In a crystal, the “twisting” of electronic wave functions in momentum space – as encoded in the Bloch band Berry curvature gives rise to a wealth of interesting “anomalous” behaviors that typify a wide new range of quantum materials. An emerging theme is how quantum geometry enables coupling between electric and magnetic degrees of freedom. I will discuss how coupled charge and magnetic degrees of freedom can conspire to produce a variety of unusual transport phenomena.
A particularly striking example occurs in gapped graphene (a nominally topologically trivial “vanilla” insulator). In vanilla/conventional insulators, carrier transport is expected to be exponentially activated, leading to a severely muted current response when an electric field is applied. I will argue that this expectation fails in gapped graphene (of with finite sample size) where its bulk free carriers in valleys with non-vanishing Berry curvature give rise to low-dissipation edge currents, which are squeezed within a distance of the order of the valley diffusion length from the edge. This happens even in the absence of edge states [topological (gapless) or otherwise], and when the bulk equilibrium carrier concentration is thermally activated across the gap. Instead, this behavior arises from the unusual coupling between charge and magnetic degrees of freedom afforded by Berry curvature.
If time permits, I will discuss another example of unusual quantum geometric behavior. This occurs in monolayer 1T’-WTe2 where a perpendicularly applied electric field induces a bulk band berry curvature and magnetic moment with a rapid switch-like behavior. Due to its low symmetry, Berry curvature and magnetic moment in 1T’-WTe2 possess a dipole-like distribution enabling (gate-tunable) quantum non-linear anomalous Hall currents and current induced magnetization (kinetic magneto-electric effect) respectively. Taken together these render it a rich two-dimensional platform for all- electrical control over quantum geometric effects as well as spin/magnetic texture.