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    THẠC SĨ Chiral P-wave Superconductivity of Sr2RuO4

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  6. 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

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