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physica status solidi (b)

Large Polarons in the Discrete SSH Model

R. Ruckh, E. Sigmund

Published May 1, 1988• 0 citations
Publisher

Abstract

Abstract Stationary polaron solutions are derived for the discrete version of the Su‐Schrieffer‐Heeger (SSH) model in two different ways. First Holstein's large polaron theory is applied. Second, the polaron solution is derived from Heisenberg's equations of motion. It turns out that the results obtained from the continuum version of the SSH Hamiltonian are different from those obtained from Holstein's molecular crystal model (MCM).

DOI
10.1002/pssb.2221470126

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Abstract Stationary polaron solutions are derived for the discrete version of the Su‐Schrieffer‐Heeger (SSH) model in two different ways. First Holstein's large polaron theory is applied. Second, the polaron solution is derived from Heisenberg's equations of motion. It turns out that the results obtained from the continuum version of the SSH Hamiltonian are different from those obtained from Holstein's molecular crystal model (MCM).
We obtain analytical expressions for the large- and small-radius polarons on the one-dimensional lattice in the TBA approximation. The equations of motion for this model are treated classically for the oscillator subsystem, while a quantum description is used for the electron. The electron-phonon interaction is considered in the linear Su--Schrieffer--Heeger approximation. Good agreement between analytical formulae and accurate numerical simulation is obtained. The dynamics of polaron formation from different initial conditions is considered. Some features of the wave function evolution, governed by the finite lattice length, are elucidated.
Nondiagonal couplings to a bosonic bath completely change polaronic dynamics, from the usual diagonally coupled paradigm of smoothly varying properties. We study, using analytic and numerical methods, a model having both diagonal Holstein and nondiagonal Su-Schrieffer-Heeger (SSH) couplings. The critical coupling found previously in the pure SSH model, at which the k=0k=0k=0 effective mass diverges, now becomes a transition line in the coupling constant plane---the form of the line depends on the adiabaticity parameter. Detailed results are given for the quasiparticle and ground-state properties, over a wide range of couplings and adiabaticity ratios. The new paradigm involves a destabilization, at the transition line, of the simple Holstein polaron to one with a finite ground-state momentum, but with everywhere a continuously evolving band shape. No ``self-trapping transition'' exists in any of these models. The physics may be understood entirely in terms of competition between different hopping terms in a simple renormalized effective band theory. The possibility of further transitions is suggested by the results.
Su-Schrieffer-Heeger (SSH) electron-phonon ($e\ensuremath{-}p\phantom{\rule{0}{0ex}}h$) interactions have been theorized to play critical roles in several novel states of matter, ranging from nontrivial topological states to high-temperature bipolaronic superconductivity. This work compares the superconducting and competing charge and bond correlations of the two-dimensional Holstein and optical (SSH) models. The authors find that near half-filling, light SSH (bi)polarons support superconductivity to larger values of $e\ensuremath{-}p\phantom{\rule{0}{0ex}}h$ coupling compared to the Holstein polaron. These results are essential for identifying and engineering bipolaronic superconductivity in quantum materials.
Abstract The wave function and energy of the ground state of a lattice described by the Su–Schrieffer–Heeger Hamiltonian with a trap were found using three different methods. In the first of these methods, the energy of the ground state was calculated by numerical minimization of the energy functional. In the second, an auxiliary Hamiltonian was constructed, the diagonalization of which determined the energy of the ground state and the wave functions. And in the third, the wave function is completely restored analytically from the asymptotics of the wave function. All the three approaches produced results that agreed with an accuracy of 10–15.
We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength λ, in all models where this coupling depends only on phonon momentum q. In the SSH model the coupling also depends on the electron momentum k; we find it has a sharp transition, at a critical coupling strength λ(c), between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at λ=λ(c). This result is representative of all polarons with coupling depending on k and q, and will have important experimental consequences (e.g., in angle-resolved photoemission spectroscopy and conductivity experiments).
We analyze Su-Schrieffer-Heeger (SSH) models using the doubling method for orthogonal polynomial sequences. This approach yields the analytical spectrum and exact eigenstates of the models. We demonstrate that the standard SSH model is associated with the doubling of Chebyshev polynomials. Extending this technique to the doubling of other finite sequences enables the construction of Hamiltonians for inhomogeneous SSH models which are exactly solvable. We detail the specific cases associated with Krawtchouk and qqq-Racah polynomials. This work highlights the utility of polynomial-doubling techniques in obtaining exact solutions for physical models.