Quantum fluctuations and the emergence of in-gap Higgs mode in superconductors

TL;DR

This paper investigates how quantum fluctuations influence the Higgs mode in s-wave superconductors, revealing a shift below the energy gap and sharper experimental signatures, with implications for various condensed matter systems.

Contribution

The study extends the Higgs mode theory to include quantum fluctuations, showing they cause a shift below the gap and produce a new undamped pole, enhancing experimental detection.

Findings

Quantum corrections shift the Higgs eigenfrequency below 2Δ.

The Higgs mode appears as an undamped pole below the quasiparticle continuum.

Fluctuation effects alter measured gaps in different experimental techniques.

Abstract

We extend the well-established action of the Higgs mode in $s$-wave superconductors to include quantum fluctuations (QFs). We find that already one-loop quantum corrections to the Higgs propagator shift its eigenfrequency below the superconducting energy gap $2\Delta$. Consequently, the Higgs mode appears as an undamped pole below the quasiparticle continuum, leading to drastically sharper experimental signatures. We demonstrate this by calculating two characteristic fingerprints of the Higgs mode, namely in Third Harmonic Generation (THG) and inelastic Raman scattering signals. More generally, gaps measured in $s$-wave superconductors with different experimental techniques (such as scanning tunneling microscope and Raman scattering) may be different due to fluctuation corrections. Since already arbitrarily weak QFs lead to the shift and to the new pole, our results shed some light on other amplitude modes even for systems with weak QFs, including charge density waves, (anti-) ferromagnets, or cold atom fermionic condensates.