Effect of orbital currents on the restricted optical sum rule

TL;DR

This paper derives a modified optical sum rule considering orbital currents, explaining temperature-dependent spectral weight behavior in high-$T_c$ cuprates and comparing normal and superconducting states.

Contribution

It introduces a new form of the restricted optical sum rule accounting for orbital currents, linking theoretical predictions with experimental observations.

Findings

The sum rule is altered by orbital currents, affecting spectral weight.

Temperature dependence of spectral weight aligns with experimental data.

Differences between normal and superconducting states are analyzed.

Abstract

We derive the restricted optical-conductivity sum rule for a model with circulating orbital currents. It is shown that an unusual coupling of the vector potential to the interaction term of the model Hamiltonian results in a non-standard form of the sum rule. As a consequence, the temperature dependence of the restricted spectral weight could be compatible with existing experimental data for high-$T_c$ cuprates above the critical temperature $T_c$. We extend our results to the superconducting state, and comment on the differences and analogies between these two symmetry-breaking phenomena.