RESUMEN
We present a general method of constructing in situ pseodopotentials from first-principles, all-electron, and full-potential electronic structure calculations of a solid. The method is applied to bcc Na, at low-temperature equilibrium volume. The essential steps of the method involve (i) calculating an all-electron Kohn-Sham eigenstate, (ii) replacing the oscillating part of the wave function (inside the muffin-tin spheres) of this state, with a smooth function, (iii) representing the smooth wave function in a Fourier series, and (iv) inverting the Kohn-Sham equation, to extract the pseudopotential that produces the state generated in steps i-iii. It is shown that an in situ pseudopotential can reproduce an all-electron full-potential eigenvalue up to the sixth significant digit. A comparison of the all-electron theory, in situ pseudopotential theory, and the standard nonlocal pseudopotential theory demonstrates good agreement, e.g., in the energy dispersion of the 3s band state of bcc Na.
RESUMEN
We show conceptually that the edge of a two-dimensional topological insulator can be used to construct a solid-state Stern-Gerlach spin splitter. By threading such a Stern-Gerlach apparatus with a magnetic flux, Aharanov-Bohm-like interference effects are introduced. Using ferromagnetic leads, the setup can be used to both measure magnetic flux and as a spintronics switch. With normal metallic leads a switchable spintronics NOT-gate can be implemented. Furthermore, we show that a sequence of such devices can be used to construct a single-qubit SU(2)-gate, one of the two gates required for a universal quantum computer. The field sensitivity, or switching field, b, is related to the characteristic size of the device, r, through b = h/(2πqr2), with q being the unit of electric charge.
RESUMEN
Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates offer a clear advantage in a much larger superconducting order parameter, but the nodal energy spectrum of a pure d-wave superconductor only allows virtual bound states. Fully gapped d-wave superconducting states have, however, been proposed in several cuprate systems thanks to subdominant order parameters producing d + is- or d + id'-wave superconducting states. Here we study both magnetic and potential impurities in these fully gapped d-wave superconductors. Using analytical T-matrix and complementary numerical tight-binding lattice calculations, we show that magnetic and potential impurities behave fundamentally different in d + is- and d + id'-wave superconductors. In a d + is-wave superconductor, there are no bound states for potential impurities, while a magnetic impurity produces one pair of bound states, with a zero-energy level crossing at a finite scattering strength. On the other hand, a d + id'-wave symmetry always gives rise to two pairs of bound states and only produce a reachable zero-energy level crossing if the normal state has a strong particle-hole asymmetry.
RESUMEN
We show that superconducting currents are generated around magnetic impurities and ferromagnetic islands proximity coupled to superconductors with finite spin-orbit coupling. Using the Ginzburg-Landau theory, T-matrix calculation, as well as self-consistent numerical simulation on a lattice, we find a strong dependence of the current on the direction and magnitude of the magnetic moment. We establish that in the case of point magnetic impurities, the current is carried by the induced Yu-Shiba-Rusinov (YSR) subgap states. In the vicinity of the phase transition, where the YSR states cross at zero energy, the current increases dramatically. Furthermore, we show that the currents are orthogonal to the local spin polarization and, thus, can be probed by measuring the spin-polarized local density of states.