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AIP conference proceedings

Excitonic instability in a strongly correlated system: A slave rotor approach

Subhasree Pradhan, A. Taraphder

Published Jan 1, 2018• 0 citations
Publisher

Abstract

Exciton formation and condensation in a two band correlated model is studied using slave rotor mean field (SRMF) theory. In the SRMF theory, charge and spin degrees are treated as independent degrees of freedom. Using this, we capture the effective many body scales beyond conventional mean-field theory. While the formation of exciton is favoured by the hybridization, it is strongy influenced by the Coulomb repulsion between electrons in the two bands. Beyond a critical value of hybridization, there is complete coheherence among the electrons and holes signalling a condensation of excitons.

DOI
10.1063/1.5033026

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Exciton formation and condensation in a two band correlated model is studied using slave rotor mean field (SRMF) theory. In the SRMF theory, charge and spin degrees are treated as independent degrees of freedom. Using this, we capture the effective many body scales beyond conventional mean-field theory. While the formation of exciton is favoured by the hybridization, it is strongy influenced by the Coulomb repulsion between electrons in the two bands. Beyond a critical value of hybridization, there is complete coheherence among the electrons and holes signalling a condensation of excitons.
The multiorbital Hubbard model is expressed in terms of quantum phase variables (``slave rotors'') conjugate to the local charge, and of auxiliary fermions, providing an economical representation of the Hilbert space of strongly correlated systems. When the phase variables are treated in a local mean-field manner, similar results to the dynamical mean-field theory are obtained, namely a Brinkman-Rice transition at commensurate fillings together with a ``preformed'' Mott gap in the single-particle density of states. The slave-rotor formalism allows to go beyond the local description and take into account spatial correlations, following an analogy to the superfluid-insulator transition of bosonic systems. We find that the divergence of the effective mass at the metal-insulator transition is suppressed by short range magnetic correlations in finite-dimensional systems. Furthermore, the strict separation of energy scales between the Fermi-liquid coherence scale and the Mott gap, found in the local picture, holds only approximately in finite dimensions, due to the existence of low-energy collective modes related to zero-sound.
We analyze the stability of excitonic ground states in the two-band Hubbard model with additional electron-phonon and Hund's rule couplings using a combination of mean-field and variational cluster approaches. We show that both the interband Coulomb interaction and the electron-phonon interaction will cooperatively stabilize a charge density wave (CDW) state which typifies an ``excitonic'' CDW if predominantly triggered by the effective interorbital electron-hole attraction or a ``phononic'' CDW if mostly caused by the coupling to the lattice degrees of freedom. By contrast, the Hund's rule coupling promotes an excitonic spin density wave. We determine the transition between excitonic charge and spin density waves and comment on a fixation of the phase of the excitonic order parameter that would prevent the formation of a superfluid condensate of excitons. The implications for exciton condensation in several material classes with strongly correlated electrons are discussed.
Building on the work by Florens and Georges [Phys. Rev. B 70, 035114 (2004)], we formulate and study a self-consistent slave rotor mean-field theory for strongly correlated systems. This approach views the electron, in the strong correlation regime, as a composite of a neutral spinon and a charged rotor field. We solve the coupled spinon-rotor model self-consistently using a cluster mean-field theory for the rotors and various Ans\"atze for the spinon ground state. We illustrate this approach with a number of examples relevant to ongoing experiments in strongly correlated electronic systems such as (i) the phase diagram of the isotropic triangular lattice organic Mott insulators, (ii) quasiparticle excitations and tunneling asymmetry in the weakly doped cuprate superconductors, and (iii) the cyclotron mass of carriers in commensurate spin-density wave and U(1) staggered flux (or ddd-density wave) normal states of the underdoped cuprates. We compare the estimated cyclotron mass with results from recent quantum oscillation experiments on ortho-II YBa2Cu3O6.5\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.5}YBa2​Cu3​O6.5​ by Doiron-Leyraud et al. [Nature (London) 447, 565 (2007)] which appear to find Fermi pockets in the magnetic field induced normal state. We comment on the relation of this normal ground state to Fermi arcs seen in photoemission experiments above Tc{T}_{c}Tc​. This slave rotor mean-field theory can be generalized to study inhomogeneous states and strongly interacting models relevant to ultracold atoms in optical lattices.
A new mean field theory is proposed for the Mott transition in the Hubbard model based on the slave rotor representation of the electron operator. This theory provides a better description of the role of the long range charge correlation in the Mott insulating state and offers a good estimation of the critical correlation strength for the Mott transition. We have constructed a new variational wave function for the Mott insulating state based on this new slave rotor mean field theory. We find this new variational wave function outperforms the conventional Jastrow type wave function with long range charge correlator in the Mott insulating state. It predicts a continuous Mott transition with non-divergent quasiparticle mass at the transition point. We also show that the commonly used on-site mean field decoupling for the slave rotor corresponds to the Gutzwiller approximation for the Gutzwiller projected wave function with only on-site charge correlator, which can not describe the Mott transition in any finite dimensional system.
Excitons are bound electron-hole pairs in semiconductors whose interactions influence optical properties and determine their collective behavior and emergent correlated phases. Despite the theoretical and experimental significance of these phenomena, a microscopic theory of exciton-exciton interactions that takes into account the full composite nature of these quasiparticles in systems with an arbitrary single-particle Hamiltonian is lacking. Here, we present a general theory of exciton-exciton interactions that builds upon our previous publication [Physical Review B 113, 155440 (2026)], which applied only to conventional semiconductors with weak band hybridization. By contrast, the theory presented here is valid in virtually any crystalline semiconducting system and can be applied to the study of biexciton formation and correlated excitonic phases in systems where band topology, quantum geometry, and moiré effects play a significant role. In addition to the analytical theory, we also present results in simple systems with flat bands with a nontrivial quantum metric and show that the biexcitonic spectrum differs strongly from that in the case without quantum geometry. Our theory paves the way for accurate quantitative calculations of biexciton spectra and excitonic many-body phases in modern condensed-matter systems.
The treatment of intershell interactions remains a major challenge in the theoretical description of strongly correlated materials. Most previous approaches considered the influence of intershell interactions at best in a static fashion, neglecting dynamic effects. In this paper, we propose a slave-rotor method that goes beyond this approximation by incorporating the effect of intershell interactions in a dynamic manner. Our method is derived and implemented as a quantum impurity solver in the context of dynamical mean field theory and benchmarked on a two-orbital model system. The results from our slave-rotor technique are found to be in good agreement with our reference calculations that include intershell interactions explicitly. We identify and analyze qualitative features emerging from the dynamic treatment. Our results thus provide qualitative new insights, revealing the ambivalent effect of intershell interactions in strongly correlated materials.