View Single Post
hesky
#1
Jan12-12, 08:03 AM
P: 7
Please help me, I need to derive exciton-photon interaction.
Here, we are using second quantization. Please refer to this paper http://prb.aps.org/abstract/PRB/v75/i3/e035405
Hamiltonian of electron-photon is
[itex]H_{el-op}=\sum_k D_k c^+_{kc}c_{kv}(a+a^+)[/itex]

[itex]c^+_{kc}c_{kv}[/itex] are creation of electron to conduction band and annihilation electron in valence band, respectively. [itex](a+a^+)[/itex] are photon annihilation and creation operator.
Exciton wave function is
[itex] |\Psi^f\rangle=\sum_k Z^n_{k_{c},k_v}c^+_{k_{c}}c_{k_v}|0\rangle [/itex]
Where Z is weighting coefficient, kc is electron state (conduction band), kv is hole state (valence band), and [itex]|0\rangle [/itex] is ground state (all electrons occupy valence) band.

Matrix element of exciton-photon is defined as
[itex] M_{ex-op}=\langle\Psi^f|H_{el-op}|0\rangle[/itex]

[itex]M_{ex-op}=\sum_k Z^{n*}_{k_{c},k_v}D_k\langle 0|a+a^+|0\rangle[/itex]
My question is, how can we prove that [itex] \langle 0|a+a^+|0\rangle=1[/itex] to get

[itex]M_{ex-op}=\sum_k Z^{n*}_{k_{c},k_v}D_k [/itex]
Phys.Org News Partner Physics news on Phys.org
Working group explores the 'frustration' of spin glasses
New analysis of oxide glass structures could guide the forecasting of melt formation in planetary interiors
Scientists characterize carbon for batteries