Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2506.13556

Superconductivity with repulsion: a variational approach

Laura Fanfarillo·Yifu Cao·Chandan Setty·Sergio Caprara·Peter J. Hirschfeld
View original source ↗Read source document ↗Export metadata ↓

Abstract

We revisit the stability of the superconducting state within mean-field theory in the presence of repulsive pairing interactions, focusing on multiband systems where such channels naturally arise. We show that, when repulsion is present, the self-consistent BCS solution appears as a saddle point of the conventional mean-field free energy, casting doubt on its physical stability. We show that this pathology is an artifact of using a non-variational functional. Recasting the problem with Bogoliubov's variational principle restores a free energy that is bounded from below and places the BCS solution at a genuine minimum. Using a two-band toy model relevant to iron-based superconductors, we demonstrate the stability of the s$_\pm$ state and clarify how projection schemes that rely only on the interaction matrix can misidentify the attractive eigenmode that drives pairing. Our results clarify the instability issue highlighted by Aase et al. and provide a consistent foundation for analyzing fluctuations in the presence of repulsive interactions.

Explore related subjects

cond-mat.supr-con

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Laura Fanfarillo, Yifu Cao, Chandan Setty, Sergio Caprara, Peter J. Hirschfeld. 2025-06-16. Superconductivity with repulsion: a variational approach. https://doi.org/10.1103/jhy9-mckg

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Anisotropic upper critical field in the van der Waals superconducting quasicrystal (Ta$_{0.7}$Nb$_{0.3}$)$_{1.6}$Te

We investigated the upper critical field of a large single grain of the Nb-substituted van der Waals layered quasicrystal (Ta$_{0.7}$Nb$_{0.3}$)$_{1.6}$Te. The sample exhibits a sharp superconducting transition at $T_{\mathrm{c}}$ = 1.35 K, the highest value reported to date among quasicrystal superconductors. The angular dependence of the critical field exhibits a pronounced criterion dependence: the field determined using the 10% $R_{\mathrm{N}}$ ($R_{\mathrm{N}}$: normal-state resistance) criterion is well described by the anisotropic Ginzburg-Landau model, whereas those determined using the 65% and 90% $R_{\mathrm{N}}$ criteria exhibit Tinkham-like angular dependence characteristic of two-dimensional superconductivity. The high-field part of the resistive transition is well described by a surface-superconductivity model and exhibits a pronounced excitation-current dependence for magnetic fields close to the $ab$ plane, supporting the presence of surface superconductivity on the quasiperiodic $ab$-plane surfaces. The bulk $H_{\mathrm{c2}}$ is strongly anisotropic, with the in-plane $H_{\mathrm{c2}}$ exceeding the weak-coupling Pauli limit by a factor of approximately 2.5. For both field orientations, $H_{\mathrm{c2}}(T)$ deviates upward from the conventional dirty-limit Werthamer-Helfand-Hohenberg prediction at low temperatures. A phenomenologically modified Ginzburg-Landau-Abrikosov-Gorkov model incorporating a spatial distribution of the electronic diffusivity substantially improves the description of $H_{\mathrm{c2}}(T)$, suggesting that spatial variations in electronic transport properties may contribute to its anomalous temperature dependence.

cond-mat.supr-con↗
arXiv2026

Field-induced incipient spin-density phase stabilized inside the nematic phase of FeSe$_{1-x}$S$_x$

Spin-density wave (SDW) order and superconductivity frequently compete and coexist in unconventional superconductors, where spin fluctuations often mediate superconducting pairing. In iron-chalcogenide superconductors, FeSe$_{1-x}$S$_x$, SDW order has only been detected under applied pressure, while both spin and nematic fluctuations are involved in determining their rich superconducting phase diagrams. Here, we report evidence for an incipient SDW phase, within the nematic state of FeSe$_{1-x}$S$_x$, revealed in magnetic fields up to 68~T. Once superconductivity is quenched, we observe sharp upturns in longitudinal resistivity accompanied by anomalies in tunnel diode oscillator frequency response and torque anisotropy, consistent with a field-induced electronic order. Dominant low-frequency quantum oscillations reveal a small reconstructed Fermi surface, consistent with a field-induced SDW order. Direct experimental comparisons with a pressure-tuned nematic, analogue, FeSe$_{0.96}$S$_{0.04}$, demonstrate that SDW phases are stabilized within the nematic phase of FeSe$_{1-x}$S$_x$ via both chemical substitution and applied pressure. These findings reveal that by weakening nematicity, the SDW orders are stabilised, which promotes the dominant superconducting pairing mechanism in iron chalcogenides.

cond-mat.supr-con↗
arXiv2026

Q-ball mechanism of electron transport and spin/phonon excitations properties of high-Tc superconductors

The Q-ball mechanism of high Tc superconductivity in cuprates, recently proposed by the author, is farther explored. Scattering on the Q-balls above Tc causes linear with temperature growth of electrical resistivity, splitting of the inplane phonon brunches into softened and hardened ones and hourglass dispersion of spin-wave excitations close to CDW and SDW wave vectors respectively. The diamagnetic response of Q-balls gas above Tc is in qualitative accord with experimental data in high Tc cuprates.

cond-mat.supr-con↗