Valley splitter and transverse valley focusing in twisted bilayer graphene

Abstract

We study transport in twisted bilayer graphene and show that electrostatic barriers can act as valley splitters, where electrons from the K (K) valley are transmitted only to, e.g., the top (bottom) layer, leading to valley-layer locked currents. We show that such a valley splitter is obtained when the barrier varies slowly on the moiré scale and induces a Lifshitz transition across the junction, i.e., a change in the Fermi-surface topology. Furthermore, we show that for a given valley the reflected and transmitted current are transversely deflected, as time-reversal symmetry is effectively broken in each valley separately, resulting in valley-selective transverse focusing at zero magnetic field.

Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models

“…In agreement with results of Ref. [46] for an abrupt barrier the momentum resolved transmission exhibits oscillations due to finite size effects. This spectral density oscillations are linked to the finite length of the central region λ B .…”

“…This model has been intensively used [46][47][48][49] due to its simplicity but, although it exhibits naturally particle/hole symmetry, due to the Wannier obstruction it lacks the characteristic symmetries of the system and leads to moiré minivalleys with vanishing net chirality.…”

“…Following Ref. [46] we truncate the hopping terms in the 2B1V model by considering just the four largest ones. As we can see in Table I, due to the particular form of the Wannier orbitals the hopping elements do not vary monotonically with distance (i.e.…”

“…Inspired by the experimental device described in Ref. [46] the potential profile Hamiltonian for a three regions junction takes the form…”

“…In the case of the 2B1V model, which goes beyond the nearest neighbors approximation, we follow Ref. [46] to set the recursive equations from However, we equivalently can express the relevant matrices for the recursive method in terms of the polynomial expansion of the Hamiltonian.…”