Abstract
Among quantum phenomena in solids at low temperatures, the superconductivity and Bose–Einstein condensation (BEC) are representatives of arising from coherent macroscopic quantum states. In this article, we discuss possible correlations between these two phenomena. It is well known that the Cooper pairs are not true bosons and then, we introduce the concept of collective electron pairs (CEP) through a unitary transformation of electron pairs. The CEP accomplish bosonic commutation relations at the dilute limit, being able to accumulate many of them at a single quantum state, in contrast to the standard Cooper pairs. An exact solution of all single CEP eigenstates is found by means of the Richardson’s equation within a multishell model. The obtained energy spectrum is used to determine the BEC temperature of CEP. In addition, we present an alternative approach to calculate the superconducting critical temperature by using the BEC formalism for a system composed by ground-state CEP, excited pairs and unpaired electrons.
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