Effect of electron-hole asymmetry on optical conductivity in \(8-Pmmn\) borophene

At the atomic-cluster scale, pure boron is markedly similar to carbon, forming simple planar molecules and cage-like fullerenes. Theoretical studies predict that two-dimensional (2D) boron sheets will adopt an atomic configuration similar to that of boron atomic clusters. We synthesized atomically thin, crystalline 2D boron sheets (i.e., borophene) on silver surfaces under ultrahigh-vacuum conditions. Atomic-scale characterization, supported by theoretical calculations, revealed structures reminiscent of fused boron clusters with multiple scales of anisotropic, out-of-plane buckling. Unlike bulk boron allotropes, borophene shows metallic characteristics that are consistent with predictions of a highly anisotropic, 2D metal.

Optical reflectivity and transmission measurements over photon energies between 0.2 and 1.2 eV were performed on single-crystal graphene samples on a SiO2 substrate. For photon energies above 0.5 eV, graphene yielded a spectrally flat optical absorbance of (2.3+/-0.2)%. This result is in agreement with a constant absorbance of pialpha, or a sheet conductivity of pie2/2h, predicted within a model of noninteracting massless Dirac fermions. This simple result breaks down at lower photon energies, where both spectral and sample-to-sample variations were observed. This "nonuniversal" behavior is explained by including the effects of doping and finite temperature, as well as contributions from intraband transitions.

The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin-orbit coupling strength. We briefly review the status of efforts to achieve long spin-relaxation times in graphene with its weak spin-orbit coupling, and to achieve large current-induced spin polarizations in topological-insulator surface states that have strong spin-orbit coupling. We also comment on differences between the magnetic responses and dilute-moment coupling properties of the two systems, and on the pseudospin analogue of giant magnetoresistance in bilayer graphene.