On Symmetry Properties of The Corrugated Graphene System

Abstract

The properties of the ballistic electron transport through a corrugated graphene system are analysed from the symmetry point of view. The corrugated system is modelled by a curved surface (an arc of a circle) connected from both sides to flat sheets. The spin–orbit couplings, induced by the curvature, give rise to equivalence between the transmission (reflection) probabilities of the transmitted (reflected) electrons with the opposite spin polarisation, incoming from opposite system sides. We find two integrals of motion that explain the chiral electron transport in the considered system.

Tunneling in a Rippled Graphene Superlattice with Spin Dependence and a Mass Term

“…After a lengthy and straightforward algebraic calculation, we obtain the transmission amplitudes for spin-up and spin-down We notice that the corrugated graphene structure supports the chiral symmetry for the transmitted electron flow that has been studied earlier in ref. [22]. We may easily verify that the probability conservation criterion…”

Rippled Graphene as an Ideal Spin Inverter

“…In this paper, we consider the most general case of the incident angle ϕ = arctan k y /k x of a ballistic electron beam, injected from the plane graphene sheet on the superlattice that consists of the curved graphene units. In contrast to semiripple configurations (a concave arc) considered in [11,12,30], our superlattice consists of the concave surface continuously connected to the convex surface. This unit is repeated N times (see Section 2).…”

“…There is an anticrossing effect between energy states characterized by the same m + quantum number, which yields an energy gap. This anticrossing is caused by the term λ y in the Hamiltonians ( 22), (23), which creates the energy gap 2λ y near the energy E = λ x at k x = 0, k y = 0 (see [10][11][12]). Let us analyze the upper and the lower limits of the energy gap, in which the evanescent modes exist in the case k x = 0, k y = 0.…”

“…More importantly, in the low-energy physics of graphene, the mean curvature generates a curvature-induced SOC [9] without any external field. Based on this fact, it was demonstrated that curvature-induced SOC [9,10] could produce a chiral transport [11,12]. In this case, the transport of ballistic electrons through periodically repeated ripples is subject to selection rules: Depending on the direction of motion, the system is transparent only for one spin polarization.…”