# Regensburg 2019 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 5: Topological insulators

### HL 5.3: Vortrag

### Montag, 1. April 2019, 10:00–10:15, H36

**The quantum rectification sum rule in time reversal invariant materials** — •Oles Matsyshyn and Inti Sodemann — Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

We derive a unifying fully quantum mechanical formula for the non-linear conductivity of metals and insulators. With this formula we establish a new sum rule for the frequency integrated rectified current which is controlled entirely by the non-abelian Berry connection and therefore depends purely on the quantum geometry of the ground state wave-function. For metals the sub-gap spectral weight contributing to this sum rule is exhausted by a sharp peak whose strength is proportional to the Berry curvature dipole introduced in Phys. Rev. Lett. 115, 216806 (2015). This offers a deeper insight into the meaning of the Berry curvature dipole as a kind non-linear analogue of the Drude weight in inversion breaking and time reversal invariant metals, which can be viewed as quantifying an acceleration of the electron liquid which is second order in electric fields. We apply our findings to understand the non-linear opto-electronic properties of Weyl semimetal materials.