# Skyrme insulators: insulators at the brink of superconductivity

## TL;DR

This paper introduces the concept of Skyrme insulators, a new class of insulating states arising from the loss of topological protection in superconductors, and applies it to explain phenomena observed in SmB$_6$.

## Contribution

It proposes the novel idea of Skyrme insulators as a topological failure of superflow and applies this framework to interpret experimental results in SmB$_6$, including its diamagnetic Fermi surface.

## Key findings

- Skyrme insulators are a new topological insulating state.
- The theory explains the diamagnetic Fermi surface in SmB$_6$.
- Predicted Meissner effect in SmB$_6$ at low magnetic fields.

## Abstract

Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected, quantized circulation. When this topological protection is absent, as in the case of $^3$He-A, the coherent quantum state no longer supports persistent superflow. Here we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. We specifically introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex vector order parameter. We apply this idea to the case of SmB$_6$, arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood in terms of a Skyrme insulator. Our theory enables us to understand the linear specific heat of SmB$_6$ in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB6 will develop a Meissner effect.