The Fe-based superconductors (Fe-SCs) have reinvigorated the community of high-Tc researchers worldwide. Like copper-oxide superconductors (Cu-SCs), they are layered compounds in proximity to an antiferromagnetic (AFM) state. The Fe-SC systems are amenable to controlled chemical doping/alloying, exhibiting coexistence of AFM and SC, as well as structural transformations versus temperature and pressure that lead to competing magnetic and structural defects. Because of this, exploration of the electronic structure of the normal (non-SC) state, and its related properties, may reveal key physics underlying connections between structure, magnetism and SC.In this thesis we study the phase stability, electronic structure, and magnetism of alloyed (Ba-Am)(Fe-Tm)2As2 superconductors involving transition metals (Tm=Co, Ni, Cu, Zn) and alkali metals (Am = K, Na) in nonmagnetic, paramagnetic, and antiferromagnetic states for the competing tetragonal and orthorhombic structures. These cover prominent electron (Tm) and hole (Am) doping scenarios studied experimentally. To accomplish this in a unified way, we utilize a Green's function approach based upon the all-electron, Korringa-Kohn-Rostoker (KKR) multiple scattering theory in combination with the coherent-potential approximation (CPA) to handle chemical (alloying) and magnetic (orientational) disorder, all implemented within a self-consistent-field, density functional theory (DFT).For $Tm$ doping, we detail the Fermi-surface evolution and nesting that dictate instabilities to the observed spin-density wave (SDW) state. For Am doping we track topological changes in the Fermi surface and connect these to transitions between SC phases. For K-doping, dissolution of electron cylinders occurs near 90%K with a Lifshitz (topological) transition, as observed, which reduces key inter-band interactions. This result reveals a transition that influences s+/- to d-like SC and suggests the origin for the deviations for the empirically identified Bud'ko-Ni-Canfield scaling. Formation energies indicate alloying at 35%K, as observed, but a tendency for segregation on the K-rich (>= 60%K) side, explaining the difficulty of controlling sample quality and conflicting results between characterized electronic structures. In addition, due to the observed proliferation of twins and magnetic twin boundaries in BaFe2As2 (and possible other operative magnetic planar defects) with temperature and pressure, we study the stability and magnetic properties of competing antiphase and domain boundaries, twins and isolated $nano$twins (twin nuclei). These nanoscale defects have very low surface energy (22-210m Jm^-2), with twins favorable to the mesoscale. The nano-twins explain features in measured pair distribution functions obtained from neutron diffraction. Notably, these low-energy defects are tied to the magneto-structural transition whose fluctuations are widely expected to drive SC.
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Electronic structure and energetics of Fe-based superconductors: Effects of chemical and magnetic disorder in (Ba-X)(Fe-Y)2As2