Motivated by high-accuracy scanning tunneling spectroscopy measurements on disordered two-dimensional electron gases in strong magnetic field, we present an exact solution for the local density of states (LDoS) of electrons moving in an arbitrary potential smooth on the scale of the magnetic length, that can be locally described up to its second derivatives. We use a technique based on coherent state Green's functions, allowing us to treat on an equal footing confining and open quantum systems. The energy-dependence of the LDoS is found to be universal in terms of local geometric properties, such as drift velocity and potential curvature. We also show that thermal effects are quite important close to saddle points, leading to an overbroadening of the tunneling trajectories.
We study the spin-charge conversion mechanisms in a two-dimensional gas of electrons moving in a smooth disorder potential by accounting for both Rashba-type and Mott's skew scattering contributions. We find that quantum interference effects between spin-flip and skew scattering give rise to anisotropic spin precession scattering (ASP), a direct spin-charge conversion mechanism that was discovered in an earlier study of graphene decorated with adatoms [C. Huang \emph{et al.} Phys.~Rev.~B \textbf{94} 085414.~(2016)]. Our findings suggest that, together with other spin-charge conversion mechanis…
We develop in detail a new formalism [as a sequel to the work of T. Champel and S. Florens, Phys. Rev. B 75, 245326 (2007)] that is well-suited for treating quantum problems involving slowly-varying potentials at high magnetic fields in two-dimensional electron gases. For an arbitrary smooth potential we show that electronic Green's function is fully determined by closed recursive expressions that take the form of a high magnetic field expansion in powers of the magnetic length l_B. For illustration we determine entirely Green's function at order l_B^3, which is then used to obtain quantum exp…
A metal-insulator transition in two-dimensional electron gases at B=0 is found in Ga(Al)As heterostructures, where a high density of self-assembled InAs quantum dots is incorporated just 3 nm below the heterointerface. The transition occurs at resistances around h/e^2 and critical carrier densities of 1.2 10^11cm^-2. Effects of electron-electron interactions are expected to be rather weak in our samples, while disorder plays a crucial role.
Transport and thermodynamic properties of disordered conductors are considerably modified when the angle through which the electron spin precesses due to spin-orbit interaction (SOI) during the mean free time becomes significant. Cooperon and Diffusion equations are solved for the entire range of strength of SOI. The implications of SOI for the electron-electron interaction and interference effects in various experimental settings are discussed.
In high-mobility two-dimensional electron gases Landau levels are already formed at very small magnetic field values. Such two-dimensional electron gases show a huge negative magnetoresistance at low temperatures and an unexpected and very strong non-linear behavior with the applied current. This non-linearity depends on carrier concentration and is explained by the subtle interplay of elastic scattering within Landau levels and in between Landau levels.
We investigate high-mobility two-dimensional electron gases in AlGaAs heterostructures by employing Schottky-gate-dependent measurements of the samples' electron density and mobility. Surprisingly, we find that two different sample configurations can be set in situ with mobilities diering by a factor of more than two in a wide range of densities. This observation is discussed in view of charge redistributions between the doping layers and is relevant for the design of future gateable high-mobility electron gases.
We investigate intra-Landau-level collective excitations in a bilayer disordered two-dimensional electron system exposed to a perpendicular magnetic field. The energy spectrum is calculated within the random phase approximation by taking into account electron-impurity scattering in the self-consistent Born approximation which includes consistent vertex corrections. Signatures of these bilayer excitations in drag and collective excitation measurements are identified.
We have observed that the tunneling magnetoconductance between two-dimensional (2D) electron gases formed at nominally identical InAs-AlSb interfaces most often exhibits two sets of Shubnikov-de Haas oscillations with almost the same frequency. This result is explained quantitatively with a model of the conductance in which the 2D gases have different densities and can tunnel between Landau levels with different quantum indices. When the epitaxial growth conditions of the interfaces are optimized, the zero-bias magnetoconductance shows a single set of oscillations, thus proving that the asymme…
We investigate the transport properties of narrow quantum wires realized in disordered two-dimensional electron gases in the presence of k-linear Rashba and Dresselhaus spin-orbit interaction (SOI), and an applied in-plane magnetic field. Building on previous work [Scheid, et al., PRL 101, 266401 (2008)], we find that in addition to the conductance, the universal conductance fluctuations also feature anisotropy with respect to the magnetic field direction. This anisotropy can be explained solely from the symmetries exhibited by the Hamiltonian as well as the relative strengths of the Rashba an…
We present magnetotransport measurements on freely suspended two-dimensional electron gases from AlGaAs/GaAs heterostructures. The technique to realize such devices relies on a specially MBE grown GaAs/AlGaAs-heterostructure including a sacrificial layer. We fabricated simple Hall-bars as well as quantum cavities and quantum dot systems. We find well-pronounced Shubnikov-de Haas oscillations and observe commensurability resonances, allowing characterization of the electron gas in these 100 nm thin membranes.
We present a variety of methods to derive the Casimir interaction in planar systems containing two-dimensional layers. Examples where this can be of use is graphene, graphene-like layers and two-dimensional electron gases. We present results for two free standing layers and for one layer above a substrate. The results can easily be extended to systems with a larger number of layers.
We have studied magnetodrag between spatially separated two dimensional electron systems due to the virtual phonon exchange with and without taking into account the screening effects. The drag rate as a function of magnetic field, temperature, and interlayer spacing is calculated.
Recent theoretical results on transport in a two-dimensional disordered electron liquid with spin and isospin degrees of freedom are reviewed. A number of experimental features in temperature dependence of resistivity at low temperatures in Si-MOSFET, n-AlAs quantum well and double quantum well heterostructures is explained. Novel behavior of low-temperature resistivity at low temperature in electron systems with isospin degrees of freedom are predicted.
The diffusion of energy that is locally deposited into two-dimensional electron gases by Joule heating generates transverse voltages across devices with broken symmetry. For mesoscopic structures characterized by device dimensions comparable to the energy diffusion length, the resulting thermopower strongly depends on details of the potential profile defined by electric gates. We discuss these mesoscopic features within a diffusion thermopower model and propose schemes to measure the energy diffusion length and its dependence on gate voltage.
We study the quantum corrections to the conductivity of the two-dimensional disordered interacting electron system in the diffusive regime due to inelastic scattering off rare magnetic impurities. We focus on the case of very different g-factors for electrons and magnetic impurities. Within the Born approximation for the inelastic scattering off magnetic impurities we find additional temperature-dependent corrections to the conductivity of the Altshuler-Aronov type. Our results demonstrate that the low temperature transport in interacting disordered electron systems with rare magnetic impuriti…
Using the partition-free time-dependent Landauer-B{ü}ttiker formalism for transient current correlations, we study the traversal times taken for electrons to cross graphene nanoribbon (GNR) molecular junctions. We demonstrate electron traversal signatures that vary with disorder and orientation of the GNR. These findings can be related to operational frequencies of GNR-based devices and their consequent rational design.
Separately contacted double layers of a 2d electron - 2d hole gases have been prepared in GaAs separated by thin AlGaAs barriers with thicknesses down to 15 nm. The molecular-beam-epitaxial growth was interrupted just before the barrier in order to use in situ focussed-ion-beam implantation to pattern contacts which extend underneath the barrier. The two charge gases form upon biasing the p- and n-type contacts underneath and above the barrier in forward direction and show independent transistor-like behavior.
The weak localization correction and the mesoscopic fluctuations of the polarizability and the capacitance of a small disordered sample are studied systematically in 2D and 3D geometries. While the grand canonical ensemble calculation gives the positive magnetopolarizability, in the canonical ensemble (appropriate for isolated samples) the sign of the effect is reversed. The magnitude of mesoscopic fluctuations for a single sample exceeds considerably the value of the weak localization correction.
We calculate the thermal conductivity of interacting electrons in disordered metals. In our analysis we point out that the interaction affects thermal transport through two distinct mechanims, associated with quantum interference corrections and energy exchange of the quasi particles with the electromagnetic environment, respectively. The latter is seen to lead to a violation of the Wiedemann-Franz law. Our theory predicts a strong enhancement of the Lorenz ratio $κ/σT$ over the value which is predicted by the Wiedemann-Franz law, when the electrons encounter a large environmental impedance.
We investigate the effect of electron-electron interactions on Aharonov-Bohm (AB) current oscillations in nanorings formed by a chain of metallic quantum dots. We demonstrate that electron-electron interactions cause electron dephasing thereby suppressing the amplitude of AB oscillations at all temperatures down to T=0. The crossover between thermal and quantum dephasing is found to be controlled by the ring perimeter. Our predictions can be directly tested in future experiments.
The localization length of a low energy tightly bound electron-hole pair (excitons) is calculated by exact diagonalization for small interacting disordered systems. The exciton localization length (which corresponds to the thermal electronic conductance) is strongly enhanced by electron-electron interactions, while the localization length (pertaining to the charge conductance) is only slightly enhanced. This shows that the two particle delocalization mechanism widely discussed for the electron pair case is more efficient close to the Fermi energy for an electron-hole pair. The relevance to exp…
We report the observation of strong electron dephasing in a series of disordered Cu$_{93}$Ge$_4$Au$_3$ thin films. A very short electron dephasing time possessing very weak temperature dependence around 6 K, followed by an upturn with further decrease in temperature below 4 K, is found. The upturn is progressively more pronounced in more disordered samples. Moreover, a ln$T$ dependent, but high-magnetic-field-insensitive, resistance rise persisting from above 10 K down to 30 mK is observed in the films. These results suggest a nonmagnetic dephasing process which is stronger than any known mech…
The nonzero bulk viscosity signals breaking of the scale invariance. We demonstrate that a disorder in two-dimensional noninteracting electron gas in a perpendicular magnetic field results in the nonzero disorder-averaged bulk viscosity. We derive analytic expression for the bulk viscosity within the self-consistent Born approximation. This residual bulk viscosity provides the lower bound for the bulk viscosity of 2D interacting electrons at low enough temperatures.
We investigate quantum corrections to the conductivity due to the interference of electron-electron (electron-phonon) scattering and elastic electron scattering in weakly disordered conductors. The electron-electron interaction results in a negative $T^2 \ln T$-correction in a 3D conductor. In a quasi-two-dimensional conductor, $d < v_F/T$ ($d$ is the thickness, $v_F$ is the Fermi velocity), with 3D electron spectrum this correction is linear in temperature and differs from that for 2D electrons (G. Zala et. al., Phys. Rev.B {\bf 64}, 214204 (2001)) by a numerical factor. In a quasi-one-dimens…
The electron--electron scattering does not affect the electrical current in Galilean--invariant systems. We show that nevertheless electron--electron collisions may contribute to the electric resistivity of systems with parabolic spectrum provided that they have multiply connected Fermi surface and there is an additional mechanism of scattering. To this end, we calculate the resistivity of a two-dimensional electron gas with two filled transverse subbands in a presence of electron--electron and impurity scattering. Though the collisions between the electrons do not directly affect the current …
Magnetic barriers in two-dimensional electron gases are shifted in B space by homogeneous, perpendicular magnetic fields. The magnetoresistance across the barrier shows a characteristic asymmetric dip in the regime where the polarity of the homogeneous magnetic field is opposite to that one of the magnetic barrier. The measurements are in quantitative agreement with semiclassical simulations, which reveal that the magnetoresistance originates from the interplay of snake orbits with E x B drift at the edges of the Hall bar and with elastic scattering.
A poly(styrene-block-methylmethacrylate) diblock copolymer in the hexagonal cylindrical phase has been used as a mask for preparing a periodic gate on top of a Ga[Al]As-heterostructure. A superlattice period of 43 nm could be imposed onto the two-dimensional electron gas. Transport measurements show a characteristic positive magnetoresistance around zero magnetic field which we interpret as a signature of electron motion guided by the superlattice potential.
We report magneto-transport studies of InAs/GaSb bilayer quantum wells in a regime where the interlayer tunneling between the electron and hole gases is suppressed. When the chemical potential is tuned close to the charge neutrality point, we observe anomalous quantum oscillations that are inversely periodic in magnetic field and that have an extremely high frequency despite the highly insulating regime where they are observed. The seemingly contradictory coexistence of a high sheet resistance and high frequency quantum oscillations in the charge neutrality regime cannot be understood within t…
We investigate ramifications of the persistent spin helix symmetry in two-dimensional hole gases in the conductance of disordered mesoscopic systems. To this end we extend previous models by going beyond the axial approximation for III-V semiconductors. For heavy-hole subbands we identify an exact spin-preserving symmetry analogous to the electronic case by analyzing the crossover from weak antilocalization to weak localization and spin transmission as a function of extrinsic spin-orbit interaction strength.
The energy relaxation in the spin-polarized disordered electron systems is studied in the diffusive regime. We derived the quantum kinetic equation in which the kernel of electron-electron collision integral explicitly depends on the electron magnetization. As the consequence, the inelastic scattering rate is found to have non-monotonic dependence on the spin polarization of the electron system.
The electronic properties of heterojunction electron gases formed in GaN/AlGaN core/shell nanowires with hexagonal and triangular cross-sections are studied theoretically. We show that at nanoscale dimensions, the non-polar hexagonal system exhibits degenerate quasi-one-dimensional electron gases at the hexagon corners, which transition to a core-centered electron gas at lower doping. In contrast, polar triangular core/shell nanowires show either a non-degenerate electron gas on the polar face or a single quasi-one-dimensional electron gas at the corner opposite the polar face, depending on th…
We investigate the possibility of an Anderson transition below two dimensions in disordered systems of non-interacting electrons with symplectic symmetry. Numerical analysis of energy level statistics and conductance statistics on Sierpinski carpets with spin-orbit coupling indicates the occurrence of an Anderson transition below two dimensions.
Using the transfer matrix technique, we investigate the propagation of electron through a two dimensional disordered sample. We find that the spatial distribution of electrons is homogeneous only in the limit of weak disorder (diffusive transport regime). In the limit of very strong disorder, we identify a narrow channel through which the electron propagates from one side of the sample to the opposite side. Even in this limit, we prove the wave character of the electron propagation.
We study the electron-phonon relaxation (dephasing) rate in disordered semiconductors and low-dimensional structures. The relaxation is determined by the interference of electron scattering via the deformation potential and elastic electron scattering from impurities and defects. We have found that in contrast to the destructive interference in metals, which results in the Pippard ineffectiveness condition for the electron-phonon interaction, the interference in semiconducting structures substantially enhances the effective electron-phonon coupling. The obtained results provide an explanation …
Magnetotransport measurements in combination with molecular dynamics (MD) simulations on two-dimensional disordered Lorentz gases in the classical regime are reported. In quantitative agreement between experiment and simulation, the magnetoconductivity displays a pronounced peak as a function of perpendicular magnetic field $B$ which cannot be explained in the framework of existing kinetic theories. We show that this peak is linked to the onset of a directed motion of the electrons along the contour of the disordered obstacle matrix when the cyclotron radius becomes smaller than the size of th…
Eigenvalues and wave functions describing free electron gases in toroidal shells are determined using a basis set expansion natural to the system geometry. Couplings between azimuthal and poloidal modes are found to be appreciable at lower values of ${m_ϕ}$, modifying single particle density distributions within the shells. Thermodynamic state functions are calculated and contrasted with those of a solid toroidal volume.
In order to model the phase-coherent scattering of electrons in two-dimensional electron gases in the presence of Rashba spin-orbit coupling, a general partial-wave expansion is developed for scattering from a cylindrically symmetric potential. The theory is applied to possible electron flow imaging experiments using a moveable scanning probe microscope tip. In such experiments, it is demonstrated theoretically that the Rashba spin-orbit coupling can give rise to spin interference effects, even for unpolarized electrons at nonzero temperature and no magnetic field.
We report a detailed study of the influence of the electron-electron interaction on physical observables (conductance, etc.) of a disordered electron liquid in double quantum well heterostructure. We find that even in the case of common elastic scattering off electrons in both quantum wells, the asymmetry in the electron-electron interaction across and within quantum wells decouples them at low temperatures. Our results are in quantitative agreement with recent transport experiments on the gated double quantum well Al$_x$Ga$_{1-x}$As/GaAs/Al$_x$Ga$_{1-x}$As heterostructures.
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit.
We report high-quality two-dimensional (2D) electron and hole gases induced at the surface of graphite by the electric field effect. The 2D carriers reside within a few near-surface atomic layers and exhibit mobilities up to 15,000 and 60,000 cm2/Vs at room and liquid-helium temperatures, respectively. The mobilities imply ballistic transport at micron scale. Pronounced Shubnikov-de Haas oscillations reveal the existence of two types of carries in both 2D electron and hole gases.
We consider the effect of electron-electron interactions on the current-in-plane (CIP) conductivity and exchange coupling energy of a disordered metallic magnetic multilayer. We analyze its dependence on the value of ferromagnetic splitting of conducting electrons and ferromagnetic layers relative magnetizations orientation. We show that contribution to the CIP conductivity and exchange coupling energy as a periodic function of the angle of magnetizations relative orientation experience $ 2π\to π$ transition depending on the characteristic energies: ferromagnetic splitting of the conducting el…
We present an efficient numerical method for simulating the low-energy properties of disordered many-particle systems. The method which is based on the quantum-chemical configuration interaction approach consists in diagonalizing the Hamiltonian in an energetically truncated basis build of the low-energy states of the corresponding Hartree-Fock Hamiltonian. As an example we investigate the quantum Coulomb glass, a model of spinless electrons in a random potential interacting via long-range Coulomb interaction. We find that the Coulomb interaction increases the conductance of strongly disordere…
We study entanglement of electron spins in many-body systems based on the Green's function approach. As an application we obtain the two-particle density matrix of a non-interacting electron gas and identify its two-spin density matrix as a Werner state. We calculate entanglement measures, a classical correlation, mutual information, and a pair distribution function of two electrons at zero and finite temperatures. We find that changes of entanglement measures are proportional to $T^2$ at low temperatures.
Electron transport phenomena in disordered electron systems with spin-orbit coupling in two dimensions and below are studied numerically. The scaling hypothesis is checked by analyzing the scaling of the quasi-1D localization length. A logarithmic increase of the mean conductance is also confirmed. These support the theoretical prediction that the two dimensional metal in systems with spin-orbit coupling has a perfect conductivity. Transport through a Sierpinski carpet is also reported.
We report the detailed study of the influence of the spin and valley splittings on such physical observables of the two-dimensional disordered electron liquid as resistivity, spin and valley susceptibilities. We explain qualitatively the nonmonotonic dependence of the resistivity with temperature in the presence of a parallel magnetic field. In the presence of either the spin splitting or the valley splitting we predict novel, with two maximum points, temperature dependence of the resistivity.
At low densities, electrons confined to two dimensions in a delta-doped heterostructure can arrange themselves into self-consistent droplets due to disorder and screening effects. We use this observation to show that at low temperatures, there should be resistance oscillations in low density two dimensional electron gases as a function of the gate voltage, that are greatly enhanced in a magnetic field. These oscillations are intrinsic to small samples and give way to variable range hopping resistivity at low temperatures in larger samples. We place our analysis in the context of recent experim…
We have experimentally studied the spin-induced time reversal symmetry (TRS) breaking as a function of the relative strength of the Zeeman energy (E_Z) and the Rashba spin-orbit interaction energy (E_SOI), in InGaAs-based 2D electron gases. We find that the TRS breaking saturates when E_Z becomes comparable to E_SOI. Moreover, we show that the spin-induced TRS breaking mechanism is a universal function of the ratio E_Z/E_SOI, within the experimental accuracy.
These lectures provide an introduction to the theory of disordered interacting electron systems. In particular, we concentrate on those aspects which are fundamental for the problem of the metal-insulator transition due to the interplay of disorder and interaction. After reviewing the problem of disordered non-interacting electrons, we examine the past and recent experimental urgency to take into account interaction effects. We describe, by using the language of standard perturbation theory, how these interactions effects lead to the picture of the renormalized disordered Fermi liquid. This al…
We consider mechanism of exchange coupling based on interaction between electrons in nonmagnetic layer. Depending on ratio of inverse time of diffusion of electrons between ferromagnetic layers and ferromagnetic splitting of conducting electrons this mechanism describes transition from ferromagnetic to noncollinear ordering of magnetizations of ferromagnetic layers.
We have generalized the scattering-matrix theory of multiple Andreev reflections in mesoscopic Josephson junctions to the multi-mode case, and applied it to short superconductor/normal metal/superconductor junctions with diffusive electron transport. Both the dc and ac current-voltage characteristics are analyzed for a wide range of bias voltages $V$. For voltages smaller than the supeconducting gap the dc differential conductance of the junction diverges as $1/\sqrt{V}$.
We have investigated the bias-voltage dependence of the phase-dependent differential resistance of a disordered T-shaped 2-dimensional electron gas coupled to two superconducting terminals. The resistance oscillations first increase upon lowering the energy. For bias voltages below the Thouless energy, the resistance oscillations are suppressed and disappear almost completely at zero bias voltage. We find a qualitative agreement with the calculated reentrant behavior of the resistance and discuss quantitative deviations.
The influence of inelastic relaxation time on the intrinsic spin Hall effects in a disordered two-dimensional electron gas with Rashba interaction is studied, which clarifies the controversy of impurity effects in the system. We reveal that, due to the existence of inelastic scattering, the spin Hall conductivity does not vanish when the impurity concentration diminishes to zero no matter it is non-magnetically or magnetically disordered. The spin accumulation is evaluated by using the obtained spin Hall conductivity, and an alternate route is suggested to verify the intrinsic spin Hall effect…
We study a penetration of an electron with high energy E<<T through strongly disordered wire of length L<<a (a being the localization length). Such an electron can loose, but not gain the energy, when hopping from one localized state to another. We have found a distribution function for the transmission coefficient t. The typical t remains exponentially small in L/a, but with the decrement, reduced compared to the case of direct elastic tunnelling. The distribution function has a relatively strong tail in the domain of anomalously high t; the average <t>~(a/L)^2 is controlled by rare configura…
Charge and thermal conductivities are the most important parameters of carbon nanomaterials as candidates for future electronics. In this paper we address the effects of Anderson type disorder in long semiconductor carbon nanotubes (CNTs) to electron charge conductivity and lattice thermal conductivity using the atomistic Green function approach. The electron and phonon transmissions are analyzed as a function of the length of the disordered nanostructures. The thermal conductance as a function of temperature is calculated for different lengths. Analysis of the transmission probabilities as a …
We study the electronic transport in the lowest Landau level of disordered two-dimensional semimetals placed in a homogeneous perpendicular magnetic field. The material system is modeled by the Bernevig-Hughes-Zhang Hamiltonian, which has zero energy Landau modes due to the material's intrinsic Berry curvature. These turn out to be crucially important for the density of states and the static conductivity of the disordered system. We develop an analytical approach to the diffusion and conductivity based on a self-consistent equation of motion for the mean squared displacement. The obtained valu…
We study collective excitations of a two-dimensional electron system consisting of two kinds of charge carriers: relativistic or Dirac electrons with linear dispersion and non-relativistic electrons with parabolic dispersion. We find that the strength of the interaction between the different charge carriers, i.e., the inter-species interaction, plays a significant role in determining the number of plasmon modes as well as their dispersions in certain parameter regimes.
We investigate the emergence of long-range electron hopping mediated by cavity vacuum fields in disordered quantum Hall systems. We show that the counter-rotating (anti-resonant) light-matter interaction produces an effective hopping between disordered eigenstates within the last occupied Landau band. The process involves a number of intermediate states equal to the Landau degeneracy: each of these states consists of a virtual cavity photon and an electron excited in the next Landau band with the same spin. We study such a cavity-mediated hopping mechanism in the dual presence of a random diso…
