Superconductor-insulator duality for the array of Josephson wires

We propose novel model system for the studies of superconductor-insulator transitions, which is a regular lattice, whose each link consists of Josephson-junction chain of $N \gg 1$ junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy $E_J$ large compared to the junctions's Coulomb energy $E_C$. Exact duality transformation is derived, which transforms the Hamiltonian of the proposed model into a standard Hamiltonian of JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter $q \approx N^2 \exp(-\sqrt{8E_J/E_C})$, with superconductive state corresponding to small $q < q_c$. The values of $q_c$ are calculated for magnetic frustrations $f= 0$ and $f= \frac12$. Temperature of superconductive transition $T_c(q)$ and $q < q_c$ is estimated for the same values of $f$. In presence of strong random offset charges, the T=0 phase diagram is controlled by the parameter $\bar{q} = q/\sqrt{N}$; we estimated critical value $\bar{q}_c$.Comment: 5 pages, 2 figure

Tunneling conductance due to discrete spectrum of Andreev states

We study tunneling spectroscopy of discrete subgap Andreev states in a superconducting system. If the tunneling coupling is weak, individual levels are resolved and the conductance $G(V)$ at small temperatures is composed of a set of resonant Lorentz peaks which cannot be described within perturbation theory over tunnelling strength. We establish a general formula for their widths and heights and show that the width of any peak scales as normal-state tunnel conductance, while its height is $\lesssim 2e^2/h$ and depends only on contact geometry and the spatial profile of the resonant Andreev level. We also establish an exact formula for the single-channel conductance that takes the whole Andreev spectrum into account. We use it to study the interference of Andreev reflection processes through different levels. The effect is most pronounced at low voltages, where an Andreev level at $E_j$ and its conjugate at $-E_j$ interfere destructively. This interference leads to the quantization of the zero-bias conductance: G(0) equals $2e^2/h$ (or 0) if there is (there is not) a Majorana fermion in the spectrum, in agreement with previous results from $S$-matrix theory. We also study $G(eV>0)$ for a system with a pair of almost decoupled Majorana fermions with splitting $E_0$ and show that at lowest $E_0$ there is a zero-bias Lorentz peak of width $W$ as expected for a single Majorana fermion (a topological NS-junction) with a narrow dip of width $E_0^2/W$ at zero bias, which ensures $G(0)=0$ (the NS-junction remains trivial on a very small energy scale). As the coupling $W$ gets stronger, the dip becomes narrower, which can be understood as enhanced decoupling of the remote Majorana fermion. Then the zero-bias dip requires extremely low temperatures $T\lesssim E_0^2/W$ to be observed.Comment: 8 pages, 3 figure

Quantum spin metal state on a decorated honeycomb lattice

We present a modification of exactly solvable spin-(1/2) Kitaev model on the decorated honeycomb lattice, with a ground state of "spin metal" type. The model is diagonalized in terms of Majorana fermions; the latter form a 2D gapless state with a Fermi-circle those size depends on the ratio of exchange couplings. Low-temperature heat capacity C(T) and dynamic spin susceptibility \chi(\omega,T) are calculated in the case of small Fermi-circle. Whereas C(T)\sim T at low temperatures as it is expected for a Fermi-liquid, spin excitations are gapful and \chi(\omega,T) demonstrate unusual behaviour with a power-law peak near the resonance frequency. The corresponding exponent as well as the peak shape are calculated.Comment: 4 pages, 3 figure