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Register a new userReal-space multiple scattering theory for superconductors with impurities
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We implement the Bogoliubov-de Gennes (BdG) equation in real-space using the screened Korringa-Kohn-Rostoker (KKR) method. This allows us to solve, self-consistently, the superconducting state for 3d crystals including substitutional impurities with a full normal-state DFT band structure. We apply the theoretical framework to bulk Nb with impurities. Without impurities, Nb has an anisotropic gap structure with two distinct peaks around the Fermi level. In the presence of non-magnetic impurities those peaks are broadened due to the scattering between the two bulk superconducting gaps, however the peaks remain separated. As a second example of self-consistent real-space solutions of the BdG equations we examine superconducting clusters embedded within a non-superconducting bulk metallic host. This allows us to estimate the coherence length of the superconductor and we show that, within our framework, the coherence length of the superconductor is related to the inverse of the gap size, just as in bulk BCS theory.
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Disorder - impurities and defects violating an ideal order - is always present in solids. It can result in interesting and sometimes unexpected effects in multiband superconductors. Especially if the superconductivity is unconventional thus having other than the usual s-wave symmetry. This paper uses the examples of iron-based pnictides and chalcogenides to examine how both nonmagnetic and magnetic impurities affect superconducting states with $s_pm$ and $s_{++}$ order parameters. We show that disorder causes the transitions between $s_pm$ and $s_{++}$ states and examine observable effects these transitions can produce.
Within the framework of the kinetic energy driven superconducting mechanism, the effect of the extended impurity scatterers on the quasiparticle transport of cuprate superconductors in the superconducting state is studied based on the nodal approximation of the quasiparticle excitations and scattering processes. It is shown that there is a cusplike shape of the energy dependent microwave conductivity spectrum. At low temperatures, the microwave conductivity increases linearly with increasing temperatures, and reaches a maximum at intermediate temperature, then decreases with increasing temperatures at high temperatures. In contrast with the dome shape of the doping dependent superconducting gap parameter, the minimum microwave conductivity occurs around the optimal doping, and then increases in both underdoped and overdoped regimes.
We implement the Bogoliubov-de Gennes (BdG) equation in a screened Korringa-Kohn-Rostoker (KKR) method for solving, self-consistently, the superconducting state for 3d crystals. This method combines the full complexity of the underlying electronic structure and Fermi surface geometry with a simple phenomenological parametrisation for the superconductivity. We apply this theoretical framework to the known s-wave superconductors Nb, Pb, and MgB$_2$. In these materials multiple distinct peaks at the gap in the density of states were observed, showing significant gap anisotropy which is in good agreement with experiment. Qualitatively, the results can be explained in terms of the k-dependent Fermi velocities on the Fermi surface sheets exploiting concepts from BCS theory.
We present an textit{ab initio} theory for superconductors, based on a unique mapping between the statistical density operator at equilibrium, on the one hand, and the corresponding one-body reduced density matrix $gamma$ and the anomalous density $chi$, on the other. This new formalism for superconductivity yields the existence of a universal functional $mathfrak{F}_beta[gamma,chi]$ for the superconductor ground state, whose unique properties we derive. We then prove the existence of a Kohn-Sham system at finite temperature and derive the corresponding Bogoliubov-de Gennes-like single particle equations. By adapting the decoupling approximation from density functional theory for superconductors we bring these equations into a computationally feasible form. Finally, we use the existence of the Kohn-Sham system to extend the Sham-Schluter connection and derive a first exchange-correlation functional for our theory. This reduced density matrix functional theory for superconductors has the potential of overcoming some of the shortcomings and fundamental limitations of density functional theory of superconductivity.
We propose a simple way to parameterize the gap function in iron pnictides. The key idea is to use orbital representation, not band representation, and to assume real-space short-range pairing. Our parameterization reproduces fairly well the structure of gap function obtained in microscopic calculation. At the same time the present parameterization is simple enough to obtain an intuitive picture and to develop a phenomenological theory. We also discuss simplification of the treatment of the superconducting state.
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