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arXiv:2301.05684 · Physical review. B./Physical review. B

Following the Higgs mode across the BCS-BEC crossover in two dimensions

Dan Phan, Andrey V. Chubukov

Published Apr 27, 2023• 15 citations
arXivHTMLPDF

Abstract

Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the amplitude (Higgs) susceptibility in the lower half plane of complex frequency. We analyze the behavior of the Higgs mode in a two-dimensional neutral fermionic superfluid at $T=0$ throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. This occurs when the dressed chemical potential $\ensuremath{\mu}$ changes sign from positive to negative. For $\ensuremath{\mu}>0$, we find a pole in the Higgs susceptibility in the lower half plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For $\ensuremath{\mu}<0$, the pole still exists but is ``hidden,'' not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.

DOI
10.1103/physrevb.107.134519

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Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the amplitude (Higgs) susceptibility in the lower half plane of complex frequency. We analyze the behavior of the Higgs mode in a two-dimensional neutral fermionic superfluid at T=0T=0T=0 throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. This occurs when the dressed chemical potential \ensuremathμ\ensuremath{\mu}\ensuremathμ changes sign from positive to negative. For \ensuremathμ>0\ensuremath{\mu}>0\ensuremathμ>0, we find a pole in the Higgs susceptibility in the lower half plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For \ensuremathμ<0\ensuremath{\mu}<0\ensuremathμ<0, the pole still exists but is ``hidden,'' not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.
In quantum many-body systems with spontaneous breaking of continuous symmetries, Higgs modes emerge as collective amplitude oscillations of order parameters. Recently, Higgs mode has been observed in the ultracold Fermi gas. In the present paper, we use the time-dependent Bogoliubov-de Gennes equations to investigate Higgs amplitude oscillations of the superfluid order parameter in a Fermi gas induced by a rapid change of the s{\it s}s-wave scattering length. In particular, we investigate the Higgs mode with different values of the initial scattering length. We find that the energy of the Higgs mode coincides with the threshold energy of the pair-breaking excitation, and exponent of the power-low decay of the Higgs mode γγγ continuously changes between γ=−1/2γ=-1/2γ=−1/2 and γ=−3/2γ=-3/2γ=−3/2 through the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. Moreover, we propose the optimal ramp speed of the scattering length for observing the clearest Higgs oscillations.
We discuss the derivation of a low-energy effective field theory of phase (Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic theory of attractive fermions. The coupled equations for Goldstone and Higgs fields are critically analyzed in the Bardeen–Cooper–Schrieffer (BCS)-to-Bose–Einstein condensate (BEC) crossover—both in three spatial dimensions and in two spatial dimensions. The crucial role of pair fluctuations is investigated, and the beyond-mean-field Gaussian theory of the BCS–BEC crossover is compared with available experimental data of the two-dimensional ultracold Fermi superfluid.
We study the observability of the Higgs mode in BEC-BCS crossover. The observability of the Higgs mode is investigated by calculating the spectral weight functions of the amplitude fluctuation below the critical transition temperature. At zero temperature, we find that there are two sharp peaks on the spectral function of the amplitude fluctuation attributed to Goldstone and Higgs modes, respectively. As the system goes from the BCS to Bose-Einstein condensate (BEC) side, there is strong enhancement of spectral weight transfer from the Higgs to Goldstone mode. However, even at the unitary regime where the Lorentz invariance is lost, the sharp feature of the Higgs mode still exists. We specifically calculate the finite-temperature spectral function of the amplitude fluctuation at the unitary regime and show that the Higgs mode is observable at the temperature that present experiments can reach.
In phase transitions, spontaneous symmetry breaking results in a nonzero order parameter and two collective excitations: the Goldstone and the amplitude mode. These modes, which define key properties of superconductors and fermionic superfluids, are well understood in homogeneous systems. However, their behavior under strong confinement remains largely unexplored, particularly when their excitation energy becomes comparable to the imposed discrete level spacing. In this scenario, hybridization between different collective modes is expected to take place. Here, we show how the amplitude mode hybridizes with a spatial mode in a confined fermionic superfluid. Using lattice modulation spectroscopy, we observe the evolution of the mode throughout the entire crossover from the Bardeen-Cooper-Schrieffer (BCS) state to Bose-Einstein condensation (BEC) of molecules. In the BCS regime, the excitation energy is located at twice the pairing gap, then gradually becomes an in-gap excitation in the strongly correlated regime. Further to the BEC limit, the excitation energy approaches twice the level spacing. The spectral weight of this mode vanishes when approaching the superfluid critical temperature. Our experimental results are in excellent agreement with an effective field theory, providing strong evidence that amplitude oscillations hybridize with and eventually transform into breathing oscillations of the order parameter. The strong modification of the excitation spectrum reveals how confinement and finite-size effects impact fundamental modes of symmetry-broken states.
In this work we present a coherent picture for the evolution of Higgs mode in neutral sss-wave fermion superfluids. As the strength of attractive interaction between fermions increases from the BCS to the Bose-Einstein condensate (BEC) regime we find that the Higgs mode in the fermionic superfluids is pushed to higher energy while at the same time, gradually loses its spectral weight, which is because the system is tuned away from Lorentz invariance. Furthermore, when damping is taken into account, the spectral weight of the Higgs mode is significantly broadened due to coupling to phase mode in the whole BEC-BCS crossover.
Abstract The Bardeen–Cooper–Schrieffer (BCS) condensation and Bose–Einstein condensation (BEC) are the two limiting ground states of paired Fermion systems, and the crossover between these two limits has been a source of excitement for both fields of high temperature superconductivity and cold atom superfluidity. For superconductors, ultra-low doping systems like graphene and Li x ZrNCl successfully approached the crossover starting from the BCS-side. These superconductors offer new opportunities to clarify the nature of charged-particles transport towards the BEC regime. Here we report the study of vortex dynamics within the crossover using their Hall effect as a probe in Li x ZrNCl. We observed a systematic enhancement of the Hall angle towards the BCS-BEC crossover, which was qualitatively reproduced by the phenomenological time-dependent Ginzburg-Landau (TDGL) theory. Li x ZrNCl exhibits a band structure free from various electronic instabilities, allowing us to achieve a comprehensive understanding of the vortex Hall effect and thereby propose a global picture of vortex dynamics within the crossover. These results demonstrate that gate-controlled superconductors are ideal platforms towards investigations of unexplored properties in BEC superconductors.