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International Journal of Modern Physics B

SURFACE POLARON WITH A BARRIER POTENTIAL: UPPER BOUND TO THE GROUND-STATE ENERGY

Nikolay N. Bogolubov, Alexey N. Kireev

Published Feb 15, 1996• 0 citations
Publisher

Abstract

A general variational method is proposed for investigating the surface polaron ground state valid for any coupling strength of an electron-surface-optical-phonon interaction and for any height of a barrier potential at the crystal boundary. The ground states of the surface polaron at the infinitely high barrier potential and of the surface polaron without the barrier potential are considered. The properties of the surface polarons are discussed in comparison with the bulk polaron theory.

DOI
10.1142/s0217979296000192

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A general variational method is proposed for investigating the surface polaron ground state valid for any coupling strength of an electron-surface-optical-phonon interaction and for any height of a barrier potential at the crystal boundary. The ground states of the surface polaron at the infinitely high barrier potential and of the surface polaron without the barrier potential are considered. The properties of the surface polarons are discussed in comparison with the bulk polaron theory.
The ground-state characterization of the polaron problem is retrieved within the framework of a variational scheme proposed previously by Devreese et al for the bound polaron. The formulation is based on the standard canonical transformation of the strong coupling ansatz and consists of a variationally determined perturbative extension serving for the theory to interpolate in the overall range of the coupling constant. Specializing our considerations to the bulk and strict two-dimensional polaron models we see that the theory yields significantly improved energy upper bounds in the strong coupling regime and, moreover, extrapolates itself successfully towards the well-established weak coupling limits for all polaron quantities of general interest.
The optical polaron bounded in a Coulomb potential is investigated within the modified variational scheme of the Lee-Low-Pines theory (1953) which is valid for the whole range of the electron-phonon coupling. The ground state energy, the mean number of phonons in the cloud around the electron and the spatial localisation of the electron for the optical polaron change abruptly at certain values of the electron-phonon coupling constant alpha and of the Coulomb potential beta . The polaron changes its state according to the values of the parameters alpha and beta . Such features are summarised in the phase diagram.
An upper bound to the ground-state energy of a tight-binding polaron (a polaron in a narrow band material) in a polar crystal is obtained, in the nonadiabatic limit, from a Hamiltonian that includes two contributions to the electron–phonon coupling: a short-range deformation potential interaction and a long-range dipolar interaction. A Debye cutoff on the phonon wave vectors is also assumed. A variational ground-state energy is deduced, using a modification of a tight-binding type Ansatz used in small-polaron theory, in the nonadiabatic limit. In the weak-coupling limit the ground state corresponds to that of a large polaron, while the strong-coupling limit gives a small-polaron state. The bandwidth greatly influences the state of the system and phase diagrams are presented that show the regions where the small and the large polarons are energetically favored. We find, in this variational context, that for a narrow band, the transition between the self-trapped state and the band state is continuous and that an intermediate-polaron state is involved. For a larger but moderate bandwidth, the system is found to switch abruptly from one state to the other, with a coexistence of both states around the transition region. Each of the two types of coupling is found to have an equivalent role in increasing the trapping energy of the electron and in reducing the bandwidth exponentially. Furthermore, their effect is cumulative.
We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest computational resources (12-digit accuracy for the one-dimensional polaron energy at intermediate coupling). We compute ground-state and low-lying excited-state properties of the model at continuous values of the wave vector k in essentially all parameter regimes. Our results for the polaron energy band, effective mass, and correlation functions compare favorably with those of other numerical techniques, including the density-matrix renormalization-group technique, the global-local method, and the exact diagonalization technique. We find a phase transition for the first excited state between a bound and unbound system of a polaron and an additional phonon excitation. The phase transition is also treated in strong-coupling perturbation theory.