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arXiv:2005.11722 · Physical review. B./Physical review. B

Effects of frustration on the nonequilibrium dynamics of photoexcited lattice systems

Nikolaj Bittner, Denis Golež, Martin Eckstein, Philipp Werner

Published Dec 31, 2020• 11 citations
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Abstract

We theoretically investigate the effects of spin frustration on the nonequilibrium dynamics of photoexcited carriers in a half-filled two-dimensional Hubbard model. Using a nonequilibrium generalization of the dynamical cluster approximation, we compare the relaxation dynamics in lattices which interpolate between the triangular lattice and square lattice configuration. To clarify the influence of the density of states of the different lattices, we also consider the corresponding single-site dynamical mean-field theory results. Our study shows that the cooling effect resulting from the disordering of the spin background is less effective in the triangular case because of the frustration. This manifests itself in a longer relaxation time of the photodoped population, as measured by the time-resolved photoemission signal, and a higher effective temperature of the photodoped carriers in the nonthermal steady state after the intra-Hubbard-band thermalization.

DOI
10.1103/physrevb.102.235169

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Journal of Physics Condensed Matter•Mar 23, 2007•0 citations
We theoretically investigate the effects of spin frustration on the nonequilibrium dynamics of photoexcited carriers in a half-filled two-dimensional Hubbard model. Using a nonequilibrium generalization of the dynamical cluster approximation, we compare the relaxation dynamics in lattices which interpolate between the triangular lattice and square lattice configuration. To clarify the influence of the density of states of the different lattices, we also consider the corresponding single-site dynamical mean-field theory results. Our study shows that the cooling effect resulting from the disordering of the spin background is less effective in the triangular case because of the frustration. This manifests itself in a longer relaxation time of the photodoped population, as measured by the time-resolved photoemission signal, and a higher effective temperature of the photodoped carriers in the nonthermal steady state after the intra-Hubbard-band thermalization.
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.
We study the photoexcitation dynamics of correlated band insulators, using nonequilibrium dynamical mean-field theory for the ionic Hubbard model. We find two distinct behaviors, depending on the ratio of the on-site interaction UUU and the bare band gap $\mathrm{\ensuremath{\Delta}}$. For small interactions, the relaxation is characterized by intraband carrier scattering in relatively rigid bands, leading to a nonthermal intermediate state with separate thermal distributions of electrons and holes. This behavior can be viewed as typical for a band insulator with weak interactions. For larger interaction, on the other hand, we observe a strong modification of the electronic spectrum and a filling-in of the gap after photoexcitation, along with a rapid thermalization of the system. The two behaviors therefore provide a dynamical distinction of a correlated band insulator and a band insulator, which can differ even when the spectra of the two systems are similar in equilibrium. The crossover happens when the interaction UUU is comparable to $\mathrm{\ensuremath{\Delta}}$.
We examine the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ and the chemical potential $\ensuremath{\mu}$, together with the spin correlation, in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling by using an exact diagonalization technique. In contrast to the case of a square lattice without frustration, the doping dependences of $\ensuremath{\mu}$ and the Drude weight indicate that the charge degree of freedom is weakly coupled to the spin degree of freedom. However, we find that $\ensuremath{\sigma}(\ensuremath{\omega})$ shows strong incoherent excitations extended to a higher energy region. This implies that geometrical frustration in strongly correlated electron systems influences incoherent charge dynamics.
We study the effect of spatially nonlocal correlations on the nonequilibrium dynamics of interacting fermions by constructing the nonequilibrium dynamical cluster theory, a cluster generalization of the nonequilibrium dynamical mean-field theory (DMFT). The formalism is applied to interaction quenches in the Hubbard model in one and two dimensions, and the results are compared with data from single-site DMFT, the time-dependent density matrix renormalization group, and lattice perturbation theory. Both in one and two dimensions the double occupancy quickly thermalizes, while the momentum distribution relaxes only on much longer time scales. For the two-dimensional square lattice we find a strongly momentum-dependent evolution of the momentum distribution around the Fermi energy, with a much faster relaxation near the momenta $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ than near $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$. This result is interpreted as reflecting the momentum-anisotropic quasiparticle lifetime of the marginal Fermi liquid. The method is further applied to the two-dimensional Hubbard model driven by a dc electric field, where the damping of the Bloch oscillation of the current is found to be less effective than predicted by DMFT and lattice perturbation theory.
Ultra-fast spectroscopy can reveal the interplay of charges with low energy degrees of freedom, which underlies the rich physics of correlated materials. As a potential glue for superconductivity, spin fluctuations in Mott insulators are of particular interest. A theoretical description of the coupled spin and charge degrees of freedom is challenging, because magnetic order is often only short-lived and short-ranged. In this work we theoretically investigate how the spin-charge interactions influence the relaxation of a two-dimensional Mott-Hubbard insulator after photo-excitation. We use a nonequilibrium variant of the dynamical cluster approximation, which, in contrast to single-site dynamical mean-field theory, captures the effect of short-range correlations. The relaxation time is found to scale with the strength of the nearest-neighbor spin correlations, and can be 10-20 fs in the cuprates. Increasing the temperature or excitation density decreases the spin correlations and thus implies longer relaxation times. This may help to distinguish the effect of spin-fluctuations on the charge relaxation from the influence of other bosonic modes in the solid.
We examine the regular part of optical conductivity in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling. A numerically exact diagonalization method based on the Lanczos technique is employed for a 21-site triangular lattice. The regular part is calculated by averaging over various twisted boundary conditions to reduce finite-size effects. We find that the spectra show strong incoherent excitations extended to a higher energy region irrespective of the sign of the hopping amplitude. This is in contrast to the case of a square lattice without frustration. The results imply that geometrical frustration in strongly correlated electron systems influences incoherent charge dynamics.