Topological phase effect on a superconductivity model: Generalized Jahn-teller problems and fractional charge

Using a toy model of the pairing hamiltonian, we show that the topological (Berry) phase leads to the fractional quantization of the pairing mode in superconductivity, which implies a fractional charge of the Cooper pair.     

Peierls transition in a quasi-one dimensional system

We study the thermodynamics of a noninteracting electron system with a half filled strongly anisotropic tight binding band in the mean field approximation. This system may exhibit a structural transition dimerizing along the high conductivity direction. The conditions for the instability to occur are given as a function of the degree of anisotropy. The relationship to the behavior of TCNQ salts is discussed.     

Strong-coupling topological Josephson effect in quantum wires

We investigate the Josephson effect for a setup with two lattice quantum wires featuring Majorana zero energy boundary modes at the tunnel junction. In the weak-coupling regime, the exact solution reproduces the perturbative result for the energy containing a contribution ～ ± cos(?/2) relative to the tunneling of paired Majorana fermions. As the tunnel amplitude g grows relative to the hopping amplitude w, the gap between the energy levels gradually diminishes until it closes completely at the critical value gc [Formula: see text]. At this point the Josephson energies have the principal values [Formula: see text], where m =- 1,0,1 and σ =± 1, a result not following from perturbation theory. It represents a transparent regime where three Bogoliubov states merge, leading to additional degeneracies of the topologically nontrivial ground state with an odd number of Majorana fermions at the end of each wire. We also obtain the exact tunnel currents for a fixed parity of the eigenstates. The Josephson current shows the characteristic 4π periodicity expected for a topological Josephson effect. We discuss the additional features of the current associated with a closure of the energy gap between the energy levels.     

Cooper pair and electron-hole pair instabilities in a quasi-one dimensional system

We calculate for an almost half-filled tight-binding band, the mean field ground state energy differences between the charge-density-wave (CDW) and BCS paired states for a truncated model Hamiltonian with zero-range instantaneous electron-electron interactions. The CDW pairing is found to be always unstable vis-à-vis BCS for a static lattice distortion of wave vector Q = (2k_F, π, π).     

Photograph of a giant structural distortion in a quasi-one dimensional organic crystal

Using a high-speed photographic technique, we have recorded directly the crystalline distortion associated with a first-order phase transition in tetrathiafulvalenium-bis-ditholene (Cu). This structural distortion, at a temperature of 238 K, has been observed as a crystal motion through an angle of the order of 10°. The phase change may be important in establishing the one-dimensional magnetic character of the crystal that leads to a spin-dimerization transition at a temperature of 12 K.     

Josephson effect without superconductivity: realization in quantum Hall bilayers

We show that a quantum Hall bilayer with the total filling nu = 1 should exhibit a dynamical regime similar to the flux flow in large Josephson junctions. This analogy may explain a conspicuous peak in the interlayer tunneling conductance [Phys. Rev. Lett. 84, 5808 (2000)]. The flux flow is likely to be spatiotemporally chaotic at low-bias voltage, which will manifest itself through broadband noise. The peak position can be controlled by an in-plane magnetic field.     

Influence of Coulomb interactions on the phase diagram of quasi-one dimensional metals

The influence of only partially screened Coulomb interactions on the phase diagram and the order parameter of quasi-one dimensional metals is investigated. Using a standard microscopic model, the free energy functional is derived by means of the heat kernel method. It is assumed that the Peierls gap and the mismatch are small compared to the band width and the reciprocal lattice vectors, respectively. Furthermore we neglect interchain to intrachain hopping elements. The resulting mean field phase diagram and the properties of the order parameter are discussed. We show in particular that the Coulomb forces are responsible for:a) a first-order transition between the incommensu-rate and the commensurate phase;b) only small deviations of the order parameter from a single plane wave over the entire incommensurate phase; andc) the approximate temperature independence of the wavelength of the modulation throughout the incommensurate phase. The possible relevance of these results for quasi-one dimensional systems exhibiting nonlinear conduction is pointed out.     

Topological order in the insulating Josephson junction array

We propose a Josephson junction array which can be tuned into an unconventional insulating state by varying external magnetic field. This insulating state retains a gap to half-vortices; as a consequence, such an array with nontrivial global geometry exhibits a ground state degeneracy. This degeneracy is protected from the effects of external noise. We compute the gaps, separating higher energy states from the degenerate ground state, and we discuss experiments probing the unusual properties of this insulator.     

Topological solitons and zero modes in high-T c superconductivity

The realization of topological solitons, zero modes, and supersymmetry in theCP ₁ nonlinear sigma model, a theory of high-T _c superconductivity, is presented.     

Spectroscopy of the fractional vortex eigenfrequency in a long Josephson 0-kappa junction

Fractional Josephson vortices carry a magnetic flux Phi, which is a fraction of the magnetic flux quantum Phi(0) approximately 2.07 x 10(-15) Wb. Their properties are very different from the properties of the usual integer fluxons. In particular, fractional vortices in 0-kappa Josephson junctions are pinned and have an oscillation eigenfrequency which is expected to be within the Josephson plasma gap. Using microwave spectroscopy, we investigate the dependence of the eigenfrequency of a fractional Josephson vortex on its magnetic flux Phi and on the bias current. The experimental results are in good agreement with the theory.     

Quantization by parts,self-adjoint extensions,and a novel derivation of the Josephson equation in superconductivity

There has been a lot of interest in generalizing orthodox quantum mechanics to include POV measures as observables, namely as unsharp obserrables. Such POV measures are related to symmetric operators. We have argued recently that only maximal symmetric operators should describe observables.¹ This generalization to maximal symmetric operators has many physical applications. One application is in the area of quantization. We shall discuss a scheme, to he called quantization by parts,which can systematically deal with what may be called quantum circuits. As a specific application we shall present a novel derivation of the famous Josephson equation for the supercurrent through a Josephson junction in a superconducting circuit. An interesting effect emerges from our quantization scheme when applied to a superconducting Y-shape circuit configuration. We also propose an experimental test for this effect which is expected to shed light on some conceptual problems on the quantum nature of the condensate.     

Two dimensional fractional projectile motion in a resisting medium

In this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter k was introduced in the derivative operator. This parameter has a dimension of inverse of seconds (sec)^?1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity v ₀ and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.     

Topological structure of the inter-band phase difference soliton in two-band superconductivity

Two-component superconductivity based on the two-band superconductor has a functional topology such as an inter-band phase difference soliton (i-soliton) to realize topological electronics (topolonics). Many gauge field theories are applied to investigate the topology of two-band superconductivity. To ease experimental and electronics applications, these theories should be refined. Weinberg–Salam theory and SU(2) (two-dimensional special unitary symmetry) gauge field theory are proper starting points. An effective extra force field because of the crystal structure and inter-band Josephson interaction, rather than spontaneous symmetry breaking, simplifies the conventional gauge field theory.     

Josephson effect in a Coulomb-blockaded SINIS junction

The problem of a Josephson current through a Coulomb-blocked nanoscale superconductor-normal-superconductor structure with tunnel contacts is reconsidered. Two different contributions to the phase-biased supercurrent I(?) are identified, which are dominant in the limits of weak and strong Coulomb interaction. Full expression for the free energy valid at arbitrary Coulomb strength is found. The current derived from this free energy interpolates between known results for weak and strong Coulomb interaction as the phase bias changes from 0 to π. In the broad range of Coulomb strength, the current-phase relation is substantially nonsinusoidal and qualitatively different from the case of semiballistic SNS junctions. The Coulomb interaction leads to the appearance of a local minimum in the current at some intermediate value of the phase difference applied to the junction.     

Higher harmonics in the Josephson effect

In the low temperature regime where macroscopic flux tunneling allows a SQUID magnetometer to follow the stable thermodynamic free energy without hysteretic dissipation, it is possible to exhibit macroscopic quantum behaviour via higher Josephson harmonic oscillations in the thermal response. A simple theory is presented here; the experimental data will appear elsewhere.     

Reveal the nematic topological superconductivity from the anisotropic unconventional Josephson effect: Theory and application to doped Bi_2Se_3

We propose a scheme to reveal the possible nematic superconducting order parameter in the doped Bi_2Se_3 by observing the anisotropic unconventional Josephson effect without an external magnetic field. We find the presence of an intrinsic π-phase in the spin-triplet channel of Andreev reflection. Its competition with the odd-parity superconducting gap phase can lead to unconventional Josephson effect in the Josephson junction, whose normal region is connected to the same side of the superconductor,called the U-shaped junction according to its geometry. For Josephson junctions with the interfaces perpendicular to the nematic direction, the competition will lead to a Josephson π-junctions. In the case where the interface is parallel to the nematic direction, it will lead to a Josephson 0-junction. Thus, this can directly reflect the nematic superconductivity. It is worth noting that Josephson coupling with the 4π period appears only in the normal injected channels. Interestingly, if the Josephson junction adopts a conventional geometry, it always exhibits a normal Josephson 0-junction regardless of the gap function taken by the doped Bi_2Se_3 and therefore cannot distinguish the pairing symmetry. We thus propose a superconducting quantum interference device containing a U-shaped Josephson junction to detect nematic superconductivity. This proposal not only can be applied to detect nematic superconductivity but also provides a feasible platform for topological quantum computation.