Exciton energy in monolayer titanium trisulfide from second-order perturbation theory
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Abstract
While numerical methods have been widely established for determining exciton
energies in various anisotropic semiconductors, this work introduces a rigorous analytical
framework based on perturbation theory, specifically tailored for monolayer titanium
trisulfide (TiS3). Recognizing the limitations of conventional perturbation theory in
accurately capturing the physics of anisotropic systems, we implement a regularized
perturbation approach. Our methodology commences with a spatial scaling transformation
that maps the kinetic anisotropy of the Hamiltonian onto the Keldysh potential.
Subsequently, a Levi-Civita transformation is employed to recast the Schrödinger equation
into an anharmonic oscillator representation, which is then formulated algebraically using
quantum creation and annihilation operators. This framework facilitates the systematic
analytical derivation of the matrix elements. By applying this regularized approach, we
construct analytical expressions for energy corrections up to the second order. Numerical
benchmarks demonstrate that our second-order results achieve remarkable precision, with
deviations from high-accuracy numerical data remaining (mostly below 1.0 meV). These
findings underscore the efficacy of the proposed method, establishing it as a robust
foundation for the analytical characterization of excitonic properties in emerging two –
dimensional anisotropic semiconductors.