Observation of the quantum valley Hall state in ballistic graphene superlattices

Abstract

A new state of matter “quantum valley Hall state” is observed by the nonlocal transport in a massive Dirac fermion.

Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents

“…This contradicts experimental observation of edge currents near the DP in isolated graphene wires with zigzag edges [28] or in G/hBN wires where some zigzag segments are present [26]. These edge currents [26] are responsible for the metallic-like resistivityρ xx in figure 2(b), which is also observed experimentally [1,25,26].…”

“…Another long-standing puzzle is the metallic-like ordinary longitudinal resistivity, ρ xx ∼10 kΩ, commonly measured experimentally [1,25] for the G/hBN channel between the two crossbars despite the expected finite gap in its bulk. This suggests the presence of additional conduction pathways, such as edge currents observed very recently [26,27], which shunt the highly insulating state at low temperatures.…”

“…• metallic-like ρ xx usually measured experimentally [1,25] despite the presumed gap opening around the DP, using ab initio quantum transport where we perform density functional theory (DFT) calculations combined with both the multiterminal LB formula (figures 2, 3 and 5) and the Kubo formula ( figure 4).…”

“…Interestingly, the very recent experiments [25] on quasiballistic hBN/G/hBN heterostructures exhibiting metallic-like r xx have measured R NL that does not scale as r µ xx 3 at low temperatures T;1.5 K (such cubic scaling is restored at T;40 K). Also, deep into the insulating regime (i.e., with large ρ xx ) R NL becomes independent of ρ xx [5].…”

“…This is because the VASP calculations for the periodic supercell of G/hBN used to construct the Wannier TBH did not include information about edges and edge passivating atoms. Nevertheless, the Wannier TBH could be useful for fully encapsulated hBN/G/hBN wires [25,26], where edges are not exposed to the environment and where a large group velocity of edge state bands near the DP in figure A1(d) would make edge currents more resilient to disorder.…”