Excitonic versus electron-hole liquid phases in Tm[Se,Te] compounds

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We discuss, from a theoretical point of view, excitonic phases at the pressure induced semiconductor-semimetal transition in TmSe₀.₄₅Te₀.₅₅,focusing, in particular, on the stability against an electron-hole liquid. The electron-hole pair density parameter rₛ(Eg,T) is calculated within the quasi-static plasmon pole approximation as a function of temperature T and energy gap Eg and converted into -Eg(rₛ,T). A comparison of this quantity, which is the electron-hole pair chemical potential, with the exciton binding energy reveals that excitons should be suppressed in contrast to experimental evidence for excitonic phases. We suspect therefore inter-valley exciton scattering and exciton-phonon scattering to substantially stabilise excitons in TmSe₀.₄₅Te₀.₅₅.