Fractional Josephson current through a Luttinger liquid with topological excitations

Recently, the Majorana fermion has received great attentions due to its promising application in the fault-tolerant quantum computation. This application requires more accessible methods to detect the motion and braiding of the Majorana fermions. We use a Luttinger liquid ring to achieve this goal, where the ring geometry is nontrivial in the sense that it leads to fermion-parity-dependent topological excitations. First, we briefly review the essential physics of the Luttinger liquid and the Majorana fermion, in order to give an introduction of the general framework used in the following main work. Then, we theoretically investigated the DC Josephson effect between two topological superconductors via a Luttinger liquid ring. A low-energy effective Hamiltonian is derived to show the existence of the fractional Josephson current. Also, we find that the amplitude of the Josephson current, which is determined by the correlation function of Luttinger liquid, exhibits different behaviors in terms of the parity of Luttinger liquid due to the topological excitations. Our results suggest a possible method to detect the Majorana fermions and their tunneling process.     

Unconventional Josephson signatures of Majorana bound states

A junction between two topological superconductors containing a pair of Majorana fermions exhibits a "fractional" Josephson effect, 4π periodic in the superconductors' phase difference. An additional fractional Josephson effect, however, arises when the Majorana fermions are spatially separated by a superconducting barrier. This new term gives rise to a set of Shapiro steps which are essentially absent without Majorana modes and therefore provides a unique signature for these exotic states.     

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: J1-J2 model

We study the ground-state phase diagram of the frustrated spin-[Formula: see text] antiferromagnet with J(2) = xJ(1) > 0 (J(1) > 0) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for x(c(1)) < x < x(c(2)), where x(c(1)) ≈ 0.207 ± 0.003 and x(c(2)) ≈ 0.385 ± 0.010. The transition at x(c(1)) to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range 0.21 ? x ? 0.24), while that at x(c(2)) is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point [Formula: see text]. The spiral phases that are present classically for all values x > 1/6 are absent for all x ? 1.     

Thermodynamic behaviour of two-dimensional vesicles revisited

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher (Phys. Rev. Lett. 59, 1989 (1987)). We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure [Formula: see text] , where [Formula: see text] = Np/4[Formula: see text] , with the number of monomers N [Formula: see text] ∞ and the pressure p [Formula: see text] 0 , keeping [Formula: see text] constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N -gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. Away from these limits, we argue that the transition is replaced by a sharp crossover. The area, however, scales with N(2) for all positive p in all such models, consistent with earlier scaling theories.     

An electron paramagnetic resonance study of the tetragonally distorted [Formula: see text] ion in [Formula: see text] and [Formula: see text

Chromium-doped [Formula: see text] and [Formula: see text] have been studied by both EPR and ENDOR spectroscopy. [Formula: see text] ions enter the fluorite structure in distorted substitution cation sites. In both matrices the distortion observed is tetragonal. X- and Q-band EPR measurements at temperatures between 4 and 300 K allowed us to determine the ion symmetry and the following spin-Hamiltonian parameters: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text]; and [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text]. For [Formula: see text], the weak superhyperfine interaction of [Formula: see text] with the surrounding [Formula: see text] ions has been studied by both EPR and ENDOR techniques for [Formula: see text]. No ENDOR signals were detected for [Formula: see text]. The results are tentatively explained in terms of a Jahn - Teller effect corresponding to [Formula: see text] coupling strongly stabilized by lattice stresses, although other possible origins for the distortion cannot be completely ruled out.     

Final-state effects in neutron Compton scattering measurements on zirconium deuteride and beryllium

We report inelastic neutron scattering measurements of the neutron Compton profile, J(y), for Be and for D in polycrystalline [Formula: see text] over a range of momentum transfers, q between 27 and [Formula: see text]. The measurements were performed using the inverse geometry spectrometer eVS which is situated at the UK pulsed spallation neutron source ISIS. We have investigated deviations from impulse approximation (IA) scattering which are generically referred to as final-state effects (FSEs) using a method described by Sears. This method allows both the magnitude and the q dependence of the FSE to be studied. Analysis of the measured data was compared with analysis of numerical simulations based on the harmonic approximation and good agreement was found for both [Formula: see text] and Be. Finally we have shown how [Formula: see text], where V is the interatomic potential, can be extracted from the antisymmetric component of J(y).     

Topological superconductivity and the fractional Josephson effect in quasi-one dimensional wires on a plane

A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one-dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin–orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of the Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle–hole symmetry. Tunneling of Majorana quasiparticle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with 4π-periodicity.     

Josephson current through a nanoscale magnetic quantum dot

We present theoretical results for the equilibrium Josephson current through an Anderson dot tuned into the magnetic regime, using Hirsch-Fye Monte Carlo simulations covering the complete crossover from Kondo-dominated physics to pi junction behavior in a numerically exact way. Within the "magnetic" regime, U/Gamma > 1 and epsilon0/Gamma < or = 1, the Josephson current is found to depend only on Delta/TK, where Delta is the BCS gap and TK the Kondo temperature. The junction behavior can be classified into four different quantum phases. We describe these behaviors, specify the associated three transition points, and identify a local minimum in the critical current of the junction as a function of Delta/TK.     

Search for heavy long-lived particles that decay to photons at CDF II

We present the first search for heavy, long-lived particles that decay to photons at a hadron collider. We use a sample of gamma + jet + missing transverse energy events in pp[over] collisions at square root[s] = 1.96 TeV taken with the CDF II detector. Candidate events are selected based on the arrival time of the photon at the detector. Using an integrated luminosity of 570 pb(-1) of collision data, we observe 2 events, consistent with the background estimate of 1.3+/-0.7 events. While our search strategy does not rely on model-specific dynamics, we set cross section limits in a supersymmetric model with [Formula: see text] and place the world-best 95% C.L. lower limit on the [Formula: see text] mass of 101 GeV/c(2) at [Formula: see text].     

Theoretical and experimental study of the nanoparticle-driven blue phase stabilisation

We have studied theoretically and experimentally the effects of various types of nanoparticles (NPs) on the temperature stability range [Formula: see text] T (BP) of liquid-crystalline (LC) blue phases. Using a mesoscopic Landau-de Gennes type approach we obtain that the defect core replacement (DCR) mechanism yields in the diluted regime [Formula: see text] T (BP)(x) [Formula: see text] 1/(1 - xb) , where x stands for the concentration of NPs and b is a constant. Our calculations suggest that the DCR mechanism is efficient if a local NP environment resembles the core structure of disclinations, which represent the characteristic property of BP structures. These predictions are in line with high-resolution ac calorimetry and optical polarising microscopy experiments using the CE8 LC and CdSe or aerosil NPs. In mixtures with CdSe NPs of 3.5nm diameter and hydrophobic coating the BPIII stability range has been extended up to 20K. On the contrary, the effect of aerosil silica nanoparticles of 7.0nm diameter and hydrophilic coating is very weak.     

Ferroelastic domain freezing and low-frequency elastic behaviour of [Formula: see text] (ALHS)

In this work elastic measurements on [Formula: see text] (ALHS) which were carried out in the low-frequency range between 1 and 50 Hz are presented. The temperature dependence of the inverse elastic compliance [Formula: see text] has been determined between 90 K and 420 K. Distinct anomalies have been found in the temperature dependence of [Formula: see text], which are connected to the motion of domain walls in the ferroelastic phase below [Formula: see text]. Around [Formula: see text] a (partial) ferroelastic `domain freezing' phenomenon has been observed. To the knowledge of the authors this is the first time that pure ferroelastic domain freezing has been reported. However, below [Formula: see text] the domain walls seem to retain a certain vibrational degree of freedom which could be responsible for an additional anomaly of the loss modulus which was observed. The elastic behaviour of a crystal of ALHS is dependent on the `history' of the given sample. During temperature cycling [Formula: see text] shows differences between the first run of heating and cooling and later runs. Finally, some basic insights concerning the domain wall motion were obtained; it was found that the domain wall mobility decreases by three orders of magnitude in the temperature region 170 - 230 K.     

Hole-doped semiconductor nanowire on top of an s-wave superconductor: a new and experimentally accessible system for Majorana fermions

Majorana fermions were envisioned by Majorana in 1935 to describe neutrinos. Recently, it has been shown that they can be realized even in a class of electron-doped semiconductors, on which ordinary s-wave superconductivity is proximity induced, provided the time reversal symmetry is broken by an external Zeeman field above a threshold. Here we show that in a hole-doped semiconductor nanowire the threshold Zeeman field for Majorana fermions can be very small for some magic values of the hole density. In contrast to the electron-doped systems, smaller Zeeman fields and much stronger spin-orbit coupling and effective mass of holes allow the hole-doped systems to support Majorana fermions in a parameter regime which is routinely realized in current experiments.     

Observation of Majorana Quasiparticles’ Edge States in Superfluid 3He

We suggest in this article the nuclear magnetic resonance (NMR) method of observation and investigations of Majorana fermions at the edge of Topological Insulator, superfluid ³He-B. The Majorana fermions form the remarkable quantum state of condensed matter where particle-like and antiparticle (hole-like) excitations are indistinguishable. They have been observed recently by deviation of the temperature dependence of the superfluid ³He-B heat capacity from the well-known exponential law for Bogoliubov quasiparticles at the world limit of ultra-low temperatures. The experimental data are well described by adding the heat capacity of Majorana quasiparticles’ edge states with zero energy gap. We report here the results of the similar experiments with extended temperature range down to 125 µK. The possible way to detect these states by means of NMR is also discussed.     

Anomalies in the ion transport of phosphoric acid in water and heavy-water environments

This paper presents the experimentally determined precise transport data - (tracer) diffusion coefficients in both water and heavy-water environments, together with molar conductivity and viscosity of (ortho)phosphoric acid in water over an extended concentration range at [Formula: see text]. The concentration (c) dependence of the diffusion coefficients (D), viscosity [Formula: see text] and molar conductivity [Formula: see text] have been analysed. An anomalous depression in the D - [Formula: see text] curve for both [Formula: see text] - [Formula: see text] and [Formula: see text] - [Formula: see text] systems in the neighbourhood of 0.8 M is observed, which is complementary to the sudden sharp rise observed in the [Formula: see text] curve in the neighbourhood of 0.8 M. Although the occurrence of such an anomaly could be inferred from the earlier conductance, e.m.f. and diffusion data, it was never conclusively inferred earlier. This new set of diffusion and viscosity data clearly delineates anomalies in the ion transport of phosphoric acid.     

Josephson junction with two superconducting current components

The properties of a Josephson junction with the 2π- and 4π-periodic superconducting current component have been analyzed. In the range of low voltages, such a junction exhibits the 4π periodicity of the phase difference for the Majorana current amplitude much smaller than the Josephson current, which makes it possible to observe Josephson current oscillations with a fractional period for small dissipation β < 1 in the hysteresis region. The effect the 4π-periodic Majorana current component is also manifested in a change in the sequence of steps in the ladder structure emerging on the current–voltage (I–V) characteristic of the junction. We have determined the interval of external electromagnetic radiation amplitudes, in which the manifestation of the fractional Josephson effect on the I–V characteristic is most significant.     

Observing Majorana bound states in p-wave superconductors using noise measurements in tunneling experiments

The zero-energy bound states at the edges or vortex cores of chiral p-wave superconductors should behave like Majorana fermions. We introduce a model Hamiltonian that describes the tunneling process when electrons are injected into such states. Using a nonequilibrium Green function formalism, we find exact analytic expressions for the tunneling current and noise and identify experimental signatures of the Majorana nature of the bound states to be found in the shot noise. We discuss the results in the context of different candidate materials that support triplet superconductivity. Experimental verification of the Majorana character of midgap states would have important implications for the prospects of topological quantum computation.     

Josephson effect throughout the BCS-BEC crossover

We study the stationary Josephson effect for neutral fermions across the BCS-BEC (Bose-Einstein condensate) crossover, by solving numerically the Bogoliubov-de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.     

Floquet Majorana fermions in superconducting quantum dots

We consider different configurations of ac driven quantum dots coupled to superconductor leads where Majorana fermions can exist as collective quasiparticles. The main goal is to tune the existence, localization and properties of these zero energy quasiparticles by means of periodically driven external gates. In particular, we analyze the relevance of the system and driving symmetry. We predict the existence of different sweet spots with Floquet Majorana fermions in configurations where they are not present in the undriven system.     

Evolution of edge states in topological superfluids during the quantum phase transition

The quantum phase transition between topological and nontopological insulators or between fully gapped superfluids/superconductors can occur without closing the gap. We consider the evolution of the Majorana edge states on the surface of topological superconductor during transition to the topologically trivial superconductor on example of non-interacting Hamiltonian describing spin-triplet superfluid ³He-B. In conventional situation when the gap is nullified at the transition, the spectrum of Majorana fermions shrinks and vanishes after the transition to the trivial state. If the topological transition occurs without the gap closing, the Majorana fermion spectrum disappears by escaping to ultraviolet, where the Green’s function approaches zero. This demonstrates the close connection between the topological transition without closing the gap and zeroes in the Green’s function. Similar connection takes place in interacting systems where zeroes may occur due to interaction.     

Scanning Josephson tunneling microscopy of single-crystal Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} with a conventional superconducting tip

We have performed both Josephson and quasiparticle tunneling in vacuum tunnel junctions formed between a conventional superconducting scanning tunneling microscope tip and overdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} single crystals. A Josephson current is observed with a peak centered at a small finite voltage due to the thermal-fluctuation-dominated superconducting phase dynamics. Josephson measurements at different surface locations yield local values for the Josephson I_{C}R_{N} product. Corresponding energy gap measurements were also performed and a surprising inverse correlation was observed between the local I_{C}R_{N} product and the local energy gap.