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Synthesis Of The Conventional Phenomenological Theories With Marginal Fermi Liquid Model

Synthesis Of The Conventional Phenomenological Theories With Marginal Fermi Liquid Model

ABSTRACT

The high temperature superconducting cuprates show some non Fermi liquid behaviour in their normal state. Also there is no generally accepted theory of high temperature superconductivity. The BCS theory has failed to explain the superconductive state properties of the cuprate superconductors. Gorter-Casimir two uid model and London theory has been very useful before the BCS theory. Varma and his co-workers propounded a ‘marginal’ Fermi liquid theory which explains the normal state properties of the cuprate superconductors. In this thesis, we have calculated some thermodynamic and electrodynamic properties of the cuprate superconductors. The method involves applying the result of electronic specic heat capacity of cuprates in the normal state obtained by Kuroda and Varma to the Gorter-Casimir two uid model using the standard variational method. We also applied the two uid scheme to the London theory and obtained an expression for the magnetic eld penetration depth. Our result was compared with other peoples’ results and experimental results.

TABLE OF CONTENTS

INTRODUCTION

1.1 General Background . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Classication of Superconductors by their Critical Temperature 4
1.2.1 Low Temperature Superconductors . . . . . . . . . . . . 4
1.2.2 High Temperature Superconductors . . . . . . . . . . . . 4
1.3 Cuprate Superconductors . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 General properties . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . 6
2 THEORIES OF SUPERCONDUCTIVITY 9
2.1 Landau Fermi Liquid theory . . . . . . . . . . . . . . . . . . . . 9
2.2 Gorter-Casimir Two Fluid Model . . . . . . . . . . . . . . . . . 15
2.3 The London Theory . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 The BCS Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Marginal Fermi Liquid Theory . . . . . . . . . . . . . . . . . . . 21
2.6 A Phenomenological Marginal Fermi Liquid Theory . . . . . . . 22
3 SYNTHESIS OF GORTER-CASIMIR TWO FLUID MODEL
WITH MFL MODEL 25
4 SYNTHESIS OF LONDON THEORY WITH MFL MODEL 32
5 DISCUSSION OF RESULTS 36
5.1 Specic heat jump . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.2 London Penetration Depth . . . . . . . . . . . . . . . . . . . . . 38
5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Bibliography 39

CHAPTER ONE

INTRODUCTION

1.1 General Background

Superconductivity is a phenomenon characterised by the disappearance of electrical resistance in various metals, alloys and compounds when they are cooled below a certain temperature usually termed the critical temperature, Tc. It is also characterised by the expulsion of the interior magnetic eld (called Meissner eect) from the superconductor.

Figure 1.1: Graph of resistance R against temperature

Figure 1.2: Meissner eect

Superconductivity was rst observed in mercury by Dutch Physicist, Heike Kamerlingh Onnes of Leiden University in 1911. When he cooled it to the temperature of liquid helium (4.2K), its resistance suddenly disappeared
(Solymar, 1993).

In 1933, German researchers, Walter Meissner and Robert Ochsenfeld discovered that a superconducting material will repel a magnetic eld.

The rst widely accepted microscopic theoretical understanding of superconductivity called BCS theory was advanced in 1957 by American Physicists; john Bardeen, Leon Cooper and Robert Schrieer.

In 1986, Alex Muller and George Bednorz, researchers at IBM research laboratory in Ruschlikon, Switzerland discovered a critical temperature of 30K when performing measurements of conductivity in ceramic (lanthanum, barium, copper and oxygen) compounds with various concentration of barium.

Higher superconducting transition temperature were reached in January 1987 by the group of C. W Chu at the University of Houston in collaboration with the group of M. K Wu at the University of Alabama by replacing yttrium for barium in the Muller and Bednorz molecule. They achieved an incredible critical temperature of 90K [Matsumoto (2010)].

High temperature superconductivity has taken the stage of modern condensed matter theory since its discovery in 1987. High temperature superconducting materials show deviations from the Fermi liquid phenomenology.

The BCS theory has not been able to explain the properties of the high Tc cuprates. On a phenomenological level, behaviour close to the optimal doping (ie the regime where the superconducting transition temperature is highest) seems to display ‘marginal Fermi liquid’ (MFL) behaviour.

Studies of electrodynamic properties provide a clear phenomenological picture, reveal information regarding the pairing state, the energy gap and density of state of the superconductor and give important information on the mechanism of high temperature superconductivity. However, there is no clear consensus about the electrodynamics of cuprates from earlier studies of YBCO and BSCCO [Peil et al (1991)]. This is due in part to their complex microstructural properties: interruption of the conductive Cu-O chains by twin boundaries in YBCO, and the short coherence length which gives rise to a plethora of weaklink phenomena [Halbritter (1990)]. The most important feature observed in experiments is the linear resistivity, which at optimal doping persists in an enormous temperature range from a few kelvin to much above room temperature.

A phenomenological model describing the marginal Fermi liquid behaviour of cuprates have been put forward by Varma and co-workers but its microscopic origin remains highly controversial. To our knowledge, no microscopic theory has so far been able to provide a microscopic explanation for the phenomenon of high temperature superconducting cuprates despite years of efforts and hundreds of papers published on the subject [Chaudhury (1995)].

This research work therefore focuses on the application of the marginal Fermi liquid model to the Gorter-Casimir two uid model/London theory.

In chapter 2 we look at the general properties of cuprates, the Fermi liquid theory, the BCS theory and some phenomenological theories including Gorter-Casimir two uid model, London-Pippard theory and the phenomenological marginal Fermi liquid model.


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