Topological kink states at a tilt boundary in gated multi-layer graphene

TL;DR

This paper demonstrates that tilt boundaries in gated multi-layer graphene host topologically protected gapless kink states, which are linked to quantum valley Hall insulators and protected by symmetries, potentially explaining sub-gap conductance.

Contribution

It identifies and characterizes topologically protected kink states at tilt boundaries in multi-layer graphene using microscopic and symmetry-based approaches, revealing their robustness and topological nature.

Findings

Tilt boundaries support gapless kink states.

Kink states are protected by symmetries and are robust against strain.

Possible phase transition between different topological states observed.

Abstract

The search for new realization of topologically protected edge states is an active area of research. We show that a tilt boundary in gated multi-layer graphene supports topologically protected gapless kink states, associated with quantum valley Hall insulator (QVH). We investigate such kink states from two perspectives: the microscopic perspective of a tight-binding model and an ab-initio calculation on bilayer, and the perspective of symmetry protected topological (SPT) states for general multi-layer. We show that a AB-BA bilayer tilt boundary supports gapless kink states that are undeterred by strain concentrated at the boundary. Further, we establish the kink states as concrete examples of edge states of {\it time-reversal symmetric} ${\mathbb Z}$-type SPT, protected by no valley mixing, electron number conservation, and time reversal $T$ symmetries. This allows us to discuss possible phase transitions upon symmetry changes from the SPT perspective. Recent experimental observations of a network of such tilt boundaries suggest that transport through these novel topological kink states might explain the long standing puzzle of sub-gap conductance. Further, recent observation of gap closing and re-opening in gated bi-layer might be the first example of a transition between two distinct SPT's: QVH and LAF.