Higgs Mode in Superconductors

Abstract: When a continuous symmetry of a physical system is spontaneously broken, two types of collective modes typically emerge: the amplitude and phase modes of the order-parameter fluctuation. For superconductors, the amplitude mode is recently referred to as the ''Higgs mode'' as it is a condensed-matter analogue of a Higgs boson in particle physics. Higgs mode is a scalar excitation of the order parameter, distinct from charge or spin fluctuations, and thus does not couple to electromagnetic fields linearly. This is why the Higgs mode in superconductors has evaded experimental observations over a half century after the initial theoretical prediction, except for a charge-density-wave coexisting system. With the advance of nonlinear and time-resolved terahertz spectroscopy techniques, however, it has become possible to study the Higgs mode through the nonlinear light-Higgs coupling. In this review, we overview recent progresses on the study of the Higgs mode in superconductors.

Higgs Mode in Superconductors: An Overview

The paper "Higgs Mode in Superconductors" by Ryo Shimano and Naoto Tsuji offers an extensive review of the understanding and experimental investigation of Higgs modes in superconductors, providing crucial insights into a realm where condensed matter physics intersects with high-energy particle physics. Historically, the identification of the Higgs mode, a scalar excitation distinct from charge or spin fluctuations, posed significant experimental challenges due to its inability to couple linearly with electromagnetic fields. The advent of nonlinear and time-resolved terahertz spectroscopy has enabled the observation of these modes, culminating in a comprehensive exploration of their properties and implications.

Nature of the Higgs Mode

In superconductors, when a continuous symmetry is spontaneously broken, two collective modes emerge: phase and amplitude fluctuations of the order parameter. While the phase mode, known as the Nambu-Goldstone mode, is typically gapless, the amplitude mode, referred to as the Higgs mode, is gapped. Its existence in superconductors was postulated theoretically as an analogue to the Higgs boson in particle physics, sharing a conceptual foundation with the framework of the standard model as a relativistic version of the Ginzburg-Landau theory. Despite its theoretical prediction, experimental observation remained elusive for decades, largely due to the Higgs mode's lack of direct interaction with external electromagnetic probes.

Breakthrough Through Terahertz Spectroscopy

The breakthrough in observing the Higgs mode experimentally was achieved through the application of nonlinear terahertz spectroscopy techniques. These advances have allowed researchers to circumvent the limitations imposed by the mode's electromagnetic coupling constraints. The nonlinear coupling facilitates observable effects in superconductors, such as third-harmonic generation (THG) and pump-probe spectroscopy, where the Higgs mode can be resonantly excited.

Experimental Observations

Various experimental strategies are reviewed:

• Raman Scattering: Initial detection of the Higgs mode in superconductors was reported in systems like 2H-NbSe2, where superconductivity coexists with charge density wave (CDW). The mode's interaction with CDW facilitates its visibility in Raman spectra, evidenced by experiments showing a peak below the superconducting gap energy.

• Terahertz Pump-Probe Spectroscopy: Such methodologies allowed the observation of Higgs mode oscillations in $s$-wave superconductors like NbN. The use of intense single-cycle terahertz pulses provided the nonadiabatic quench necessary for inducing the mode oscillations, reflecting the temporal dynamics and spectral weight variations expected theoretically.

• Multicycle THz Driving and THG: The resonance conditions ($2\omega = 2\Delta$) for THG experiments highlighted the two-photon processes enabled by the Higgs mode, suggesting both quasiparticle and scalar excitation contributions in nonlinear optical responses.

• Supercurrents: The injection of supercurrents in thin films, coupled with THz probing, has demonstrated the Higgs mode's linear coupling to electromagnetic fields under specific conditions, offering a new method of direct observation.

Theoretical Implications and Speculation for Future Developments

The paper discusses how recent theoretical advancements have refined understanding of the Higgs mode. Efforts beyond BCS mean-field calculations, acknowledging impurity scattering and phonon retardation, have illuminated the Higgs mode's enhanced contribution to nonlinear optical phenomena. The review extends to non-$s$-wave superconductors, proposing future exploration of various unconventional symmetries and multiband interactions.

Future Directions:

1. Exploration in Multiband Superconductors: Understanding interactions among multiple condensates and identifying the Leggett modes can yield insights into complex band structures.
2. Investigation in Unconventional Superconductors: High-$T_c$ and spin-triplet superconductors present opportunities to study Higgs modes linked to diverse order parameter symmetries.
3. Nonequilibrium Phenomena: Observing Higgs modes within photoinduced states could substantiate transient superconductivity claims and reveal insights into competition among various quantum phases.

This thorough review of the Higgs mode in superconductors lays a foundation for continued study, particularly focusing on theoretical implications and new experimental techniques that expand understanding of the interplay between symmetry breaking and collective excitations in condensed matter physics.