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Symmetry breaking driven by petahertz electron acceleration in a centrosymmetric organic superconductor

Charge acceleration during an intense light field application to solids attracts much attention as elementary processes in high-harmonic generation and photoelectron emission [1-7]. For manipulating such attosecond dynamics of charge, carrier-envelope-phase (CEP:relative phase between carrier oscillation of light field and its envelope function) control has been employed in insulators, nanometal and graphene [8-10]. In superconducting materials, collective control of charge motion is expected because of its strongly coherent nature of quasi-particles. Here, in a layered organic superconductor, second harmonic generation (SHG) is observed by using a single-cycle 6 femtosecond near infrared pulse, which is in contrast to the common belief that even harmonics are forbidden in the centrosymmetric system. The SHG shows a CEP sensitive nature and an enhancement near the superconducting temperature. The result and its quantum many-body analysis indicate that a polarized current is induced by non-dissipative acceleration of charge, which is amplified by superconducting fluctuations. This will lead to petahertz functions of superconductors and of strongly correlated systems.


3
An electromagnetic oscillation of light cannot directly access a spatial symmetry breaking because of its symmetric nature on the time axis (i. e., the time average of the oscillation is zero). However, recent developments of ultrashort laser technologies enable us to control the direction of charge motion by carrier-envelope phase (CEP) control of a strong light field [8][9][10].
Considering non-perturbative and non-dissipative light-matter interactions during an ultrashort pulse, we can expect petahertz control of the spatial inversion symmetry in solids.
In the non-dissipative regime (before electron scatterings occur substantially), a current j(t) driven by a light field ( ) = 0 ( )sin ( − CEP ) [E0 (t): envelope of a single-cycle pulse, CEP : CEP] [ Fig. 1 Fig. 1(b)], indicating that an induced current can be modulated by the CEP. This is in contrast to the fact that a net current driven by a light-field is zero in the dissipative regime ( ) =  (t), where  is conductivity. Such a non-dissipative current can break the symmetry of a charge density in the momentum space [or equivalently a breaking of the spatial inversion symmetry in the sense that the induced current is no longer described as an odd function of E(t) of the moment], resulting in current induced SHG [11-13, for conventional (dissipative-)current-induced SHG].

(a)] is given by
Thus, the SHG (and the spatial inversion symmetry breaking) is induced even in the centrosymmetric system, if the non-dissipative current is driven by light.
Our target material is a layered organic superconductor -(BEDT-TTF)2Cu[N(CN)2]Br [14][15][16][17][18] with a transition temperature TSC=11.6 4 K ( Fig. 1(c)). Superconducting fluctuations above TSC (TSC<T<2TSC) have been discussed in analogy with a pseudogap in high-TSC superconducting cuprates in the temperature-t/Udimer phase diagram [17,18], where t/Udimer is the ratio of an inter-dimer transfer integral t to the effective on-site Coulomb energy for a dimer Udimer, as shown in Fig. 1(c). In superconductors, optical responses have been discussed in terms of non-equilibrium quasi-particle dynamics on the time scale of picosecond [19][20][21][22], coherent excitation of the Higgs mode [23] and light-induced superconductivity [24,25]. On the other hand, petahertz light functions driven by charge dynamics during a light pulse is also expected, reflecting the large energy scale of electron correlation (ca. 1 eV) [26].
In this letter, we report SHG for a strong light field ( in a conventional perturbation theory. 5 As shown in the upper panel of Fig. 2 Fig. 3(d).
On the other hand, the observed anisotropy of the SHG [ Fig. 2  In summary, this letter demonstrates that SHG is induced by the non-dissipative current in the centrosymmetric organic superconductor We performed SHG and THG measurements for the single crystal using a 6 fs pulse with a reflection geometry (incident angle is smaller than 3-degree).
The intensity and polarization of the fundamental (excitation range :0.01 to 2 mJ/cm 2 ) pulse are controlled by a pair of wire-grid CaF2 polarizers [30]. The SHG and the THG are detected by an photomuliplier tube (Hamamatsu R13456) after passing through a spectrometer (JASCO, M10). The CEP of the fundamental pulse is controlled by a pair of glass plates with the incidence angle of  ( Fig. 3(a)) and detected by the 2f-3f interferometer (2f and 3f are generated using -BBO ) [Figs. 3(b) and 3(c)]. 10 Data Availability The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.  1909-1910 (1999).     When we fully take electron correlations into account by employing the exact diagonalization method, we find that inter-site repulsive interactions substantially reduce the coherence of the charge oscillations that are responsible for the SHG, just as they reduce the coherence of the nonlinear charge oscillations that are responsible for the stimulated emission [S1]. On the other hand, we also find that they do not affect the THG so much. In the main text, we employ the time-dependent Hartree-Fock approximation, which cannot treat such decoherence effects, so that the SHG is overestimated and thus comparable with the THG.

Anisotropy of SHG
The SHG is polarized to the c-axis (ESH||c) for both fundamental polarizations (EFund||c, EFund ||a ) as shown in Fig. 2(b), although the THG shows the usual polarization (ETH||c for, Efund ||c and ETH||a for Efund ||a).
As described in the main text, the observed anisotropy of the SHG (ESH||c Thus, charge motion along the c-axis is actually driven by Epu||a as well. The microscopic reason for the induction of j||c by Efund ||a remains unclear. However, it is reasonable to consider that the induction of j||c by The blue, black and red dashed lines indicate I 2.0 (blue and black) and I 2.9 (red). Thus, the discrepancy between the observation ( ∝ 2.1 ) and the theory ( ∝ 2.9 ) would be due to the intra-molecular charge redistribution.
The energy range (0.6-2 eV) is known as a "spectral window" between inter-molecular (< 0.5 eV) and intra-molecular (> 2.3 eV) charge transfer bands in the organic superconductors [S4-S6], i.e., we have no large reflectivity or absorption bands except for a peak at 1.5 eV as shown in references [S7, S8]. We measure a transmittance spectrum of a thin film [S9] to investigate the influence of the absorption to the SHG, because it is difficult to estimate an absorption coefficient by Kramers-Kronig analysis of a reflectivity in such a "transparent" spectral region. The electronic coherence after the field application is also seen in another strong light field effect in this compound [26]. We perform a transient reflectivity (R/R) measurement with a double-pump pulse to make an insight of coherence induced by a strong-light field. This method has been employed for elucidating electronic and vibrational coherence [S11-S13].
Here, the coherence of the non-linear charge motion, which has been assigned as the origin of stimulated emission [26], is discussed.