Current-Voltage Characteristic and Shot Noise of Shift Current Photovoltaics

We theoretically study the current-voltage relation, the $I-V$ characteristic, of the photovoltaics due to the shift current, i.e., the photocurrent generated without the external dc electric field in noncentrosymmetric crystals through the Berry connection of the Bloch wave functions. We find that the $I-V$ characteristic and shot noise are controlled by the difference of group velocities between conduction and valence bands, i.e., $v_{11}-v_{22}$, and the relaxation time $\tau$. Since the shift current itself is independent of these quantities, there are a wide variety of possibilities to design it to maximize the energy conversion rate and also to suppress the noise. We propose that the Landau levels in noncentrosymmetric two-dimensional systems are a promising candidate for energy conversion.

Figure 1

Schematic picture of $I-V$ characteristics and photodetection in shift current photovoltaics. (a) Setup to measure $I-V$ and photocurrent. (b) $I-V$ characteristics of shift current photovoltaics. In this Letter, we consider current density $J$ as a function of the electric field $E$. (c) Shot noise in shift current photovoltaics. When the light is off, current fluctuates around zero due to thermal noise which can be neglected in zero temperature. When light is on, shift current flows and additional current fluctuation appears due to photocarriers in the nonequilibrium steady state.

Figure 2

Optical transitions in LLs in inversion broken 2D systems realized in (a) graphene with staggered potential, and (b) TI surface states. (c) Shift current in TI surface states. We plot the nonlinear conductivity ${\sigma }_{yyy}$ as a function of frequency. The inset is for linear conductivity ${\sigma }_{yy}(\omega )$. Relaxation time is set to $1/\tau =0.05{\omega }_c$.

Figure 3

(a) $I-V$ characteristic of flat band systems. (b) Photoexcitation in zero electric field. (c) Photoexcitation in $E=-E_{\max }$. Real space shift $R$ causes energy shift of $eER$.