Quantum Phase Transitions in Josephson Junction Chains

We investigate the quantum phase transition in a one-dimensional chain of ultra-small superconducting grains, considering both the self- and junction capacitances. At zero temperature, the system is transformed into a two-dimensional system of classical vortices, where the junction capacitance introduces anisotropy in the interaction between vortices. This leads to the superconductor-insulator transition of the Berezinskii-Kosterlitz-Thouless type, as the ratios of the Josephson coupling energy to the charging energies are varied. It is found that the junction capacitance plays a role similar to that of dissipation and tends to suppress quantum fluctuations; nevertheless the insulator region survives even for arbitrarily large values of the junction capacitance.Comment: REVTeX+5 EPS figures, To appear in PRB Rapid

Escape from a zero current state in a one dimensional array of Josephson junctions

A long one dimensional array of small Josephson junctions exhibits Coulomb blockade of Cooper pair tunneling. This zero current state exists up to a switching voltage, Vsw, where there is a sudden onset of current. In this paper we present histograms showing how Vsw changes with temperature for a long array and calculations of the corresponding escape rates. Our analysis of the problem is based on the existence of a voltage dependent energy barrier and we do not make any assumptions about its shape. The data divides up into two temperature regimes, the higher of which can be explained with Kramers thermal escape model. At low temperatures the escape becomes independent of temperature.Comment: 4 pages 5 figure

Parity Effect and Charge Binding Transition in Submicron Josephson Junction Arrays

We reconsider the issue of Berezinskii-Kosterlitz-Thouless (BKT) transition into an insulating state in the Coulomb-dominated Josephson junction arrays. We show that previously predicted picture of the Cooper-pair BKT transtion at T = T_2 is valid only under the condition that T_2 is considerably below the parity-effect temperature (which is usually almost 10 times below the value of superconductive transition temperature), and even in this case it is not a rigorous phase transition but only a crossover, whereas the real phase transition takes place at T_1 = T_2/4. Our theory is in agreement with available experimental data on Coulomb-dominated Josephson arrays and also sheds some light on the origin of unusual reentrant temperature dependence of resistivity in the array with nearly-criticial ratio of Coulomb to Josephson energies.Comment: 4 pages, Revtex, to be published in JETP Letters, April 9

Quantum superconductor-metal transition in a proximity array

A theory of the zero-temperature superconductor-metal transition is developed for an array of superconductive islands (of size d) coupled via a disordered two-dimensional conductor with the dimensionless conductance g>>1. At T=0 macroscopically superconductive state of the array with the lattice spacing b>>d is destroyed at g < g_c \approx 0.1 ln^2(b/d). At high temperatures the normal-state resistance between neighboring islands at b=b_c is much smaller than h/4e^2.Comment: RevTeX, 7 pages, 2 eps figure

Top-transmon: hybrid superconducting qubit for parity-protected quantum computation

Qubits constructed from uncoupled Majorana fermions are protected from decoherence, but to perform a quantum computation this topological protection needs to be broken. Parity-protected quantum computation breaks the protection in a minimally invasive way, by coupling directly to the fermion parity of the system --- irrespective of any quasiparticle excitations. Here we propose to use a superconducting charge qubit in a transmission line resonator (a socalled transmon) to perform parity-protected rotations and read-out of a topological (top) qubit. The advantage over an earlier proposal using a flux qubit is that the coupling can be switched on and off with exponential accuracy, promising a reduced sensitivity to charge noise.Comment: 7 pages, 5 figure

Quantum Glass Transition in a Periodic Long-Range Josephson Array

We show that the ground state of the periodic long range Josephson array frustrated by magnetic field is a glass for a sufficiently large Josephson energies despite the absence of a quenched disorder. Like superconductors, this glass state has non-zero phase stiffness and Meissner response; for smaller Josephson energies the glass "melts" and the ground state loses the phase stiffness and becomes insulating. We find the critical scaling behavior near this quantum phase transition: the excitation gap vanishes as (J-J_c)^2, the frequency-dependent magnetic susceptibility behaves as \chi(\omega) ~ \sqrt{\omega}\ln{\omega}.Comment: 9 pages, Latex, 3 figures in separated eps-file

First experimental evidence of one-dimensional plasma modes in superconducting thin wires

We have studied niobium superconducting thin wires deposited onto a SrTiO$_{3}$ substrate. By measuring the reflection coefficient of the wires, resonances are observed in the superconducting state in the 130 MHz to 4 GHz range. They are interpreted as standing wave resonances of one-dimensional plasma modes propagating along the superconducting wire. The experimental dispersion law, $\omega$ versus $q$, presents a linear dependence over the entire wave vector range. The modes are softened as the temperature increases close the superconducting transition temperature. Very good agreement are observed between our data and the dispersion relation predicted by Kulik and Mooij and Sch\"on.Comment: Submitted to Physical review Letter

Magnetic-field-dependent zero-bias diffusive anomaly in Pb oxide-n-InAs structures: Coexistence of two- and three-dimensional states

The results of experimental and theoretical studies of zero-bias anomaly (ZBA) in the Pb-oxide-n-InAs tunnel structures in magnetic field up to 6T are presented. A specific feature of the structures is a coexistence of the 2D and 3D states at the Fermi energy near the semiconductor surface. The dependence of the measured ZBA amplitude on the strength and orientation of the applied magnetic field is in agreement with the proposed theoretical model. According to this model, electrons tunnel into 2D states, and move diffusively in the 2D layer, whereas the main contribution to the screening comes from 3D electrons.Comment: 8 double-column pages, REVTeX, 9 eps figures embedded with epsf, published versio

Electron Glass in Ultrathin Granular Al Films at Low Temperatures

Quench-condensed granular Al films, with normal-state sheet resistance close to 10 k$\Omega/\Box$, display strong hysteresis and ultraslow, non-exponential relaxation in the resistance when temperature is varied below 300 mK. The hysteresis is nonlinear and can be suppressed by a dc bias voltage. The relaxation time does not obey the Arrhenius form, indicating the existence of a broad distribution of low energy barriers. Furthermore, large resistance fluctuations, having a 1/f-type power spectrum with a low-frequency cut-off, are observed at low temperatures. With decreasing temperature, the amplitude of the fluctuation increases and the cut-off frequency decreases. These observations combine to provide a coherent picture that there exists a new glassy electron state in ultrathin granular Al films, with a growing correlation length at low temperatures.Comment: RevTeX 3.1, 4 pages, 4 figures (EPS files) (Minor Additions

Coulombically Interacting Electrons in a One-dimensional Quantum Dot

The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is investigated as a function of the electron number and of the system length. The limitations of a description in terms of a capacitance are demonstrated. The energetically lowest lying excitations are physically explained as vibrational and tunneling modes. The limits of a dilute, Wigner-type arrangement of the electrons, and a dense, more homogeneous charge distribution are discussed.Comment: 10 pages (excl. Figures), Figures added in POSTSCRIPT, LaTe