arXiv subjects

B. I. Shklovskii

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

At least 37 records · Page 2Linked to original sources

arXiv2018

Mobility and quantum mobility of modern GaAs/AlGaAs heterostructures

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 well, flanked by narrow AlAs layers which capture excess electrons from donors. We show that each excess electron is localized in a compact dipole atom with the nearest donor. Nevertheless, excess electrons screen both the remote donors and background impurities. When the fraction of remote donors filled by excess electrons $f$ is small, the remote donor limited quantum mobility grows as $f^{3}$ and becomes larger than the background impurity limited one at a characteristic value $f_c$. We also calculate both the mobility and the quantum mobility limited by the screened background impurities with concentrations $N_1$ in Al$_x$Ga$_{1-x}$As and $N_2$ in GaAs, which allows one to estimate $N_1$ and $N_2$ from the measured mobilities. Taken together, our findings should help to identify avenues for further improvement of modern heterostructures.

cond-mat.mes-hall↗

arXiv2018

ZnO Nanocrystal Networks Near the Insulator-Metal Transition: Tuning Contact Radius and Electron Density with Intense Pulsed Light

Networks of ligand-free semiconductor nanocrystals (NCs) offer a valuable combination of high carrier mobility and optoelectronic properties tunable via quantum confinement. In principle, maximizing carrier mobility entails crossing the insulator-metal transition (IMT), where carriers become delocalized. A recent theoretical study predicted that this transition occurs at nρ^3 ~ 0.3, where n is the carrier density and ρis the interparticle contact radius. In this work, we satisfy this criterion in networks of plasma-synthesized ZnO NCs by using intense pulsed light (IPL) annealing to tune n and ρindependently. IPL applied to as-deposited NCs increases ρby inducing sintering, and IPL applied after the NCs are coated with Al2O3 by atomic layer deposition increases n by removing electron-trapping surface hydroxyls. This procedure does not substantially alter NC size or composition and is potentially applicable to a wide variety of nanomaterials. As we increase nρ^3 to at least twice the predicted critical value, we observe conductivity scaling consistent with arrival at the critical region of a continuous quantum phase transition. This allows us to determine the critical behavior of the dielectric constant and electron localization length at the IMT. However, our samples remain on the insulating side of the critical region, which suggests that the critical value of nρ^3 may in fact be significantly higher than 0.3.

cond-mat.mtrl-sci↗

arXiv2018

Disorder From the Bulk Ionic Liquid in Electric Double Layer Transistors

Ionic liquid gating has a number of advantages over solid-state gating, especially for flexible or transparent devices and for applications requiring high carrier densities. However, the large number of charged ions near the channel inevitably results in Coulomb scattering, which limits the carrier mobility in otherwise clean systems. We develop a model for this Coulomb scattering. We validate our model experimentally using ionic liquid gating of graphene across varying thicknesses of hexagonal boron nitride, demonstrating that disorder in the bulk ionic liquid often dominates the scattering.

cond-mat.mes-hall↗

arXiv2017

Roughness scattering induced insulator-metal-insulator transition in a quantum wire

We have theoretically investigated the influence of interface roughness scattering on the low temperature mobility of electrons in quantum wires when electrons fill one or many subbands. We find the Drude conductance of the wire with length $\mathcal{L}$ first increases with increasing linear concentration of electrons $η$ and then decreases at larger concentrations. For small radius $R$ of the wire with length $\mathcal{L}$ the peak of the conductance $G_{max}$ is below $e^2/h$ so that electrons are localized. The height of this peak grows as a large power of $R$, so that at large $R$ the conductance $G_{max}$ exceeds $e^2/h$ and a window of concentrations with delocalized states (which we call the metallic window) opens around the peak. Thus, we predict an insulator-metal-insulator transition with increasing concentration for large enough $R$. Furthermore, we show that the metallic domain can be sub-divided into three smaller domains: 1) single-subband ballistic conductor, 2) many-subband ballistic conductor 3) diffusive metal, and use our results to estimate the conductance in these domains. Finally we estimate the critical value of $R_c(\mathcal{L})$ at which the metallic window opens for a given length $\mathcal{L}$ and find it to be in reasonable agreement with experiment.

cond-mat.mes-hall↗

arXiv2017

Anomalous Thermodynamic Properties of Electron Accumulation Layer in SrTiO$_{3}$

Due to the nonlinear dielectric response within SrTiO$_{3}$ (STO), an accumulation layer created by positive charges at the surface of the STO sample ($x=0$) has an electron density profile $n(x)$ that slowly decays as $1/x^{12/7}$. Here we show that the long tail of $n(x)$ causes the magnetization and the specific heat of the accumulation layer to diverge at large $x$. We explore the truncation of the tail by the finite sample width $W$, the transition from the nonlinear to linear dielectric response with dielectric constant $κ$, and the use of a back gate with a negative voltage $-|V|$. We find that both the magnetization and specific heat are anomalously large and obey nontrivial power law dependences on $W$, $κ$, or $|V|$. We conclude with a discussion of how the capacitance as a function of the back gate voltage may be used to study the shape of the $n(x)$ tail in thin samples.

cond-mat.mes-hall↗

arXiv2017

Universality of Electron Mobility in LaAlO$_3$/SrTiO$_3$ and bulk SrTiO$_3$

Metallic LaAlO$_3$/SrTiO$_3$ (LAO/STO) interfaces attract enormous attention, but the relationship between the electron mobility and the sheet electron density, $n_s$, is poorly understood. Here we derive a simple expression for the three-dimensional electron density near the interface, $n_{3D}$, as a function of $n_s$ and find that the mobility for LAO/STO-based interfaces depends on $n_{3D}$ in the same way as it does for bulk doped STO. It is known that undoped bulk STO is strongly compensated with $N \simeq 5 \times 10^{18}~\rm{cm^{-3}}$ background donors and acceptors. In intentionally doped bulk STO with a concentration of electrons $n_{3D} < N$ background impurities determine the electron scattering. Thus, when $n_{3D} < N$ it is natural to see in LAO/STO the same mobility as in the bulk. On the other hand, in the bulk samples with $n_{3D} > N$ the mobility collapses because scattering happens on $n_{3D}$ intentionally introduced donors. For LAO/STO the polar catastrophe which provides electrons is not supposed to provide equal number of random donors and thus the mobility should be larger. The fact that the mobility is still the same implies that for the LAO/STO the polar catastrophe model should be revisited.

cond-mat.mtrl-sci↗

arXiv2017

Exciton Transfer in Array of Epitaxially Connected Nanocrystals

Recently, epitaxially connected at facets semiconductor nanocrystals (NCs) have been introduced to fascilitate the electron transport between nanocrystals. To fully deploy their potential a better understanding of the exciton transfer between connected NCs is needed. We go beyond the two well-known transfer mechanisms suggested by Förster and Dexter and propose a third mechanism of exciton tandem tunneling. The tandem tunnelling occurs through the intermediate state in which electron and hole are in different NCs. The corresponding rate for exciton hops is larger than the Dexter rate and for Si is even much larger that the Förster one.

cond-mat.mes-hall↗

arXiv2016

Electron Accumulation Layer in Ultrastrong Magnetic Field

When a three-dimensional electron gas is subjected to a very strong magnetic field, it can reach a quasi-one-dimensional state in which all electrons occupy the lowest Landau level. This state is referred to as the extreme quantum limit (EQL) and has been studied in the physics of pulsars and bulk semiconductors. Here we present a theory of the EQL phase in electron accumulation layers created by an external electric field $E$ at the surface of a semiconductor with a large Bohr radius such as InSb, PbTe, SrTiO$_3$ (STO), and particularly in the LaAlO$_3$/SrTiO$_3$ (LAO/STO) heterostructure. The phase diagram of the electron gas in the plane of the magnetic field strength and the electron surface concentration is found for different orientations of the magnetic field. We find that in addition to the quasi-classical metallic phase (M), there is a metallic EQL phase, as well as an insulating Wigner crystal state (WC). Within the EQL phase, the Thomas-Fermi approximation is used to find the electron density and the electrostatic potential profiles of the accumulation layer. Additionally, the quantum capacitance for each phase is calculated as a tool for experimental study of these phase diagrams.

cond-mat.mes-hall↗

arXiv2016

Anomalous conductivity, Hall factor, magnetoresistance, and thermopower of accumulation layer in $\text{SrTiO}_3$

We study the low temperature conductivity of the electron accumulation layer induced by the very strong electric field at the surface of $\text{SrTiO}_3$ sample. Due to the strongly nonlinear lattice dielectric response, the three-dimensional density of electrons $n(x)$ in such a layer decays with the distance from the surface $x$ very slowly as $n(x) \propto 1/x^{12/7}$. We show that when the mobility is limited by the surface scattering the contribution of such a tail to the conductivity diverges at large $x$ because of growing time electrons need to reach the surface. We explore truncation of this divergence by the finite sample width, by the bulk scattering rate, or by the crossover to the bulk linear dielectric response with the dielectric constant $κ$. As a result we arrive at the anomalously large mobility, which depends not only on the rate of the surface scattering, but also on the physics of truncation. Similar anomalous behavior is found for the Hall factor, the magnetoresistance, and the thermopower.

cond-mat.mes-hall↗

arXiv2016

Surface roughness scattering in multisubband accumulation layers

Accumulation layers with very large concentrations of electrons where many subbands are filled became recently available due to ionic liquid and other new methods of gating. The low temperature mobility in such layers is limited by the surface roughness scattering. However theories of roughness scattering so far dealt only with the small-density single subband two-dimensional electron gas (2DEG). Here we develop a theory of roughness-scattering limited mobility for the multisubband large concentration case. We show that with growing 2D electron concentration $n$ the surface dimensionless conductivity $σ/(2e^2/h)$ first decreases as $\propto n^{-6/5}$ and then saturates as $\sim(da_B/Δ^2)\gg 1$, where $d$ and $Δ$ are the characteristic length and height of the surface roughness, $a_B$ is the effective Bohr radius. This means that in spite of the shrinkage of the 2DEG width and the related increase of the scattering rate, the 2DEG remains a good metal. Thus, there is no re-entrant metal-insulator transition at high concentrations conjectured by Das Sarma and Hwang [PRB 89, 121413 (2014)].

cond-mat.mes-hall↗

arXiv2016

Metal-insulator transition in films of doped semiconductor nanocrystals

To fully deploy the potential of semiconductor nanocrystal films as low-cost electronic materials, a better understanding of the amount of dopants required to make their conductivity metallic is needed. In bulk semiconductors, the critical concentration of electrons at the metal-insulator transition is described by the Mott criterion. Here, we theoretically derive the critical concentration $n_c$ for films of heavily doped nanocrystals devoid of ligands at their surface and in direct contact with each other. In the accompanying experiments, we investigate the conduction mechanism in films of phosphorus-doped, ligand-free silicon nanocrystals. At the largest electron concentration achieved in our samples, which is half the predicted $n_c$, we find that the localization length of hopping electrons is close to three times the nanocrystals diameter, indicating that the film approaches the metal-insulator transition.

cond-mat.mes-hall↗

arXiv2016

Percolation via combined electrostatic and chemical doping in complex oxide films

Stimulated by experimental advances in electrolyte gating methods, we investigate theoretically percolation in thin films of inhomogenous complex oxides, such as La$_{1-x}$Sr$_{x}$CoO$_{3}$ (LSCO), induced by a combination of bulk chemical and surface electrostatic doping. Using numerical and analytical methods, we identify two mechanisms that describe how bulk dopants reduce the amount of electrostatic surface charge required to reach percolation: (i) bulk-assisted surface percolation, and (ii) surface-assisted bulk percolation. We show that the critical surface charge strongly depends on the film thickness when the film is close to the chemical percolation threshold. In particular, thin films can be driven across the percolation transition by modest surface charge densities \emph{via} surface-assisted bulk percolation. If percolation is associated with the onset of ferromagnetism, as in LSCO, we further demonstrate that the presence of critical magnetic clusters extending from the film surface into the bulk results in considerable volume enhancement of the saturation magnetization, with pronounced experimental consequences. These results should significantly guide experimental work seeking to verify gate-induced percolation transitions in such materials.

cond-mat.mes-hall↗

arXiv2016

Dielectric Constant and Charging Energy in Array of Touching Nanocrystals

We calculate the effective macroscopic dielectric constant $\varepsilon_a$ of a periodic array of spherical nanocrystals (NCs) with dielectric constant $\varepsilon$ immersed in the medium with dielectric constant $\varepsilon_m \ll \varepsilon$. For an array of NCs with the diameter $d$ and the distance $D$ between their centers, which are separated by the small distance $s=D-d \ll d$ or touch each other by small facets with radius $ρ\ll d$ what is equivalent to $s < 0$, $|s| \ll d$ we derive two analytical asymptotics of the function $\varepsilon_a(s)$ in the limit $\varepsilon/\varepsilon_m \gg 1$. Using the scaling hypothesis we interpolate between them near $s=0$ to obtain new approximated function $\varepsilon_a(s)$ for $\varepsilon/\varepsilon_m \gg 1$. It agrees with existing numerical calculations for $\varepsilon/\varepsilon_m =30$, while the standard mean-field Maxwell-Garnett and Bruggeman approximations fail to describe percolation-like behavior of $\varepsilon_a(s)$ near $s = 0$. We also show that in this case the charging energy $E_c$ of a single NC in an array of touching NCs has a non-trivial relationship to $\varepsilon_a $, namely $E_c = αe^2/\varepsilon_a d$, where $α$ varies from 1.59 to 1.95 depending on the studied three-dimensional lattices. Our approximation for $\varepsilon_a(s)$ can be used instead of mean field Maxwell-Garnett and Bruggeman approximations to describe percolation like transitions near $s=0$ for other material characteristics of NC arrays, such as conductivity.

cond-mat.mes-hall↗

arXiv2015

Hopping conductivity and insulator-metal transition in films of touching semiconductor nanocrystals

This paper is focused on the the variable-range hopping of electrons in semiconductor nanocrystal (NC) films below the critical doping concentration $n_c$ at which it becomes metallic. The hopping conductivity is described by the Efros-Shklovskii law which depends on the localization length of electrons. We study how the localization length grows with the doping concentration $n$ in the film of touching NCs. For that we calculate the electron transfer matrix element $t(n)$ between neighboring NCs for two models when NCs touch by small facets or just one point. We study two sources of disorder: variations of NC diameters and random Coulomb potentials originating from random numbers of donors in NCs. We use the ratio of $t(n)$ to the disorder-induced NC level dispersion to find the localization length of electrons due to the multi-step elastic co-tunneling process. We found three different phases at $n<n_c$ depending on the strength of disorder, the material, sizes of NCs and their facets: 1) "insulator" where the localization length of electrons increases monotonically with $n$ and 2) "oscillating insulator" when the localization length (and the conductivity) oscillates with $n$ from the insulator base and 3) "blinking metal" where the localization length periodically diverges. The first two phases were seen experimentally and we discuss how one can see the more exotic third one. In all three the localization length diverges at $n=n_c$. This allows us to find $n_c$.

cond-mat.mes-hall↗

arXiv2015

Electron gas induced in SrTiO$_3$

This mini-review is dedicated to the 85th birthday of Prof. L. V. Keldysh, from whom we have learned so much. In this paper we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO$_3$ (STO) in the cases of planar, spherical and cylindrical geometries. The electron gas can be created by applying an induction $D_0$ to the STO surface. We describe the lattice dielectric response of STO using the Landau-Ginzburg free energy expansion and employ the Thomas-Fermi (TF) approximation for the electron gas. For the planar geometry we arrive at the electron density profile $n(x) \propto (x+d)^{-12/7}$, where $d \propto D_0^{-7/5} $. We extend our results to overlapping electron gases in GTO/STO/GTO multi-heterojunctions and electron gases created by spill-out from NSTO (heavily $n$-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with nuclear charge $Ze$, where $Z > 170$, electrons collapse onto the nucleus resulting in a net charge $Z_n < Z$. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius $R$ when its total charge number $Z$ exceeds the critical value $Z_c \simeq R/a$, where $a$ is the lattice constant. The net charge $eZ_n$ grows with $Z$ until $Z$ exceeds $Z^* \simeq (R/a)^{9/7}$. After this point, the charge number of the compact core $Z_n$ remains $\simeq Z^*$, with the rest $Z^*$ electrons forming a sparse Thomas-Fermi electron atmosphere around it. We extend our results to the case of long cylindrical clusters as well.

cond-mat.mes-hall↗

arXiv2015

Hopping Conduction via Ionic Liquid Induced Silicon Surface States

In order to clarify the physics of the gating of solids by ionic liquids (ILs) we have gated lightly doped $p$-Si, which is so well studied that it can be called the "hydrogen atom of solid state physics" and can be used as a test bed for ionic liquids. We explore the case where the concentration of induced holes at the Si surface is below $10^{12}\text{cm}^{-2}$, hundreds of times smaller than record values. We find that in this case an excess negative ion binds a hole on the interface between the IL and Si becoming a surface acceptor. We study the surface conductance of holes hopping between such nearest neighbor acceptors. Analyzing the acceptor concentration dependence of this conductivity, we find that the localization length of a hole is in reasonable agreement with our direct variational calculation of its binding energy. The observed hopping conductivity resembles that of well studied $\text{Na}^{+}$ implanted Si MOSFETs.

cond-mat.mes-hall↗

arXiv2015

Collapse of electrons to a donor cluster in SrTiO$_3$

It is known that a nucleus with charge $Ze$ where $Z>170$ creates electron-positron pairs from the vacuum. These electrons collapse onto the nucleus resulting in a net charge $Z_n<Z$ while the positrons are emitted. This effect is due to the relativistic dispersion law. The same reason leads to the collapse of electrons to the charged impurity with a large charge number $Z$ in narrow-band gap semiconductors and Weyl semimetals as well as graphene. In this paper, a similar effect of electron collapse and charge renormalization is found for donor clusters in SrTiO$_3$ (STO), but with a very different origin. At low temperatures, STO has an enormously large dielectric constant. Because of this, the nonlinear dielectric response becomes dominant when the electric field is not too small. We show that this leads to the collapse of surrounding electrons into a charged spherical donor cluster with radius $R$ when its total charge number $Z$ exceeds a critical value $Z_c\simeq R/a$ where $a$ is the lattice constant. Using the Thomas-Fermi approach, we find that the net charge $Z_ne$ grows with $Z$ until $Z$ exceeds another value $Z^*\simeq(R/a)^{9/7}$. After this point, $Z_n$ remains $\sim Z^*$. We extend our results to the case of long cylindrical clusters. Our predictions can be tested by creating discs and stripes of charge on the STO surface.

cond-mat.mes-hall↗

arXiv2015

Accumulation, inversion, and depletion layers in SrTiO$_3$

We study potential and electron density depth profiles in accumulation, inversion and depletion layers in crystals with large and nonlinear dielectric response such as $\mathrm{SrTiO_3}$. We describe the lattice dielectric response using the Landau-Ginzburg free energy expansion. In accumulation and inversion layers we arrive at new nonlinear dependencies of the width $d$ of the electron gas on applied electric field $D_0$. Particularly important is the predicted electron density profile of accumulation layers (including the $\mathrm{LaAlO_3/SrTiO_3}$ interface) $n(x) \propto (x+d)^{-12/7}$, where $d \propto D_0^{-7/5}$ . We compare this profile with available data and find satifactory agreement. For a depletion layer we find an unconventional nonlinear dependence of capacitance on voltage. We also evaluate the role of spatial dispersion in the dielectric response by adding a gradient term to the Landau-Ginzburg free energy.

cond-mat.str-el↗