On the phase transitions for the electronic excitations in semiconductors |
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Authors: | H Haug |
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Institution: | (1) Institut für Theoretische Physik, Universität Frankfurt/Main, Robert-Mayer-Straße 8, D-6000 Frankfurt/Main, Germany |
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Abstract: | A model Hamiltonian for a system of interacting electrons, holes and Wannier excitons is derived. This system of electronic excitations is assumed to be in a quasi-equilibrium state. With the aid of Bogolubov's variational principal the thermodynamic potential is calculated. Using the most general mean-field Hamiltonian as a trial Hamiltonian, a set of coupled integral equations is obtained for the self-energies. These equations are solved numerically for equal effective masses of the electrons and holes. Below a critical temperature ofk
B
T
c 0.65E
ex
b
whereE
ex
b
is the exciton binding energy, we find a first order phase transition from an exciton rich phase into a degenerate electron-hole phase. The mechanical and thermal stability of both phases is proven. Below a critical temperaturek
B
T
c 0.11E
ex
b
the exciton system becomes degenerate (Bose-Einstein condensation). A complete phase diagram of these three phases is given.This is a project of the Sonderforschungsbereich Frankfurt/Darmstadt, financed by special funds of the Deutsche Forschungsgemeinschaft |
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Keywords: | |
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