Topological transition of graphene from a quantum Hall metal to a quantum Hall insulator at ν = 0

Abstract

An exciting theme in condensed matter physics is the search for new states of matter. Over the last few years, a new class of topological states has been discovered—the topological insulator—which greatly expands our knowledge about quantum states. One important topic is the transition from the new topological state to other known states, such as the superconductor or normal band insulator. Graphene at filling factor ν = 0 was known to be a topological insulator (called a quantum Hall metal (QH-metal)) protected by the electron–hole symmetry. A recent surprising experiment indicates that graphene can also be a normal band insulator (called a quantum Hall insulator (QH-insulator)) at ν = 0 in a strong magnetic field. Here we show that a transition from a topological insulator to a band insulator can occur in graphene at ν = 0. The topological transition results from the competition between the magnetic field-driven Peierls-type lattice distortion (originating from the Landau level degeneracy) and random bond fluctuations from the intrinsic sheet-buckling. The critical field that separates a QH-metal from a QH-insulator depends on the strength of bond fluctuation. The picture explains well why the field required for observing the QH-insulator is lower for a cleaner sample.