Non-linear Optics and Quantum Geometry of the Exciton State

The quantum geometry of single-particle Bloch states has played a central role in the description of emergent phenomena in condensed matter. Discussions on quantum geometry in the many-body regime have thus far been limited. In this work, we provide fresh perspectives on the concept of quantum geometry in correlated exciton states. We show that the quantum geometry of the many-body state cannot be simply attributed to the quantum geometry of the constituent single-particle states, but additional physics arises from the phase coherence of the many-body state. The quantum geometry of excitons plays a key role in experimentally accessible non-linear optical properties and leads to an enhancement in the non-linear optical response. In the case of the shift current (a direct current arising from optically-induced real-space shifts of the charge centres), the quantum many-body geometric term may be interpreted as a many-body analogue of the well-known Berry phase. Predictions from first principles calculations within the GW-BSE approximation will be presented for a range of non-linear optical responses and the many-body quantum geometric contribution will be quantified.

References

1. M. Lai, F. Xuan, S. Y. Quek, arXiv:2402.02002

2. F. Xuan. M. Lai, S.Y. Quek, PRL 132, 246902 (2024)