Resonant transport through midgap states in voltage-biased Josephson junctions of d-wave superconductors

We study theoretically the ac Josephson effect in voltage-biased planar junctions of d-wave superconductors. For some orientations of the superconductors a current peak is found at finite voltage in the current–voltage characteristics. We pick out the relevant physical processes and write down an analytical formula for the current which clearly shows how the midgap state acts as a resonance and produces the peak. We present a possible explanation for the zero-bias conductance peak, recently found in experiments on grain boundary junctions of high-temperature superconductors, in terms of resonant transmission through midgap state of quasiparticles undergoing multiple Andreev reflections. We note that within our framework the zero-bias conductance peak appears in rather transparent Josephson junctions of d-wave superconductors.     

Controlled dynamics of sine-Gordon breather in long Josephson junctions

A possible definition of the specific heat of open quantum systems is based on the reduced partition function of the system. For a free damped quantum particle, it has been found that under certain conditions, this specific heat can become negative at low temperatures. In contrast to the conventional approaches focusing on the system degree of freedom, here we concentrate on the changes induced in the environment when the system is coupled to it. Our analysis is carried out for an Ohmic environment consisting of harmonic oscillators and allows to identify the mechanism by which the specific heat becomes negative. Furthermore, the formal condition for the occurrence of a negative specific heat is given a physical interpretation in terms of the total mass of bath oscillators and the system mass.     

Resonant effects in ballistic Josephson junctions

We study the Josephson effect in ballistic double-barrier SINIS planar junctions, consisting of bulk superconductors (S), a clean normal metal or semiconductor (N), and insulating interfaces (I) modeled as a δ-function potential-energy barriers. We solve the scattering problem based on the Bogoliubov-de Gennes equations and derive a general expression for the dc Josephson current, valid for arbitrary interfacial transparency, the Fermi wave vectors mismatch, and for different effective band masses. The effect of transmission resonances on the Josephson current and on the normal conductance is analyzed for short junctions. Curvature of the temperature dependence of the critical Josephson current is related to the presence of resonances at the Fermi level and to the interfacial transparency. For thin semiconductor layers with negative effective masses of the carriers, finite interfacial transparency and large Fermi wave vectors mismatch we find that an unusual and significant enhancement of both the normal conductance and the critical Josephson current occurs at low temperatures due to the presence of an evanescent mode localized at interfaces.     

Possible dynamic states in inductively coupled intrinsic Josephson junctions of layered high-Tc superconductors

Based on computer simulations and theoretical analysis, a new dynamic state is found in inductively coupled intrinsic Josephson junctions in the absence of an external magnetic field. In this state, the plasma oscillation is uniform along the c axis with the fundamental frequency satisfying the ac Josephson relation. There are (2m+1)pi phase kinks around the junction center, with m being an integer, periodic and thus nonuniform in the c direction. In the IV characteristics, the state manifests itself as current steps occurring at all cavity modes. Inside the current steps, the plasma oscillation becomes strong, which generates several harmonics in frequency spectra at a given voltage. The recent experiments on terahertz radiations from the mesa of a Bi{2}Sr{2}CaCu{2}O{8+delta} single crystal can be explained in terms of this state.     

Synthesis of maximally entangled mixed states and disentanglement in coupled Josephson charge qubits

We analyze a controllable generation of maximally entangled mixed states of a circuit containing two-coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Illustrative variational calculations were performed to demonstrate the effect on the two-qubits entanglement. At sufficiently deviation between the Josephson energies of the qubits and/or strong coupling regime, maximally entangled mixed states at certain instances of time is synthesized. We show that entanglement has an interesting subsequent time evolution, including the sudden death effect. This enables us to completely characterize the phenomenon of entanglement sharing in the coupling of two superconducting charge qubits, a system of both theoretical and experimental interest.     

Quasistable states in globally coupled tent map systems

The characteristics of long lasting but not perpetual chaotic states appear in a wide parameter region in a globally coupled overcritical tent map system are exhibited. The lifetime of the transient state has essential relevance with the system size. In some parameter region, the lifetime saturates at a certain level, while in another region it seems to diverge as the size of the system grows. In order to uncover the dynamical structures in large system size limit, the dynamics of one-body distribution is investigated as an idealized model for the infinitely large coupled map system. Obtained numerical results indicate the correspondence between the characteristics of long transient behavior in finite size system and that of the attractor or the ruin of attractor in the idealized model.     

The confined breather: Quantized states from classical field theory

The energy of a sine-Gordon breather moving in a square-well potential is studied. The ideally reflecting walls of the well are simulated by two trains of breathers moving with opposite velocity and opposite phase, the solution being found by use of the appropriate Bäcklund transformation. The confined breather shows discrete energy levels identical with those obtained from the Schrödinger equation for a particle confined in such a potential. The breather, however, is governed by a classical, non-linear field equation for the extended field u, which is subject to classical interpretation in contrast to the statistical interpretation of the ψ-wave of quantum mechanics.     

Resonant Andreev reflection in a normal-metal/quantum-dot/superconductor system with coupled Majorana bound states

Andreev reflection(AR) in a normal-metal/quantum-dot/superconductor(N–QD–S) system with coupled Majorana bound states(MBSs) is investigated theoretically. We find that in the N–QD–S system, the AR can be enhanced when coupling to the MBSs is incorporated. Fano line-shapes can be observed in the AR conductance spectrum when there is an appropriate QD–MBS coupling or MBS–MBS coupling. The AR conductance is always e~2/2h at the zero Fermi energy point when only QD–MBSs coupling is considered. In addition, the resonant AR occurs when the MBS–MBS coupling roughly equals to the QD energy level. We also find that an AR antiresonance appears when the QD energy level approximately equals to the sum of the QD–MBS coupling and the MBS–MBS coupling. These features may serve as characteristic signatures for the probe of MBSs.     

The stability boundary of synchronized states in globally coupled dynamical systems

The stability boundary of synchronized states in families of globally coupled map lattices and differential equations are studied. It is shown that this boundary may have a very complicated structure in a wide variety of systems. This explains why states can go through sequences of desynchronization and resynchronization as a parameter is varied: in `typical' systems, between any two parameter values at which synchronized states are unstable there are parameter values at which synchronized states are stable!     

Resonant Josephson tunneling through S-I-S junctions of arbitrary size

The Josephson tunneling current in S-I-S structures where the main current transport channel is resonant tunneling through an isolated localized state is calculated using the Bogolyubov-de Gennes equations. It is shown that the efficiency of equilibrium Josephson resonant tunneling is determined only by the ratio of the width of the resonance level to the absolute value of the order parameter for the superconducting electrodes with arbitrary relationships among the system parameters. Zh. éksp. Teor. Fiz. 112, 342–352 (July 1997)     

Resonant states and their uses

The paper shows, for a simple model, how the wave functions belonging to complex energy eigenvalues (resonance states) can be regarded as part of a complete set of states, containing also bound states and a continuum of (generally complex) wave functions. This forms the basis of an expansion, which is used to describe inelastic scattering in the plane-wave Born approximation, taking the same simple model for the target.     

Transitions in two sinusoidally coupled Josephson junction rotators

We investigate the dynamics of two sinusoidally coupled Josephson junction rotators to provide a clear knowledge of the behaviors in different regions of the parameter space. The dynamical states are identified, and the transitions among these states are studied. The properties of the current–voltage curves are investigated. Further more, we observed the chaotic states in some regions of parameter space. We conjecture it may caused by the competition of two periodic potentials: one is the external field, another is the interacting of two particles.     

Resonant escape over an oscillating barrier in underdamped Josephson tunnel junctions

The escape from a metastable state over an oscillating barrier of an underdamped Josephson tunnel junction has been experimentally investigated with oscillation frequency well separated from the plasma frequency of the junction. The resonant escape, namely, a minimum of the average escape time as a function of the oscillation frequency, was observed. For the oscillation frequency much smaller than the "resonant frequency," the average escape time is the average of the times required to cross over each of the barriers. On the other hand, for the oscillation frequency much greater than the "resonant frequency," the average escape time is that required to cross the average barrier.     

Resonant regions of Josephson junction equation in case of large damping

The dynamics of Josephson junction equation in case of damping α>2 is investigated numerically. In this case the second-order system can be asymptotically reduced in the large to a one-dimensional circle map. We study the parametric dependence of the resonances of this system and plot the resonant regions in two-dimensional parameter space. The periodic variation of the widths of harmonic regions with increase of the periodic driving force is observed. In the limit of infinite damping, we study a first order system through suitable re-scaling and the same property is observed. We conjecture this may caused by the competition between the periodic potential and the periodic external driving in these systems.     

Resonant states in heterostructures of graphene nanoribbons

We study the transport properties of heterostructures of armchair graphene nanoribbons (AGNR) forming a double symmetrical barrier configuration. The systems are described by a single-band tight-binding Hamiltonian and Green's functions formalism, based on real-space renormalization techniques. We present results for the quantum conductance and the current for distinct configurations, focusing our analysis on the dependence of the transport with geometrical effects such as separation, width and transverse dimension of the barriers. Our results show the apparition of a series of resonant peaks in the conductance, showing a clear evidence of the presence of resonant states in the conductor. Changes in the barrier dimensions allow the modulation of the resonances in the conductance, making possible to obtain a complete suppression of electron transmission for determined values of the Fermi energy. The current–voltage curves show the presence of a negative differential resistance effect with a threshold voltage that can be controlled by varying the separation between the barriers and by modulating its confinement potential.     

Incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media

We theoretically investigate the propagation of incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media. It is found that multipole-mode soliton pairs with arbitrary different orders of Hermite-Gaussian shape can exist when the total power of two beams equals the critical power and the ratio of the beam widths for the Gaussian part is inversely proportional to the square root of the ratio of the wave numbers. When the total power does not equal the critical power, the Hermite-Gaussian breather pair exists and their beam widths evolve analogously. For general cases where the ratio of the beam widths is arbitrary, soliton-breather pairs or breather-breather pairs can be formed and their beam widths evolve synchronously in-phase or out-of-phase. Numerical simulations directly based on the nonlocal nonlinear Schrödinger equation are conducted for comparison with our theoretical predictions. The numerical stability analysis shows the higher-order Hermite-Gaussian solitons can not be stable for small nonlocality or for some media like liquid crystals.