Weak localisation driven by pseudospin-spin entanglement

Abstract

At low temperatures, quantum corrections, originating from the interference of the many paths an electron may take between two points, tend to dominate the transport properties of two-dimensional conductors. These quantum corrections increase the resistivity in systems such as two-dimensional electron gases (2DEGs) without spin–orbit coupling (SOC), a phenomenon called weak localisation. Including symmetry-breaking SOC leads to a change from weak localisation (WL) to weak anti-localisation (WAL) of the electronic states, i.e. a WL-to-WAL transition. Here, we revisit the Cooperon, the propagator encoding quantum corrections, within the context of ultra-clean graphene-based van der Waals heterostructures with strong symmetry-breaking Bychkov-Rashba SOC to yield two completely counter-intuitive results. Firstly, we find that quantum corrections vary non-monotonically with the SOC strength, a clear indication of non-perturbative physics. Secondly, we observe the exact opposite of that seen in 2DEGs with strong SOC: a WAL-to-WL transition. This dramatic reversal is driven by mode entanglement of the pseudospin and spin degrees of freedom describing graphene’s electronic states. We obtain these results by constructing a non-perturbative treatment of the Cooperon, and observe distinct features in the SOC dependence of the quantum corrections to the electrical conductivity that would otherwise be missed by standard perturbative approaches.