Abstract
Bloch electrons in multiorbital systems carry nontrivial quantum geometric information characteristic of their orbital composition as a function of their wave vector. When such electrons form Cooper pairs, the resultant superconducting state naturally inherits aspects of the quantum geometry. In this paper, we study how this geometric character is revealed in the intrinsic optical response of the superconducting state. In particular, due to the superconducting gap opening, interband optical transitions involving states around the Fermi level are forbidden. This generally leads to an anomalous suppression of the optical conductivity at frequencies matching the band separation -- which could be significantly higher than the superconducting gap energy. We discuss how the predicted anomaly may have already emerged in two earlier measurements on an iron-based superconductor. When interband Cooper pairing is present, intraband optical transitions may be allowed and finite conductivity emerges at low frequencies right above the gap edge. These conductivities depend crucially on the off-diagonal elements of the velocity matrix in the band representation, i.e. the interband velocity -- which is related to the non-Abelian Berry connection of the Bloch states.
Highlights
In a multiorbital system, Bloch electrons on the individual energy bands are generally not featureless particles
The anomalous suppression is not necessarily restricted to a narrow width of 1 above ωF, but could potentially take place at all frequencies associated with indirect band separations, which amount to a frequency span as wide as the bandwidth of the unpaired band
As we focus on translation invariant models, we only consider interband Cooper pairs formed between electrons of opposite wave vectors
Summary
Bloch electrons on the individual energy bands are generally not featureless particles They exhibit nontrivial internal structure, in the sense that they possess quantum geometric information associated with their varying orbital composition as a function of the wave vector. The object i m, k|∂kμ |n, k is known as the non-Abelian Berry connection and is involved in the definition of the quantum geometric tensor [1,2,3,4,5,6] It is finite provided the orbital composition of the Bloch states, i.e., the rela-. We demonstrate how the geometric character of the superconducting electrons influences the intrinsic optical conductivity
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