2025/08/18 by Kim, Kyung-Su · 2 citations
#FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2508.13149
We study how an out-of-plane magnetic field B(\bf r) and a Berry curvature Ω(\bf k) modify the exchange interactions in a two-dimensional Wigner crystal (WC) using a semi-classical large-rs expansion. When only a magnetic field is present, ring-exchange processes arise from multi-particle tunneling through \it complex trajectories which constitute \it complex instanton solutions of the coordinate-space path integral. To leading order in B, each exchange constant Ja acquires an Aharonov-Bohm phase along the zero-field tunneling trajectory. When a Berry curvature is present, the multi-particle tunneling must be considered in a complexified phase space (\bf r, \bf k). To leading order in Ω, Ja acquires a Berry phase along a \it purely imaginary momentum-space trajectory. When B and Ω are both present, in addition to having both Aharonov-Bohm and Berry phases, the exchange magnitude |Ja| is also modified due to an effective-mass renormalization. These effects could be relevant for the WC and proximate phases recently observed in rhombohedral multilayer graphene.