First-principles calculation of shift current in chalcopyrite semiconductor ${\mathrm{ZnSnP}}_2$

The bulk photovoltaic effect generates intrinsic photocurrents in materials without inversion symmetry. Shift current is one of the bulk photovoltaic phenomena related to the Berry phase of the constituting electronic bands: photoexcited carriers coherently shift in real space due to the difference in the Berry connection between the valence and conduction bands. Ferroelectric semiconductors and Weyl semimetals are known to exhibit such nonlinear optical phenomena. Here we consider the chalcopyrite semiconductor ${\mathrm{ZnSnP}}_2$, which lacks inversion symmetry, and calculate the shift-current conductivity. We find that the magnitude of the shift current is comparable to the recently measured values on other ferroelectric semiconductors and an order of magnitude larger than bismuth ferrite. The peak response for both optical and shift-current conductivity, which mainly comes from P-$3p$ and Sn-$5p$ orbitals, is several eV above the band gap.

Figure 1

Unit cell of the chalcopyrite ${\mathrm{ZnSnP}}_2$ (CH-ZSP) lattice: (a) side view and (b) top view. It has two twofold glide rotational and mirror symmetries $C_2\left(x\right)$, $C_2\left(y\right)$, $M_{xy}$, and $M_{x-y}$. (c) Brillouin zone (BZ) along with the high-symmetric points.

Figure 2

(a) The band structure from GGA and $\mathrm{GGA}+U$, showing a direct band gap at $\mathrm{\Gamma }$. The GGA band gap is $\sim 0.69\mathrm{eV}$, whereas the $\mathrm{GGA}+U$ band gap is $\sim 1.05\mathrm{eV}$, obtained with $U_d=10\mathrm{eV}$ and $U_p=2\mathrm{eV}$ (see text for details). (b) The total and partial density of states within $\mathrm{GGA}+U$. (c) Comparison of band structures obtained within $\mathrm{GGA}+\mathrm{\Delta }$ and TB-mBJ calculations. For comparison, the GGA conduction bands have been scissor shifted by $\mathrm{\Delta }=0.71\mathrm{eV}$ (bottom panel) to match the band gap, and $\mathrm{\Delta }=0.45\mathrm{eV}$ in an energy range of 1 and 5 eV (top panel), showing the qualitative and quantitative agreement between the two methods in the description of the conduction-band states.

Figure 3

The real and imaginary parts of the dielectric constant as a function of the incident photon energy obtained within the (a),(b) $\mathrm{GGA}+U$ and (c),(d) TB-mBJ scheme, showing overall agreement.

Figure 4

The optical conductivity (a) ${\sigma }_{xx}$ and (b) ${\sigma }_{zz}$ from $\mathrm{GGA}+U$ and $\mathrm{GGA}+\mathrm{\Delta }$ ($\mathrm{\Delta }=0.36\mathrm{eV}$). The shift-current conductivity (c) $\sigma {}_{yz}^x$ and (d) $\sigma {}_{xy}^z$ from $\mathrm{GGA}+U$ and $\mathrm{GGA}+\mathrm{\Delta }$. (e) Both the optical and shift-current conductivity from $\mathrm{GGA}+U$ are plotted on the same scale.

Figure 5

A comparison of the scalar relativistic (no SOC) and full relativistic (SOC) band structures for ${\mathrm{ZnSnP}}_2$.