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arXiv:1202.3616 · New Journal of Physics

Dynamics of a single exciton in strongly correlated bilayers

Louk Rademaker, Kai Wu, Jan Zaanen

Published Aug 31, 2012• 9 citations
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Abstract

We formulated an effective theory for a single interlayer exciton in a bilayer quantum antiferromagnet, in the limit when the holon and doublon are strongly bound onto one interlayer rung by the Coulomb force. Upon using a rung linear spin-wave approximation of the bilayer Heisenberg model, we calculated the spectral function of the exciton for a wide range of the interlayer Heisenberg coupling α = J ⊥ / Jz . In the disordered phase at large α , a coherent quasi-particle peak appears, representing free motion of the exciton in a spin singlet background. In the Néel phase, which applies to more realistic model parameters, a ladder spectrum arises due to Ising confinement of the exciton. The exciton spectrum is visible in measurements of the dielectric function, such as c -axis optical conductivity measurements.

DOI
10.1088/1367-2630/14/8/083040

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We formulated an effective theory for a single interlayer exciton in a bilayer quantum antiferromagnet, in the limit when the holon and doublon are strongly bound onto one interlayer rung by the Coulomb force. Upon using a rung linear spin-wave approximation of the bilayer Heisenberg model, we calculated the spectral function of the exciton for a wide range of the interlayer Heisenberg coupling α = J ⊥ / Jz . In the disordered phase at large α , a coherent quasi-particle peak appears, representing free motion of the exciton in a spin singlet background. In the Néel phase, which applies to more realistic model parameters, a ladder spectrum arises due to Ising confinement of the exciton. The exciton spectrum is visible in measurements of the dielectric function, such as c -axis optical conductivity measurements.
We formulated an effective theory for a single interlayer exciton in a bilayer quantum antiferromagnet, in the limit that the holon and doublon are strongly bound onto one interlayer rung by the Coulomb force. Upon using a rung linear spin wave approximation of the bilayer Heisenberg model, we calculated the spectral function of the exciton for a wide range of the interlayer Heisenberg coupling α = J⊥/Jz. In the disordered phase at large α, a coherent quasiparticle peak appears representing free motion of the exciton in a spin singlet background. In the N´eel phase, which applies to more realistic model parameters, a ladder spectrum arises due to Ising confinement of the exciton. The exciton spectrum is visible in measurements of the dielectric function, such as c-axis optical conductivity measurements.
We develop a nonequilibrium multi-orbital extension of the two-particle self-consistent theory and apply it to the bilayer Hubbard model as a minimal platform to investigate correlation effects in the presence of interlayer interactions and tunneling. The method determines vertex corrections in the spin and charge channels self-consistently at the two-particle level, thereby avoiding the spurious finite-temperature phase transitions that limit dynamical mean-field theory in two dimensions. We derive the spectral self-energy and implement the framework directly on the real-frequency axis within the Keldysh nonequilibrium Green's function formalism, enabling the treatment of both equilibrium and non-equilibrium steady states without relying on numerical analytic continuation. As an application, we demonstrate that a pseudogap can emerge in the bilayer Hubbard model when spin, charge, or excitonic fluctuations become sufficiently strong. Instabilities in different channels are also evaluated in an unbiased manner across the parameter space. Remarkably, we find that the excitonic susceptibility grows with increasing interlayer bias, before it gets suppressed at large biases by the charge imbalance between the layers. This work establishes a versatile and computationally efficient framework for investigating correlated multi-orbital systems under nonequilibrium conditions.
We studied the possibility of exciton condensation in Mott insulating bilayers. In these strongly correlated systems, an exciton is the bound state of a double occupied and empty site. In the strong coupling limit, the exciton acts as a hard-core boson. Its physics is captured by the exciton ttt-JJJ model, containing an effective XXZXXZXXZ model describing the exciton dynamics only. Using numerical simulations and analytical mean-field theory, we constructed the ground-state phase diagram. Three homogeneous phases can be distinguished: the antiferromagnet, the exciton checkerboard crystal, and the exciton superfluid. For most model parameters, however, we predict macroscopic phase separation between these phases. The exciton superfluid exists only for large exciton hopping energy. Additionally, we studied the collective modes and susceptibilities of the three phases. In the superfluid phase, we find the striking feature that the bandwidth of the spin-triplet excitations, potentially detectable by resonant inelastic x-ray scattering (RIXS), is proportional to the superfluid density. The superfluid phase mode is visible in the charge susceptibility, measurable by RIXS or electron energy loss spectroscopy (EELS).
The two-layer square lattice quantum antiferromagnet with spins 12\frac{1}{2}21​ shows a magnetic order-disorder transition at a critical ratio of the interplane to intraplane couplings. We investigate the dynamics of a single hole in a bilayer antiferromagnet described by a $t\ensuremath{-}J$ Hamiltonian. To model the spin background we propose a ground-state wave function for the undoped system that covers both magnetic phases and includes transverse as well as longitudinal spin fluctuations. The photoemission spectrum is calculated using the spin-polaron picture for the whole range of the ratio of the magnetic couplings. This allows for the study of the hole dynamics on both sides of the magnetic order-disorder transition. For small interplane coupling we find a quasiparticle with properties known from the single-layer antiferromagnet, e.g., the dispersion minimum is at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).$ For large interplane coupling the hole dispersion is similar to that of a free fermion (with reduced bandwidth). The crossover between these two scenarios occurs inside the antiferromagnetic phase, which indicates that the hole dynamics is governed by the local environment of the hole.
A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon interlayer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping ${\ensuremath{\delta}}_{c}$ due to the formation of excitons. A spin-liquid-insulator (SLI) phase is thus realized without the lattice frustration. The critical value ${\ensuremath{\delta}}_{c}$ sensitively depends on the interlayer interaction strength. In the $t\text{\ensuremath{-}}J$ model description of each layer with the ddd-wave pairing, ${\ensuremath{\delta}}_{c}$ marks the crossover between SLI and ddd-wave superconductor. The SLI phase, despite being nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the $t\text{\ensuremath{-}}J$ model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.
This work investigates the exciton property of the bilayer Hubbard model by using the con- strained-path Monte Carlo method. The calculated results show that when the doping density is lower than 0.08, the local exciton characterized by interlayer single particle tunneling is enhanced by the interlayer Coulomb interaction V, and the enhancement becomes stronger with decreasing the doping density. However, when the doping density is higher than 0.08, the local exciton is sup- pressed by V. This result exhibits significant differences from the published results at finite tem- peratures. Further analysis shows that the long-range exciton correlation function is reduced with increasing V, demonstrating that there does not exist exciton condensation in the studied model. In addition, the interlayer Coulomb interaction V is shown to have a rather weak effect on local magnetic moment.