Bulk photovoltaic effect in 2D materials with electron-phonon interactions from first-principles

The generation of a direct current in a solid under a uniform oscillating light field is a non-linear optical phenomenon known as bulk photovoltaic effect (BPVE). In non-magnetic materials under a linearly polarized field, the BPVE has two frequency-dependent contributions: the shift current, an intrinsic quantity derived from electrons in the perfect lattice; and the ballistic current, which arises from scattering processes (in particular the electron-phonon interaction). The possibility of realizing this inherently quantum effect in homogeneous, non-centrosymmetric materials has made BPVE an increasingly important topic in photovoltaics, but realistic numerical calculations have not been possible until recent years. Here we present a symmetry analysis of the atomistic expressions for the shift current and the phonon-assisted ballistic current, which allows to obtain convenient local selection rules in the Brillouin zone (BZ) as well as efficient implementations in the irreducible part of the BZ. These general results are then applied to the calculation of these two quantities in two-dimensional materials, such as an insulating single layer of GaSe, from first-principles electron and phonon calculations with the software Crystal. This is, to our knowledge, one of the first instances in which the phonon-assisted ballistic current has been computed in 2D materials. The impact of in- and out-of-plane strain on the shift current is also demonstrated, in regards to both numerical magnitudes and local selection rules.