# Ising quantum criticality in Majorana nanowires

## TL;DR

This paper investigates the finite-size scaling behavior of Majorana zero modes in topological superconductor nanowires near the quantum critical point, linking Ising criticality with realistic experimental conditions.

## Contribution

It introduces a universal finite-size scaling framework for Majorana modes at the topological transition, applicable to realistic nanowire models with spin-orbit coupling and Zeeman splitting.

## Key findings

- Derived the finite-size scaling laws near the topological quantum critical point.
- Applied the scaling to a synthetic superconductor model with realistic parameters.
- Proposed experimental methods to detect the topological quantum critical point.

## Abstract

Finite-length one-dimensional topological superconductor wires host localized Majorana zero modes at their ends. In realistic models, these appear only after a topological quantum critical point is crossed by external tuning of parameters. Thus, there is a universal finite-size scaling, governed by the critical point, that dictates the evolution of the energy of the Majorana modes near the transition. We first describe this scaling, then apply it in detail to an explicit synthetic topological superconductor model. Our work not only connects Ising quantum criticality with realistic nanowires in the presence of spin-orbit coupling, Zeeman splitting and superconductivity, but also provides a viable experimental route for discerning the existence of the topological quantum critical point.