Hall Effect In Two-dimensional Systems Research Articles

Classification of spin Hall effect in two-dimensional systems

Classification of spin Hall effect in two-dimensional systems

Direct and inverse superspin Hall effect in two-dimensional systems: Electrical detection of spin supercurrents

A useful experimental signature of the ordinary spin Hall effect is the spin accumulation it produces at the sample edges. The superspin Hall current [Phys. Rev. B 96, 094512 (2017)] is a transverse equilibrium spin current which is induced by a charge supercurrent. We study the superspin Hall current numerically, and find that it does not give rise to a similar edge magnetization. We also predict and numerically confirm the existence of the inverse superspin Hall effect, which produces a transverse charge supercurrent in response to an equilibrium spin current. We verify the existence of the inverse superspin Hall effect both for a spin-polarized charge supercurrent and an exchange spin current, and propose that a $\phi_0$ junction produced by the inverse superspin Hall effect can be used to directly and electrically measure the spin polarization of a charge supercurrent. This provides a possible way to solve the long-standing problem of how to directly detect the spin-polarization of supercurrents carried by triplet Cooper pairs.

Hall effect in two-dimensional systems with hopping transport and strong disorder

We reconsider the theory of Hall effect in the systems with hopping conduction. The purpose of the present study is to compare the percolation approach based on the optimal triad model with numerical simulations and recent experimental results. We show that, in the nearest neighbor hopping regime, the results of the percolation theory agree to the simulation. However, in the variable range hopping (VRH) regime, the optimal triad model fails to describe the numerical results. It is related to the extremely small probability to find the optimal triad of sites in the percolation cluster in the VRH regime. The contribution of these triads to the Hall effect appears to be small. We describe the Hall mobility in the VRH regime with the empirical law obtained from the numerical results. The law is in agreement with our recent experimental data in 2D quantum dot arrays with the hopping transport.

Spin Hall effect in two-dimensional systems within the relativistic phase shift model

Spin Hall effect in two-dimensional systems within the relativistic phase shift model

Anomalous Hall effect in two-dimensional systems with magnetization: The roles of electron-impurity and electron-phonon scatterings

We present a kinetic equation approach to investigate the anomalous Hall effect in two-dimensional systems with magnetization considering both electron-impurity and electron-phonon scatterings. In our study, the spin-orbit interaction due to the external driving electric field as well as the extrinsic spin-orbit couplings induced by electron-impurity and electron-phonon scatterings are taken into account, while the intrinsic Rashba and Dresselhaus spin-orbit couplings are ignored. We derive the side-jump contributions to anomalous Hall current in terms of the distribution function and obtain the skew-scattering contribution by considering electron-impurity (and electron-phonon) scattering up to the second Born approximation. By performing a numerical calculation for InSb-based quantum wells, the temperature dependencies of the various components of anomalous Hall current are examined. We also discuss the roles of electron-impurity and electron-phonon scatterings in contributing to the total anomalous Hall current.

Quantization of the Hall Conductance in a Three-Dimensional Layer

Quantization of the Hall conductance is observed in epitaxial layers of heavily doped $n$-type GaAs with thickness $(\ensuremath{\approx}100\mathrm{nm})$ larger than both the screening length and the mean free path of the conduction electrons. Therefore, the single-particle spectrum of the electrons is three dimensional. Analogous to the quantum Hall effect in two-dimensional systems, the magnetic field $B$ dependence of the Hall conductance ${G}_{\mathrm{xy}}$ shows, below 1 K, steps at quantized values ${\mathrm{ie}}^{2}/h$ for $i\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,4,6$ together with pronounced minima in the transverse conductance ${G}_{\mathrm{xx}}$. The minima in ${G}_{\mathrm{xx}}$ and $|{\mathrm{dG}}_{\mathrm{xy}}/\mathrm{dB}|$ appear in magnetic fields where, at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4\mathrm{K}$, ${G}_{\mathrm{xy}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}ie}^{2}/h$.

Influence of localization on the Hall effect in narrow-gap, bulk semiconductors.

Our transport study of the narrow-gap, bulk (three-dimensional) semiconductors ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Cd}}_{\mathit{x}}$Te and InSb reveals incipient, nonquantized ``Hall plateaus'' which coincide with minima of the Shubnikov--de Haas oscillations, analogous to the quantum Hall effect in two-dimensional systems. We attribute this effect to the existence of quasi-mobility-gaps at the bottom of each Landau level, originating from localization due to shallow hydrogenic donors and disorder.

Fractionally quantized Hall effect in two-dimensional systems of extreme electron concentration

We report magnetotransport measurements, down to 0.050 K and up to 20 T, in two-dimensional systems with dilute and dense electron densities. The emphasis is on the latter regime, where the Hall resistance shows quantization for level filling factors at $\ensuremath{\nu}=\frac{4}{3} \mathrm{and} \frac{5}{3}$, and the magnetoresistance presents well-defined structures at $\ensuremath{\nu}=\frac{7}{3} \mathrm{and} \frac{8}{3}$. These results indicate that the fractional quantum Hall effect is a general phenomenon not restricted to the lowest-orbital Landau level.