Tunneling Anomaly in Superconductor above Paramagnetic Limit

We study the tunneling density of states (DoS) in the superconducting systems driven by Zeeman splitting E_Z into the paramagnetic phase. We show that, even though the BCS gap disappears, superconducting fluctuations cause a strong DoS singularity in the vicinity of energies -E^* for electrons polarized along the magnetic field and E^* for the opposite polarization. The position of the singularity E^*=(1/2) (E_Z + \sqrt{E_Z^2- \Delta^2}) (where \Delta is BCS gap at E_Z=0) is universal. We found analytically the shape of the DoS for different dimensionality of the system. For ultrasmall grains the singularity has the form of the hard gap, while in higher dimensions it appears as a significant though finite dip. Our results are consistent with recent experiments in superconducting films.Comment: 4 pages, 2 .eps figures include

Effect of Time Reversal Symmetry Breaking on the Density of States in Small Superconducting Grains

We show that in ultra-small superconducting grains any concentration of magnetic impurities or infinitely small orbital effect of magnetic field leads to destruction of the hard gap in the tunneling density of states. Instead, though exponentially suppressed at low energies, the tunneling density of states exhibits the ``soft gap'' behavior, vanishing linearly with excitation energy, as the energy approaches zero.Comment: 4 pages, 1 eps figur

A dc voltage step-up transformer based on a bi-layer \nu=1 quantum Hall system

A bilayer electron system in a strong magnetic field at low temperatures, with total Landau level filling factor nu =1, can enter a strongly coupled phase, known as the (111) phase or the quantum Hall pseudospin-ferromagnet. In this phase there is a large quantized Hall drag resistivity between the layers. We consider here structures where regions of (111) phase are separated by regions in which one of the layers is depleted by means of a gate, and various of the regions are connected together by wired contacts. We note that with suitable designs, one can create a DC step-up transformer where the output voltage is larger than the input, and we show how to analyze the current flows and voltages in such devices