Photo-induced gap closure in an excitonic insulator

We study the dynamical phase transition out of an excitonic insulator phase after photo-excitation using a time-dependent extension of the selfconsistent GW method. We connect the evolution of the photoemission spectra to the dynamics of the excitonic order parameter and identify two dynamical phase transition points marked by a slowdown in the relaxation: one critical point is connected with the trapping in a nonthermal state with reduced exciton density and the second corresponds to the thermal phase transition. The transfer of kinetic energy from the photoexcited carriers to the exciton condensate is shown to be the main mechanism for the gap melting. We analyze the low energy dynamics of screening, which strongly depends on the presence of the excitonic gap, and argue that it is difficult to interpret the static component of the screened interaction as the effective interaction of some low energy model. Instead we propose a phenomenological measure for the effective interaction which indicates that screening has minor effects on the low energy dynamics

Low rank compression in the numerical solution of the nonequilibrium Dyson equation

We propose a method to improve the computational and memory efficiency of numerical solvers for the nonequilibrium Dyson equation in the Keldysh formalism. It is based on the empirical observation that the nonequilibrium Green's functions and self energies arising in many problems of physical interest, discretized as matrices, have low rank off-diagonal blocks, and can therefore be compressed using a hierarchical low rank data structure. We describe an efficient algorithm to build this compressed representation on the fly during the course of time stepping, and use the representation to reduce the cost of computing history integrals, which is the main computational bottleneck. For systems with the hierarchical low rank property, our method reduces the computational complexity of solving the nonequilibrium Dyson equation from cubic to near quadratic, and the memory complexity from quadratic to near linear. We demonstrate the full solver for the Falicov-Kimball model exposed to a rapid ramp and Floquet driving of system parameters, and are able to increase feasible propagation times substantially. We present examples with 262144 time steps, which would require approximately five months of computing time and 2.2 TB of memory using the direct time stepping method, but can be completed in just over a day on a laptop with less than 4 GB of memory using our method. We also confirm the hierarchical low rank property for the driven Hubbard model in the weak coupling regime within the GW approximation, and in the strong coupling regime within dynamical mean-field theory.Comment: 14 page

Photoinduced gap closure in an excitonic insulator

We study the dynamical phase transition out of an excitonic insulator phase after photoexcitation using a time-dependent extension of the self-consistent GW method. We connect the evolution of the photoemission spectra to the dynamics of the excitonic order parameter and identify two dynamical phase transition points marked by a slowdown in the relaxation: one critical point is connected with the trapping in a nonthermal state with reduced exciton density and the second corresponds to the thermal phase transition. The transfer of kinetic energy from the photoexcited carriers to the exciton condensate is shown to be the main mechanism for the gap melting. We analyze the low energy dynamics of screening, which strongly depends on the presence of the excitonic gap, and argue that it is difficult to interpret the static component of the screened interaction as the effective interaction of some low energy model. Instead we propose a phenomenological measure for the effective interaction which indicates that screening has minor effects on the low energy dynamics

Photoinduced enhancement of excitonic order

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

Comparing the generalized Kadanoff-Baym ansatz with the full Kadanoff-Baym equations for an excitonic insulator out of equilibrium

We investigate out-of-equilibrium dynamics in an excitonic insulator (EI) with a finite momentum pairing perturbed by a laser-pulse excitation and a sudden coupling to fermionic baths. The transient dynamics of the excitonic order parameter is resolved using the full nonequilibrium Green's function approach and the generalized Kadanoff-Baym ansatz (GKBA) within the second-Born approximation. The comparison between the two approaches after a laser pulse excitation shows a good agreement in the weak and the intermediate photo-doping regime. In contrast, the laser-pulse dynamics resolved by the GKBA does not show a complete melting of the excitonic order after a strong excitation. Instead we observe persistent oscillations of the excitonic order parameter with a predominant frequency given by the renormalized equilibrium bandgap. This anomalous behavior can be overcome within the GKBA formalism by coupling to an external bath, which leads to a transition of the EI system towards the normal state. We analyze the long-time evolution of the system and distinguish decay timescales related to dephasing and thermalization.Comment: 13 pages, 12 figure

Hund’s coupling driven photocarrier relaxation in the two-band Mott insulator

We study the relaxation dynamics of photocarriers in the paramagnetic Mott insulating phase of the half-filled two-band Hubbard model. Using nonequilibrium dynamical mean-field theory, we excite charge carriers across the Mott gap by a short hopping modulation, and simulate the evolution of the photodoped population within the Hubbard bands. We observe an ultrafast charge-carrier relaxation driven by the emission of local spin excitations with an inverse relaxation time proportional to the Hund's coupling. The photodoping generates additional side-bands in the spectral function, and for strong Hund's coupling, the photodoped population also splits into several resonances. The dynamics of the local many-body states reveals two effects, thermal blocking and kinetic freezing, which manifest themselves when the Hund's coupling becomes of the order of the temperature or the bandwidth, respectively. These effects, which are absent in the single-band Hubbard model, should be relevant for the interpretation of experiments on correlated materials with multiple active orbitals. In particular, the features revealed in the nonequilibrium energy distribution of the photocarriers are experimentally accessible, and provide information on the role of the Hund's coupling in these materials