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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

Inspired by empirical evidence of the existence of pair-density-wave (PDW) order in certain underdoped cuprates, we investigate the collective modes in systems with unidirectional PDW order with momenta $\pm {Q}$ and a $d$-wave form-factor…

Strongly Correlated Electrons · Physics 2025-01-27 Yi-Ming Wu , Andrey V. Chubukov , Yuxuan Wang , Steven A. Kivelson

The pair density wave (PDW) superconducting state has been proposed to explain the layer- decoupling effect observed in the compound La$_{2-x}$Ba$_x$CuO$_4$ at $x=1/8$ (Phys. Rev. Lett. 99, 127003). In this state the superconducting order…

Superconductivity · Physics 2017-06-07 Rodrigo Soto-Garrido , Yuxuan Wang , Eduardo Fradkin , S. Lance Cooper

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

Pair density waves (PDW) are novel forms of superconducting states that exhibit periodically modulated pairing. A remaining challenge is to elucidate how intrinsic PDW order can emerge robustly in strongly correlated electrons. Here we…

Superconductivity · Physics 2025-12-09 Hao-Xin Wang , Yi-Jian Hu , Wen Huang , Hong Yao

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

Interior-gap superconductivity has long been discussed as an exotic paired state in the presence of Fermi-surface mismatch, but its realization in canonical strongly correlated models has remained elusive. Here we present evidence that the…

Strongly Correlated Electrons · Physics 2026-05-01 Yuto Hirose , Shunsuke C. Furuya , Yasuhiro Tada

Unconventional superconductors have been long sought for their potential applications in quantum technologies and devices. A key challenge impeding this effort is the difficulty associated with probing and characterizing candidate materials…

Superconductivity · Physics 2022-08-23 Jonathan B. Curtis , Nicholas R. Poniatowski , Amir Yacoby , Prineha Narang

The concept of "broken symmetry", that the symmetry of the vacuum may be lower than the Hamiltonian of a quantum theory, plays an important role in modern physics. A manifestation of this phenomena is the Higgs boson in particle physics…

Superconductivity · Physics 2012-06-05 Yafis Barlas , C. M. Varma

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

Since their discovery, it has been suggested that pairing in pnictides can be mediated by spin fluctuations between hole and electron bands. In this view, multiband superconductivity would substantially differ from other systems like MgB2,…

Superconductivity · Physics 2014-01-14 M. Marciani , L. Fanfarillo , C. Castellani , L. Benfatto

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

We develop a microscopic and gauge-invariant theory for collective modes resulting from the phase of the superconducting order parameter in non-centrosymmetric superconductors. Considering various crystal symmetries we derive the…

Superconductivity · Physics 2015-12-02 Nikolaj Bittner , Dietrich Einzel , Ludwig Klam , Dirk Manske

Higgs modes in condensed matter physics have drawn attention because of analogies to the Higgs bosons of particle physics. Here we use a microscopic time-dependent mean-field theory to study the collective mode spectra of two-dimensional…

Mesoscale and Nanoscale Physics · Physics 2020-09-02 Fei Xue , Fengcheng Wu , Allan H. MacDonald

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

The proximity effect in hybrid superconducting - normal metal structures is shown to affect strongly the coherent oscillations of the superconducting order parameter $\Delta$ known as the Higgs modes. The standard Higgs mode at the…

Superconductivity · Physics 2019-09-18 V. L. Vadimov , I. M. Khaymovich , A. S. Mel'nikov

We study dynamics of a superconducting condensate in the presence of a domain wall defect in the order parameter. We find that broken translation and reflection symmetries result in new collective excitations, bound to the domain wall…

Superconductivity · Physics 2016-02-23 Andrew R. Hammer , Anton B. Vorontsov

The concept of mass-generation via the Higgs mechanism was strongly inspired by earlier works on the Meissner-Ochsenfeld effect in superconductors. In quantum field theory, the excitations of longitudinal components of the Higgs field…

We study collective excitations in three- and four-band superconductors with inter-band frustration, which causes neither 0 nor $\pi$ inter-band phases in the superconducting state. Using a low-energy spin-Hamiltonian originating from a…

Superconductivity · Physics 2014-01-03 Keita Kobayashi , Masahiko Machida , Yukihiro Ota , Franco Nori

Elucidation of the symmetry and structure of order parameter(OP) is a fundamental subject in the study of superconductors. Recently, a growing number of superconducting materials have been identified that suggest additional spontaneous…

Superconductivity · Physics 2025-07-22 Haruki Matsumoto , Silvia Neri , Tomoki Kobayashi , Atsutaka Maeda , Dirk Manske , Ryo Shimano
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