple Wannier-orbital-based real-space diagnosis to unambiguously capture the corresponding higher-order topology. We further identify and characterize a variety of conventional topological phases in our minimal model, including a weak topological superconductor and a nodal topological superconductor with chiral-symmetry protection. The disorder effect is also systematically studied to demonstrate the robustness of higher-order bulk-boundary correspondence. Our theory lays the groundwork for predicting and diagnosing $C_2$-protected higher-order topology in class DIII superconductors.

cond-mat.supr-con↗

arXiv2020

Quantum Phase Diagram of a Moiré-Hubbard Model

We theoretically study a generalized Hubbard model on moiré superlattices of twisted bilayers, and find very rich filling-factor-dependent quantum phase diagrams tuned by interaction strength and twist angle. Strong long-range Coulomb interaction in the moiré-Hubbard model induces Wigner crystals at a series of fractional filling factors. The effective lattice of the Wigner crystal is controlled by the filling factor, and can be triangle, rectangle, honeycomb, kagome, etc, providing a single platform to realize many different spin models on various lattices by simply tuning carrier density. In addition to Wigner crystals that are topologically trivial, interaction-induced Chern insulators emerge in the phase diagram. This finding paves a way for engineering interaction-induced quantum anomalous Hall effect in moiré-Hubbard systems where the corresponding single-particle moiré band is topologically trivial.

cond-mat.str-el↗

arXiv2020

Fermi-surface topology and renormalization of bare ellipticity in an interacting anisotropic electron gas

We investigate effects of electron-electron interactions on the shape of the Fermi surface in an anisotropic two-dimensional electron gas using the `RPA-GW' self-energy approximation. We find that the interacting Fermi surface deviates from an ellipse, but not in an arbitrary way. The interacting Fermi surface has only two qualitatively distinct shapes for most values of $r_s$. The Fermi surface undergoes two distinct transitions between these two shapes as $r_s$ increases. For larger $r_s$, the degree of the deviation from an ellipse rapidly increases, but, in general, our theory provides a justification for the widely used elliptical Fermi surface approximation even for the interacting system since the non-elliptic corrections are quantitatively rather small except for very large $r_s$.

cond-mat.mes-hall↗

arXiv2020

The two-dimensional electron self-energy: Long-range Coulomb interaction

The electron self-energy for long-range Coulomb interactions plays a crucial role in understanding the many-body physics of interacting electron systems (e.g. in metals and semiconductors), and has been studied extensively for decades. In fact, it is among the oldest and the most-investigated many body problems in physics. However, there is a lack of an analytical expression for the self-energy $Re Σ^{(R)}( \varepsilon,T)$ when energy $\varepsilon$ and temperature $k_{B} T$ are arbitrary with respect to each other (while both being still small compared with the Fermi energy). We revisit this problem and calculate analytically the self-energy on the mass shell for a two-dimensional electron system with Coulomb interactions in the high density limit $r_s \ll 1$, for temperature $ r_s^{3/2} \ll k_{B} T/ E_F \ll r_s$ and energy $r_s^{3/2} \ll |\varepsilon |/E_F \ll r_s$. We provide the exact high-density analytical expressions for the real and imaginary parts of the electron self-energy with arbitrary value of $\varepsilon /k_{B} T$, to the leading order in the dimensionless Coulomb coupling constant $r_s$, and to several higher than leading orders in $k_{B} T/r_s E_F$ and $\varepsilon /r_s E_F$. We also obtain the asymptotic behavior of the self-energy in the regimes $|\varepsilon | \ll k_{B} T$ and $|\varepsilon | \gg k_{B} T$. The higher-order terms have subtle and highly non-trivial compound logarithmic contributions from both $\varepsilon $ and $T$, explaining why they have never before been calculated in spite of the importance of the subject matter.

cond-mat.str-el↗

arXiv2020

Hofstadter butterfly and Floquet topological insulators in minimally twisted bilayer graphene

We theoretically study the Hofstadter butterfly of a triangular network model in minimally twisted bilayer graphene (mTBLG). The band structure manifests periodicity in energy, mimicking that of Floquet systems. The butterfly diagrams provide fingerprints of the model parameters and reveal the hidden band topology. In a strong magnetic field, we establish that mTBLG realizes low-energy Floquet topological insulators (FTIs) carrying zero Chern number, while hosting chiral edge states in bulk gaps. We identify the FTIs by analyzing the nontrivial spectral flow in the Hofstadter butterfly, and by explicitly computing the chiral edge states. Our theory paves the way for an effective practical realization of FTIs in equilibrium solid state systems.

cond-mat.mes-hall↗

arXiv2020

Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems

The ability to perform gates in multiqubit systems that are robust to noise is of crucial importance for the advancement of quantum information technologies. However, finding control pulses that cancel noise while performing a gate is made difficult by the intractability of the time-dependent Schrodinger equation, especially in multiqubit systems. Here, we show that this issue can be sidestepped by using a formalism in which the cumulative error during a gate is represented geometrically as a curve in a multi-dimensional Euclidean space. Cancellation of noise errors to leading order corresponds to closure of the curve, a condition that can be satisfied without solving the Schrodinger equation. We develop and uncover general properties of this geometric formalism, and derive a recursion relation that maps control fields to curvatures for Hamiltonians of arbitrary dimension. We demonstrate examples by using the geometric method to design dynamically corrected gates for a class of two-qubit Hamiltonians that is relevant for both superconducting transmon qubits and semiconductor spin qubits. We propose this geometric formalism as a general technique for pulse-induced error suppression in quantum computing gate operations.

quant-ph↗

arXiv2020

Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer WSe$_2$

We present a theoretical study of single-particle and many-body properties of twisted bilayer WSe$_2$. For single-particle physics, we calculate the band topological phase diagram and electron local density of states (LDOS), which are found to be correlated. By comparing our theoretical LDOS with those measured by scanning tunneling microscopy, we comment on the possible topological nature of the first moiré valence band. For many-body physics, we construct a generalized Hubbard model on a triangular lattice based on the calculated single-particle moiré bands. We show that a layer potential difference, arising, for example, from an applied electric field, can drastically change the non-interacting moiré bands, tune the spin-orbit coupling in the Hubbard model, control the charge excitation gap of the Mott insulator at half filling, and generate an effective Dzyaloshinskii-Moriya interaction in the effective Heisenberg model for the Mott insulator. Our theoretical results agree with transport experiments on the same system in several key aspects, and establish twisted bilayer WSe$_2$ as a highly tunable system for studying and simulating strongly correlated phenomena in the Hubbard model.

cond-mat.str-el↗

arXiv2020

Resistivity saturation in an electron-doped cuprate

We report the observation of resistivity saturation in lightly doped ($x\sim 0.10)$ as-grown samples of the electron-doped cuprate La$_{2-x}$Ce$_x$CuO$_4$ (LCCO). The saturation occurs at resistivity values roughly consistent with the phenomenological Mott-Ioffe-Regel criterion once the low effective carrier density of these materials is included in the analysis. These results imply that, at least for light doping, the high-temperature metallic phase of these materials is not necessarily strange and may be understood as simply a low-density metal.

cond-mat.str-el↗

arXiv2020

Landau poles in condensed matter systems

The existence or not of Landau poles is one of the oldest open questions in non-asymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the $ϕ^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the $ϕ^6$ potential, can significantly change the fate of the Landau pole in the $ϕ^4$ theory. We obtain the coupled beta functions of a $ϕ^4 + ϕ^6$ potential at both small and large orders. Already from the 1-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a $ϕ^6$ term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in 2+1 dimensional Dirac fermions with Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to 2 loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a $ϕ^4$ theory, so graphene is free from Landau poles if the $ϕ^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.

cond-mat.str-el↗

arXiv2020

Tunneling conductance of long-range Coulomb interacting Luttinger liquid

The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynamic range of temperature and bias voltage, the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale-dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.

cond-mat.str-el↗

arXiv2020

Collective ground states in small lattices of coupled quantum dots

Motivated by recent developments on the fabrication and control of semiconductor-based quantum dot qubits, we theoretically study a finite system of tunnel-coupled quantum dots with the electrons interacting through the long-range Coulomb interaction. When the inter-electron separation is large and the quantum dot confinement potential is weak, the system behaves as an effective Wigner crystal with a period determined by the electron average density with considerable electron hopping throughout the system. For stronger periodic confinement potentials, however, the system makes a crossover to a Mott-type strongly correlated ground state where the electrons are completely localized at the individual dots with little inter-dot tunneling. In between these two phases, the system is essentially a strongly correlated electron liquid with inter-site electron hopping constrained by strong Coulomb interaction. We characterize this Wigner-Mott-liquid quantum crossover with detailed numerical finite-size diagonalization calculations of the coupled interacting qubit system, showing that these phases can be smoothly connected by tuning the system parameters. Experimental feasibility of observing such a hopping-tuned Wigner-Mott-liquid crossover in currently available semiconductor quantum dot qubits is discussed. In particular, we connect our theoretical results to recent quantum-dot-based quantum emulation experiments where collective Coulomb blockade was demonstrated. One conclusion of our theory is that currently available realistic quantum dot arrays are unable to explore the low-density Wigner phase with only the Mott-liquid crossover being accessible experimentally.

cond-mat.mes-hall↗

arXiv2020

Electron-phonon and electron-electron interaction effects in twisted bilayer graphene

By comparing with recently available experimental data from several groups, we critically discuss the manifestation of continuum many body interaction effects in twisted bilayer graphene (tBLG) with small twist angles and low carrier densities, which arise naturally within the Dirac cone approximation for the non-interacting band structure. We provide two specific examples of such continuum many body theories: one involving electron-phonon interaction and one involving electron-electron interaction. In both cases, the experimental findings are only partially quantitatively consistent with rather clear-cut leading-order theoretical predictions based on well-established continuum many body theories. We provide a critical discussion, based mainly on the currently available tBLG experimental data, on possible future directions for understanding many body renormalization involving electron-phonon and electron-electron interactions in the system. One definitive conclusion based on the comparison between theory and experiment is that the leading order 1-loop perturbative renormalization group theory completely fails to account for the electron-electron interaction effects in the strong-coupling limit of flatband moiré tBLG system near the magic twist angle even at low doping where the Dirac cone approximation should apply. By contrast, approximate nonperturbative theoretical results based on Borel-Padé resummation or $1/N$ expansion seems to work well compared with experiments, indicating rather small interaction corrections to Fermi velocity or carrier effective mass. For electron-phonon interactions, however, the leading-order continuum theory works well except when van Hove singularities in the density of states come into play.

cond-mat.mes-hall↗

arXiv2020

Three-Dimensional Topological Twistronics

We introduce a theoretical framework for the new concept of three-dimensional (3D) twistronics by developing a generalized Bloch band theory for 3D layered systems with a constant twist angle $θ$ between successive layers. Our theory employs a nonsymmorphic symmetry that enables a precise definition of an effective out-of-plane crystal momentum, and also captures the in-plane moiré pattern formed between neighboring twisted layers. To demonstrate the novel topological physics that can be achieved through 3D twistronics, we present two examples. In the first example of chiral twisted graphite, Weyl nodes arise because of inversion-symmetry breaking, with $θ$-tuned transitions between type-I and type-II Weyl fermions, as well as magic angles at which the in-plane velocity vanishes. In the second example of twisted Weyl semimetal, the twist in the lattice structure induces a chiral gauge field $\boldsymbol{\mathcal{A}}$ that has a vortex-antivortex lattice configuration. Line modes bound to the vortex cores of the $\boldsymbol{\mathcal{A}}$ field give rise to 3D Weyl physics in the moiré scale. We also discuss possible experimental realizations of 3D twistronics.

cond-mat.mes-hall↗

arXiv2020

Ferromagnetism and superconductivity in twisted double bilayer graphene

We present a theory of competing ferromagnetic and superconducting orders in twisted double bilayer graphene (TDBG). In our theory, ferromagnetism is induced by Coulomb repulsion, while superconductivity with intervalley equal-spin pairing can be mediated by electron-acoustic phonon interactions. We calculate the transition temperatures for ferromagnetism and superconductivity as a function of moiré band filling factor, and find that superconducting domes can appear on both the electron and hole sides of the ferromagnetic insulator at half filling. We show that the ferromagnetic insulating gap has a dome shape dependence on the layer potential difference, which provides an explanation to the experimental observation that the ferromagnetic insulator only develops over a finite range of external displacement field. We also verify the stability of the half-filled ferromagnetic insulator against two types of collective excitations, i.e., spin magnons and valley magnons.

cond-mat.str-el↗

arXiv2020

One-dimensional few-electron effective Wigner crystal in quantum and classical regimes

A system of confined charged electrons interacting via the long-range Coulomb force can form a Wigner crystal due to their mutual repulsion. This happens when the potential energy of the system dominates over its kinetic energy, i.e., at low temperatures for a classical system and at low densities for a quantum one. At $T=0$, the system is governed by quantum mechanics, and hence, the spatial density peaks associated with crystalline charge localization are sharpened for a lower average density. Conversely, in the classical limit of high temperatures, the crystalline spatial density peaks are suppressed (recovered) at a lower (higher) average density. In this paper, we study those two limits separately using an exact diagonalization of small one-dimensional (1D) systems containing few ($<10$) electrons and propose an approximate method to connect them into a unified effective phase diagram for Wigner few-electron crystallization. The result is a qualitative quantum-classical crossover phase diagram of an effective 1D Wigner crystal. We show that the spatial density peaks associated with the quasi-crystallization should be experimentally observable in a few-electron 1D system. We find that the effective crystalline structure slowly disappears with both the crossover average density and crossover temperature for crystallization decreasing with increasing particle number, consistent with the absence of any true long-range 1D order. In fact, one peculiar aspect of the effective finite-size nature of 1D Wigner crystallization we find is that even a short-range interaction would lead to a finite-size 1D crystal, except that the crystalline order vanishes much faster with increasing system size in the short-range interacting system compared with the long-range interacting one.

cond-mat.mes-hall↗