Classification and characterization of nonequilibrium Higgs modes in unconventional superconductors

Abstract

Recent findings of new Higgs modes in unconventional superconductors require a classification and characterization of the modes allowed by nontrivial gap symmetry. Here we develop a theory for a tailored nonequilibrium quantum quench to excite all possible oscillation symmetries of a superconducting condensate. We show that both a finite momentum transfer and quench symmetry allow for an identification of the resulting Higgs oscillations. These serve as a fingerprint for the ground state gap symmetry. We provide a classification scheme of these oscillations and the quench symmetry based on group theory for the underlying lattice point group. For characterization, analytic calculations as well as full scale numeric simulations of the transient optical response resulting from an excitation by a realistic laser pulse are performed. Our classification of Higgs oscillations allows us to distinguish between different symmetries of the superconducting condensate.

Phase-resolved Higgs response in superconducting cuprates

“…Experimental detection of the Higgs mode has also been hampered by its lack of electric and magnetic dipole moments in most superconductors. Recently, it was proposed that the Higgs mode may reveal the superconducting gap symmetry and multiplicity [4][5][6] , unveil coupled collective modes 7 , or explain aspects of light-induced superconductivity 8 . Novel methods for exciting and detecting the superconducting Higgs mode were also demonstrated using ultrafast terahertz techniques in the meantime 9,10 .…”

Momentum-resolved analysis of condensate dynamic and Higgs oscillations in quenched superconductors with time-resolved ARPES

“…4(b) and 4(d). The usual 2 Higgs mode corresponds to an oscillation in the ground state symmetry channel, whereas the low-lying Higgs mode corresponds to an oscillation in another symmetry channel [28]. The energies of these two modes are controlled by different quantities.…”

“…In addition, multiband systems show frequencies for each band and also for the frequency of the relative phase mode (Leggett mode) [26,27]. Excited in an asymmetric way, nontrivial gap symmetries can show additional oscillation frequencies as a result of an oscillation of the condensate in a different symmetry channel [28]. Finally, composite order parameters [29], excitations of subleading pairing channels [30] as well as coupling to other coexisting modes [20] might show up as additional frequencies.…”

“…The idea behind such quenches is to model the net effect of pump pulses in a controlled way, which act on the condensate momentum-dependently. These might be realized experimentally by tuning polarization and pulse direction [28] or could be implemented in more complex approaches like transient grating [39,40] or four-wave mixing [41] setups.…”

“…Quenching superconductors with such an approach, where the symmetry of the condensate is altered with respect to the ground state, can result in dynamically created additional Higgs modes [28]. It is important to note that we ensure that the order parameter always keeps its ground state symmetry and only the underlying condensate is modified.…”