Topological Quantum Phases in Organic Batteries: Analysis of the SSH-Extended Hubbard Model
Abstract
Topological phases of matter show that quantum states can be classified through global topological invariants rather than conventional local order parameters. Although the theory of non-interacting topological phases is now well established, understanding the fate of topological invariants in the presence of strong electron-electron interactions remains a central challenge. This thesis addresses this issue through a unified theoretical framework applied to sp²-hybridized organic materials, namely cyclooctatetraene rings and poly-bi-[8]-annulenylene. These systems are described within the Su-Schrieffer-Heeger Extended Hubbard Model, and their topological properties are investigated using three complementary approaches spanning different interaction regimes: a Green’s-function formalism valid for arbitrary interaction strengths, a mean-field treatment incorporating interaction-renormalized hopping amplitudes, and a strong-coupling mapping onto a Heisenberg model. The interaction parameters are determined from first principles using the HP module of Quantum ESPRESSO, yielding U = 3.4506eV, V_intra = 0.4262eV, V_inter = 0.2331eV. These values place the polymers within the Mott-spin-density-wave (Mott-SDW) regime. However, they are not universal, as they depend on the choice of pseudopotential and projector. Furthermore, the interaction asymmetry, V_intra =/= V_inter, which originates from the bond alternation inherent to the COT ring, is the principal interaction-driven mechanism that shifts the system toward the topological phase boundary. Finally, this work links topological properties to the electrochemical performance of these materials as battery electrodes and points to applications of COT-based polymers in molecular electronics, LEDs, and rechargeable energy storage.
Mohamed Taha Rouabah
Associate Professor of Physics
ARISE Fellow, Principal Investigator at Constantine Quantum Technologies, Associate Professor at University of Constantine 1 (Algeria).