Resonant Photovoltaic Effect in Doped Magnetic Semiconductors

The rectified nonlinear response of a clean, time-reversal symmetric, undoped semiconductor to an ac electric field includes a well known intrinsic shift current. We show that when Kramers degeneracy is broken, a distinct second order rectified response appears due to Bloch state anomalous velocities in a system with an oscillating Fermi surface. This effect, which we refer to as the resonant photovoltaic effect, produces a resonant galvanic current peak at the interband absorption threshold in doped semiconductors or semimetals with approximate particle-hole symmetry. We evaluate the resonant photovoltaic effect for a model of the surface states of a magnetized topological insulator.

Figure 1

(a) Resonant photovoltaic effect induced by linearly polarized light incident on the surface of a warped topological insulator on a ferromagnet with an in-plane magnetization. (b) Carriers excited from the valence band to the oscillating Fermi surface.

Figure 2

(a) Constant energy contour showing the breaking of Kramers degeneracy by an in-plane magnetization, with $\lambda =200\mathrm{eV}{\AA }^3$ and $M=0.05\mathrm{eV}$. (b) Schematic picture showing the displacement of the hexagonally distorted Fermi surface.

Figure 3

(a) RPE for magnetized TI surface states with different warping coefficients $\lambda$ using ${ϵ}_F=250\mathrm{meV}$, $A=2.55\mathrm{eV}\AA$, $T=1\mathrm{K}$, $M=10\mathrm{meV}$, $\tau =1\mathrm{ps}$. Blue: experimental value of $\lambda$ for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. (b) Blue: peak value of RPE for $\lambda =250\mathrm{eV}{\AA }^3$ as a function of ${ϵ}_F$ in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Red: quadratic fit.