掺杂磁性半导体中的谐振光伏效应

The interband coherence responses of crystals to dc and ac driving electric fifields have both been studied extensively in recent years. The intrinsic anomalous velocity dc response, which is due to interband coherence and related to momentum-space Berry curvature, is essential for the chiral anomaly  in Weyl semimetals, and that it often dominates the anomalous Hall effffect of magnetic materials . Separately a number of conceptually novel non-linear response effffects  have been identifified recently that involve interband coherence. Notably, the non-linear optical response of a semiconductor at frequencies above the band gap includes an intrinsic dc photocurrent associated with an interband coherence related shift of intra-cell coordinates. The intrinsic shift current has received particular attention because it is closely related to topological band characteristics , and has been identifified experimentally in some noncentrosymmetric ferroelectrics . In this Letter, we identify a new non-linear response effffect by showing that the dc galvanic photocurrent in doped semiconductors can contain an anomalous velocity contribution.

The understanding of interband coherence and its relation to disorder in the non-linear optical response of semiconductors is still in its infancy. Most studies to date have focused on undoped materials, although possible Fermi surface effffects in doped systems have started to gain attention very recently. The resonant photovoltaic effffect (RPE) mechanism for rectifified response to linearly polarized light (Fig. 1(a)) is due to the combination of Bloch state anomalous velocities and Fermi surface shifts, which both oscillate when driven by an ac fifield as indicated in Fig. 1(b) and produce a current with a non-zero time average. The RPE involves an interplay between Bloch state wave function topology, disorder, and interband optical excitation. The RPE is active in doped semiconductors with broken time-reversal symmetry, and strongest in semiconductors with approximate particle-hole symmetry. It is therefore especially strong in magnetized topological materials whose surface states have approximate particle-hole symmetry, reflflecting the fundamental connection between non-linear response and non-trivial band topology , and the importance of the Berry curvature in non-linear optical response . The RPE is related in part to the non-linear Hall conductivity, which contains a related intrinsic contribution proportional to the Berry curvature dipole but may also have extrinsic contributions . Non-linear phenomena in topological materials have been discussed previously e.g. the observation of the non-linear Hall effffect , the prediction of a non-linear anomalous Hall effffect , and valley-driven second harmonic generation.

Fig1

For experimental observation the TI layer should be as thin as possible so as to enable a strong proximity effect. Strictly speaking, our model applies to fifilms thicker than 3nm with no tunneling between the top and bottom surfaces . Yet the effffect will be very strong even in thinner fifilms, and our model is still approximately applicable since εF is much larger than the interlayer tunneling strength. We expect a strong RPE in Bi2−xMnxTe3 synthesized recently. If, instead of ferromagnetism, an in-plane magnetic fifield is used to break time reversal symmetry, in a geometry very similar to Ref., the effffect will be observable but relatively small due to the inherent smallness of the Bohr magneton. The RPE can occur in conventional semiconductors, yet due to the large asymmetry between the valence and conduction bands and the smallness of the Fermi energy we expect it to be much weaker than in TIs.

In summary, we have developed the general formalism describing the second order optical response and identi- fified a resonance in the dc photocurrent at ¯hω = 2εF with a height and width determined by the relaxation time scale. The theory will be extended to second harmonic generation, circularly polarized light, and other materials such as transition metal dichalcogenides .