Double Andreev Reflections in Type-II Weyl Semimetal-Superconductor Junctions

We study the Andreev reflections (ARs) at the interface of the type-II Weyl semimetal-superconductor junctions and find double ARs when the superconductor is put in the Weyl semimetal band tilting direction, which is similar to the double reflections of light in anisotropic crystals. The directions of the double (retro and specular) ARs are symmetric about the normal due to the hyperboloidal Fermi surface near the Weyl nodes, but with different AR amplitudes depending on the direction and energy of the incident electron. When the normal direction of the Weyl semimetal-superconductor interface is changed from parallel to perpendicular with the tilt direction, the double ARs gradually evolve from one retro-AR and one specular AR, passing through double retro-ARs, one specular AR and one retro-AR, into one retro AR and one normal reflection, resulting in an anisotropic conductance which can be observed in experiments.Comment: 12 pages, 7 figure

Block Spins for Partial Differential Equations

We investigate the use of renormalisation group methods to solve partial differential equations (PDEs) numerically. Our approach focuses on coarse-graining the underlying continuum process as opposed to the conventional numerical analysis method of sampling it. We calculate exactly the coarse-grained or `perfect' Laplacian operator and investigate the numerical effectiveness of the technique on a series of 1+1-dimensional PDEs with varying levels of smoothness in the dynamics: the diffusion equation, the time-dependent Ginzburg-Landau equation, the Swift-Hohenberg equation and the damped Kuramoto-Sivashinsky equation. We find that the renormalisation group is superior to conventional sampling-based discretisations in representing faithfully the dynamics with a large grid spacing, introducing no detectable lattice artifacts as long as there is a natural ultra-violet cut off in the problem. We discuss limitations and open problems of this approach.Comment: 8 pages, RevTeX, 8 figures, contribution to L.P. Kadanoff festschrift (J. Stat. Phys

Theory of Defects in n-Type Transparent Conducting Oxides

A range of computational modelling techniques are employed to explore the structures, defect and electronic properties of three transparent conducting oxides (TCOs): SnO₂, In₂O₃ and ZnO. Bulk interatomic potential (IP) based calculations are carried out to model point defects in SnO₂ and In₂O₃. We report new IPs for the two binary oxides, which offer an improvement over the previously available models, and give defect formation energies comparable with those obtained using density functional theory (DFT). The intrinsic point defects in ZnO are investigated in detail using a hybrid quantum mechanical/molecular mechanical (QM/MM) embedded cluster approach. The formation energies show the oxygen vacancy to be the most favourable under O-poor conditions and zinc vacancies under O-rich conditions. Our calculations are also able to assign several of the widely studied luminescence bands to defect states. For extrinsic dopants, including in ZnO, we compute the structure and formation energies of Li and H dopants in both substitutional and interstitial form and their complexes, the Li_{Zn}-Lii_{(oct)} complex has the lowest formation energy in Zn-poor conditions. The HO is energetically favoured compared to Hi. Using QM/MM calculations, we investigate the native point defect on the electrical and optical properties of In₂O₃. The oxygen vacancy is the lowestenergy donor defect, with a predicted luminescence peak at 2.12 eV using the B97-2 functional. Finally, we study the solid-solution of In₂O₃ and SnO₂ over a range of dopant concentrations, which provide local structure information