Remarks on sine-Gordon kink -- fermion system: localized modes and scattering

Abstract

We study numerically the kink-fermion interactions in a 1+1 dimensional toy model, which describes sine-Gordon kinks coupled to the massless Dirac fermions with backreaction. We show that the spectrum of fermionic modes strongly depends on the choice of the coupling, in particular, there are no localized modes for a minimal Yukawa coupling. We analyze the scattering of the fermionic packet by the kink. We demonstrate that the outcome of the collision dynamically depends on the phase of the incoming fermion packet, it results in alternating regimes of positive and negative acceleration of the kink.

Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion

“…[32,33,34]. The recent studies including the back-reaction were mainly performed using numerical methods [35,36]. In a recent work the analytical scattering states of the fermion on a prescribed sine-Gordon kink has been considered [37].…”