Electrostatically-induced topological phase transitions in polyacetylene molecules

Abstract

We study the electronic properties of a linear trans-polyacetylene (tPA) molecule capacitively coupled to an external gate voltage $V_g$ of width $d$. We describe this system using the Takayama-Lin-Liu-Maki (TLM) model in the continuum, and analyze it within the Abelian bosonization formalism, which allows us to treat both electronic and lattice degrees of freedom and to incorporate the effects of repulsive Coulomb interactions among electrons. The global ground state describing simultaneously the electronic charge-density field as well as the lattice dimerization field of a tPA molecule is shown to consist of multikink solutions of a modified sine-Gordon equation for the charge-density field, which is controlled by $V_g$, the width $d$, and the Luttinger parameter $K$ encoding the strength of electron-electron interactions. These solutions belong to distinct topological sectors labeled by an integer invariant $q$ that simultaneously quantifies both the bound charge and the number of domain walls in the dimerization pattern induced at the gated region. Increasing $V_g$ drives a sequence of topological phase transitions characterized by abrupt changes in $q$. We further examine the effect of repulsive Coulomb interactions on the resulting topological phase diagram, and finally, we discuss the relevance of our findings for potential nanoelectronic devices based on gated tPA molecules.

Figures (5)

• Figure 1: (Color online) (a) Schematic representation of the device. A linear tPA molecule capacitively coupled to a potential gate. The dotted lines represent the formation of DWs. (b) Electrostatic potential well of width $d$ and depth $V_g$ induced by the gate.
• Figure 2: (Color online) Solutions in the topological sector $q=1$ (induced charge $Q=-e$). (a) Profiles of three different solutions of Eq. (\ref{['eq:EOM phic final']}) obtained for fixed $d=2\xi_c$ and for different values of $\xi_c/\xi_g$. (b) The associated charge densities $\rho_c(c)$. In both plots, the gray-shaded region denotes the region $R_2$ (gated region). By smoothly varying the gate potential $V_g$ the shape of the solutions changes smoothly, but the topological properties remain unchanged. Dataset available in Ref. dataset
• Figure 3: (Color online) Ground-state configuration of the field $\phi_c(x)$ and the associated (staggered) lattice dimerization field $\Delta(x)$, obtained for different values of the gate potential $V_g$. As $V_g$ is increased, a sequence of topological phase transitions are produced, in which the value $\phi_c(-L/2)$ jumps in units of $\sqrt{2}/\pi$ while simultaneously a new DW appears in the gated region (gray-shaded areas). Dataset available in Ref. dataset
• Figure 4: (Color online) (a) Dimensionless ground-state energy $\epsilon_\text{gs}$ and (b) total induced charge $Q$ as functions of the ratio $\xi_c/\xi_g \sim V_g$ for fixed $d=2\xi_c$. In panel (a), the solid lines correspond to the ground-state energy in a given topological sector, whereas the dashed lines correspond to the first excited state. Topological quantum phase transitions occur at critical voltages where energy levels cross. Whenever this transition occurs,the total charge $Q$ changes jumps by $-e$. Dataset available in Ref. dataset
• Figure 5: (Color online) Topological phase diagram in the $(d/\xi_c,\xi_c/\xi_g)$ plane. Each coloured region corresponds to a different topological sector. The black line corresponds to a parametric curve generated as the parameters $d/\xi_c$ and $\xi_c/\xi_g$ get renormalized by the interaction parameter $g$ [see Eqs. (\ref{['eq:xic_renormalized']})-(\ref{['eq:xic_xig_renormalized']})], where the arrow indicates de direction in which $g$ increase. Dataset available in Ref. dataset