A fresh view on Frenkel excitons: Electron-hole pair exchange and many-body formalism

Abstract

We here present a fresh approach to Frenkel excitons in cubic semiconductor crystals, with a special focus on the spin and spatial degeneracies of the electronic states. This approach uses a second quantization formulation of the problem in terms of creation operators for electronic states on all lattice sites -- their creation operators being true fermion operators in the tight-binding limit valid for semiconductors hosting Frenkel excitons. This operator formalism avoids using cumbersome ($6N_s$ x $6N_s$) Slater determinants -- 2 for spin, 3 for spatial degeneracy and $N_s$ for the number of lattice sites -- to represent state wave functions out of which the Frenkel exciton eigenstates are derived. A deep understanding of the tricky Coulomb physics that takes place in the Frenkel exciton problem, is a prerequisite for possibly diagonalizing this very large matrix analytically. This is done in three steps: (i) the first diagonalization, with respect to lattice sites, follows from transforming excitations on the $N_s$ lattice sites ${\mathbf{R}}_{\ell }$ into $N_s$ exciton waves ${\mathbf{K}}_n$, by using appropriate phase prefactors; (ii) the second diagonalization, with respect to spin, follows from the introduction of spin-singlet and spin-triplet electron-hole pair states, through the commonly missed sign change when transforming electron-absence operators into hole operators; (iii) the third diagonalization, with respect to threefold spatial degeneracy, leads to the splitting of the exciton level into one longitudinal and two transverse modes, that result from the singular interlevel Coulomb scattering in the small ${\mathbf{K}}_n$ limit.

80 pages, 21 figures

References in corpus (6)

• Microscopic derivation of Frenkel excitons in second quantization
• Composite boson many-body theory for Frenkel excitons
• Signature of electromagnetic quantum fluctuations in exciton physics
• Ground state energy of N Frenkel excitons
• Missing understanding of the phase factor between valence-electron and hole operators
• Effect of Pauli blocking on coherent states of composite bosons

Cited by in corpus (1)

• Squeezed states for Frenkel-like two-fermion composite bosons