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The condition for the occurrence of excitonic phases is examined. It is shown that even for a simple band structure of two isotropic conduction band minima and a single isotropic valence band maximum the excitonic phase occurs only when the effective mass of an electron is 0.7 times heavier than that of a hole and that the condition for occurrence of excitonic phases becomes more severe for more complicated band structures. It is suggested that the first order semiconductor-semimetal transition bypassing excitonic phases is likely to occur in many real indirect gap semiconductors when one reduces the energy gap continuously.
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Kamimura et al. (2013) studied this question.
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