Characterization of two-dimensional fermionic insulating states

Understand

Inspired by the duality picture between superconductivity and insulator in two spatial dimension, we conjecture that the order parameter, suitable for characterizing 2D fermionic insulating state, is the disorder operator, usually known in the context of statistical transformation.

• Namely, the change of the phase of the disorder operator along a closed loop measures the particle density accommodating inside this loop.
• Thus, identifying this (doped) particle density with the dual counterpart of the magnetic induction in 2D SC, we can naturally introduce the disorder operator as the dual order parameter of 2D insulators.
• The disorder operator has a branch cut emitting from this ``vortex'' to the single infinitely far point.