Friedel oscillations in graphene gapped by breaking P and T symmetries: Topological and geometrical signatures of electronic structure

Abstract

The measurement of Friedel oscillations (FOs) is conventionally used to recover the energy dispersion of electronic structure. Besides the energy dispersion, the modern electronic structure also embodies other key ingredients such as the geometrical and topological properties; it is one promising direction to explore the potential of FOs for the relevant measurement. Here, we present a comprehensive study of FOs in substrate-supported graphene under off-resonant circularly polarized light, in which a valley-contrasting feature and topological phase transition occur due to the combined breaking of inversion ($\mathcal{P}$) and time reversal ($\mathcal{T}$) symmetries. Depending on the position of the Fermi level, FOs may be contributed by electronic backscattering in one single valley or two valleys. In the single-valley regime, the oscillation periods of FOs can be used to determine the topological phase boundary of electronic structure, while the amplitudes of FOs distinguish trivial insulators and topological insulators in a quantitative way. In the two-valley regime, the unequal Fermi surfaces lead to a beating pattern (robust two-wave-front dislocations) of FOs contributed by intravalley (intervalley) scattering. This study implies the great potential of FOs in characterizing topological and geometrical properties of the electronic structure of two-dimensional materials.