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Journal of Physics C Solid State Physics

Polaron density of states of a hole in a narrow band of an alternate lattice of fermions

Gilles Montambaux

Published Jul 30, 1982• 0 citations
Publisher

Abstract

Studies the problem of a single hole propagating in an alternative lattice of fermions, in the atomic limit of the Hubbard model, for inhomogeneous spin configurations. An estimate of the band shape is deduced from the development of the Green function. It seems that in a spin polaron configuration, the band presents peaks at the extremities. Such peaks stabilise the polaron state.

DOI
10.1088/0022-3719/15/21/017

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Studies the problem of a single hole propagating in an alternative lattice of fermions, in the atomic limit of the Hubbard model, for inhomogeneous spin configurations. An estimate of the band shape is deduced from the development of the Green function. It seems that in a spin polaron configuration, the band presents peaks at the extremities. Such peaks stabilise the polaron state.
The problem of the single-hole motion in a two-dimensional quantum Heisenberg antiferromagnet is examined in the t-J model. By introducing a kind of slave-fermion representation for Hubbard operators a hole is treated as a spinless fermion strongly interacting with spin-1/2 degrees of freedom. We suggest an analytic approach based on a decoupling procedure for two-time fermionic Green functions that allows us to describe a hole as a magnetic polaron of a minimal size (i.e., involving one-step ``string'' spin excitations) and reproduce the main features characteristic of a one-hole band in a quantum antiferromagnet. A generalization of the procedure in the spirit of the Lanczos approach to extend the internal structure of the magnetic polaron is discussed.
We discuss the approximate calculation of a Green's function and its spectral density from its low-order moments by the use of ratio-extrapolation techniques to estimate and factor off the dominant shape of the band edges. The techniques are illustrated, following Brinkman and Rice, on the problem of a single hole propagating in ferromagnetic, antiferromagnetic, and random electron-spin configurations in the atomic limit of the Hubbard model; the methods are, however, of wider applicability.
We consider a Hubbard model in which electrons are locally coupled to the lattice and form polarons. The frequency-dependent polaron conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{pot}}$(\ensuremath{\omega}) is calculated in the narrow-band limit as a function of electron density. There are two contributions: a band term that arises from coherent motion of dressed electrons and a hopping term that describes the incoherent process by which electrons ``shake off'' their polaron distortion. The possible relevance of these results to the structure in \ensuremath{\sigma}(\ensuremath{\omega}) observed in high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors is briefly discussed.
The interactions between holes in the Hubbard model, in the low density, intermediate- to strong-coupling limit, are investigated by systematically improving mean field calculations. The configuration-interaction basis set is constructed by applying to local unrestricted Hartree-Fock configurations all lattice translations and rotations. It is shown that this technique reproduces, correctly, the properties of the Heisenberg model, in the limit of large U. Upon doping, dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. The numerical results also show that when more than two holes are added to the system, they do not tend to cluster, but rather hole pairs remain far apart. Hole-hole correlations are also calculated and shown to be in qualitative agreement with exact calculations for $4\ifmmode\times\else\texttimes\fi{}4$ clusters. In particular our results indicate that for intermediate coupling the hole-hole correlation attains a maximum when the holes are in the same sublattice at a distance of 2\sqrt{2}2​ times the lattice spacing, in agreement with exact results and the $t\ensuremath{-}J$ model. The method is also used to derive known properties of the quasiparticle band structure of isolated spin polarons.
We consider a narrow one-dimensional tight-binding chain with intra-atomic Coulomb repulsions described in the Hubbard model. The electrons at each site are furthermore assumed to be coupled to a high-frequency local oscillator. In the limit where the oscillator frequency is large compared to the bandwidth, and in the extreme-band-narrowing regime, for various electron densities, we find that: the half-filled-band ground state is an antiferromagnetic insulator; the one-third-filled-band ground state is a diamagnetic insulator; and the one-quarter-filled-band ground state is a weakly coupled system of bound singlet pairs somewhat reminiscent of superconductivity.
The motion of a single hole in a two-dimensional Heisenberg antiferromagnet (hAF) is studied in a representation where holes are described as spinless fermions (holons) and spins as normal bosons. Assuming long-range AF order the spin dynamics is treated in linear spin-wave theory. The formulation highlights the close relation with the conventional polaron problem. The holon Green's function is calculated self-consistently within the Born approximation using finite-cluster geometries for the numerical solution. As a remarkable result we find close agreement with the spectral function A(k,\ensuremath{\omega}) of a hole calculated by exact diagonalization methods. A(k,\ensuremath{\omega}) is characterized by a narrow quasiparticle (QP) peak at the low-energy side of the spectrum, which is well separated from the incoherent part for large enough J values. A complete characterization of our solution is given, including the spectral weight, the dispersion relation, and effective masses of the QP state. A finite-size-scaling study gives a nonvanishing spectral weight of the QP in the thermodynamic limit for values J/t typical for copper oxide superconductors. Our calculations indicate that the self-consistent Born approximation is a valuable scheme for characterizing the dynamics of a hole in the t-J model, even in the strong-coupling regime.