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We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for…

Superconductivity · Physics 2019-06-26 Mikhail Silaev

We theoretically investigate coherent optical excitations of collective modes in two-band BCS superconductors, which accommodate two Higgs modes and one Leggett mode corresponding, respectively, to the amplitude and relative-phase…

Superconductivity · Physics 2017-03-06 Yuta Murotani , Naoto Tsuji , Hideo Aoki

We study optical responses of Leggett modes in multiband superconductors in the linear response regime. The Leggett mode is a collective mode unique to multiband superconductors that arises from relative phase fluctuations of…

Strongly Correlated Electrons · Physics 2022-04-12 Takumi Kamatani , Sota Kitamura , Naoto Tsuji , Ryo Shimano , Takahiro Morimoto

Multiband superconductors can host collective excitations with marked differences with respect to their single-band counterpart. We first study the spectrum of collective amplitude fluctuations in a clean two-bands superconductor, showing…

Superconductivity · Physics 2022-09-26 Jacopo Fiore , Mattia Udina , Marco Marciani , Goetz Seibold , Lara Benfatto

We study the contribution of the Higgs amplitude mode on the nonlinear optical response of superconductors beyond the BCS approximation by taking into account the retardation effect in the phonon-mediated attractive interaction. To evaluate…

Superconductivity · Physics 2017-01-02 Naoto Tsuji , Yuta Murakami , Hideo Aoki

We study collective amplitude modes of the superconducting order parameter in strongly-coupled electron-phonon systems described by the Holstein model using the nonequilibrium dynamical mean-field theory with the self-consistent Migdal…

Superconductivity · Physics 2017-06-19 Yuta Murakami , Philipp Werner , Naoto Tsuji , Hideo Aoki

The quest for new functionalities in quantum materials has recently been extended to non-equilibrium states, which are interesting both because they exhibit new physical phenomena and because of their potential for high-speed device…

Lifshitz invariant is a symmetry invariant composed of multiple order parameters that contain a single spatial derivative in a Ginzburg-Landau (GL) free energy, which may induce a nonuniform configuration of the order parameters. In…

Superconductivity · Physics 2025-07-11 Raigo Nagashima , Titouan Mouilleron , Naoto Tsuji

The recent observation of a transmitted Thz pulse oscillating at three times the frequency of the incident light paves the way to a new protocol to access resonant excitations in a superconductor. Here we show that this non-linear optical…

Superconductivity · Physics 2016-06-01 T. Cea , C. Castellani , L. Benfatto

Collective excitation modes are a characteristic feature of symmetry-broken phases of matter. For example, superconductors exhibit an amplitude Higgs mode and a phase mode, which are the radial and angular excitations in the Mexican-hat…

Superconductivity · Physics 2016-06-22 H. Krull , N. Bittner , G. S. Uhrig , D. Manske , A. P. Schnyder

Recently, several groups have reported observations of collective modes of the charge order present in underdoped cuprates. Motivated by these experiments, we study theoretically the oscillations of the order parameters, both in the case of…

Superconductivity · Physics 2015-12-22 Zachary M. Raines , Valentin G. Stanev , Victor M. Galitski

This work investigates amplitude-dependent nonlinear corrections to the dissipative conductivity in superconductors, using the Keldysh--Usadel theory of nonequilibrium superconductivity, which captures the nonequilibrium dynamics of both…

Superconductivity · Physics 2025-12-25 Takayuki Kubo

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…

Superconductivity · Physics 2020-03-19 Ryo Shimano , Naoto Tsuji

We theoretically investigate the resonance of third harmonic generation (THG) that has been observed at frequency being half of the superconducting gap in a multiband disordered superconductor NbN. The central question is whether the…

Superconductivity · Physics 2020-10-09 Naoto Tsuji , Yusuke Nomura

We study nonlinear response of conventional superconducting alloys with weak magnetic impurities to an external alternating electromagnetic field. In particular, we calculate a correction to superconducting order parameter up to the second…

Superconductivity · Physics 2024-02-23 Yantao Li , Maxim Dzero

We study nonlinear optical responses in superconducting systems with inversion ($\mathcal{I}$) symmetry-breaking order parameters. We first show that any superconducting system with $\mathcal{I}$ and time-reversal ($\mathcal{T}$) symmetries…

Superconductivity · Physics 2019-12-11 Tianrui Xu , Takahiro Morimoto , Joel E. Moore

The nonlinear magneto-optical response of $s$- and $d$-wave superconductors is discussed. We carry out the symmetry analysis of the nonlinear magneto-optical susceptibility in the superconducting state. Due to the surface sensitivity of the…

Condensed Matter · Physics 2009-10-28 J. Schmalian , W. Hübner

Higgs mode in superconductors, i.e. the collective amplitude mode of the order parameter does not associate with charge nor spin fluctuations, therefore it does not couple to the electromagnetic field in the linear response regime. On the…

Superconductivity · Physics 2019-07-02 Sachiko Nakamura , Yudai Iida , Yuta Murotani , Ryusuke Matsunaga , Hirotaka Terai , Ryo Shimano

Intensive research has revealed intriguing optical responses in topological materials. This paper focuses on the optical responses in $s$-wave superconductors with a Rashba spin-orbit coupling and a magnetic field, one of the platforms of…

Superconductivity · Physics 2025-10-07 Hiroto Tanaka , Youichi Yanase

The dynamics of Higgs mode in superconductors, manifested as coherent oscillations of the superconducting order parameter amplitude, provides vital insights into the nature of the superconducting gap structure and symmetry. Here we utilize…

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