Pairing in the quantum Hall system

TL;DR

This paper draws an analogy between skyrmion states in quantum Hall systems and BCS superconductivity, proposing that skyrmions originate from electronic pairing and analyzing their stability under magnetic fields and temperature.

Contribution

It introduces a novel analogy between skyrmions and BCS superconductors and models the critical magnetic field's temperature dependence in the quantum Hall system.

Findings

Skyrmion phase is unstable above a critical magnetic field.

The critical field depends on temperature as B_c(T)/B_c(0) ≈ [1-(T/T_c)^3]^{1/2}.

Electronic pairing underpins the skyrmion state.

Abstract

We find an analogy between the single skyrmion state in the quantum Hall system and the BCS superconducting state and address that the quantum mechanical origin of the skyrmion is electronic pairing. The skyrmion phase is found to be unstable for magnetic fields above the critical field $B_{c}(T)$ at temperature $T$, which is well represented by the relation $B_c(T)/B_{c}(0) \approx {[1-(T/T_c)^3]}^{1/2}$.