Curvature-induced pseudogauge fields from time-dependent geometries in graphene

The massless Dirac equation is studied in curved space-time on the (2+1)-dimensional graphene sheet in time-dependent geometries. Emergent pseudogauge fields are found both in the adiabatic regime and, for high-frequency periodic geometries, in the nonadiabatic regime for a generic Friedmann-Lemaitre-RobertsonWalker metric in Fermi normal coordinates. The former extends the conventionally understood homogeneous pseudogauge field to include weak temporal inhomogeneities. The latter, through the usage of Floquet theory, represents another class of emergent pseudogauge field and is argued to potentially provide a condensed matter realization of cosmological high-frequency geometries.