Lifshitz transition and magnetic superconductivity in flat band systems
Abstract
A Lifshitz transition is a class of non-symmetry-breaking transitions typically associated with metallic systems wherein the Fermi surface changes its connectivity as the chemical potential sweeps through a band extremum or a saddle point. The phenomenology naturally adapts itself to the superconducting state, where the object that reconstructs is the manifold of minimum quasiparticle energy rather than the Fermi surface. This paper concerns Lifshitz-type transitions in multi-band superconductors. Thus, we focus on the attractive Hubbard--Kondo model on the two-dimensional Lieb lattice, with classical core spins coupled to the itinerant electrons, by laying recourse to a real-space Bogoliubov--de Gennes mean-field theory and an analytic Green's function calculation. The competition between the Kondo and pairing channels yields a magnetic superconductor throughout, with (π,π) order near half filling giving way to (0,π) and then, at stronger Kondo coupling, to an incommensurate spiral (0,q). In such a multiband superconductor hosting a flat band, we identify two inequivalent Lifshitz-type transitions. With the core spins decoupled (the Kondo coupling set to zero), the minimum energy contour deforms with chemical potential, a hole pocket about M opening into a perfectly nested square at μ=−2t and reconnecting into pockets about Γ; this nesting fixes where (π,π) order sets in. At finite Kondo coupling, for certain chemical potential, the dimension of the manifold itself drops. We obtain it analytically for each magnetic order and show that only the spiral carries the minimum energy through zero, nucleating nodes and leaving a gapless magnetic superconductor, with clear signatures in the density of states and the spectral function.
Related
- Spin–orbit–controlled flat-band transition, thermodynamic and magnetic response in a disordered Lieb-5 lattice
- Higher derivative Hořava-Lifshitz fermions: from superconductivity to atomic spectroscopy
- Fermi surface and field-induced Lifshitz transition in the antiferromagnet NbMnP exhibiting an anomalous Hall effect
- A cascade of orbital-field-driven phases with a Lifshitz-type transition to unidirectional spiral order
- From a Lifshitz Transition to Spin-Density-Wave Order: Sr2RuO4 under Uniaxial Strain
BibTeX
@misc{pal2026lifshitz,
title = {{Lifshitz transition and magnetic superconductivity in flat band systems}},
author = {Sudeshna Pal and K. B. Yogendra and Madhuparna Karmakar and Rajesh Narayanan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06140},
eprint = {2610.06140},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06140},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lifshitz transition and magnetic superconductivity in flat band systems
AU - Sudeshna Pal
AU - K. B. Yogendra
AU - Madhuparna Karmakar
AU - Rajesh Narayanan
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06140
UR - https://arxiv.org/abs/2610.06140
AB - A Lifshitz transition is a class of non-symmetry-breaking transitions typically associated with metallic systems wherein the Fermi surface changes its connectivity as the chemical potential sweeps through a band extremum or a saddle point. The phenomenology naturally adapts itself to the superconducting state, where the object that reconstructs is the manifold of minimum quasiparticle energy rather than the Fermi surface. This paper concerns Lifshitz-type transitions in multi-band superconductors. Thus, we focus on the attractive Hubbard--Kondo model on the two-dimensional Lieb lattice, with classical core spins coupled to the itinerant electrons, by laying recourse to a real-space Bogoliubov--de Gennes mean-field theory and an analytic Green's function calculation. The competition between the Kondo and pairing channels yields a magnetic superconductor throughout, with (π,π) order near half filling giving way to (0,π) and then, at stronger Kondo coupling, to an incommensurate spiral (0,q). In such a multiband superconductor hosting a flat band, we identify two inequivalent Lifshitz-type transitions. With the core spins decoupled (the Kondo coupling set to zero), the minimum energy contour deforms with chemical potential, a hole pocket about M opening into a perfectly nested square at μ=−2t and reconnecting into pockets about Γ; this nesting fixes where (π,π) order sets in. At finite Kondo coupling, for certain chemical potential, the dimension of the manifold itself drops. We obtain it analytically for each magnetic order and show that only the spiral carries the minimum energy through zero, nucleating nodes and leaving a gapless magnetic superconductor, with clear signatures in the density of states and the spectral function.
ER -