Odd-frequency superconducting pairing in topological insulators

We discuss the appearance of odd-frequency spin-triplet s-wave superconductivity, first proposed by Berezinskii [{\it JETP} {\bf 20}, 287 (1974)], on the surface of a topological insulator proximity coupled to a conventional spin-singlet s-wave superconductor. Using both analytical and numerical methods we show that this disorder robust odd-frequency state is present whenever there is an in-surface gradient in the proximity induced gap, including superconductor-normal state (SN) junctions. The time-independent order parameter for the odd-frequency superconductor is proportional to the in-surface gap gradient. The induced odd-frequency component does not produce any low-energy states.Comment: 6 pages, 5 figures. v2 contains minor changes + supplementary materia

Entanglement and quantum state engineering in the optically driven two-electron double-dot structure

We study theoretically the quantum dynamics of two interacting electrons in the symmetric double-dot structure under the influence of the bichromatic resonant pulse. The state vector evolution is studied for two different pulse designs. It is shown that the laser pulse can generate the effective exchange coupling between the electron spins localized in different dots. Possible applications of this effect to the quantum information processing (entanglement generation, quantum state engineering) are discussed.Comment: 28 pages, 3 figure

Flexoelectric effect in finite samples

Static flexoelectric effect in a finite sample of a solid is addressed in terms of phenomenological theory for the case of a thin plate subjected to bending. It has been shown that despite an explicit asymmetry inherent to the bulk constitutive electromechanical equations which take into account the flexoelectric coupling, the electromechanical response for a finite sample is "symmetric". "Symmetric" means that if a sensor and an actuator are made of a flexoelectric element, performance of such devices can be characterized by the same effective piezoelectric coefficient. This behavior is consistent with the thermodynamic arguments offered earlier, being in conflict with the current point of view on the matter in literature. This result was obtained using standard mechanical boundary conditions valid for the case where the polarization vanishes at the surface. It was shown that, for the case where there is the polarization is nonzero at the surface, the aforementioned symmetry of electromechanical response may be violated if standard mechanical boundary conditions are used, leading to a conflict with the thermodynamic arguments. It was argued that this conflict may be resolved when using modified mechanical boundary conditions. It was also shown that the contribution of surface piezoelectricity to the flexoelectric response of a finite sample is expected to be comparable to that of the static bulk contribution (including the material with high values of the dielectric constant) and to scale as the bulk value of the dielectric constant (similar to the bulk contribution). This finding implies that if the experimentally measured flexoelectric coefficient scales as the dielectric constant of the material, this does not imply that the measured flexoelectric response is controlled by the static bulk contribution to the flexoelectric effect