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Spectral geometry
Published in Peter B. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, 2018
Let m = 2n and let RPm = Sm/Z2 be real projective space. We use the spin representation to define Clifford matrices {ei} for 0 ≤ i ≤ m on a complex vector space V of dimension 2n. More explicitly, if m = 2, let: () e0,2:=(100−1),a1,2:=(0110),a2,2:=(0−1−−10).
Autocorrelation of quasiparticle spectral intensities and its connection with quasiparticle scattering interference in cuprate superconductors
Published in Philosophical Magazine, 2019
Deheng Gao, Yingping Mou, Yiqun Liu, Shuning Tan, Shiping Feng
The present discussion of the ARPES autocorrelation and its connection with QSI is based on the framework of the kinetic-energy-driven superconductivity [39–41]. This kinetic-energy-driven SC mechanism is developed early within the t-J model in the charge-spin separation fermion-spin representation, where the charge carriers are held together in the pairs in the particle-particle channel by the effective interaction that originates directly from the kinetic energy of the t-J model by the exchange of spin excitations, then the electron pairs originating from the charge-carrier pairing state are due to the charge-spin recombination [42], and their condensation reveals the SC-state. In particular, this same interaction also generates the pseudogap state in the particle-hole channel [41], leading to a coexistence of the SC-state and pseudogap state below the SC transition temperature in the whole SC dome. Following these previous works, the single-particle diagonal and off-diagonal Green's functions and of cuprate superconductors in the SC-state can be obtained as [42],where is the bare band structure, with , , the nearest-neighbour (NN) and next NN electron hopping integrals t and in the t-J model, respectively, the number of the NN or next NN sites on a square lattice Z, and the chemical potential μ. The electron self-energies in the particle-hole channel in Equation (2), which describes the single-particle coherence, and in the particle-particle channel, which is defined as the energy and momentum-dependence of the SC gap [43–45], , can be obtained in terms of the full charge-spin recombination, and are given explicitly in Ref. [42]. In this paper, the parameters are chosen as and , where J is the AF exchange in the t-J model for a pair of NN spins. The magnitude of J and the lattice constant of the square lattice are the energy and length units, respectively. However, when necessary to compare with the experimental data, we take J = 100 meV [1–6].