Two-orbital Hubbard Model Research Articles

Spin Seebeck effect in nonmagnetic excitonic insulators

We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneously hybridized. Using the generalized spin-wave theory and Boltzmann transport equation, we find that a spin current generated by a thermal gradient is observed in the excitonic insulating state without magnetic fields. The spin Seebeck effect originates from spin-split collective excitation modes although the ground state does not exhibit any magnetic orderings. This peculiar phenomenon is inherent in the excitonic insulating state, whose order parameter is time-reversal odd and yields a spin splitting for the collective excitation modes. We also find that the spin current is strongly enhanced and its direction is inverted in the vicinity of the phase transition to another magnetically ordered phase. We suggest that the present phenomenon is possibly observed in perovskite cobaltites with the $\mathrm{Gd}\mathrm{Fe}{\mathrm{O}}_{3}$-type lattice distortion.

Fractional Fermi liquid in a generalized t−J model

Inspired by the recent discovery of superconductivity in the nickelate Nd$_{1-x}$Sr$_x$NiO$_2$, we study a generalized $t-J$ model to investigate the correlated phases induced by doping spin-one Ni$^{2+}$ into a spin $1/2$ Mott insulator formed by Ni$^{1+}$. Based on a three-fermion parton mean field analysis, we identify a robust fractional Fermi liquid (FL*) phase for almost every doping level. The FL* state is characterized by a small Fermi pocket on top of a spin liquid, which violates the Luttinger theorem of a conventional Fermi liquid and is an example of a symmetric pseudogap metal. Furthermore, we verify our theory in one dimension through density matrix renormalization group (DMRG) simulations on both the generalized $t-J$ model and a two-orbital Hubbard model. The fractional Fermi liquid reduces to fractional Luttinger liquid (LL*) in one dimension, which is connected to the conventional Luttinger liquid through a continuous quantum phase transition by tuning interaction strength. Our findings offer new insights into correlated electron phenomena in nickelate superconductors and other multi-orbital transition metal oxide with spin-triplet $d^8$ state.

Nonequilibrium-DMFT based RIXS investigation of the two-orbital Hubbard model

Resonant inelastic X-ray scattering (RIXS) detects various types of high- and low-energy elementary excitations in correlated solids, and this tool will play an increasingly important role in investigations of time-dependent phenomena in photo-excited systems. While theoretical frameworks for the computation of equilibrium RIXS spectra are well established, the development of appropriate methods for nonequilibrium simulations is an active research field. Here, we apply a recently developed nonequilibrium dynamical mean field theory (DMFT) based approach to compute the RIXS response of photo-excited two-orbital Mott insulators. The results demonstrate the feasibility of multi-orbital nonequilibrium RIXS calculations and the sensitivity of the quasi-elastic fluorescence-like features and excitation peaks on the nonequilibrium population of the Hubbard bands.

Destabilization of ferromagnetism by frustration and realization of a nonmagnetic Mott transition in the quarter-filled two-orbital Hubbard model

The two-orbital Hubbard model on a square lattice at quarter filling (electron number per site $n=1$) is investigated by the variational Monte Carlo method. For the variational wave function, we include short-range doublon-holon binding factors. We find that the energy of this wave function is lower than that of the density-density Jastrow wave function partially including long-range correlations used in a previous study. We introduce frustration to the model by the next-nearest-neighbor hopping $t'$ in addition to the nearest-neighbor hopping $t$. For $t'=0$, a ferromagnetic state with staggered orbital order occurs by increasing the Coulomb interaction $U$ before the Mott transition takes place. By increasing $t'$, the region of this ferromagnetic phase shrinks, and the Mott transition without magnetic order occurs.

Electronic structure and two-band superconductivity in unconventional high- Tc cuprates Ba2 CuO3+δ

The recently discovered cuprate superconductor Ba$_2$CuO$_{3+\delta}$ exhibits a high $T_c\simeq73$K at $\delta\simeq0.2$. The polycrystal grown under high pressure has a structure similar to La$_2$CuO$_4$, but with dramatically different lattice parameters due to the CuO$_6$ octahedron compression. The crystal field in the compressed Ba$_2$CuO$_4$ leads to an inverted Cu $3d$ $e_g$ complex with the $d_{x^2-y^2}$ orbital sitting below the $d_{3z^2-r^2}$ and an electronic structure highly unusual compared to the conventional cuprates. We construct a two-orbital Hubbard model for the Cu $d^9$ state at hole doping $x=2\delta$ and study the orbital-dependent strong correlation and superconductivity. For the undoped case at $x=0$, we found that strong correlation drives an orbital-polarized Mott insulating state with the spin-$1/2$ moment of the localized $d_{3z^2-r^2}$ orbital. In contrast to the single-band cuprates where superconductivity is suppressed in the overdoped regime, hole doping the two-orbital Mott insulator leads to orbital-dependent correlations and the robust spin and orbital exchange interactions produce a high-$T_c$ antiphase $d$-wave superconductor even in the heavily doped regime at $x=0.4$. We conjecture that Ba$_2$CuO$_{3+\delta}$ realizes mixtures of such heavily hole-doped superconducting Ba$_2$CuO$_4$ and disordered Ba$_2$CuO$_{3}$ chains in a single-layer or predominately separated bilayer structure. Our findings suggest that unconventional cuprates with liberated orbitals as doped two-band Mott insulators can be a direction for realizing high-T$_c$ superconductivity with enhanced transition temperature $T_c$.

Nonthermal excitonic condensation near a spin-state transition

We consider a two-orbital Hubbard model with Hund coupling and crystal-field splitting and show that in the vicinity of the high-spin/low-spin transition, crystal-field quenches can induce an excitonic condensation at initial temperatures above the highest ordering temperature in equilibrium. This condensation is the effect of an increase in the spin entropy and an associated cooling of the effective electronic temperature. We identify a dynamical phase transition and show that such quenches can result in long-lived nonthermal excitonic condensates which have no analogue in the equilibrium phase diagram. The results are interpreted by means of an effective pseudo-spin model.

Low-Temperature Phases in Two-Orbital Hubbard Model Realized with Ultracold Atoms in Optical Lattices

Low-Temperature Phases in Two-Orbital Hubbard Model Realized with Ultracold Atoms in Optical Lattices

Photoinduced dynamics of excitonic order and Rabi oscillations in the two-orbital Hubbard model

We investigate the condition for the photoinduced enhancement of an excitonic order in a two-orbital Hubbard model, which has been theoretically proposed in our previous work [Phys. Rev. B 97, 115105 (2018)], and analyze it from the viewpoint of the Rabi oscillation. Within the mean-field approximation, we simulate real-time dynamics of an excitonic insulator with a direct gap, where the pair condensation in the initial state is of BEC nature and the photoexcitation is introduced by electric dipole transitions. We first discuss that in the atomic limit our model is reduced to a two-level system that undergoes the Rabi oscillation, so that for single cycle pulses physical quantities after the photoirradiation are essentially determined by the ratio of the Rabi frequency to the pump-light frequency. Then, it is shown that this picture holds even in the case of nonzero transfer integrals where each one-particle state exhibits the Rabi oscillation leading to the enhancement of the excitonic order. We demonstrate that effects of electron-phonon interactions do not alter the results qualitatively. We also examine many-body dynamics by the exact diagonalization method on small clusters, which strongly suggests that our mechanism for the enhancement of the exctionic order survives even when quantum fluctuations are taken into account.

Strong enhancement of magnetic susceptibility induced by spin-nematic fluctuations in an excitonic insulating system with spin-orbit coupling

Effects of the spin-orbit coupling (SOC) and magnetic field on excitonic insulating (EI) states are investigated. We introduce the two-orbital Hubbard model with the crystalline field splitting, which is a minimal model for discussing the exciton condensation in strongly correlated electron systems, and analyze its effective Hamiltonian in the strong correlation limit by using the mean-field theory. In the absence of the SOC and magnetic field, the ground state changes from the nonmagnetic band-insulating state to the EI state by increasing the Hund coupling. In an applied magnetic field, the magnetic moment appears in the EI state, which is continuously connected to the forced ferromagnetic state. On the other hand, in the presence of the SOC, they are separated by a phase boundary. We find that the magnetic susceptibility is strongly enhanced in the EI phase near the boundary with a small SOC. This peculiar behavior is attributed to the low-energy fluctuation of the spin nematicity inherent in the high-spin local state stabilized by the Hund coupling. The present study not only reveals the impact of the SOC for the EI state but also sheds light on the role of quantum fluctuations of the spin nematicity for the EI state.

Slave-rotor theory on magic-angle twisted bilayer graphene

We investigate the correlated electrons in the magic-angle twisted bilayer graphene by using the slave-rotor mean-field theory. Owing to the extended figure of Wannier orbitals, we study the two-orbital cluster Hubbard model with spin-valley fourfold degeneracy, focusing around half filling of valence bands below the neutrality point. The theory predicts multiple Mott insulator phases at fractional fillings not only for integer charges per moir{\'e} site, and it demonstrates that long-range electron hopping is highly suppressed because multiple-charge excitations are induced. Furthermore, the Kekul{\'e} valence bond order is investigated and is found to extend the Mott insulator phases to occupy a finite doping region. Adjacent to Mott insulator phases, superconducting domes emerges by virtue of spin-valley fluctuations. This work has provided a primal understanding and interesting phenomena of the correlated system, and for its novel interaction the model might produce plenty of possibilities waiting to be explored.

Emergence of pure spin current in doped excitonic magnets

An excitonic magnet hosts a condensate of spin-triplet excitons composed of conduction-band electrons and valence-band holes, and may be described by the two-orbital Hubbard model. When the Hamiltonian has the nearest-neighbor interorbital hopping integrals with $d$-wave symmetry and the number of electrons is slightly away from half filling, the $\boldsymbol{k}$-space spin texture appears in the excitonic phase with a broken time-reversal symmetry. We then show that, applying electric field to this doped excitonic magnet along a particular direction, a pure spin current emerges along its orthogonal direction. We discuss possible experimental realization of this type of the pure spin current in actual materials.

Emergence of superconductivity in doped multiorbital Hubbard chains

We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our ansatz is an optimized linear superposition of Affleck–Kennedy–Lieb–Tasaki valence-bond states, rendering the combination a valence-bond liquid dubbed orbital resonant valence bond. We show that the undoped (one-electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Anderson’s resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile, leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths—W the carrier’s bandwidth—could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.

Metal-insulator transition and dominant d+id pairing symmetry in twisted bilayer graphene

Motivated by recent experimental studies that have found signatures of a correlated insulator phase and tuning superconductivity in twisted bilayer graphene, we study the temperature-dependent conductivity, the spin correlation and the superconducting pairing correlation within a two-orbital Hubbard model on an emergent honeycomb lattice. The evaluation of the temperature dependence of the conductivity demonstrates that there is a metal-insulator transition, and the Mott phase at strong coupling is accompanied by antiferromagnetic order. The electronic correlation drives a $d+id$ superconducting pairing to be dominant over a wide filling region. All of the dc conductivity, the spin correlation and the superconductivity are suppressed as the interlayer coupling strength increases, and the critical $U_c$ for the metal-insulator transition is also reduced. Our intensive numerical results reveal that twisted bilayer graphene should be a uniquely tunable platform for exploring strongly correlated phenomena.

Optical response in the excitonic insulating state: Variational cluster approach

Optical responses in an excitonic insulating (EI) system with strong electron correlation are studied. We adopt the two-orbital Hubbard model with a finite energy difference between the two orbitals where the spin state degree of freedom exists. This model is analyzed by the variational cluster approach. In order to include the local electron correlation effect, the vertex correction is taken into account in the formulation of the optical conductivity spectra. We calculate a finite-temperature phase diagram, in which an EI phase appears between a low-spin band insulating state and a high-spin Mott insulating state. Characteristic components of the optical conductivity spectra consisting of a sharp peak and continuum appear in the EI phase. Integrated intensity almost follows the order parameter of the EI state, suggesting that this component is available to identify the EI phases and transitions.

Quantum Monte Carlo study of magnetic ordering and superconducting pairing symmetry in twisted bilayer graphene

To understand correlated insulating and unconventional superconducting states in twisted bilayer graphene, we perform a systematic study of spin and pairing correlations in an effective two-orbital Hubbard model, by using the ground-state constrained-path quantum Monte Carlo method. Our numerical simulations reveal that when only the on-site Hubbard $U$ is considered, the long-range magnetic order develops for $U\ensuremath{\ge}3.2t$ at half filling. Upon doping away from half filling, an analysis based on the pairing correlations and corresponding vertex contributions identifies that pairing with the $d+id$ symmetry is the dominant pairing channel. As the on-site Coulomb interaction is increased, both spin correlation and effective pairing interaction are enhanced simultaneously, indicating the intimate relation between magnetism and superconductivity. An inclusion of nearest neighbor Coulomb interaction $V$ results in a suppression of the $d+id$ superconductivity, but it can survive in the small $V$ regime. Our findings are useful for clarifying the ongoing controversy on the superconducting pairing symmetry in twisted bilayer graphene.

Doublon-holon excitations split by Hund's rule coupling within the orbital-selective Mott phase

Multiorbital interactions have the capacity to produce an interesting kind of doublon-holon bound state that consists of a single-hole state in one band and a doubly-occupied state in another band. Interband doublon-holon pair excitations in the two-orbital Hubbard model are studied by using dynamical mean-field theory with the Lanczos method as the impurity solver. We find that the interband bound states may provide several in-gap quasiparticle peaks in the density of states of the narrow band in the orbital-selective Mott phase with a small Hund's rule coupling ($J$). There exists a corresponding energy relation between the in-gap states of the narrow band and the peaks in the excitation spectrum of the doublon for the wide band. We also find that the spin flip and pair-hopping Hund interactions can divide one quasiparticle peak into two peaks, where the splitting energy increases linearly with increasing $J$. Strong Hund's rule coupling can move the interband doublon-holon pair excitations outside the Mott gap and restrict the bound states by suppressing the orbital selectivity of the doubly-occupied and single-hole states.

Spin-Orbital Density Wave and a Mott Insulator in a Two-Orbital Hubbard Model on a Honeycomb Lattice

Inspired by the recent discovery of correlated insulating states in twisted bilayer graphene, we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group simulation, we identify a metal-insulator transition around U_{c}/t=2.5-3. In the vicinity of U_{c}, we find strong spin-orbital density wave fluctuations at commensurate wave vectors, accompanied by weaker incommensurate charge density wave fluctuations. The spin-orbital density wave fluctuations are enhanced with increasing system sizes, suggesting the possible emergence of long-range order in the two-dimensional limit. At larger U, our calculations indicate a possible nonmagnetic Mott insulator phase without spin or orbital polarization. Our findings offer new insight into correlated electron phenomena in twisted bilayer graphene and other multiorbital honeycomb materials.

Spin-valley density wave in moiré materials

We introduce and study a minimum two-orbital Hubbard model on a triangular lattice, which captures the key features of both the trilayer ABC-stacked graphene-boron nitride heterostructure and twisted transition metal dichalcogenides in a broad parameter range. Our model comprises first- and second-nearest neighbor hoppings with valley-contrasting flux that accounts for trigonal warping in the band structure. For the strong-coupling regime with one electron per site, we derive a spin-orbital exchange Hamiltonian and find the semiclassical ground state to be a spin-valley density wave. We show that a relatively small second-neighbor exchange interaction is sufficient to stabilize the ordered state against quantum fluctuations. Effects of spin- and valley Zeeman fields as well as thermal fluctuations are also examined.

Model-mapped random phase approximation to evaluate superconductivity in the fluctuation exchange approximation from first principles

We have applied the model-mapped random phase approximation (RPA) [H. Sakakibara et al., J. Phys. Soc. Jpn. 86, 044714 (2017)] to the cuprate superconductors ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}$, resulting in two-orbital Hubbard models. All the model parameters are determined based on first-principles calculations. For the model Hamiltonians, we perform fluctuation exchange calculation. Results explain relative height of ${T}_{c}$ observed in experiment for ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}$. In addition, we give some analyses for the interaction terms in the model, especially comparisons with those of the constrained RPA.

Spin-triplet f -wave pairing in twisted bilayer graphene near 14 -filling

We investigate the twisted bilayer graphene by a two-orbital Hubbard model on the honeycomb lattice. The model is studied near 1/4 band filling by using the singular-mode functional renormalization group theory. Spin-triplet $f$-wave pairing is found from weak to moderate coupling limit of the local interactions, and is associated with the Hund's rule coupling and incommensurate spin fluctuations at moderate momenta.