Third harmonic generation from collective modes in disordered superconductors

Abstract

Recent experiments with strong THz fields in both conventional and unconventional superconductors have clearly evidenced a marked third-harmonic generation below the superconducting temperature T c . Its interpretation challenged substantial theoretical work aimed at establishing the relative efficiency of quasiparticle excitations and collective modes in triggering such a resonant response. Here we compute the nonlinear current by implementing a time-dependent Bogoljubov-de Gennes approach, with the twofold aim to account nonperturbatively for the effect of local disorder, and to include the contribution of all collective modes, i.e., superconducting amplitude (Higgs) and phase fluctuations, and charge fluctuations. We show that, in agreement with previous work, already at small disorder the quasiparticle response is dominated by paramagnetic effects. We further demonstrate that paramagnetic processes mediate also the response of all collective modes, with a substantial contribution of charge/phase fluctuations. These processes, which have been overlooked so far, turn out to dominate the third-order current at strong disorder. In addition, we show that disorder strongly influences the polarization dependence of the nonlinear response, with a marked difference between the clean and the disordered case. Our results are particularly relevant for recent experiments in cuprates, whose band structure is in a first approximation reproduced by our lattice model.

Optical response of Higgs mode in superconductors at clean limit

“…Moreover, while the density-related effect is hard to handle in the quasiclassical Eilenberger equation, the vanishing chargedensity fluctuation in the second-order response, which agrees with the charge conservation, is obtained within the GIKE and path-integral approach. Consequently, the present work resolves the controversies among various studies in the literature (whether the experimentally observed third-harmonic current [26][27][28][29][30][31][32] is attributed to the Higgs-mode [29][30][31][32][33]48 or charge-density-fluctuation [49][50][51] generation, and whether one has to rely on impurity to explain the experimentally observed Higgs-mode generation 33,45,[48][49][50][51]54,55,57,58 ), and can therefore help understanding the experimental findings.…”

“…However, rather than straightening out the situation, these theoretical descriptions make the understanding of the existing and growing experimental findings muddled. Specifically, early theoretical studies of the nonlinear optical response in superconductors have used the Bloch [26][27][28][29][30][34][35][36][37][38][39][40] or Liouville [41][42][43][44][45] equation derived in Anderson pseudospin picture 46 , with the vector potential A alone. The second-order light-matter interaction H p = e 2 A 2 τ 3 /(2m) naturally emerges in these descriptions [26][27][28][29][30][34][35][36][37][38][39][41][42][43][44] as a pseudo field along z direction, with τ i being the Pauli matrices in Nambu space.…”

“…However, an isotropic optical response is experimentally observed [29][30][31][32] , giving firm evidence to support the previous observation of the Higgs mode. Recent theoretical attention then tends to focus on and emphasize the important role of the impurity scattering to mediate the Higgs-mode generation 45,54,55,57,58 . To handle the microscopic scattering seriously, Silaev 55,56 used the Eilenberger equation [59][60][61][62][63] that only involves the drive effect H d by vector potential.…”

Флуктуационно-Диссипативная Теорема И Частотные Моменты Функций Реакции Плотной Плазмы На Электромагнитное Поле

“…д. ), связанные с нелинейным взаимодействием электромагнитных (ЭМ) волн (см., например, [1][2][3][4]). В то же время недостаточно изучены нелинейные явления в плотных заряженных системах (кулоновских системах и плазме), вызванные квадратичной реакцией на электромагнитное поле -генерация второй гармоники (ГВГ), параметрическая генерация излучения (ПГИ) (см.…”

Third-harmonic generation in excitonic insulators

“…Recently, collective natures of materials are investigated by nonlinear optical spectroscopies. For example, in BCS superconductors, the amplitude (Higgs) mode, which is dark in linear response regime, is activated by the nonlinear optical drive and the resulting resonance emerges in third-harmonic generation (THG) [59][60][61][62][63][64]. Actually, the enhancement of the THG intensity at the resonant frequency has been observed by the terahertz pump-probe experiments [65][66][67][68][69].…”