We study the effect of strong electron-phonon interactions on the damping of the Higgs amplitude mode in superconductors by means of nonequilibrium dynamical mean-field simulations of the Holstein model. In contrast to the BCS dynamics, we find that the damping of the Higgs mode strongly depends on the temperature, becoming faster as the system approaches the transition temperature. The damping at low temperatures is well described by a power law, while near the transition temperature the damping shows exponential-like behavior. We explain this crossover in terms of a temperature-dependent quasiparticle lifetime caused by the strong electron-phonon coupling, which smears the superconducting gap edge and makes the relaxation of the Higgs mode into quasiparticles more efficient at elevated temperatures. We also reveal that the phonon dynamics can soften the Higgs mode, which results in a slower damping.We study the effect of strong electron-phonon interactions on the damping of the Higgs amplitude mode in superconductors by means of nonequilibrium dynamical mean-field simulations of the Holstein model. In contrast to the BCS dynamics, we find that the damping of the Higgs mode strongly depends on the temperature, becoming faster as the system approaches the transition temperature. The damping at low temperatures is well described by a power law, while near the transition temperature the damping shows exponential-like behavior. We explain this crossover in terms of a temperature-dependent quasiparticle lifetime caused by the strong electron-phonon coupling, which smears the superconducting gap edge and makes the relaxation of the Higgs mode into quasiparticles more efficient at elevated temperatures. We also reveal that the phonon dynamics can soften the Higgs mode, which results in a slower damping.

arXiv:1604.08073Physical review. B./Physical review. BSep 12, 201618 citations

Highly anisotropic collective modes of altermagnetic superconductors with Bogoliubov Fermi surfaces

Huaisong Zhao, Peng Zou, Xia-Ji Liu +1 more

We investigate collective modes in charge-neutral altermagnetic superconductors with $d$ -wave spin-split bands, focusing on the impact of emergent Bogoliubov Fermi surfaces. In the absence of a magnetic field, the BCS state supports collective modes that inherit the underlying $d$ -wave symmetry, resulting in pronounced momentum-space anisotropy. The broken time-reversal symmetry further couples these modes to spin-density fluctuations, allowing their signatures to emerge in the spin dynamical structure factor. Upon applying a magnetic field, Bogoliubov Fermi surfaces emerge and qualitatively reshape the collective-mode dynamics through gapless particle-hole excitations and strongly anisotropic Landau damping. The damping is strongest along the momentum-space diagonal, where it can suppress the low-energy phonon mode at small momenta. Remarkably, the suppressed phonon is accompanied by the emergence of an in-gap structure in the Higgs mode and an associated pronounced enhancement of the spin response. These results establish Bogoliubov Fermi surfaces as a mechanism for generating highly anisotropic collective-mode dynamics and identify spin response as a sensitive probe of in-gap Higgs excitations in altermagnetic superconductors.We investigate collective modes in charge-neutral altermagnetic superconductors with $d$-wave spin-split bands, focusing on the impact of emergent Bogoliubov Fermi surfaces. In the absence of a magnetic field, the BCS state supports collective modes that inherit the underlying $d$-wave symmetry, resulting in pronounced momentum-space anisotropy. The broken time-reversal symmetry further couples these modes to spin-density fluctuations, allowing their signatures to emerge in the spin dynamical structure factor. Upon applying a magnetic field, Bogoliubov Fermi surfaces emerge and qualitatively reshape the collective-mode dynamics through gapless particle-hole excitations and strongly anisotropic Landau damping. The damping is strongest along the momentum-space diagonal, where it can suppress the low-energy phonon mode at small momenta. Remarkably, the suppressed phonon is accompanied by the emergence of an in-gap structure in the Higgs mode and an associated pronounced enhancement of the spin response. These results establish Bogoliubov Fermi surfaces as a mechanism for generating highly anisotropic collective-mode dynamics and identify spin response as a sensitive probe of in-gap Higgs excitations in altermagnetic superconductors.

arXiv:2610.01011Oct 1, 20260 citations

Damping Rate of a Coupled One Dimensional Electron-Phonon System

E. H. Hwang, S. Das Sarma, Ben Yu-Kuang Hu

APSMar 1, 19960 citations

Collective excitation transfer dynamics due to locally non-thermal phonon environmentII

Ryo Okada, Tomoaki Yazaki, Kazuharu Uchiyama +3 more

The Japan Society of Applied PhysicsFeb 3, 20170 citations

Collective versus single-particle motion in quantum many-body systems from the perspective of an integrable model

Jens Hämmerling, Boris Gutkin, Thomas Guhr

We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transition strengths induced by the collective mode is determined by its classical dynamics.We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transition strengths induced by the collective mode is determined by its classical dynamics.

arXiv:0911.2724Journal of Physics A Mathematical and TheoreticalJun 2, 20107 citations

We investigate collective modes in charge-neutral altermagnetic superconductors with

d

-wave spin-split bands, focusing on the impact of emergent Bogoliubov Fermi surfaces. In the absence of a magnetic field, the BCS state supports collective modes that inherit the underlying

d

-wave symmetry, resulting in pronounced momentum-space anisotropy. The broken time-reversal symmetry further couples these modes to spin-density fluctuations, allowing their signatures to emerge in the spin dynamical structure factor. Upon applying a magnetic field, Bogoliubov Fermi surfaces emerge and qualitatively reshape the collective-mode dynamics through gapless particle-hole excitations and strongly anisotropic Landau damping. The damping is strongest along the momentum-space diagonal, where it can suppress the low-energy phonon mode at small momenta. Remarkably, the suppressed phonon is accompanied by the emergence of an in-gap structure in the Higgs mode and an associated pronounced enhancement of the spin response. These results establish Bogoliubov Fermi surfaces as a mechanism for generating highly anisotropic collective-mode dynamics and identify spin response as a sensitive probe of in-gap Higgs excitations in altermagnetic superconductors.