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# The Non-linear Hall Effect in Time-Reversal-Invariant Materials and the Shear Sound of Metals

### Inti Sodemann (MPIPKS Dresden)

#### 19.12.2019 at 12:15

In the first part of the talk, we will describe a correction to Newton’s second law when electrons move in Bloch bands without inversion symmetry, whereby, their acceleration acquires a term proportional to the square of the electric field and orthogonal to it. This "non-linear Hall acceleration" gives rise to a "non-linear Hall effect" in time reversal invariant materials that is controlled by a quantum geometric tensor called the "Berry curvature dipole”. We will also discuss a remarkable "quantum rectification sum rule” according to which the frequency integrated rectification conductivity is entirely controlled by the Berry geometry and is independent of the band energies. In the second part, we will review the bosonization approach to Fermi liquids above one dimension and use it to study a sharp change in the excitation spectrum of fermi liquids that occurs beyond a critical interaction strength whereby an unconventional collective mode exits the particle-hole continuum. This mode is a collective shear wave that features purely transverse current oscillations, in analogy to the transverse sound of crystals. We will argue that the shear sound might be “hiding`' in several metals and describe experimental strategies to probe it, including the appearance of sharp conductivity dips in ultra-clean narrow channels and its coupling to charge-fluctuations under weak magnetic fields.

A 450, Theresienstr. 37