Intermittent superconductivity in three-dimensional mesoscopic rings

Three-dimensional mesoscopic rings are investigated by the phenomenological Ginzburg–Landau theory in the presence of an externally applied magnetic-field. By solving an eigenvalue problem and minimizing systematic free energy, we find that the superconducting and normal states cyclically appear, and that between the state L and the state L + 1 the field extent of existing normal state increases with increase of vorticity L. The dimensional phase diagram with the maximum vorticity and existing normal state between two superconducting states is given. The normal state can be controlled by the medium with surface enhancement or suppression of superconductivity.     

Quantum Superposition of Two Coherent States in a Mesoscopic Josephson Junction

We study a mesoscopic Josephson junction in a circular superconducting ring which encloses a magneto static flux. It is shown that with the junction being initially prepared in vacuum state, the state of the junction can evolve into a quantum superposition of two coherent states.     

Stable and metastable states in a mesoscopic superconducting “eight” loop in presence of an external magnetic field

The stable and metastable states of different configurations of a mesoscopic loop in the form of an eight is studied in the presence of a magnetic field. We find that for certain configurations the current is equal to zero for any value of the magnetic field leading to a magnetic field independent superconducting state. The state with fixed phase circulation becomes unstable when the momentum of the superconducting electrons reaches a critical value. At this moment the kinetic energy of the superconducting condensate becomes of the same order as the potential energy of the Cooper pairs and it leads to an instability. Numerical analysis of the time-dependent Ginzburg–Landau equations shows that the absolute value of the order parameter changes gradually at the transition from a state with one phase circulation to another although the vorticity change occurs abruptly.     

Metastability and paramagnetism in superconducting mesoscopic disks

A projected order parameter is used to calculate not only local minima of the Ginzburg-Landau energy functional but also saddle points or energy barriers responsible for the metastabilities observed in superconducting mesoscopic disks [A. K. Geim et al., Nature (London) 396, 144 (1998)]. We calculate the local minima magnetization and find the energetic instability points between vortex configurations with different vorticity. We also find that, for any vorticity, the supercurrent can reverse its flow direction on decreasing the magnetic field before one vortex can escape.     

Superconducting state evolution with applied magnetic flux in mesoscopic rings

The magnetic flux dependence of the vortex state for small mesoscopic superconducting rings surrounded by a medium is investigated by the phenomenological Ginzburg-Landau theory. The influences of the ring size and the surface superconductivity on the free energy and total supercurrent are studied. For narrow rings, the persistent current evolves towards a periodic behaviour with magnetic flux. The complete paramagnetic or diamagnetic state, corresponding to positive or negative current flowing in the whole ring, can occur. A remarkable intermittent superconducting behaviour for the ground-state transition is found when the strength of surface-suppressed superconductivity is enlarged or the ring size is decreased. Consequently, a pure superconducting state with positive total current can be obtained.     

三维介观超导环的涡旋结构

在Ginzburg-Landan理论的框架下, 运用有限差分法研究了在圆环电流产生磁场下的介观超导圆环内的涡旋结构, 讨论了超导圆环尺寸和不同空间分布的磁场对涡旋形成的影响, 得到在一般超导圆环体内的基态多是巨涡旋态、而多涡旋态多以激发态形式存在的结论, 说明磁场一般从超导圆环的环孔穿过, 而很难穿过超导圆环体.     

Electric Charges in Superconducting Mesoscopic Samples

The distribution of the electric charge density in mesoscopic superconducting disks and cylinders is studied within the phenomenological Ginzburg-Landau approach. We found that even in the Meissner state the mesoscopic sample exhibits a non-uniform charge distribution such that a region near the sample edge becomes negatively charged. When vortices are inside the sample there is a superposition of the negative charge located at the vortex core and this Meissner charge, and, as a result, the charge at the sample edge changes sign as a function of the applied magnetic field.     

Experimental distinction between giant vortex and multivortex states in mesoscopic superconducting squares

We study the distinction between giant vortex states and multivortex states in a thin mesoscopic superconducting square by using the temperature dependence of the vortex expulsion fields. We find that the results agree well with those obtained from the multiple-small-tunnel-junction method, indicating that the distinction by the temperature dependence of the vortex expulsion fields is applicable to superconducting squares.     

Quantum Magnetoresistive (hc/2e)/m-Periodic Oscillations in a Superconducting Ring

JETP Letters - It has been found experimentally that quantum magnetoresistive hc/2e-periodic Little-Parks oscillations in a mesoscopic superconducting ring with a decrease in the temperature and an...     

Local density of states of vortex state in mesoscopic superconductors

We study local density of states (LDOS) of vortex state in mesoscopic square superconductors with Bogoliubov-de Gennes (BdG) equation. We develop one effective numerical method based on the finite element method to self-consistently solve the BdG equation. The LDOS for various vortex states is obtained. Our results about the single vortex show that the LDOS has the particle-hole asymmetry and the results for one- and two-vortex state agree very well with the experimental observation. Besides, we predict the LDOS of multi-vortex states, which is crucial for the further STM/STS experimental study of vortex state in mesoscopic superconducting system.     

Relaxation processes in mesoscopic superconductors

We investigate the possibility of a novel kind of optical pump probe spectroscopy where the two laser pulses are focused on different areas of the sample. The response to the destruction of the superconducting state in a large part of a mesoscopic ring is studied numerically. We use the time dependent Ginzburg-Landau equations with periodic boundary conditions and external magnetic field. We evaluate the relaxation rates of the superconducting order parameter as well as the voltage induced by the charge imbalance. Computer simulations confirm that the perturbation of superconductivity on one part of the ring induces a voltage which decelerates the superconducting electrons on the other part of the ring. This deceleration results in the decrease of the superconducting current and the superfluid density. The relaxation times are of the order of the picosecond, the induced voltage of few millivolts and the variation of the superconducting gap of 10% which we believe to be suitable for time resolved femtosecond optical spectroscopy.     

Josephson transport in complex mesoscopic structures

A universal spectral equation is derived for Andreev bound states in superconducting quantum junctions, relating bound state energies with the normal electron scattering amplitudes. The equation is applied to calculation of d.c. Josephson effect in mesoscopic S-2DEG-S junctions.     

薄介观超导环中的涡旋电荷分布

本文用Ginzburg-Landau理论研究在薄介观超导环中的涡旋电荷分布．对于巨涡旋态，我们发现随着外场的增加，内半径附近的电荷会从负号变为正号．本文表明，是顺磁迈斯纳效应和抗磁迈斯纳效应的竞争决定了涡旋电荷的分布．     

Effects of geometrical symmetry on the vortex in mesoscopic superconductors

We first systematically study the multivortex states in mesoscopic superconductors via self-consistent Bogoliubov-de Gennes equations. Our work focuses on how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors and find that the key parameter determining the entrance of the vortex is the current density at the hot spots on the edge of sample. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconductors with their topological geometries, and they can be easily generalized to the confined superfluids and Bose-Einstein condensates.     

Two-dimensional mesoscopic vortex clusters in a superconducting ring: Shell structure and melting

The structure and phase transitions in the mesoscopic system of vortices in a quasi-two-dimensional superconducting ring are investigated. The shell structure of the mesoscopic system of vortices is studied, and its variation with the number of vortices and the parameters of the superconducting ring is analyzed. Two mechanisms of formation of new shells in vortex clusters with an increasing number of vortices in an increasing magnetic field are discovered: the generation of a new shell in a cluster and the splitting of the internal shell into two shells. The melting of vortex clusters and their thermodynamic parameters are analyzed using the Monte Carlo method. It is found that the melting of shell-type clusters occurs in two stages, orientation melting taking place at the lower temperature (during which nearly crystalline adjacent shells start rotating relative to each other) and blurring of the vortex structure occurring at the higher temperature. The shells obtained by splitting upon an increase in the number of vortices do not participate in orientational melting. The two-stage form of melting is associated with the smaller height of potential barriers being surmounted during the rotation of shells relative to one another as compared to the barrier for vortices jumping from one shell to another.     

Mesoscopic entangled coherent states implemented with a circuit quantum electrodynamics system

We show a scheme to generate entangled coherent states in a circuit quantum electrodynamics system, which consists of a nanomechanical resonator, a superconducting Cooper-pair box (CPB), and a superconducting transmission line resonator. In the system, the CPB plays the role of a nonlinear medium and can be conveniently controlled by a gate voltage including direct-current and alternating-current components. The scheme provides a powerful tool for preparing the multipartite mesoscopic entangled coherent states.     

三维介观超导环涡旋态的研究

通过数值求解非线性金兹堡-朗道(G-L)方程组,研究了三维介观超导环中的涡旋态。发现了在细环中只能存在巨涡旋态,以及存在顺磁、抗磁迈斯纳效应和间隙性超导现象。在粗环中,发现了多涡旋态和巨涡旋态共存的混合态。相应讨论有助于理解介观超导环中涡旋态相变。     

Non-rigid hole band in the extended t-J model

Based on a simple matrix method, we investigate the effects of Fermi vector mismatch and elastic barrier on the dc Josephoson current through a ballistic, normal, one-dimensional quantum channel in contact with two superconducting electrodes. The coexistence of Andreev reflection and normal reflection forms quasibound states with open gaps in the normal conductor. The quantum transmission of individual electrons (or holes) gives new features to this mesoscopic system. The critical current character of a 2DEG coupled superconducting heterostructure with a length of sevral m0 is extensively studied. More importantly, our theoritical results are able to account for the recent anomalous experimental results.     

Levitating states of superconducting rings in the field of a fixed ring with constant current

We consider the possibility of designing a plasma trap with a magnetic system formed by super-conducting rings and coils levitating in the field of a fixed coaxial coil carrying constant current. An analytic dependence of the potential energy of such a system with one or two levitating superconducting rings having trapped preset magnetic fluxes on their coordinates in the uniform gravitational field is obtained in the thin ring approximation. Calculations performed in the Mathcad system show that equilibrium states of such a system exist for certain values of parameters. Levitating states of a single superconducting ring and two superconducting rings in the field of the coil with constant current are observed experimentally in positions corresponding to calculated values.     

Excess resistance in the superconducting transition of a mesoscopic Al disk

We report resistance measurements on a mesoscopic Al disk whose size is comparable to the superconducting coherence length. As the magnetic field increases, resistance peaks successively appear and some of the peak resistances are larger than the normal state value R_N. These peaks are ascribed to the transitions between different vortex states in the superconducting Al disk. The experimental results suggest that some anomalous energy dissipation is caused by the dynamics of the vortices in the confined geometry.