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arXiv:2408.06514 · Physical review. B./Physical review. B

Photoinduced charge, spin, and orbital order in the two-orbital extended Hubbard model

Sujay Ray, Philipp Werner

Published Dec 20, 2024• 2 citations
arXivHTMLPDF

Abstract

Nonequilibrium control of electronically ordered hidden phases may lead to the development of ultrafast switches and memory devices. In this study, we demonstrate tunable hidden orders in the half-filled photodoped two-orbital extended Hubbard model. Using steady-state nonequilibrium dynamical mean-field theory, we clarify the coexistence and interplay of nonthermal charge, spin, and orbital order. The hidden state at low effective temperature and sufficiently high photodoping is reminiscent of Kugel-Khomskii order in the two-orbital Hubbard model at $\frac{1}{4}$ and $\frac{3}{4}$ filling, but it emerges out of a nonequilibrium charge-ordered state and exhibits a different magnetic structure. A low-energy effective Hamiltonian is used to analyze the exchange processes that stabilize the nonthermal order.

DOI
10.1103/physrevb.110.214433

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Nonequilibrium control of electronically ordered hidden phases may lead to the development of ultrafast switches and memory devices. In this study, we demonstrate tunable hidden orders in the half-filled photodoped two-orbital extended Hubbard model. Using steady-state nonequilibrium dynamical mean-field theory, we clarify the coexistence and interplay of nonthermal charge, spin, and orbital order. The hidden state at low effective temperature and sufficiently high photodoping is reminiscent of Kugel-Khomskii order in the two-orbital Hubbard model at 14\frac{1}{4}41​ and 34\frac{3}{4}43​ filling, but it emerges out of a nonequilibrium charge-ordered state and exhibits a different magnetic structure. A low-energy effective Hamiltonian is used to analyze the exchange processes that stabilize the nonthermal order.
The search for hidden orders in photoexcited lattice systems is an active research field driven by experimental reports of light-induced or light-stabilized phases. In this study, we investigate hidden electronic orders in strongly correlated two-orbital Hubbard models with orbital-dependent bandwidths. In equilibrium, the half-filled systems are antiferromagnetically ordered. Using nonequilibrium dynamical mean field theory we demonstrate the appearance of nonthermal ferromagnetic order in the photodoped state, if the two bandwidths are sufficiently different, and its coexistence with spin-singlet $\ensuremath{\eta}$ superconductivity in the high photodoping region. Spin-triplet $\ensuremath{\eta}$-superconducting order appears instead if the two bandwidths are comparable. The rich nonequilibrium phasediagram uncovered in this work shows that Mott insulating multiorbital systems provide an interesting platform for the realization of nonthermal electronic orders.
Photo-induced hidden phases are often observed in materials with intertwined orders. Understanding the formation of these non-thermal phases is challenging and requires a resolution of the cooperative interplay between different orders on the ultra-short timescale. In this work, we demonstrate that non-equilibrium photo-excitations can induce a state with spin-orbital orders entirely different from the equilibrium state in the three-quarter-filled two-band Hubbard model. We identify a general mechanism governing the transition to the hidden state, which relies on a non-thermal partial melting of the intertwined orders mediated by photoinduced charge excitations in the presence of strong spin-orbital exchange interactions. Our study theoretically confirms the crucial role played by orbital degrees of freedom in the light-induced dynamics of strongly correlated materials and it shows that the switching to hidden states can be controlled already on the fs timescale of the electron dynamics.
Multiorbital Hubbard models with Hund coupling and crystal-field splitting exhibit an instability toward spin-triplet excitonic order in the parameter regime characterized by strong local spin fluctuations. Upon chemical doping, two distinct types of excitonic ferromagnetism have been reported. Using steady-state nonequilibrium dynamical mean-field theory, we demonstrate that photo-doped half-filled systems can host nonthermal counterparts of these excitonic phases and exhibit a rich phase diagram in the space of photo-doping and crystal field splitting. Photo-doping a spin-triplet excitonic insulator provides a route towards nonequilibrium control of magnetic order.
Superconductivity in laser-excited correlated electron systems has attracted considerable interest due to reports of light-induced superconductinglike states. Here we explore the possibility of nonthermal superconducting order in strongly interacting multiorbital Hubbard systems, using nonequilibrium dynamical mean field theory. We find that a staggered $\ensuremath{\eta}$-type superconducting phase can be realized on a bipartite lattice in the high photodoping regime, if the effective temperature of the photocarriers is sufficiently low. The $\ensuremath{\eta}$ superconducting state is stabilized by Hund coupling---a positive Hund coupling favors orbital-singlet spin-triplet $\ensuremath{\eta}$ pairing, whereas a negative Hund coupling stabilizes spin-singlet orbital-triplet $\ensuremath{\eta}$ pairing.
Photodoped states are widely observed in laser-excited Mott insulators, in which charge excitations are quickly created and can exist beyond the duration of the external driving. Despite the fruitful experimental explorations, theoretical studies on the microscopic models face the challenge to simultaneously deal with exponentially separated time scales, especially in multiband systems, where the longtime behaviors are often well beyond the reach of state-of-the-art numerical tools. Here, we address this difficulty by introducing a steady-state description of photodoped Mott insulators using an open-system setup, where the photodoped system is stabilized as a nonequilibrium steady state by a weak external driving. Taking advantage of the stationarity, we implement and discuss the details of an efficient numerical tool using the steady-state dynamical mean-field theory combined with the noncrossing approximation. We demonstrate that these stationary photodoped states exhibit the same properties of their transient counterparts, while being solvable with reasonable computational efforts. Furthermore, they can be parametrized by just a few physical quantities, including the effective temperature and the density of charge excitations, which confirms the universal nature of photodoped states indeed independent of the excitation protocols. As a first application, we consider the stationary photodoped states in a two-band Hubbard model with intertwined spin-and-orbital ordering and find a family of hidden phases unknown from the previous studies, implying an apparently unexplored time regime of the relaxation of the intertwined orders.
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.