Exact solution of an exciton energy for a monolayer medium
Ramazan Şahin, PhD · · 1 min read · Updated
Exact energy solutions for two interacting relativistic fermions in 2+1 dimensions, applied to excitons in a free-standing monolayer.
The paper derives exact solutions for the energy spectrum of two interacting particles treated as relativistic fermions in 2+1-dimensional space-time. Starting from the 2×2 spinor equations for two fermions bound by a general central potential, the authors separate relative and centre-of-mass motion covariantly, reduce the coupled first-order radial equations to one second-order equation and solve it for the Coulomb potential.
The solution is then applied to excitons in a free-standing monolayer. Because the exciton is modelled as an isolated pair of interacting fermions, outside influences such as a substrate are left out. The binding energies obtained agree with values reported in the literature, and the exciton's decay time also emerges directly from the calculation.
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