Superconducting gap anomaly in heavy fermion systems

G C ROUT^1,*, M S OJHA² and S N BEHERA^3,4

¹Condensed Matter Physics Group, Government Science College, Chatrapur 761 020, India

²Department of Physics, S.C.S. College, Puri 752 001, India

³Physics Enclave, H.I.G. 23/1, Housing Board Phase-1, Chandrasekharpur,

Bhubaneswar 751 016, India

⁴Present address: Institute of Materials Science, Planetarium Building,

Bhubaneswar 751 013, India

^*Corresponding author. E-mail: gcr@iopb.res.in

Abstract.The heavy fermion system (HFS) is described by

the periodic Anderson model (PAM), treating the Coulomb correlation between

the $f$-electrons in the mean-field Hartree--Fock approximation.

Superconductivity is introduced by a BCS-type

pairing term among the conduction electrons. Within this approximation

the equation for the superconducting gap is derived, which depends on

the effective position of the energy level of the $f$-electrons

relative to the Fermi level. The latter in turn depends on the

occupation probability $n^{\rm f}$ of the $f$-electrons. The gap

equation is solved self-consistently with the equation for $n^{\rm

f}$; and their temperature dependences are studied for different

positions of the bare $f$-electron energy level, with respect to the

Fermi level. The dependence of the superconducting gap on the

hybridization leads to a re-entrant behaviour with increasing

strength. The induced pairing between the $f$-electrons and the

pairing of mixed conduction and $f$-electrons due to hybridization

are also determined. The temperature dependence of the hybridization

parameter, which characterizes the number of electrons with mixed

character and represents the number of heavy electrons is studied.

This number is shown to be small. The quasi-particle density of

states (DOS) shows the existence of a pseudo-gap due to

superconductivity and the signature of a hybridization gap at the

Fermi level. For the choice of the model parameters, the DOS shows

that the HFS is a metal and undergoes a transition to the gap-less

superconducting state.

Keywords. Heavy fermion superconductor; Narrow band system;

Valence fluctuation.

PACS Nos 74.70.Tx; 71.28.+d; 75.30.Mb