Photoinduced Enhancement of Excitonic Order

Abstract

We study the dynamics of excitonic insulators coupled to phonons using the time-dependent mean-field theory. Without phonon couplings, the linear response is given by the damped amplitude oscillations of the order parameter with a frequency equal to the minimum band gap. A phonon coupling to the interband transfer integral induces two types of long-lived collective oscillations of the amplitude, one originating from the phonon dynamics and the other from the phase mode, which becomes massive. We show that, even for small phonon coupling, a photoinduced enhancement of the exciton condensation and the gap can be realized. Using the Anderson pseudospin picture, we argue that the origin of the enhancement is a cooperative effect of the massive phase mode and the Hartree shift induced by the photoexcitation. We also discuss how the enhancement of the order and the collective modes can be observed with time-resolved photoemission spectroscopy. [7][8][9][10][11][12]. An EI state is formed by the macroscopic condensation of electron-hole pairs [13,14], and its theoretical description is analogous to the BCS or Bose-Einstein condensate (BEC) theory for SC. Although the idea of exciton condensation was proposed already in the 1960s [13][14][15], the interest in this topic has been renewed recently by the study of some candidate materials such as 1T-TiSe 2 and Ta 2 NiSe 5 (TNS) [16][17][18][19][20][21]. Their analogy to SC makes the EI an interesting system for nonequilibrium studies. In particular, for TNS, time-and angle-resolved photoemission spectroscopy (trARPES) experiments showed that the direct band gap can be either decreased or increased depending on the pump fluence [11], which was interpreted in terms of a photoinduced enhancement or suppression of excitonic order. A more recent report of the amplitude mode [12] provides further confirmation of an EI state in TNS.So far, the theoretical works on EIs have mainly focused on the equilibrium properties such as the BEC-BCS crossover [22,23], the coupling of the EI to phonons [24][25][26], linear susceptibilities [27][28][29], and the effect of strong interactions and new emergent phases [30][31][32]. In contrast, the nonequilibrium investigation of EIs has just begun [10]. In this work, using TNS as a model system, we clarify two basic effects of the electron-phonon (e-ph) coupling on the dynamics of EIs: (i) the effect on collective modes and (ii) the impact on the excitonic order after

Nonequilibrium dynamics in the pump-probe spectroscopy of excitonic insulators

“…The time evolution of the system induced by the laser pulse is calculated in the time-dependent mean-field approximation [25,34,35]. We define the uniform excitonic order parameter as…”

Nonthermal switching of charge order: Dynamical slowing down and optimal control

“…This concept has provided an intuitive picture of related problems [13,43,[58][59][60]. Note that the pseudospin encodes the sublattice structure, while the physical spin need not be treated explicitly in the paramagnetic case.…”

“…Here, 1 is a penalty parameter for the slope, whereas 2 denotes the penalty with respect to the absorbed energy E abs . In order to evaluate the functionals (12) or (13), one has to perform the time propagation up to a sufficiently large time T max (we set T max = 500), and compute the fitting parameters a, b and the absorbed energy. This procedure depends on the parameters N b , 1 , 2 and the pulse duration T p .…”

“…Important examples include the transient enhancement of superconductivity (SC) [1][2][3][4][5][6][7][8][9], light-controlled order of excitonic condensates [10][11][12][13], or the transient manipulation of spin [14,15], orbital [16] and charge order [17][18][19][20]. Since charge-density-wave (CDW) order directly couples to external electric fields, it provides an ideal platform for inducing and tracing photoinduced phase transitions.…”

“…The dynamics after a generic excitation can exhibit qualitative changes-such as transitions from transiently trapped to vanishing order-beyond some critical excitation strength which cannot be explained in terms of the total energy of the system within an equilibrium picture. Such dynamical phase transitions [34][35][36] have been studied for various kinds of ordered phases such as superconductors [37][38][39][40], excitonic insulators [13], antiferromagnetic [41][42][43], ferromagnetic [36,44,45], and bosonic [46] systems.…”