## *** Note the change in location *** Magnetization Dynamics and Peierls Instability in Topological Josephson Structures

#### by Prof. Alexander Shnirman

*KIT*

##### at Special seminar

Tue, 30 May 2023, 14:00

Ilse Katz Institute for Nanoscale Science & Technology (51), room 015

#### Abstract

We study a long topological Josephson junction with a ferromagnetic stripe between the superconductors.

The low-energy theory exhibits a non-local in time and space interaction between chiral Majorana fermions,

mediated by the magnonic excitations in the ferromagnet. The spontaneous breaking of a Z2-symmetry at the

mean-field level leads to a tilting of the magnetization and the opening of a fermionic gap (Majorana mass).

This is equivalent to the Peierls instability in the commensurate Fröhlich model.

Within a Gaussian fluctuation analysis, we identify critical values for the temporal and spatial non-locality of the interaction,

beyond which the symmetry breaking is stable at zero temperature – despite the effective one-dimensionality of the model. We conclude that non-locality, i.e., the stiffness of the magnetization in space and time, stabilizes the symmetry breaking. In the stabilized regime, we expect the current-phase relation to exhibit an experimen- tally accessible discontinuous jump.

At nonzero temperatures, as usual in the 1D Ising model, the long-range order is destroyed by solitonic excitations,

which in our case carry each a Majorana zero mode.

Created on 23-05-2023 by Schechter, Moshe (smoshe)

Updaded on 29-05-2023 by Schechter, Moshe (smoshe)