Dual vortex theory of doped Mott insulators

We present a general framework for describing the quantum phases obtained by doping paramagnetic Mott insulators on the square lattice. The undoped insulators are efficiently characterized by the projective transformations of various fields under the square lattice space group (the PSG). We show that the PSG also imposes powerful constraints on the doped system, and on the effective action for the vortex and Bogoliubov quasiparticle excitations of superconducting states. This action can also be extended across transitions to supersolid or insulating states at non-zero doping. For the case of a valence bond solid (VBS) insulator, we show that the doped system has the same PSG as that of elementary bosons with density equal to the density of electron Cooper pairs. We also discuss aspects of the action for a d-wave superconductor obtained by doping a “staggered-flux” spin liquid state.     

Helical liquids and Majorana bound states in quantum wires

We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical electron liquid in single-channel quantum wires, with spin and velocity perfectly correlated. We argue that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional s-wave superconductor. This occurs when the external magnetic field, the superconducting gap, or, most simply, the chemical potential vary along the wire. These Majorana states do not require the presence of a vortex in the system. Experimental consequences of the helical liquid and the Majorana states are also discussed.     

Proposal for direct measuring of the Majorana number in a topological superconductor using a quantum dot

We propose to directly measure the Majorana number for one-dimensional topological superconductors using a quantum dot. The setup consists of two topological superconducting wires with four Majorana zero modes, which are coupled to an external quantum dot. The measurement is achieved by utilizing the definition of the Majorana number, which is the charge-parity flipping when changing the boundary condition for the topological superconductor. We consider a control of the boundary condition with voltage gates. When the voltage on the gate are modulated sequentially, the boundary conditions changes and the parity of the superconducting state flips. We demonstrate that this parity flipping will change the electron occupation probability of the quantum dot, which reflects the value of the Majorana number.     

Theory of pairing symmetry in the vortex states

We investigate pairing symmetry in an Abrikosov vortex and vortex lattice. It is shown that the Cooper pair wave function at the center of an Abrikosov vortex with vorticity m has a different parity with respect to frequency from that in the bulk if m is an odd number, while it has the same parity if m is an even number. As a result, in a conventional vortex with m = 1, the local density of states at the Fermi energy has a maximum (minimum) at the center of the vortex core in an even (odd)-frequency superconductor. In the vortex lattice of s-wave superconductor, we find that only odd-frequency pairing is present at the core centers, while at the midpoint of the vortex lines, only even-frequency pairing exists. Thus, the odd and even-frequency pairings also form the lattice in the vortex lattice state. We also propose a scanning tunneling microscope experiment using a superconducting tip to explore odd-frequency superconductivity.     

Massless and quantized modes of kinks in the phase space of superconducting gaps

We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory.     

First and second order quantum phase transitions in multi-band superconductors

In multi-band and inter-metallic materials superconductivity can be destroyed by applying external pressure in these systems. In many cases the critical temperature is driven continuously to zero, the superconducting to normal transition being associated with a superconducting quantum critical point (SQCP). In this paper we propose a model for this type of SQCP based on the increase of hybridization as pressure is applied in the material. We study a two-band superconductor with hybridization V between these bands. We use a BCS approximation and include both inter- and intra-band attractive interactions. We show that for negligible inter-band interactions, as hybridization increases there is a second order phase transition from a superconductor to a normal state at zero temperature at a critical value of the hybridization V_c. This SQCP can be reached by pressure, since this external parameter controls hybridization in the system. We also find discontinuous transitions at zero temperature and the appearance of a gapless superconducting (GS) phase in a certain range of hybridization in the case of inter-band interactions being dominant.     

Vortex structure in superconductors with a many-component order parameter

Abstract

The phenomenological theory of superconductors with a many-component order parameter (OP) is developed. On the basis of a generalized Ginzburg-Landau functional, equations for a two-component-OP superconductor are derived. It is shown that such a superconductor is specified by three length dimensionality parameters—penetration depth λ, correlation length ζ, and width d of the boundary between two superconducting-phase domains. With λ ? d ? ζ, the equations for the OP of a superconductor in a magnetic field can be explored analytically. The transition from the superconducting to the mixed phase may occur not only by the formation of ordinary Abrikosov vortices, but also owing to vortices that have two cores, each transferring a half-integral flux quantum. The total flux transferred by a vortex certainly constitutes an integral quantum. The cores of such a dimer are interconnected by two domain walls, which exercise confinement within the dimer. The distance between the cores in the dimer is of the order of d. Within a domain wall that separates two superconducting-phase domains, a dimer may fall apart into two vortices with a half-integral flux quantum.

For many-component-OP superconductors in a magnetic field, vortex structures of a more complicated nature than a dimer may occur. An individual core may transfer a fractional flux quantum, but the structure as a whole transfers an integral flux quantum. Confinement of individual cores occurs owing to a complicated system of domain walls determined by the topological charges of these vortices.

Under certain conditions, on attaining field H _c1, vortices may arise first in the domain walls, carrying a fractional flux quantum, and then within the superconducting domains.     

A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors

We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux-quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum space construction of the zero-mode solution presented here is complementary to the approximate real space solution of the Bogoliubov-de Gennes equations at a vortex core (Sau et al., arXiv:0907.2239 [17]), proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.     

Confinement of monopole field lines in a superconductor at T ≠ 0

We apply the Bogoliubov-de Gennes equations to the confinement of a monopole-antimonopole pair in a superconductor. This is related to the problem of a quark-antiquark pair bound by a confining string, consisting of a colour-electric flux tube, dual to the magnetic vortex of type-II superconductors. We study the confinement of the field lines due to the superconducting state and calculate the effective potential between the two monopoles. The monopoles can be simulated in a real experiment inserting two long and thin magnetic rods. At short distances the potential is Coulombic and at large distances the potential is linear, as previously determined solving the Ginzburg-Landau equations. The magnetic field lines and the string tension are also studied as a function of the temperature T. Because we take into account the explicit fermionic degrees of freedom, this work may open new perspectives to the breaking of chiral symmetry or to colour superconductivity.     

Designing current-strain-assisted superconductor-ferromagnet multi-bit memories

Current superconducting memory devices lack the basic quality of high memory density for practical memories, mainly due to the size limitations of superconducting quantum interference devices. Here, we propose a superconductor-ferromagnet bilayer device with strain-pulse-assisted multi-bit ladder-type memory, by using strain-engineered ferromagnet domain structure to control carrier concentration in the superconductor, which is simulated by coupled Landau-Lifshitz-Gilbert and Ginzburg-Landau equations. Current- and strain-pulses are observed to deterministically control the resistivity of superconductor for one and two-bit device arrangements. The average carrier concentration of superconductor is observed to have multiple metastable states that can be controllably switched using current-pulse and strain-pulse to determine multiple resistivity states. These findings confirm the eligibility of superconductor-ferromagnet bilayers to be used as ladder-type multibit memories and open a new way for further theoretical and experimental investigations of the cryogenic memories.     

Avoidance of Majorana resonances in periodic topological superconductor-nanowire structures

Semiconducting nanowires in proximity to superconductors are promising experimental systems for Majorana fermions which may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental realization of the Majorana fermion in these semiconductor-superconductor-nanowire structures is tuning the semiconductor chemical potential in close proximity to the metallic superconductor. We show that presently realizable structures in experiments with tunable chemical potential lead to Majorana resonances, which are interesting in their own right, but do not manifest non-Abelian statistics. To resolve this crucial barrier to the solid state realization of Majorana fermions, we propose a new topological superconducting array structure where introducing the superconducting proximity effect from adjacent nanowires generates Majorana fermions with non-Abelian statistics.     

Bogoliubov angle and visualization of particle-hole mixture in superconductors

Superconducting excitations—Bogoliubov quasiparticles—are the quantum mechanical mixture of negatively charged electron (−e) and positively charged hole (+e). Depending on the applied voltage bias in scanning tunneling microscope (STM) one can sample the particle and hole content of such a superconducting excitation. Recent STM experiments offer a unique insight into the inner workings of the superconducting state of superconductors. We propose a new observable quantity for STM studies that is the manifestation of the particle-hole dualism of the quasiparticles. We call it a Bogoliubov angle. This angle measures the relative weight of particle and hole amplitude in the superconducting (Bogoliubov) quasiparticle. We propose that this quantity can be measured locally by comparing the ratio of tunneling currents at positive and negative biases locally. This Bogoliubov angle allows one to measure directly the energy and position dependent particle-hole admixture and therefore visualize robustness of superconducting state locally. It may also allow one to measure the particle-hole admixture of excitations in normal state above critical temperature and thus may be used to measure superconducting correlations in pseudogap state.     

Coherent transmission of nodal Dirac fermions through a graphene-based superconducting double barrier junction

Transport characteristics of relativistic electrons through graphene-based d-wave superconducting double barrier junction and ferromagnet/d-wave superconductor/normal metal double junction have been investigated based on the Dirac–Bogoliubov–de Gennes equation. We have first presented the results of superconducting double barrier junction. In the subgap regime, both the crossed Andreev and nonlocal tunneling conductance all oscillate with the bias voltage due to the formation of Andreev bound states in the normal metal region. Moreover, the critical voltage beyond which the crossed Andreev conductance becomes to zero decreases with increasing value of superconducting pair potential α. In the presence of the ferromagnetism, the MR through graphene-based ferromagnet/ d-wave superconductor/normal metal double junction has been investigated. It is shown that the MR increases from exchange splitting h ₀=0 to h ₀=E _F (Fermi energy), and then it goes down. At h ₀=E _F, MR reaches its maximum 100. In contrast to the case of a single superconducting barrier, Andreev bound states also manifest itself in the zero bias MR, which result in a series of peaks except the maximum one at h ₀=E _F. Besides, the resonance peak of the MR can appear at certain bias voltage and structure parameter. Those phenomena mean that the coherent transmission can be tuned by superconducting pair potential, structure parameter, and external bias voltage, which benefits the spin-polarized electron device based on the graphene materials.     

Anomalous Josephson current via Majorana bound states in topological insulators

We propose a setup involving Majorana bound states (MBS) hosted by a vortex on a superconducting surface of a 3D topological insulator (TI). We consider a narrow channel drilled across a TI slab with both sides covered by s-wave superconductor. In the presence of a vortex pinned to such a channel, it acts as a ballistic nanowire connecting the superconducting surfaces, with a pair of MBS localized in it. The energies of the MBS possess a 4π-periodic dependence on the superconductive phase difference φ between the surfaces. It results in the appearance of an anomalous term in the current-phase relation I(a)(φ) for the supercurrent flowing along the channel between the superconductive surfaces. We have calculated the shape of the 4π-periodic function I(a)(φ), as well as the dependence of its amplitude on temperature and system parameters.     

Quantum phase transitions and vortex dynamics in superconducting networks

Josephson-junction arrays are ideal model systems to study a variety of phenomena such as phase transitions, frustration effects, vortex dynamics and chaos. In this review, we focus on the quantum dynamical properties of low-capacitance Josephson-junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated with the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy needed to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single-electron effects with the Josephson effect. They give rise to (quantum) superconductor–insulator phase transitions that occur when the ratio between the coupling constants is varied or when the external fields are varied. We describe the dependence of the various control parameters on the phase diagram and the transport properties close to the quantum critical points. On the superconducting side of the transition, vortices are the topological excitations. In low-capacitance junction arrays these vortices behave as massive particles that exhibit quantum behavior. We review the various quantum–vortex experiments and theoretical treatments of their quantum dynamics.     

Electron entanglement detected by quantum spin Hall systems

We propose a promising electron entanglement detector consisting of two quantum spin Hall systems weakly coupled to a superconductor. The detection of electron spins along various polarization directions, which is a prerequisite for testing Bell's inequality on solid state spins, can be achieved in an all-electrical-controlled manner utilizing the helical edge states. It is found that the violation of Bell's inequality exists in a large range of the tunneling parameters, which can be realized in mercury telluride quantum wells.     

Disorder and quantum fluctuations in superconducting films in strong magnetic fields

We find that the upper critical field in a two-dimensional disordered superconductor can increase essentially at low temperatures. This happens due to the formation of local superconducting islands weakly coupled via the Josephson effect. The distribution of the superconducting islands is derived. It is shown that the value of the critical field is determined by the interplay of the proximity effect and quantum phase fluctuations. The shift of the upper critical field is connected with the pinning properties of a superconductor.     

约瑟夫森器件中的宏观量子现象及超导量子计算

超导体中的电子结成库珀对，凝聚到可以用一个宏观波函数来描绘的能量基态，该波函数的位相是代表了成百万库珀对集体运动的宏观变量．以约瑟夫森结为基础元件的超导约瑟夫森器件，使人们能够控制并测量一个超导体的位相和库珀对数目，因此是研究宏观量子现象的理想系统．文章回顾了约瑟夫森器件中的宏观量子现象研究的发展历程，介绍了当前超导约瑟夫森器件在量子计算中的重要应用，并对它们的未来作了简要的展望．     

Vortex Pinning due to Dynamic Spin-Vortex Interaction in aSuperconductor/Ferromagnet Multilayer

We investigate the mutual interaction between superconductivity and ferromagnetism in a Nb/Ni81 Ee19 multilayer by ac susceptibility measurements. Compared with a pure superconducting Nb film, the critical current density of the multilayer is apparently enhanced in a low magnetic field region but remains nearly the same in high magnetic fields, which indicates that a continuous ferromagnetic layer with in-plane magnetization can produce strong vortex pinning in a low field region. We interpret this unusual vortex-pinning phenomenon as a consequence of dynamic spin vortex interaction which induces a spin rotation following vortex movement. In addition, we propose that this dynamic interaction could be used for spin manipulation via a superconductor.     

Implementation of a Quantum Conditional Phase Gate for the Quantum Fourier Transform in Circuit QED

It is well known that multiple superconducting charge qubits coupled to a transmission line resonator can be controlled to achieve quantum logic gates between two arbitrary qubits. We propose a scheme to realize a quantum conditional phase gate with a geometric property by circuit electrodynamics, and it is applied naturally to reaJize the quantum Fourier transform with high fidelity. It is also demonstrated that the application is feasible and considerable under the present experimental technology.