Algebra of Majorana Doubling

TL;DR

This paper explores the algebraic structure behind Majorana modes at junctions, revealing a doubled spectrum and nonlinear mode operators, which could enable new control methods for these quantum states.

Contribution

It introduces a novel algebraic framework for Majorana modes at junctions, highlighting the nonlinear nature of mode operators in interacting systems.

Findings

Emergent mode creation operators are highly nonlinear in original operators.

The algebraic structure leads to a doubled spectrum of Majorana modes.

Potential for controlled dynamical manipulation of Majorana modes.

Abstract

Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly non-linear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.