Superconducting nanowires: quantum confinement and spatially dependent Hartree-Fock potential

It is well-known that in bulk, the solution of the Bogoliubov-de Gennes equations is the same whether or not the Hartree-Fock term is included. Here the Hartree-Fock potential is position independent and, so, gives the same contribution to both the single-electron energies and the Fermi level (the chemical potential). Thus, the single-electron energies measured from the Fermi level (they control the solution) stay the same. It is not the case for nanostructured superconductors, where quantum confinement breaks the translational symmetry and results in a position dependent Hartree-Fock potential. In this case its contribution to the single-electron energies depends on the relevant quantum numbers. We numerically solved the Bogoliubov-de Gennes equations with the Hartree-Fock term for a clean superconducting nanocylinder and found a shift of the curve representing the thickness-dependent oscillations of the critical superconducting temperature to larger diameters

Absolute Negative Conductivity in Two-Dimensional Electron Systems Associated with Acoustic Scattering Stimulated by Microwave Radiation

We discuss the feasibility of absolute negative conductivity (ANC) in two-dimensional electron systems (2DES) stimulated by microwave radiation in transverse magnetic field. The mechanism of ANC under consideration is associated with the electron scattering on acoustic piezoelectric phonons accompanied by the absorption of microwave photons. It is demonstrated that the dissipative components of the 2DES dc conductivity can be negative ($\sigma_{xx} = \sigma_{yy} < 0$) when the microwave frequency $\Omega$ is somewhat higher than the electron cyclotron frequency $\Omega_c$ or its harmonics. The concept of ANC associated with such a scattering mechanism can be invoked to explain the nature of the occurrence of zero-resistance ``dissipationless'' states observed in recent experiments.Comment: 7 pager, 2 figure

Electric-Field Breakdown of Absolute Negative Conductivity and Supersonic Streams in Two-Dimensional Electron Systems with Zero Resistance/Conductance States

We calculate the current-voltage characteristic of a two-dimensional electron system (2DES) subjected to a magnetic field at strong electric fields. The interaction of electrons with piezoelectric acoustic phonons is considered as a major scattering mechanism governing the current-voltage characteristic. It is shown that at a sufficiently strong electric field corresponding to the Hall drift velocity exceeding the velocity of sound, the dissipative current exhibits an overshoot. The overshoot of the dissipative current can result in a breakdown of the absolute negative conductivity caused by microwave irradiation and, therefore, substantially effect the formation of the domain structures with the zero-resistance and zero-conductance states and supersonic electron streams.Comment: 5 pages, 4 figure

Radiation induced oscillations of the Hall resistivity in two-dimensional electron systems

We consider the effect of microwave radiation on the Hall resistivity in two-dimension electron systems. It is shown that the photon-assisted impurity scattering of electrons can result in oscillatory dependences of both dissipative and Hall components of the conductivity and resistivity tensors on the ratio of radiation frequency to cyclotron frequency. The Hall resistivity can include a component induced by microwave radiation which is an even function of the magnetic field. The phase of the dissipative resistivity oscillations and the polarization dependence of their amplitude are compared with those of the Hall resistivity oscillations. The developed model can clarify the results of recent experimental observations of the radiation induced Hall effect.Comment: 4 pages, 1 figur

Nonlinear effects in microwave photoconductivity of two-dimensional electron systems

We present a model for microwave photoconductivity of two-dimensional electron systems in a magnetic field which describes the effects of strong microwave and steady-state electric fields. Using this model, we derive an analytical formula for the photoconductivity associated with photon- and multi-photon-assisted impurity scattering as a function of the frequency and power of microwave radiation. According to the developed model, the microwave conductivity is an oscillatory function of the frequency of microwave radiation and the cyclotron frequency which turns zero at the cyclotron resonance and its harmonics. It exhibits maxima and minima (with absolute negative conductivity) at the microwave frequencies somewhat different from the resonant frequencies. The calculated power dependence of the amplitude of the microwave photoconductivity oscillations exhibits pronounced sublinear behavior similar to a logarithmic function. The height of the microwave photoconductivity maxima and the depth of its minima are nonmonotonic functions of the electric field. It is pointed to the possibility of a strong widening of the maxima and minima due to a strong sensitivity of their parameters on the electric field and the presence of strong long-range electric-field fluctuations. The obtained dependences are consistent with the results of the experimental observations.Comment: 9 pages, 6 figures Labeling of the curves in Fig.3 correcte