On the Bloch Theorem Concerning Spontaneous Electric Current

TL;DR

This paper revisits the Bloch theorem on the absence of spontaneous electric currents in interacting electron systems, extending its applicability to systems with magnetic fields and analyzing implications for surface currents and $d$-wave superconductivity.

Contribution

It demonstrates that the Bloch theorem remains valid even with magnetic fields induced by electric currents and applies this to surface currents, challenging recent proposals of $d$-wave superconductivity with surface flow.

Findings

Bloch theorem applies with magnetic fields from electric currents

Surface currents in $d$-wave superconductors are excluded

Recent $d$-wave proposals are inconsistent with the theorem

Abstract

We study the Bloch theorem which states absence of the spontaneous current in interacting electron systems. This theorem is shown to be still applicable to the system with the magnetic field induced by the electric current. Application to the spontaneous surface current is also examined in detail. Our result excludes the possibility of the recently proposed $d$-wave superconductivity having the surface flow and finite total current.