QUANTUM TUNNELING EFFECTS IN THE SSH MODEL OF ELECTRON-PHONON INTERACTIONS

Abstract

We examine the Su-Schrieffer-Heeger (SSH) model of electron-phonon (e-p) interactions as an example of a theory in which commensurate and incommensurate bond-order wave (BOW) ground states are generated (in the quasi-one-dimensional (quasi 1-D) case) by an intersite e-p coupling. We focus primarily on the two-fold commensurate situation, in view of its applicability to the important quasi 1-D conducting polymer trans-polyacetylene (trans — (CH) x). Using a coherent state formalism to model the quantum fluctuation corrections to the adiabatic ground state, we study the quantum tunneling of the SSH “solitons” (viewed as discommensurations created in the two-fold commensurate ground state) and show that, as a result of this tunneling, the energy of the discommensurations can become negative for e-p couplings below a certain critical coupling. We argue that this negative defect energy is an indication of the instability of the underlying adiabatic commensurate BOW state. The critical e-p coupling for this transition depends on the phonon frequency and, for general commensurability, on the commensurability ratio. Thus, in real trans — (CH) x chains where the e-p coupling and the bare phonon frequency are fixed, the transition we describe can occur as a function of doping (which can change the effective commensurability) and may explain the BOW-to-quasimetal transition in doped (CH) x. For quasi-1-D systems, we also estimate the critical e-p couplings for the three-fold commensurate and incommensurate cases. We conclude by mentioning possible extensions of our approach and results to the new family of “fullerenes”, C n(n≥60).