EXCITON ENERGIES IN TITANIUM TRISULFIDE MONOLAYERS: A SECOND-ORDER PERTURBATION THEORY APPROACH
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Abstract
Numerical methods have been widely used to calculate exciton energies in anisotropic semiconductors. This study develops an analytical framework based on perturbation theory for monolayer titanium trisulfide (TiS3). Because conventional perturbation theory does not accurately describe anisotropic systems, we use a regularized perturbation approach. First, a spatial scaling transformation maps the kinetic anisotropy of the Hamiltonian onto the Rytova-Keldysh potential. A Levi-Civita transformation then converts the Schrödinger equation into an anharmonic oscillator representation, which is formulated algebraically using quantum creation and annihilation operators. This framework allows the matrix elements to be derived analytically. We then construct analytical expressions for energy corrections up to second order. Numerical tests show that most deviations of the second-order results from high-accuracy numerical data are below 1.0 meV. These findings support the use of second-order perturbation theory to derive analytical expressions for exciton energies in anisotropic semiconductor monolayers.
Keywords
algebraic formulation, analogous creation and annihilation operators, anisotropic semiconductors, monolayer titanium trisulfide, regularized perturbation theory
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References
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