Thạc Sĩ Chiral P-wave Superconductivity of Sr2RuO4

Contents
1 Introduction 1
2 Structure and Properties of Sr 2 RuO 4 1
3 Hubbard Model for Spin Triplet P-wave Model of Sr 2 RuO 4 2
3.1 Hopping integrals . 3
3.2 Bogolubov equations . 5
3.3 Gap Function . 6
4 Band Structure of Quasi-2D Model 8
4.1 Periodic Boundary Conditions 8
4.2 Strip Geometry 10
5 Band Structure of Quasi-1D Model 14
5.1 Periodic Boundary Conditions 14
5.2 Strip Geometry 17
6 Spectra of Sr 2 RuO 4 In The Presence of Spin Orbit And Interlayer Coupling 20
6.1 Spin Orbit Coupling . 20
6.2 Spectra Of Sr 2 RuO 4 With Spin Orbit Coupling and Interlayer Coupling 21
7 Conclusions and Future Work 23
vBlank page
vi1 Introduction
The search for non-cuprate layered perovskite superconductors has been an active area of research
since the rst high-T c cuprate superconductor La 2ưx Ba x CuO 4 was found in 1986 [1]. In 1994, the
rst such material was found to be Strontium Ruthenate (Sr 2 RuO 4 ), which has the same crystal
structure as La 2ưx Ba x CuO 4 [1][2].
Figure 1: The common crystal structures of Sr 2 RuO 4 and La 2ưx Ba x CuO 4 [1]
The microscopic theory of superconductivity is the BCS theory [3]. In this theory, the Cooper
pair has an important role in explaining the microscopic picture of superconductors. The Cooper
pair can be in either a singlet or triplet state. All the conventional and unconventional supercon-
ductors that have been discovered have the spin-singlet state with even orbital parity, which means
that its antisymmetric spin state is accompanied by a symmetric orbital wave function. However,
the superconducting state of Sr 2 RuO 4 is a spin triplet with odd orbital parity (the symmetric spin
state is acompanied by an antisymmetric orbital wave function) [1]. Moreover, the simplest case
of triplet pairing is p-wave pairing and some experimental evidence points toward p-wave pairing
in Sr 2 RuO 4 .
In this Essay, we investigate the chiral P-wave superconductivity of Sr 2 RuO 4 . In section 2,
we describe the crystal structure and the superconducting properties of Sr 2 RuO 4 . Then, we
discuss the appropriate Hubbard model for Strontium Ruthenate in section 3. We will use these
results to nd the quasi-particle excitation spectra of the quasi-1D and quasi-2D models of P-wave
superconductivity in Sr 2 RuO 4 in section 4 and section 5. In the last section, we nd the excitation
spectra in the presence of spin orbit coupling and interlayer coupling.
2 Structure and Properties of Sr 2 RuO 4
Strontium Ruthenate is a body-centered tetragonal crystal and its structure is shown in gure
2. The highest occupied electron orbitals in Sr 2 RuO 4 contain electrons in the low-lying Ru 4+ 4d
1