Eliashberg equations

We are now able to estimate Tc for the hydrocarbon monoanions by using the approximate solution of the Eliashberg equation [20]. On the basis of the calculated BCS electron-phonon coupling constants [21], we estimate Tc s using McMillan s formula [22,23]. McMillan s formula was derived from a three-dimensional formalism, while the electron carriers in acene-edge-type molecules form a quasi-two-dimensional system. But we believe that McMillan s formula is still available for qualitative discussions. For A < 1.5, this is available for an approximate solution to the Eliashberg equations... 

In the remainder of this paper we consider the A phase and compute rFJd from the full set of nonlinear Eliashberg equations. Our starting point is the spin-fermion model, which describes the interaction of low-energy fermions with their own spin degrees of freedom, Sq, whose propagator is peaked at q = 0 [7, 3-5, 8]. The model is described by the Hamiltonian... 

We can now calculate the superconductive transition temperature through the approximate solution of the Eliashberg equation, given the intra-molccular deformation potentials These, and the vibrational frequencies, were calculated using the quahtum-chemical MNDO semi-empirical technique (IS). This method has been successfully used previously on a wide variety of... 

We now present an approximate calculation of Tp. For X < 1, McMillan (13) has given a very good (23) approximate solution to the Eliashberg equations (12)... 

As the mechanism of superconductivity in these doped fullerites was not clear, the greatest attention was directed to the standard mechanism of superconductivity. The conventional theory is based on the electron-phonon interaction and generalized in the Eliashberg equations which include the Bardeen, Cooper and Schrieffer (BCS) equation as a weak-coupling limit [78]. For real superconductors the ratio for the weak-coupling limit is close to the value of 3.52, and for stronger coupling materials it increases up to about 5.1... 

Fig. 41. Calculated tunneling DOS Ng using isotropic Eliashberg equations and the retarded potential of eq. (89). Nn is the DOS in the normal state, (a) The various lines correspond to temperatures T/Tq = 0.25,0.6,0.9,0.95 from top to bottom at eV/A = 2. (b) Enlarged strong coupling anomaly due to magnetic exciton exchange for T = 0.25...

The quantity Xei-pi, enters two important physical relations. It gives the electron-phonon enhancement of the low-temperature electronic heat capacity as Q = jT = ybandT(l + Xei ph), where JiwiT is the heat capacity obtained from the electron band structure without regard to the electron-phonon interaction. The other important relation, of particular interest here, is the connection between Xei.ph and the transition temperature T. An accurate calculation of requires the solution of the Eliashberg equations, which explicitly take into account the shape of a F(co). In many practical applications one instead obtains F from a semiempirical relation containing a F(co) in the form of the average Xei.ph, Eq. (25). The most frequently used such relation is that due to McMillan (31). It reads... 

They are coupled to each other through Eliashberg-type equations, which can be expressed, in the position and the Matzubara (ojn) representations, as ... 

The emergence of superconductivity in electronic systems close to a ferromagnetic instability has recently been studied by solving a linearized gap equation within the Eliashberg formalism [3-5], In both two- (2D) and three-dimensional (3D) systems, it was found that the superconducting transition temperature, Tlc (T stands for linearized) substantially decreases as the sys-... 

---