Weak localisation driven by pseudospin-spin entanglement

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.