Universal behavior of the condensation energy of Superconducting BCS Bose gases

Using the Boson-Fermion formalism of superconductivity we calculate the condensation energy for several superconductors ranging from conventional to unconventional, or high temperature superconductors. It is calculated as the difference between the Helmholtz free energies of the superconducting and the normal state, which is a gas of N attractive electron gas, while the superconducting state is formed by the condensed Cooper pairs taken as composite bosons, coming from a fraction of the electrons inside the Debye shell, plus those electrons inside and outside the Debye shell that are unable to pair. After giving the analytic expressions for the internal energy U and the entropy S we obtain the Helmholtz free energy F = U -TS for both the superconducting and the normal states as functions of temperature. In the search for universalities, we calculate the ratio of the condensation energy at T=0 to the Sommerfeld constant (the normal state electronic specific heat over the temperature when T it's almost zero) using two different methods: the Boson-Fermion formalism developed here, as well as an analytical expression deduced from a combination of the BCS and Ginzburg-Landau theories. We find for the Boson-Fermion formalism $E_{cond}/γ_0= 0.252\,T_{c}^{1.997}$ , which is the same behavior described by the experimental fit of Kim et al $E_{cond}/γ_0= 0.2\,T_{c}^{2.06}$ and by the one recently reported by Tallon et al for overdoped cuprate superconductors; while for the Ginzburg-Landau-BCS we get the expression $E_{cond}/γ_0= 0.236\,T_{c}^{2}$ , also in very good agreement with the partifirst method.Using the Boson-Fermion formalism of superconductivity we calculate the condensation energy for several superconductors ranging from conventional to unconventional, or high temperature superconductors. It is calculated as the difference between the Helmholtz free energies of the superconducting and the normal state, which is a gas of N attractive electron gas, while the superconducting state is formed by the condensed Cooper pairs taken as composite bosons, coming from a fraction of the electrons inside the Debye shell, plus those electrons inside and outside the Debye shell that are unable to pair. After giving the analytic expressions for the internal energy U and the entropy S we obtain the Helmholtz free energy F = U -TS for both the superconducting and the normal states as functions of temperature. In the search for universalities, we calculate the ratio of the condensation energy at T=0 to the Sommerfeld constant (the normal state electronic specific heat over the temperature when T it's almost zero) using two different methods: the Boson-Fermion formalism developed here, as well as an analytical expression deduced from a combination of the BCS and Ginzburg-Landau theories. We find for the Boson-Fermion formalism $E_{cond}/γ_0= 0.252\,T_{c}^{1.997}$, which is the same behavior described by the experimental fit of Kim et al $E_{cond}/γ_0= 0.2\,T_{c}^{2.06}$ and by the one recently reported by Tallon et al for overdoped cuprate superconductors; while for the Ginzburg-Landau-BCS we get the expression $E_{cond}/γ_0= 0.236\,T_{c}^{2}$, also in very good agreement with the partifirst method.

arXiv:2606.25316Jun 24, 20260 citations

BCS and Bose-Einstein condensates in superconductivity and superfluidity

M. Grether, Mauricio Fortes, FJ Sevilla +5 more

Jan 1, 20011 citation

Superconductivity and superfluidity as universal emergent phenomena

Mike Guidry, Yang Sun

Superconductivity (SC) or superfluidity (SF) is observed across a remarkably broad range of fermionic systems: in BCS, cuprate, iron-based, organic, and heavy-fermion superconductors, and in superfluid helium-3 in condensed matter; in a variety of SC/SF phenomena in low-energy nuclear physics; in ultracold, trapped atomic gases; and in various exotic possibilities in neutron stars. The range of physical conditions and differences in microscopic physics defy all attempts to unify this behavior in any conventional picture. Here we propose a unification through the shared symmetry properties of the emergent condensed states, with microscopic differences absorbed into parameters. This, in turn, forces a rethinking of specific occurrences of SC/SF such as high-T c SC in cuprates, which becomes far less mysterious when seen as part of a continuum of behavior shared by a variety of other systems.Superconductivity (SC) or superfluidity (SF) is observed across a remarkably broad range of fermionic systems: in BCS, cuprate, iron-based, organic, and heavy-fermion superconductors, and in superfluid helium-3 in condensed matter; in a variety of SC/SF phenomena in low-energy nuclear physics; in ultracold, trapped atomic gases; and in various exotic possibilities in neutron stars. The range of physical conditions and differences in microscopic physics defy all attempts to unify this behavior in any conventional picture. Here we propose a unification through the shared symmetry properties of the emergent condensed states, with microscopic differences absorbed into parameters. This, in turn, forces a rethinking of specific occurrences of SC/SF such as high-T c SC in cuprates, which becomes far less mysterious when seen as part of a continuum of behavior shared by a variety of other systems.

arXiv:1508.04092Frontiers of PhysicsAug 1, 20159 citations

Generalized Bose–Einstein Condensation in Superconductivity

MANUEL DE LLANO

Journal of Superconductivity and Novel MagnetismJan 15, 20100 citations

GENERALIZED BOSE-EINSTEIN CONDENSATION IN SUPERCONDUCTIVITY

MANUEL DE LLANO

Mar 1, 20110 citations

E_{cond}/γ_0= 0.252\,T_{c}^{1.997}

, which is the same behavior described by the experimental fit of Kim et al

E_{cond}/γ_0= 0.2\,T_{c}^{2.06}

and by the one recently reported by Tallon et al for overdoped cuprate superconductors; while for the Ginzburg-Landau-BCS we get the expression

E_{cond}/γ_0= 0.236\,T_{c}^{2}

, also in very good agreement with the partifirst method.