The electronic heat capacity of YBa2Cu3O7−δ superconductor

Anu Singh,B D Indu,Hempal Singh

doi:10.1063/1.4958303

Abstract

The contributions due to the point defects or disorder and anharmonicities which play deterministic role in the understanding of electronic heat capacity (EHC) of high temperature superconductors (HTS) have been investigated via electron density of states (EDOS) approach on the basis of quantum dynamical many body theory. The evaluation of EDOS has been carried out with the help of most versatile method of double time temperature dependent electron Green’s functions (GF) via a Hamiltonian (non BCS type) which includes the effects of electrons, phonons, defects, anharmonicity, and electron-phonon interactions which enables to account the effects of cubic anharmonicity besides with both the force constant changes and mass difference caused by the impurities in developing the results for EDOS and EHC. The new results reveal some striking features of EHC of HTS.

Highlights

It is well known that the heat capacity of solids Cv(T) can be assumed as the contribution due to Phonon heat capacity Cph(T), electronic heat capacity (EHC) Cel(T) and magnon heat capacity Cm(T) and is given by Cv(T) = Cph(T) + Cel(T) + Cm(T)
The evaluation of electron density of states (EDOS) has been carried out with the help of most versatile method of double time temperature dependent electron Green’s functions (GF) via a Hamiltonian which includes the effects of electrons, phonons, defects, anharmonicity, and electron-phonon interactions which enables to account the effects of cubic anharmonicity besides with both the force constant changes and mass difference caused by the impurities in developing the results for EDOS and EHC
It is useful to point out that experimental and theoretical developments on EHC of high Tc cuprate superconductors face several difficulties, namely; (i) The phonon heat capacity due to the elevated superconducting transition temperature is large compared with the electronic contribution and it becomes difficult to isolate the electronic part of the specific heat(Cph(T) > Cel(T)); (ii) The difference between EHC in superconducting and normal states is very small; (iii) In the compounds like, Y Ba2Cu3O7−δ, the low temperature value of EHC is 10 to 100 times lower than phonon heat capacity

Summary

INTRODUCTION

EHC still appears as one of the most important thermodynamic property of HTS, which over a wide range of temperature provides the gain insight into the normal and superconducting states and may provide the essential clue in the understanding of microscopic behavior and identification of the pairing symmetry of high temperature superconductivity (HTSC).[1,2] It is useful to point out that experimental and theoretical developments on EHC of high Tc cuprate superconductors face several difficulties, namely; (i) The phonon heat capacity due to the elevated superconducting transition temperature is large compared with the electronic contribution and it becomes difficult to isolate the electronic part of the specific heat(Cph(T) > Cel(T)); (ii) The difference between EHC in superconducting and normal states is very small (around 2-4% of phononic contribution); (iii) In the compounds like, Y Ba2Cu3O7−δ, the low temperature value of EHC is 10 to 100 times lower than phonon heat capacity. The remarkable feature of the present formulation is the temperature dependence of EDOS with various distribution functions

THEORETICAL FRAMEWORK OF THE PROBLEM

THE HAMILTONIAN AND GREEN’S FUNCTION

Electron Density of States

EVALUATION OF ELECTRON ENERGY

THE ELECTRONIC HEAT CAPACITY OF HIGH TEMPERATURE SUPERCONDUCTORS

CONCLUSIONS