No abstract

A generic theory of the quasiparticle superconducting gap in underdoped cuprates is derived in the strong-coupling limit, and found to describe the experimental ''second gap'' in absolute scale. In drastic contrast to the standard pairing gap associated with Bogoliubov quasiparticle excitations, the quasiparticle gap is shown to originate from anomalous kinetic (scattering) processes, with a size unrelated to the pairing strength. Consequently, the k dependence of the gap deviates significantly from the pure d x 2 Ày 2 wave of the order parameter. Our study reveals a new paradigm for the nature of the superconducting gap, and is expected to reconcile numerous apparent contradictions among existing experiments and point toward a more coherent understanding of high-temperature superconductivity. The recent exciting discovery of the superconducting gap in the underdoped cuprates by angle-resolved photoemission spectroscopy (ARPES) [1][2][3][4][5][6][7][8][9][10][11][12] and scanning tunneling microscopy [13][14][15][16][17][18][19] reveals critical clues for the puzzling high-temperature superconductivity, which has proven to be one of the most important yet challenging problems of condensed matter physics for more than two decades. Indeed, unlike the larger pseudogap, the superconducting gap closes exactly at the transition temperature T c [12], and shows strong correlation to the doping dependence of T c [3,4,[20][21][22]]. Yet, some experiments found intriguing indications that the k dependence of the superconducting gap might not follow the well-established pure d wave of the order parameter [12,20]. Obviously, a deeper understanding of the properties of the superconducting gap seen in the quasiparticle excitation spectra holds an essential key to a resolution to the long-standing problem of hightemperature superconductivity in underdoped cuprates.Despite the intensive experimental studies, to date there have been limited attempts [20,[23][24][25][26][27]] to understand the superconducting gap, which greatly contrasts with the numerous efforts made to address the pseudogap phenomenon [28][29][30][31]. Furthermore, the existing understanding for the superconducting gap remains within the scope of the weakcoupling BCS framework, which was shown to be insufficient [32] in the underdoped regime to account for the essential phase fluctuation of the order parameter. As a result, most of the key questions remain open, including those regarding the energy scale that controls the size of the superconducting gap, the nature of the sharp quasiparticle at the edge of the superconducting gap, and the precise k dependence of the superconducting gap, among others.Here we address the above key questions regarding the superconducting gap by deriving rigorously a generic description in the strong-coupling limit, in which the realspace pairs of holes are assumed to be tightly bound in nearest neighboring sites. With a rigorous separation of the Hilbert space into bosonic and fermionic portions that describe the bound pairs and un...

The properties of Mn-doped GaAs are studied at several doping levels and hole compensations, using a real-space Hamiltonian on an fcc lattice that reproduces the valence bands of undoped GaAs. Large-scale Monte Carlo (MC) simulations on a Cray XT3 supercomputer, using up to a thousand nodes, were needed to make this effort possible. Our analysis considers both the spin-orbit interaction and the random distribution of the Mn ions. The hopping amplitudes are functions of the GaAs Luttinger parameters. At the coupling J∼1.2 eV deduced from photoemission experiments, the MC Curie temperature and the shape of the magnetization curves are in agreement with experimental results for annealed samples. Although there are sizable differences with mean-field predictions, the system is found to be closer to a hole-fluid regime than to localized carriers.