Dissipation and quantum phase transitions of a pair of Josephson junctions

A model system consisting of a mesoscopic superconducting grain coupled by Josephson junctions to two macroscopic superconducting electrodes is studied. We focus on the effects of Ohmic dissipation caused by resistive shunts and superconducting-normal charge relaxation within the grain. As the temperature is lowered, the behavior crosses over from uncoupled Josephson junctions, similar to situations analyzed previously, to strongly interacting junctions. The crossover temperature is related to the energy-level spacing of the grain and is of the order of the inverse escape time from the grain. In the limit of zero temperature, the two-junction system exhibits five distinct quantum phases, including a novel superconducting state with localized Cooper pairs on the grain but phase coherence between the leads due to Cooper pair cotunneling processes. In contrast to a single junction, the transition from the fully superconducting to fully normal phases is found to be controlled by an intermediate-coupling fixed point whose critical exponents vary continuously as the resistances are changed. The model is analyzed via two-component sine-Gordon models and related Coulomb gases that provide effective low-temperature descriptions in both the weak and strong Josephson coupling limits. The complicated phase diagram is consistent with symmetries of the two component sine-Gordon models, which include weak- to strong-coupling duality and permutation triality. Experimental consequences of the results and potential implications for superconductor to normal transitions in thin wires and films are discussed briefly

Chaotic quantum dots with strongly correlated electrons

Quantum dots pose a problem where one must confront three obstacles: randomness, interactions and finite size. Yet it is this confluence that allows one to make some theoretical advances by invoking three theoretical tools: Random Matrix theory (RMT), the Renormalization Group (RG) and the 1/N expansion. Here the reader is introduced to these techniques and shown how they may be combined to answer a set of questions pertaining to quantum dotsComment: latex file 16 pages 8 figures, to appear in Reviews of Modern Physic

A Universal Interacting Crossover Regime in Two-Dimensional Quantum Dots

Interacting electrons in quantum dots with large Thouless number $g$ in the three classical random matrix symmetry classes are well-understood. When a specific type of spin-orbit coupling known to be dominant in two dimensional semiconductor quantum dots is introduced, we show that a new interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.Comment: 4 pages, 1 figur

Superconductor-to-Metal Transitions in Dissipative Chains of Mesoscopic Grains and Nanowires

The interplay of quantum fluctuations and dissipation in chains of mesoscopic superconducting grains is analyzed, and the results are also applied to nanowires. It is shown that in 1-d arrays of resistively shunted Josephson junctions, the superconducting-normal charge relaxation within the grains plays an important role. At zero temperature, two superconducting phases can exist, depending primarily on the strength of the dissipation. In the fully superconducting phase (FSC), each grain acts superconducting, and the coupling to the dissipative conduction is important. In the SC* phase, the dissipation is irrelevant at long wavelengths. The phase transitions between these two superconducting phases and the normal metallic phase may be either local or global, and possess rich and complex critical properties. These are inferred from both weak and strong coupling renormalization group analyses. At intermediate temperatures, near either superconductor-to-normal phase transition, there are regimes of super-metallic behavior, in which the resistivity first decreases gradually with decreasing temperature before eventually increasing as temperature is lowered further. The results on chains of Josephson junctions are extended to continuous superconducting nanowires and the subtle issue of whether these can exhibit an FSC phase is considered. Potential relevance to superconductor-metal transitions in other systems is also discussed.Comment: 42 pages, 14 figure

Pseudospin-Resolved Transport Spectroscopy of the Kondo Effect in a Double Quantum Dot

We report measurements of the Kondo effect in a double quantum dot (DQD), where the orbital states act as pseudospin states whose degeneracy contributes to Kondo screening. Standard transport spectroscopy as a function of the bias voltage on both dots shows a zero-bias peak in conductance, analogous to that observed for spin Kondo in single dots. Breaking the orbital degeneracy splits the Kondo resonance in the tunneling density of states above and below the Fermi energy of the leads, with the resonances having different pseudospin character. Using pseudospin-resolved spectroscopy, we demonstrate the pseudospin character by observing a Kondo peak at only one sign of the bias voltage. We show that even when the pseudospin states have very different tunnel rates to the leads, a Kondo temperature can be consistently defined for the DQD system.Comment: Text and supplementary information. Text: 4 pages, 5 figures. Supplementary information: 4 pages, 4 figure

Electron Pair Resonance in the Coulomb Blockade

We study many-body corrections to the cotunneling current via a localized state with energy $\epsilon_d$ at large bias voltages $V$. We show that the transfer of {\em electron pairs}, enabled by the Coulomb repulsion in the localized level, results in ionization resonance peaks in the third derivative of the current with respect to $V$, centered at $eV=\pm 2\epsilon_d/3$. Our results predict the existence of previously unnoticed structure within Coulomb-blockade diamonds.Comment: 5 pages, 4 figure

Quantum criticality near the Stoner transition in a two-dot with spin-orbit coupling

We study a system of two tunnel-coupled quantum dots, with the first dot containing interacting electrons (described by the Universal Hamiltonian) not subject to spin-orbit coupling, whereas the second contains non-interacting electrons subject to spin-orbit coupling. We focus on describing the behavior of the system near the Stoner transition. Close to the critical point quantum fluctuations become important and the system enters a quantum critical regime. The large-$N$ approximation allows us to calculate physical quantitites reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi liquid regime and the quantum critical regime.Comment: 19 pages, 5 figure

Level-occupation switching of the Quantum Dot, and phase anomalies in mesoscopic interferometry

For a variety of quantum dots, the widths of different single-particle levels may naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. We found that in this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation of the salient features of the behavior of the transmission phase in an interferometer with a QD. The theory of this effect will be reviewed with special emphasis on the role of the interactions. New results on the dot-charging measurements and the fine structure of occupation switchings will be presented, accompanied by the unified description of the whole series of CB peaks caused by a single broad level. We then discuss the case where the system approaches the Kondo regime.Comment: 30 pages in IOP format, 11 figure