Two-impurity helical Majorana problem

TL;DR

This paper predicts observable signatures of helical Majorana fermions in topological superconductors by analyzing a two-impurity system with quantum dots, revealing universal oscillatory spin dynamics after a magnetic quench.

Contribution

It formulates and solves the low-energy theory for a two-impurity helical Majorana system including RKKY interactions, highlighting long-range antiferromagnetic Ising coupling effects.

Findings

Universal weakly damped oscillations in spin dynamics after magnetic quench

Long-range antiferromagnetic Ising coupling mediated by edge modes

Predicts experimentally accessible signatures of helical Majorana fermions

Abstract

We predict experimentally accessible signatures for helical Majorana fermions in a topological superconductor by coupling to two quantum dots in the local moment regime (corresponding to spin-$1/2$ impurities). Taking into account RKKY interactions mediated by bulk and edge modes, where the latter cause a long-range antiferromagnetic Ising coupling, we formulate and solve the low-energy theory for this two-impurity helical Majorana problem. In particular, we show that the long-time spin dynamics after a magnetic field quench displays weakly damped oscillations with universal quality factor.