SciPost Submission Page
Collective modes in superconductors including Coulomb repulsion
by Joshua Althüser, Götz S. Uhrig
Submission summary
| Authors (as registered SciPost users): | Joshua Althüser · Götz S. Uhrig |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2503.05494v2 (pdf) |
| Date accepted: | Aug. 18, 2025 |
| Date submitted: | June 23, 2025, 8:38 a.m. |
| Submitted by: | Joshua Althüser |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We numerically study the collective excitations present in isotropic superconductors including a screened Coulomb interaction. By varying the screening strength, we analyze its impact on the system. We use a formulation of the effective phonon-mediated interaction between electrons that depends on the energy transfer between particles, rather than being a constant in a small energy shell around the Fermi edge. This justifies considering also rather large attractive interactions. We compute the system's Green's functions using the iterated equations of motion (iEoM) approach, which ultimately enables a quantitative analysis of collective excitations. For weak couplings, we identify the well-known amplitude (Higgs) mode at the two-particle continuum's lower edge and the phase (Anderson-Bogoliubov) mode at $\omega = 0$ for a neutral system, which shifts to higher energies as the Coulomb interaction is switched on. As the phononic coupling is increased, the Higgs mode separates from the continuum, and additional phase and amplitude modes appear, persisting even in the presence Coulomb interactions.
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List of changes
by Tolmachev, and Morel and Anderson.
Below Eq. (23): We added a sentence, noting that the operators, and hence, the collective modes are isotropic and at zero center-of-mass momentum.
The paragraph just before section 4.3: We added that the detachment of the Higgs mode from the quasiparticle continuum has also been observed by Barankov and Levitov.
The bottom of page 21: We added a recap of the aforementioned results by Barankov and Levitov and compare our results to theirs explicitly.
The top of page 22: We added a paragraph elucidating the similarities and differences between the results obtained by Bardasis and Schrieffer and our results.
We added the following references:
[49] V. V. Tolmachev, Logarithmic criterion for superconductivity, Dokl. Akad. Nauk SSSR 140, 563 (1961).
[58] R. A. Barankov and L. S. Levitov, Excitation of the dissipationless Higgs mode in a fermionic condensate (arXiv:0704.1292) (2007), doi:10.48550/arXiv.0704.1292, 0704.1292.
[64] M. A. Müller and I. M. Eremin, Signatures of Bardasis-Schrieffer mode excitation in third-harmonic generated currents, Physical Review B 104(14), 144508 (2021), doi:10.1103/PhysRevB.104.144508.
Published as SciPost Phys. 19, 067 (2025)