A Superconducting Peierls Instability
Abstract
The Peierls instability is a foundational mechanism in condensed matter physics, showing how the electron--phonon interaction can transform a simple metal into an insulating state with a new lattice periodicity. In a one-dimensional (1D) metal the Peierls instability follows from the enhanced electronic response at wavevector Q=2kF (connecting the Fermi points) producing a Kohn anomaly: a softening of the phonon mode at the same wavevector. Condensation of this mode then generates the tell-tale Peierls periodic lattice distortion and charge-density wave (CDW) that gaps the electronic spectrum. Here we show an analogous instability at the edge of a two-dimensional (2D) superconductor, where a dispersing Andreev bound state (ABS) hosts Bogoliubov Fermi points at ± kc. The enhanced quasiparticle response at the connecting wavevector Q=2kc couples directly to pairing-fluctuations and produces a superconducting Kohn anomaly: a softening of a pairing mode at the same wavevector. Condensation of this mode then generates an edge pair-density wave (PDW) that gaps the ABS. We refer to this as a superconducting Peierls instability and identify the boundary quasiparticle structure that enables it. As a concrete realization, we consider a square-lattice extended Hubbard model whose mixed-symmetry s+d+ip state hosts a dispersing ABS with zero-energy crossings at finite edge momenta. Using self-consistent Bogoliubov--de Gennes (BdG) calculations we show that the order parameter develops an edge PDW, with the wavevector set by the superconducting Kohn anomaly, that gaps the ABS crossings. Our results identify a novel mechanism for spontaneous translation-symmetry breaking in a superconductor. As this superconducting Peierls mechanism does not require an extensive zero-energy flat band or topologically protected edge states, it may apply broadly to unconventional superconductors.
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BibTeX
@misc{yapa2026superconducting,
title = {{A Superconducting Peierls Instability}},
author = {Pramodh Senarath Yapa and Joseph Maciejko and Frank Marsiglio and Annica M. Black-Schaffer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04164},
eprint = {2609.04164},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04164},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Superconducting Peierls Instability
AU - Pramodh Senarath Yapa
AU - Joseph Maciejko
AU - Frank Marsiglio
AU - Annica M. Black-Schaffer
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04164
UR - https://arxiv.org/abs/2609.04164
AB - The Peierls instability is a foundational mechanism in condensed matter physics, showing how the electron--phonon interaction can transform a simple metal into an insulating state with a new lattice periodicity. In a one-dimensional (1D) metal the Peierls instability follows from the enhanced electronic response at wavevector Q=2k_F (connecting the Fermi points) producing a Kohn anomaly: a softening of the phonon mode at the same wavevector. Condensation of this mode then generates the tell-tale Peierls periodic lattice distortion and charge-density wave (CDW) that gaps the electronic spectrum. Here we show an analogous instability at the edge of a two-dimensional (2D) superconductor, where a dispersing Andreev bound state (ABS) hosts Bogoliubov Fermi points at ± k_c. The enhanced quasiparticle response at the connecting wavevector Q=2k_c couples directly to pairing-fluctuations and produces a superconducting Kohn anomaly: a softening of a pairing mode at the same wavevector. Condensation of this mode then generates an edge pair-density wave (PDW) that gaps the ABS. We refer to this as a superconducting Peierls instability and identify the boundary quasiparticle structure that enables it. As a concrete realization, we consider a square-lattice extended Hubbard model whose mixed-symmetry s+d+ip state hosts a dispersing ABS with zero-energy crossings at finite edge momenta. Using self-consistent Bogoliubov--de Gennes (BdG) calculations we show that the order parameter develops an edge PDW, with the wavevector set by the superconducting Kohn anomaly, that gaps the ABS crossings. Our results identify a novel mechanism for spontaneous translation-symmetry breaking in a superconductor. As this superconducting Peierls mechanism does not require an extensive zero-energy flat band or topologically protected edge states, it may apply broadly to unconventional superconductors.
ER -