Superconductivity in Two-Band System With Low Carrier Density

Abstract

In the article a review over the theory of superconductors with energy bands that overlap on Fermi surface at arbitrary densities of charge carriers (including reduced and very low) is done. All pairings of electrons that result in formation Cooper pairs of electrons from different energy bands as well as in every energy band are considered.The system of equations for four order parameters ∆ 11 , ∆ 22 , ∆ 12 , ∆ 21 and chemical potential µ is derived. Self-consistent approach is strictly necessary at µ ∼ ∆ nm . Transition to the effective four-band model leading to the temperature of superconducting transition is performed. Analytic and numeric solutions have been performed for two mechanisms of superconducting pairing -non-phonon and phonon one. The account of the additional in regards to Moscalenco model pairings of electrons from different bands or their hybridization gives an option to obtain the high values of T C even at reduced density of charge carriers. This hybridization influences greatly the form of the dependence of the quantity T C on the density of charge carriers as well as the jump of the electron heat capacity at the point T = T C . High and low values of the relative jump of electronic heat capacity at the point An application of the path integral method to the two-band model is developed and on this basis, the process of transition from the Fermi to the Bose pattern of elementary exitations at T = 0 in the presence of a two-particll bound state in the system is demonstratied.The expression for the temperature of Bose condensation T k is obtained and the contribution of the residual boson interactions is estimated for systems with different dimensions.The overlappining of the energy bands on the fermi surface is favorable for superconductivity and intensify some peculiarities of thermodinamic properties at low carrier density. This halps to their experimental confirmation.

The theory of thermodynamic and magnetic properties of multi-band superconductors

“…The critical temperature T c , the chemical potential µ, the heat capacity (C S − C N ) at the point T = T c as a functions of the carrier density are shown [47,67,75]. This theory is used to describe the properties of the compounds MgB 2 where magnesium and boron are replaced by different elements of the periodic table.…”

“…The path integral method as applied to the two-band model is also developed; on this basis, the procedure for the transition from the Fermi to Bose elementary excitations at T = 0 is given [75,78,79]. The Bose system condensation temperature T k is also determined.…”

Выход За Рамки Теоремы Мигдала В Теории Двухзонной Сверхпроводимости

“…Решение этой системы и термодина-мические свойства двухзонного сверхпроводника без учета эффектов неадиабатич-ности можно найти в работах [22]. Заметим, что при таком подходе учитываются всевозможные сверхпроводящие спаривания как между электронами в каждой зоне, так и между электронами различных энергетических зон.…”

Analytical solutions of the microscopic two-band theory for the temperature dependence of the upper critical fields of pure MgB2 compared with experimental data

“…Many books and a lot of articles concerning this problem were published. Let us mention some publications related to the history of multiband superconductivity: books [3][4][5][6] reviews [7][8][9], and articles [10][11][12]. These works contain the names of scientists from various countries who have contributed to the development of the theory of two-band superconductivity.…”

“…We can see from the above mentioned links that a lot of studies had been carried out long before the discovery of high temperature superconductivity and, moreover, before the discovery of superconductivity in MgB 2 . The two-band theory of superconductivity can explain many anomalies of the physical properties of real superconductors (see, for example, [3,8,9]) and it can be regarded as a classical theory. It is obvious that for any application it needs to be clarified, developed and generalized.…”