Large Bulk Photovoltaic Effect and Spontaneous Polarization of Single-Layer Monochalcogenides

We use a first-principles density functional theory approach to calculate the shift current and linear absorption of uniformly illuminated single-layer Ge and Sn monochalcogenides. We predict strong absorption in the visible spectrum and a large effective three-dimensional shift current ($\sim 100\mu \mathrm{A}/{\mathrm{V}}^2$), larger than has been previously observed in other polar systems. Moreover, we show that the integral of the shift-current tensor is correlated to the large spontaneous effective three-dimensional electric polarization ($\sim 1.9\mathrm{C}/{\mathrm{m}}^2$). Our calculations indicate that the shift current will be largest in the visible spectrum, suggesting that these monochalcogenides may be promising for polar optoelectronic devices. A Rice-Mele tight-binding model is used to rationalize the shift-current response for these systems, and its dependence on polarization, in general terms with implications for other polar materials

Figure 1

The crystal structure of single-layer group-IV monochalcogenides $MX$, where $M=\mathrm{Ge}$, Sn, and $X=\mathrm{S}$, Se. In (a) we show the 3D view of the single-layer and in (b)–(d) the projections of the single-layer crystal on the Cartesian axes. Structures with $0$, $\pm P_0$ polarizations are also shown in inset (b) and (d). A twofold rotation along $z$ (plus translations) determines the polarization axis, see text.

Figure 2

Shift-current spectra (a), shift vector integrated over $\mathbf{k}$ (b), and linear absorption (c) of single-layer GeS. The large in-plane shift-current response in the visible range is dominated by the shift vector and corresponds to the large absorption along $zz$ and $yy$.

Figure 3

Nonmonotonic dependence of the integral of the shift-current tensor vs electric polarization for GeS; the integral is normalized by $-3\times 10^{10}{\mathrm{As}}^{-1}{\mathrm{V}}^{-2}$, its value at the ground state with polarization $P_0=1.9\mathrm{C}/{\mathrm{m}}^2$. The tensor components $zzz$, $zyy$, and $zxx$ are shown in black, green, and blue points, respectively. For small $P$ the integral is directly proportional to polarization (dashed lines), but it is nonmonotonic for large $P$. The integral reaches it maxima at $P({\delta }_m)$, which is close to $P_0$.