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arXiv:2209.04094 · Physical review. B./Physical review. B

Excitonic density waves, biexcitons, and orbital-selective pairing in two-orbital correlated chains

Chun Yang, Adrian E. Feiguin

Published Jul 19, 2018• 7 citations
arXivHTMLPDF

Abstract

We present a comprehensive study of a one-dimensional two-orbital model at and below quarter filling that realizes a number of unconventional phases. In particular, we find an excitonic density wave in which excitons quasicondense with finite center-of-mass momentum and an order parameter that changes phase with wave vector $Q$. In this phase, excitons behave as hard-core bosons without charge order. In addition, excitons can pair to form biexcitons in a state that is close to a charge- density-wave instability. When pairing dominates over the interorbital repulsion, we encounter a regime in which one orbital is metallic, while the other forms a spin-gapped superconductor, a genuine orbital-selective paired state. All these results are supported by both analytical and numerical calculations. By assuming a quasiclassical approximation, we solve the three-body hole-electron-spinon problem and show that excitons are held together by forming a bound state with spinons. In order to preserve the antiferromagnetic background, excitons acquire a dispersion that has a minimum away from $k=0$. The full characterization of the different phases is obtained by means of extensive density-matrix renormalization-group calculations.

DOI
10.1103/physrevb.98.035128

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We present a comprehensive study of a one-dimensional two-orbital model at and below quarter filling that realizes a number of unconventional phases. In particular, we find an excitonic density wave in which excitons quasicondense with finite center-of-mass momentum and an order parameter that changes phase with wave vector QQQ. In this phase, excitons behave as hard-core bosons without charge order. In addition, excitons can pair to form biexcitons in a state that is close to a charge- density-wave instability. When pairing dominates over the interorbital repulsion, we encounter a regime in which one orbital is metallic, while the other forms a spin-gapped superconductor, a genuine orbital-selective paired state. All these results are supported by both analytical and numerical calculations. By assuming a quasiclassical approximation, we solve the three-body hole-electron-spinon problem and show that excitons are held together by forming a bound state with spinons. In order to preserve the antiferromagnetic background, excitons acquire a dispersion that has a minimum away from k=0k=0k=0. The full characterization of the different phases is obtained by means of extensive density-matrix renormalization-group calculations.
Motivated by exploring superconductivity in multi-orbital systems, we study two orbital models of spinful fermions representing (px,pyp_x,p_ypx​,py​) or (dxz,dyz)d_{xz}, d_{yz})dxz​,dyz​) orbitals on the square lattice. For minimal interorbital ttt-JJJ or ttt-VVV on-site interactions, a random phase approximation uncovers regimes of instability towards incommensurate dxyd_{xy}dxy​ pair density wave (ddd-PDW) superconductivity with driven by interband pairing. We study the competition of PDW order with uniform nodal dxyd_{xy}dxy​ pairing states and magnetic and charge density wave (CDW) instabilities. At strong coupling, we derive an effective hard-core Cooper pair Hamiltonian which we study using a bosonic Gutzwiller ansatz to reveal a period-222 PDW over a wide range of fillings as well as a checkerboard CDW at quarter-filling. Our results apply to correlated multi-orbital materials with quasi-1D bands, Hubbard models on the square-octagon lattice, and atomic fermions in ppp-orbitals. Our work highlights the role of the orbital content and multiband Fermi surfaces in stabilizing interband PDW states.
Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space real-time evolution of an excitonic wave packet using a two-orbital Hubbard model in a chain. The exciton is created by exciting an electron from a lower-energy half-filled orbital to a higher-energy empty orbital. We carry out the real-time dynamics of the resulting excitonic wave packet using the time-dependent density matrix renormalization group. We find clear evidence of charge-spin and spin-orbit separation in real space, by tracking the time evolution of local observables. We show that the velocity of the orbiton can be tuned varying the interorbital interactions. We also present a comparative study of the dynamics of a hole in one-orbital and two-orbital Hubbard models. Moreover, we analyze the dynamics of an exciton with spin-flip excitation, where we observe fractionalized spinons induced by Hund's interaction.
Excitonic condensation and stripe formation are two distinct manifestations of electronic correlations. While excitonic order naturally arises in multi-orbital systems, stripe order is a prominent feature of doped correlated-electron models. Here, we investigate an excitonic analogue of stripe order in the two--orbital Hubbard-Kanamori model on the square lattice, characterized by a spatial modulation of inter-orbital particle-hole coherence and, in the orbital-parity-symmetric limit, spontaneous breaking of a relative orbital Z2\mathbb{Z}_2Z2​ symmetry. Using unrestricted real-space Hartree-Fock calculations complemented by random-phase-approximation instability analysis, we determine how the Kanamori interactions select different excitonic channels. The sign of Hund's exchange controls the spin character of the condensate: ferromagnetic Hund coupling favors triplet excitonic order, whereas antiferromagnetic Hund coupling stabilizes singlet excitonic order. Upon doping, commensurate excitonic density waves develop incommensurate textures, including excitonic stripes and, in the triplet sector, spiral excitonic density waves. We further show that crystal-field splitting strongly reorganizes the excitonic instability by modifying inter-orbital nesting and can stabilize triplet excitonic order even in the absence of pair hopping. Our results establish excitonic stripes as a distinct symmetry-broken state of multi-orbital correlated systems and identify microscopic routes for their stabilization.
Excitonic phases described by the quantum condensation of electron-hole pairs (or excitons) are studied in the two-orbital Hubbard model with the Hund's rule coupling J . Using the variational cluster approximation, we calculate the ground-state energy and order parameters, and show that the Hund's rule coupling always stabilizes the excitonic spin-density- wave state and destabilizes the excitonic charge-density-wave state. The pair coherence lengths calculated in the spin-singlet and spin-triplet states indicate that only the spin-triplet excitons are paired more tightly with increasing J . The single-particle spectrum and density of states are also calculated to clarify the characters of these excitonic density-wave states.
We show that an interesting of pairing occurs for spin-imbalanced Fermi gases under a specific experimental condition---the spin up and spin down Fermi levels lying within the pxp_xpx​ and sss orbital bands of an optical lattice, respectively. The pairs condense at a finite momentum equal to the sum of the two Fermi momenta of spin up and spin down fermions and form a ppp-orbital pair condensate. This 2kF2k_F2kF​ momentum dependence has been seen before in the spin- and charge- density waves, but it differs from the usual ppp-wave superfluids such as 3^33He, where the orbital symmetry refers to the relative motion within each pair. Our conclusion is based on the density matrix renormalization group analysis for the one-dimensional (1D) system and mean-field theory for the quasi-1D system. The phase diagram of the quasi-1D system is calculated, showing that the ppp-orbital pair condensate occurs in a wide range of fillings. In the strongly attractive limit, the system realizes an unconventional BEC beyond Feynman's no-node theorem. The possible experimental signatures of this phase in molecule projection experiment are discussed.
The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and interlayer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π,π) charge density wave state. We extract the Berezinskii-Kosterlitz-Thouless transition temperature from superfluid density and a finite-size scaling analysis of the correlation functions and explain our results in terms of an effective biexcitonic hard-core boson model.