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Franz X. Bronold and Holger Fehske
The possibility of an excitonic insulator (EI), separating, below a critical temperature, a semiconductor (SC) from a semimetal (SM), has been anticipated by theorists more than three decades ago. Experimental efforts, however, to establish this phase largely failed. It is only until recently, that experimental studies of the SC/SM transition in Tm[Te,Se] and related chalcogenide alloys (which is controlled by a pressure-sensitive indirect energy gap/overlap E_g) suggested the existence of an EI.In particular, the increase of the electrical resistivity in a narrow pressure range around 8 kbar [1] strongly pointed towards an (almost room temperature) EI. The linear increase of the thermal diffusivity below 10K revealed moreover a condensate at low temperatures [2]. The interpretation of the experimental data is however not generally accepted because it is based on a crude pairing theory valid only for T=0. Excitons outside the condensate, e.g., are completely ignored. These excitons, however, must play an important role at the temperatures of the experiments. In fact, we show that the experimentally observed ``high-temperature EI'' is a non-degenerate gas of excitons which at low enough temperatures becomes degenerate and enters a condensate in the sense of Bose-Einstein condensation. Our theory is based on a two-band model for valence and conduction band electrons interacting via long-range Coulomb forces. Employing a matrix propagator formalism, we derived, within a (screened) T-matrix approximation for the selfenergy, a selfconsistency equation for the anomalous (off-diagonal) selfenergy, which serves as an order parameter, and an equation for the chemical potential. These two equations enable us to probe the stability of the condensed phase versus (i) a Fermi gas of unbound electrons and holes and (ii) a gas of excitons. The former gives the phase boundary T_EI(E_g) of the EI at the scale of the dissociation energy of an exciton, whereas the latter determines the phase boundary T_C(E_g) << T_EI(E_g) of the condensate. Taking moderate polaron effects phenomenologically into account, we obtained good agreement with the experimental data and conclude that an EI has been finally found [3]. [1] J. Neuenschwander and P. Wachter, Phys.Rev.B 41 (1990) 12693. [2] P. Wachter, B. Bucher, and J. Malar, Phys. Rev. B 69 (2004) 094502. [3] F. X. Bronold and H. Fehske, in preparation. |
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