Geometric valley Hall effect and valley filtering through a singular Berry flux

Abstract

Conventionally, a basic requirement to generate valley Hall effect (VHE) is that the Berry curvature for conducting carriers in the momentum space be finite so as to generate anomalous deflections of the carriers originated from distinct valleys into different directions. We uncover a geometric valley Hall effect (gVHE) in which the valley-contrasting Berry curvature for carriers vanishes completely except for the singular points. The underlying physics is a singular non-π fractional Berry flux located at each conical intersection point in the momentum space, analogous to the classic AharonovBohm effect of a confined magnetic flux in real space. We demonstrate that, associated with gVHE, exceptional skew scattering of valley-contrasting quasiparticles from a valley-independent, scalar type of impurities can generate charge neutral, transverse valley currents. As a result, the massless nature of the quasiparticles and their high mobility are retained. We further demonstrate that, for the particular Berry flux of π/2, gVHE is considerably enhanced about the skew scattering resonance, which is electrically controllable. A remarkable phenomenon of significant practical interest is that, associated with gVHE, highly efficient valley filtering can arise. These phenomena are robust against thermal fluctuations and disorders, making them promising for valleytronics applications.

Atomistic Band-Structure Computation for Investigating Coulomb Dephasing and Impurity Scattering Rates of Electrons in Graphene

“…Here, represents the areal density of ionized impurity atoms in the crystal, and comes from the randomly-impurity scattering of electron in the second-order Born approximation [ 48 , 62 ]. Explicitly, the random impurity-interaction matrix elements are calculated as where is the charge number of ionized impurity atoms.…”

“…In recent years, by using the low-energy Dirac Hamiltonian [ 4 ], we have extensively explored varieties of dynamical properties of electrons in graphene and other two-dimensional materials, including Landau quantization [ 18 , 31 , 32 , 33 , 34 , 35 ], many-body optical effects [ 36 , 37 , 38 , 39 , 40 , 41 ], band and tunneling transports [ 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 ], etc. In this paper, we particularly focus on the application of computed electronic states and band structures from a tight-binding model to the calculations of Coulomb and impurity scatterings of electrons in graphene on the basis of a many-body theory [ 3 , 4 ], where the former and latter determine the lineshape [ 1 ] of an absorption peak and the transport mobility [ 44 ], respectively.…”

Electrical confinement in a spectrum of two-dimensional Dirac materials with classically integrable, mixed, and chaotic dynamics

“…To generate an annular structure on an α-T 3 sheet, we apply the following electrical potential: (11) where the two circles have radius R 1 and R 2 , respectively, and their centers are For all three types of cavities, there is a resonant peak in the total cross section for α = 0.1, but no such peak appears for α = or α = 1, implying a much stronger ability to confine electrons for the α-T 3 (α = 0.1) cavity than for the graphene or pseudospin-1 cavity. Fully developed classical chaos can smooth out the resonance to some extent, but it is still pronounced.…”

“…Because of the existence of three distinct bands, the low-energy excitations need to be described by a spinor wave function of three components, corresponding effectively to pseudospin-1 quasiparticles that obey the Dirac-Weyl equation. In between the pseudospin-1/2 and pseudospin-1 extremes lies a spectrum of pseudospin quasiparticles that can be generated by the corresponding spectrum of α-T 3 lattices [6][7][8][9][10][11][12][13][14][15][16].…”

“…As the value of the pseudospin parameter α increases from zero to one, the nature of the quasiparticles of the system changes from pseudospin-1/2 to hybrid and finally to pseudospin-1. For α = 0, 1, the time-reversal symmetry (T -symmetry) is broken [11].…”