The conditions for zero-energy Andreev surface bound states to exist are found for the lattice model of d-wave superconductor with arbitrary surface orientation. Both nearest neighbors and next nearest neighbors models are considered. It is shown that the results are very sensitive to the surface orientation. In particular, for half-filled (hl0)-surfaceâ€¦ (More)

These are the notes for my quarter-long course on basic stability theory at UCLA (MATH 285D, Winter 2015). The presentation highlights some relations to set theory and cardinal arithmetic, reflecting my impression about the tastes of the audience. We develop the general theory of local stability instead of specializing to the finite rank case, and touch onâ€¦ (More)

The quasiclassical theory in terms of equations for the Greenâ€™s functions (Eilenberger equations) is generalized in order to allow for quantitative description of the magneto-electric effects and proximity-induced triplet correlations in the presence of spin-orbit coupling in hybrid superconducting systems. The formalism is valid under the condition thatâ€¦ (More)

By now it is known that in a singlet superconductor-ferromagnet (S-F) structure the superconducting correlations carried by opposite-spin pairs penetrate into the ferromagnet over a short distance of the order of magnetic coherence length. The long-range proximity effect (LRPE), taking place on the length scale of the normal metal coherence length, can onlyâ€¦ (More)