Berry curvature of low-energy excitons in rhombohedral graphene

We investigate low-energy excitons in rhombohedral pentalayer graphene encapsulated by hexagonal boron nitride (hBN/R5G/hBN), focusing on the regime at the experimental twist angle <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>θ</a:mi> <a:mo>=</a:mo> <a:mn>0</a:mn> <a:mo>.</a:mo> <a:msup> <a:mn>77</a:mn> <a:mo>∘</a:mo> </a:msup> </a:mrow> </a:math> and with an applied electric field. We introduce a new low-energy two-band model of rhombohedral graphene that captures the band structure more accurately than previous models while keeping the number of parameters low. Using this model, we show that the centres of the Wannier functions are displaced from the moiré unit cell origin —they are instead localized at <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>C</b:mi> <b:mn>3</b:mn> </b:msub> </b:math> -symmetric points on the boundary. We also find that the exciton shift is electrically tunable: by varying the electric field strength, the exciton Wannier center can be exchanged between inequivalent corners of the moiré unit cell. Our results suggest the possibility of detecting excitonic corner or edge modes, as well as novel excitonic crystal defect responses in hBN/R5G/hBN. Lastly, we find that the excitons in hBN/R5G/hBN inherit excitonic Berry curvature from the underlying electronic bands, enriching their semiclassical transport properties. Our results position rhombohedral graphene as a compelling tunable platform for probing exciton topology in moiré materials.