Van Hove scenario of anisotropic transport in a two-dimensional spin-orbit coupled electron gas in an in-plane magnetic field

Abstract

We study electronic transport in two-dimensional spin-orbit coupled electron gas subjected to an in-plane magnetic field. The interplay of the spin-orbit interaction and the magnetic field leads to the Van Hove singularity of the density of states and strong anisotropy of Fermi contours. We develop a method that allows one to exactly calculate the nonequilibrium distribution function for these conditions within the framework of the semiclassical Boltzmann equation without using the scattering time approximation. The method is applied to calculate the conductivity tensor and the tensor of spin polarization induced by the electric field (Aronov-Lyanda-Geller-Edelstein effect). It is found that both the conductivity and the spin polarization have a sharp singularity as functions of the Fermi level or magnetic field, which occurs when the Fermi level passes through the Van Hove singularity. In addition, the transport anisotropy dramatically changes near the singularity.

Magnetic field driven topological transitions in the noncentrosymmetric energy spectrum of the two-dimensional electron gas with Rashba-Dresselhaus spin-orbit interaction

“…From the properties of energy spectrum which have been discussed in Sec. III some general conclusions related to isoenergetic contours follow: 1) There are no more when two separate contours for given energy E. At fixed energy E magnetic field moves the energy of branch contact E 0 (11) and energies of critical points (25) resulting in Lifshitz electron transition of both types - (1); ϕ h = π, blue dashed contours (2). b) Isoenergetic contours at and for the energy corresponding to the minimum of the parabola (11) ǫ min cont = E = 0.0868: h = 0.3, red shortdashed contour (1); h = 0.5, solid contour (2); h = 0.7, blue long-dashed contours (3).…”

“…from which an interesting observation follows: at E = E 0 the extremal radii of the contours k (1,2) + = 2λ (1,2) , for whichλ (1,2) = 0, give energies (25) and positions (22) of critical points on total surfaces ǫ = ǫ 1,2 .…”

“…(25),(A.1) for any value of magnetic field the energy of the branch ǫ = ǫ 2 has the minimum ǫ h) = ǫ crit1 (h) , f Energy spectrum (3) for the magnetic field directed along kx = −ky axis, ϕ h = 3π/4, (a,b) and along kx = ky axis, ϕ h = π/4, (c,d). a,c)h = 0.5 <hc1 = 1.28,hc2 = 1.44; b,d)h = 1.5 >hc1,hc2.…”

Determination of the Rashba and Dresselhaus Spin–Orbit Interaction Parameters and g‐Factor from the Critical Points of the Spectrum in a 2D Electron Gas in an In‐Plane Magnetic Field

“…[14][15][16] A method allowing to solve this problem in the semiclassical approximation for low temperatures and elastic scattering of electrons by impurities with a short-range potential was developed in the article. [17] The point is that the integral kinetic equation is the Fredholm integral equation with a degenerate kernel. Therefore, it reduces to an algebraic one and can be exactly solved.…”

Two‐Particle Scattering and Resistivity of Rashba Electron Gas

“…This coupling spin-splits the dispersion curve into the upper and lower helicity bands. It was found that in the low-density regime when only the lower band is filled, the impurity-related resistivity exhibits an unconventional electron-density dependence [11][12][13] . Apparently, this system is not Galilean-invariant and is described at the same time by a minimum number of independent parameters.…”