arXiv subjects

B. I. Shklovskii

Publications and source records attributed to B. I. Shklovskii.

At least 19 recordsLinked to original sources

arXiv2025

Phase diagram of solution of oppositely charged polyelectrolytes

We study a solution of long polyanions (PA) with shorter polycations (PC) and focus on the role of Coulomb interaction. A good example is solutions of DNA and PC which are widely studied for gene therapy. In the solution, each PA attracts many PCs to form a complex. When the ratio of total charges of PA and PC in the solution, $x$, equals to 1, complexes are neutral and they condense in a macroscopic drop. When $x$ is far away from 1, complexes are strongly charged. The Coulomb repulsion is large and free complexes are stable. As $x$ approaches to 1, PCs attached to PA disproportionate themselves in two competing ways. One way is inter-complex disproportionation, in which PCs make some complexes neutral and therefore condensed in a macroscopic drop while other complexes become even stronger charged and stay free. The other way is intra-complex disproportionation, in which PCs make one end of a complex neutral and condensed in a small droplet while the rest of the complex forms a strongly charged tail. Thus each complex becomes a "tadpole". These two ways can also combine together to give even lower free energy. We get a phase diagram of PA-PC solution in a plane of $x$ and inverse screening radius of the monovalent salt, which includes phases or phase coexistence with both kinds of disproportionation.

cond-mat.soft↗

arXiv2024

Half century of Efros-Shklovskii Coulomb gap. Romance with Coulomb interaction and disorder

Efros-Shklovskii (ES) Coulomb gap in density of localized states and ES law of the variable range hopping conductivity were coined 50 years ago. The theory and its first confirmations were reviewed in our monograph 40-years ago. This paper reviews the subsequent experimental evidence, theoretical advancements, and novel applications. Out of hundreds of experimental validations of the ES law in a diverse range of materials, I focus on those where the dynamic range of conductivity exceeds four orders of magnitude. These include three- and two-dimensional semiconductors under both zero and high magnetic fields, localized phases in the quantum Hall effect, granular metals, nanocrystal arrays, and conducting polymers. Additionally, this review discusses the Coulomb gap near insulator-metal transition and in non-ohmic ES law. Recent developments of other concepts of the ES book are also discussed.

cond-mat.mtrl-sci↗

arXiv2024

Electron binding energy of a donor in bilayer graphene with gate-tunable gap

In gapped bilayer graphene, similarly to conventional semiconductors, Coulomb impurities (such as nitrogen donors) may determine the activation energy of its conductivity and provide low temperature hopping conductivity. However, in spite of the importance of Coulomb impurities, nothing is known about their electron binding energy $E_b$ in the presence of gates. To close this gap, we study numerically the electron binding energy $E_b$ of a singly charged donor in BN-enveloped bilayer graphene with the top and bottom gates at distance $d$ and gate-tunable gap $2Δ$. We show that for $10 < d < 200$ nm and $1 < Δ< 100$ meV the ratio $E_b/Δ$ changes from 0.4 to 1.5. The ratio $E_b/Δ$ stays close to unity because of the dominating role of the bilayer polarization screening which reduces the Coulomb potential well depth to values $\sim Δ$. Still the ratio $E_b/Δ$ somewhat decreases with growing $Δ$, faster at small $Δ$ and slower at large $Δ$. On the other hand, $E_b/Δ$ weakly grows with $d$, again faster at small $Δ$ and slower at large $Δ$. We also studied the effect of trigonal warping and found only a small reduction of $E_b/Δ$.

cond-mat.mes-hall↗

arXiv2022

Biexciton crystal in a two-dimensional semiconductor heteropentalayer

This paper is written for the Special Issue in Honor of Emmanuel Rashba. We study the gas of indirect dipolar excitons created by an interband illumination of a pentalayer WSe$_2$/MoSe$_2$/WSe$_2$/MoSe$_2$/WSe$_2$. We show that two colinear indirect excitons bind into a linear biexciton with twice larger dipole moment. Two biexcitons with opposite dipole directions attract each other at large distances and repel each other at short distances. Therefore, biexcitons form a staggered crystal with anti-ferroelectric square lattice. The electrostatic energy of this crystal per biexciton has a minimum at the biexciton concentration $n =n_c=0.14d^{-2}$, where $d \sim 0.7$ nm is a single layer thickness. At small illumination intensity, biexcitons condense into sparse crystallites with $n = n_c$, where photoluminescence frequency is red shifted and independent on the light intensity. We also study a capacitor made of five identical semiconductor monolayers separated by hBN spacers where a critical voltage applied between layers 1, 3, 5, and 2, 4 abruptly creates a similar biexciton crystal. At this voltage, the differential capacitance diverges.

cond-mat.mes-hall↗

arXiv2022

Conductivity of two-dimensional small gap semiconductors and topological insulators in strong Coulomb disorder

We are honored to dedicate this article to Emmanuel Rashba on the occasion of his 95 birthday. In the ideal disorder-free situation, a two-dimensional band gap insulator has an activation energy for conductivity equal to half the band gap, $Δ$. But transport experiments usually exhibit a much smaller activation energy at low temperature, and the relation between this activation energy and $Δ$ is unclear. Here we consider the temperature-dependent conductivity of a two-dimensional narrow gap semiconductor on a substrate containing Coulomb impurities, mostly focusing on the case when amplitude of the random potential $Γ\gg Δ$. We show that the conductivity generically exhibits three regimes and only the highest temperature regime exhibits an activation energy that reflects the band gap. At lower temperatures, the conduction proceeds through nearest-neighbor or variable-range hopping between electron and hole puddles created by the disorder. We show that the activation energy and characteristic temperature associated with these processes steeply collapse near a critical impurity concentration. Larger concentrations lead to an exponentially small activation energy and exponentially long localization length, which in mesoscopic samples can appear as a disorder-induced insulator-to-metal transition. We arrive at a similar disorder driven steep insulator-metal transition in thin films of three-dimensional topological insulators with very large dielectric constant, where due to confinement of electric field internal Coulomb impurities create larger disorder potential. Away from neutrality point this unconventional insulator-to-metal transition is augmented by conventional metal-insulator transition at small impurity concentrations, so that we arrive at disorder-driven re-entrant metal-insulator-metal transition.

cond-mat.mes-hall↗

arXiv2022

Scattering mechanisms in state-of-the-art GaAs/AlGaAs quantum wells

Motivated by recent breakthrough in molecular beam epitaxy of GaAs/AlGaAs quantum wells [Y. J. Chung \textit{et al.}, Nature Materials \textbf{20}, 632 (2021)], we examine contributions to mobility and quantum mobility from various scattering mechanisms and their dependencies on the electron density. We find that at lower electron densities, $n_e \lesssim 1 \times 10^{11}$ cm$^{-2}$, both transport and quantum mobility are limited by unintentional background impurities and follow a power law dependence, $\propto n_e^α$, with $α\approx 0.85$. Our predictions for quantum mobility are in reasonable agreement with an estimate obtained from the resistivity at filling factor $ν= 1/2$ in a sample of Y. J. Chung \textit{et al.} with $n_e = 1 \times 10^{11}$ cm$^{-2}$. Consideration of other scattering mechanisms indicates that interface roughness (remote donors) is a likely limiting factor of transport (quantum) mobility at higher electron densities. Future measurements of quantum mobility should yield information on the distribution of background impurities in GaAs and AlGaAs.

cond-mat.mes-hall↗

arXiv2022

Plasmons in semiconductor and topological insulator wires with large dielectric constant

The dispersion law of plasmons running along thin wires with radius $a$ is known to be practically linear. We show that in a wire with a dielectric constant $κ$ much larger than that of its environment $κ_e$, such dispersion law crosses over to a dispersionless three-dimensional-like law when the plasmon wavelength becomes shorter than the length $(a/2) \sqrt{(κ/κ_e)\ln(κ/2κ_e)}$ at which the electric field lines of a point charge exit from the wire to the environment. This happens both in trivial semiconductor wires and wires of three-dimensional topological insulators.

cond-mat.mes-hall↗

arXiv2022

Conductivity of two-dimensional narrow gap semiconductors subjected to strong Coulomb disorder

In the ideal disorder-free situation, a two-dimensional band gap insulator has an activation energy for conductivity equal to half the band gap $Δ$. But transport experiments usually exhibit a much smaller activation energy at low temperature, and the relation between this activation energy and $Δ$ is unclear. Here we consider the temperature-dependent conductivity of a two-dimensional insulator on a substrate containing Coulomb impurities, with random potential amplitude $Γ\gg Δ$. We show that the conductivity generically exhibits three regimes of conductivity, and only the highest temperature regime exhibits an activation energy that reflects the band gap. At lower temperatures, the conduction proceeds through activated hopping or Efros-Shklovskii variable-range hopping between electron and hole puddles created by the disorder. We show that the activation energy and characteristic temperature associated with these processes steeply collapse near a critical impurity concentration. Larger concentrations lead to an exponentially small activation energy and exponentially long localization length, which in mesoscopic samples can appear as a disorder-induced insulator-to-metal transition. We also arrive at a similar steep disorder driven insulator-metal transition in thin films of three-dimensional topological insulators with large dielectric constant, for which Coulomb impurities inside the film create a large disorder potential due to confinement of their electric field inside the film.

cond-mat.mes-hall↗

arXiv2021

Disorder effects in topological insulator nanowires

Three-dimensional topological insulator (TI) nanowires with quantized surface subband spectra are studied as a main component of Majorana bound states (MBS) devices. However, such wires are known to have large concentration $N \sim 10^{19}$ cm$^{-3}$ of Coulomb impurities. It is believed that a MBS device can function only if the amplitude of long-range fluctuations of the random Coulomb potential $Γ$ is smaller than the subband gap $Δ$. Here we calculate $Γ$ for recently experimentally studied large-dielectric-constant (Bi$_{1-x}$Sb$_x$)$_2$Te$_{3}$ wires in a small-dielectric-constant environment (no superconductor). We show that provided by such a dielectric-constant contrast, the confinement of electric field of impurities within the wire allows more distant impurities to contribute into $Γ$, leading to $Γ\sim 3Δ$. We also calculate a TI wire resistance as a function of the Fermi level and carrier concentration due to scattering on Coulomb and neutral impurities, and do not find observable discrete subband-spectrum related oscillations at $N \gtrsim 10^{18}$ cm$^{-3}$.

cond-mat.mes-hall↗

arXiv2021

Metal-Insulator Transition in $n$-type bulk crystals and films of strongly compensated SrTiO$_3$

We start by analyzing experimental data of Spinelli [A. Spinelli, M. A. Torija, C. Liu, C. Jan, and C. Leighton, Phys. Rev. B 81, 155110 (2010)] for conductivity of $n$-type bulk crystals of SrTiO$_3$ (STO) with broad electron concentration $n$ range of $4\times 10^{15}$ - $4 \times10^{20} $ cm$^{-3}$, at low temperatures. We obtain good fit of the conductivity data, $σ(n)$, by the Drude formula for $n \geq n_c \simeq 3 \times 10^{16} $ cm$^{-3}$ assuming that used for doping insulating STO bulk crystals are strongly compensated and the total concentration of background charged impurities is $N = 10^{19}$ cm$^{-3}$. At $n< n_c$, the conductivity collapses with decreasing $n$ and the Drude theory fit fails. We argue that this is the metal-insulator transition (MIT) in spite of the very large Bohr radius of hydrogen-like donor state $a_B \simeq 700$ nm with which the Mott criterion of MIT for a weakly compensated semiconductor, $na_B^3 \simeq 0.02$, predicts $10^{5}$ times smaller $n_c$. We try to explain this discrepancy in the framework of the theory of the percolation MIT in a strongly compensated semiconductor with the same $N=10^{19}$ cm$^{-3}$. In the second part of this paper, we develop the percolation MIT theory for films of strongly compensated semiconductors. We apply this theory to doped STO films with thickness $d \leq 130$ nm and calculate the critical MIT concentration $n_c(d)$. We find that, for doped STO films on insulating STO bulk crystals, $n_c(d)$ grows with decreasing $d$. Remarkably, STO films in a low dielectric constant environment have the same $n_c(d)$. This happens due to the Rytova-Keldysh modification of a charge impurity potential which allows a larger number of the film charged impurities to contribute to the random potential.

cond-mat.mtrl-sci↗

arXiv2021

Disorder effects in topological insulator thin films

Thin films of topological insulators (TI) attract large attention because of expected topological effects from the inter-surface hybridization of Dirac points. However, these effects may be depleted by unexpectedly large energy smearing $Γ$ of surface Dirac points by the random potential of abundant Coulomb impurities. We show that in a typical TI film with large dielectric constant $\sim 50$ sandwiched between two low dielectric constant layers, the Rytova-Chaplik-Entin-Keldysh modification of the Coulomb potential of a charge impurity allows a larger number of the film impurities to contribute to $Γ$. As a result, $Γ$ is large and independent of the TI film thickness $d$ for $d > 5$ nm. In thinner films $Γ$ grows with decreasing $d$ due to reduction of screening by the hybridization gap. We study the surface conductivity away from the neutrality point and at the neutrality point. In the latter case, we find the maximum TI film thickness at which the hybridization gap is still able to make a TI film insulating and allow observation of the quantum spin Hall effect, $d_{\max} \sim 7$ nm.

cond-mat.mes-hall↗

arXiv2020

Hidden Quantum Hall Stripes in Al$_{x}$Ga$_{1-x}$As/Al$_{0.24}$Ga$_{0.76}$As Quantum Wells

We report on transport signatures of hidden quantum Hall stripe (hQHS) phases in high ($N > 2$) half-filled Landau levels of Al$_{x}$Ga$_{1-x}$As/Al$_{0.24}$Ga$_{0.76}$As quantum wells with varying Al mole fraction $x < 10^{-3}$. Residing between the conventional stripe phases (lower $N$) and the isotropic liquid phases (higher $N$), where resistivity decreases as $1/N$, these hQHS phases exhibit isotropic and $N$-independent resistivity. Using the experimental phase diagram we establish that the stripe phases are more robust than theoretically predicted, calling for improved theoretical treatment. We also show that, unlike conventional stripe phases, the hQHS phases do not occur in ultrahigh mobility GaAs quantum wells, but are likely to be found in other systems.

cond-mat.mes-hall↗

arXiv2020

Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition

We study the spectral rigidity of the non-Hermitian analog of the Anderson model suggested by Tzortzakakis, Makris and Economou (TME). This is a $L\times L \times L$ tightly bound cubic lattice, where both real and imaginary parts of on-site energies are independent random variables uniformly distributed between $-W/2$ and $W/2$. The TME model may be used to describe a random laser. In a recent paper we proved that this model has the Anderson transition at $W= W_c \simeq 6$ in three dimension. Here we numerically diagonalize TME $L \times L \times L$ cubic lattice matrices and calculate the number variance of eigenvalues in a disk of their complex plane. We show that on the metallic side $W < 6$ of the Anderson transition, complex eigenvalues repel each other as strongly as in the complex Ginibre ensemble only in a disk containing $N_c(L,W)$ eigenvalues. We find that $N_c(L,W)$ is proportional to $L$ and grows with decreasing $W$ similarly to the number of energy levels $N_c$ in the Thouless energy band of the Anderson model.

cond-mat.dis-nn↗

arXiv2020

Isotropically conducting (hidden) quantum Hall stripe phases in a two-dimensional electron gas

Quantum Hall stripe (QHS) phases, predicted by the Hartree-Fock theory, are manifested in GaAs-based two-dimensional electron gases as giant resistance anisotropies. Here, we predict a ``hidden'' QHS phase which exhibits \emph{isotropic} resistivity whose value, determined by the density of states of QHS, is independent of the Landau index $N$ and is inversely proportional to the Drude conductivity at zero magnetic field. At high enough $N$, this phase yields to an Ando-Unemura-Coleridge-Zawadski-Sachrajda phase in which the resistivity is proportional to $1/N$ and to the ratio of quantum and transport lifetimes. Experimental observation of this border should allow one to find the quantum relaxation time.

cond-mat.mes-hall↗

arXiv2020

Anderson transition in three-dimensional systems with non-Hermitian disorder

We study the Anderson transition for three-dimensional (3D) $N \times N \times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and $W/2$. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25\% smallest-modulus complex eigenvalues we find the average ratio $r$ of distances to the first and the second nearest neighbor as a function of $W$. For a given $N$ the function $r(W)$ crosses from $0.72$ to 2/3 with a growing $W$ demonstrating a transition from delocalized to localized states. When plotted at different $N$ all $r(W)$ cross at $W_c = 6.0 \pm 0.1$ (in units of nearest neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover.

cond-mat.dis-nn↗

arXiv2019

Giant violation of Wiedemann-Franz law in doping layers of modern AlGaAs heterostructures

We analyze the data of the recent paper Nature 559, 205 (2018) and show that it contains an observation of thermal and electric conductivities of the doping layers in GaAs/AlGaAs heterostructures which violates the Wiedemann-Franz law. Namely, the measured thermal conductivity of the doping layers is similar to that of a metal while the electrical conductivity is exponentially small. We find that these results may be related to the exciton contribution to thermal conductivity calculated in several recent theoretical works for metallic samples.

cond-mat.mes-hall↗

arXiv2019

Attraction of indirect excitons in van der Waals heterostructures with three semiconducting layers

We study a capacitor made of three monolayers of transition metal dichalcogenide (TMD) separated by hexagonal Boron Nitride (hBN). We assume that the structure is symmetric with respect to the central layer plane. The symmetry includes the contacts: if the central layer is contacted by the negative electrode, both external layers are contacted by the positive one. As a result a strong enough voltage $V$ induces electron-hole dipoles (indirect excitons) pointing towards one of the external layers. Antiparallel dipoles attract each other at large distances. Thus, the dipoles alternate in the central plane forming a 2D antiferroelectric with negative binding energy per dipole. The charging of a three-layer device is a first order transition, and we show that if $V_1$ is the critical voltage required to create a single electron-hole pair and charge this capacitor by $e$, the macroscopic charge $Q_c = eSn_c$ ($S$ is the device area) enters the three-layer capacitor at a smaller critical voltage $V_{c} < V_{1}$. In other words, the differential capacitance $C(V)$ is infinite at $V = V_{c}$. We also show that in a contact-less three-layer device, where the chemically different central layer has lower conduction and valence bands, optical excitation creates indirect excitons which attract each other, and therefore form antiferroelectric exciton droplets. Thus, the indirect exciton luminescence is red shifted compared to a two-layer device.

cond-mat.mes-hall↗

arXiv2018

Excess electron screening of remote donors and mobility in modern GaAs/AlGaAs herostructures

In modern GaAs/Al$_x$Ga$_{1-x}$As heterostructures with record high mobilities, a two-dimensional electron gas (2DEG) in a quantum well is provided by two remote donor $δ$-layers placed on both sides of the well. Each $δ$-layer is located within a narrow GaAs layer, flanked by narrow AlAs layers which capture excess electrons from donors but leave each of them localized in a compact dipole atom with a donor. Still excess electrons can hop between host donors to minimize their Coulomb energy. As a result they screen the random potential of donors dramatically. We numerically model the pseudoground state of excess electrons at a fraction $f$ of filled donors and find both the mobility and the quantum mobility limited by scattering on remote donors as universal functions of $f$. We repeat our simulations for devices with additional disorder such as interface roughness of the doping layers, and find the quantum mobility is consistent with measured values. Thus, in order to increase the quantum mobility this additional disorder should be minimized.

cond-mat.mes-hall↗