Suppression of Andreev conductance in a topological insulator–superconductor nanostep junction

When two three-dimensional topological insulators(TIs) are brought close to each other with their surfaces aligned,the surfaces form a line junction. Similarly, three TI surfaces, not lying in a single plane, can form an atomic-scale nanostep junction. In this paper, Andreev reflection in a TI–TI–superconductor nanostep junction is investigated theoretically. Because of the existence of edge states along each line junction, the conductance for a nanostep junction is suppressed. When the incident energy(ε) of an electron is larger than the superconductor gap(?), the Andreev conductance in a step junction is less than unity while for a plane junction it is unity. The Andreev conductance is found to depend on the height of the step junction. The Andreev conductance exhibits oscillatory behavior as a function of the junction height with the amplitude of the oscillations remaining unchanged when ε = 0, but decreasing for ε = ?, which is different from the case of the plane junction. The height of the step is therefore an important parameter for Andreev reflection in nanostep junctions, and plays a role similar to that of the delta potential barrier in normal metal–superconductor plane junctions.     

Effective manipulation of Andreev bound states,zero mode Majorana fermion and Josephson current in a superconductor–normal–superconductor junction on the surface of a topological insulator

We study the effective manipulation of the Andreev bound states (ABS), zero mode Majorana fermion and Josephson current (JC) in a superconductor–normal–superconductor junction on the surface of a topological insulator in unexplored regime of parameters. It is found that the energy of the ABS changes dramatically with the phase difference between both superconductors (SCs) in a certain range of the incident angle of quasiparticles. It is shown that the velocity of Majorana fermion and the JC can be effectively tuned in a wide range of the chemical potential in the normal region (_μN${\mu }_N$) and the separation width (L  ) of the two SCs. In addition, we expose that the critical JC and its product with the normal resistance are, respectively, a quarter and the same to those in a graphene-based Josephson junction. The dependence of the critical JC on the chemical potential in the superconducting region is not monotonous: it increases (decreases) for small (large) _μN${\mu }_N$.     

A wire-form emitter metal–insulator–semiconductor tunnel junction

Physical effects arising due to change of configuration of a MIS system from planar to cylindrical, are theoretically analyzed. Attention is paid to the voltage partitioning and all the components of tunneling current. A simple simulation model is developed enabling prediction of the band diagram details and calculation of the currents. The trends expected with decreasing system radius are elucidated. Cylindrical geometry can be faced with when quantum wire is used as an electron emitter. Similar form may also be roughly attributed to an edge region of conventional MIS capacitors.     

Effective field theory of a topological insulator and the Foldy–Wouthuysen transformation

Employing the Foldy–Wouthuysen transformation, it is demonstrated straightforwardly that the first and second Chern numbers are equal to the coefficients of the 2+1 and 4+1 dimensional Chern–Simons actions which are generated by the massive Dirac fermions coupled to the Abelian gauge fields. A topological insulator model in 2+1 dimensions is discussed and by means of a dimensional reduction approach the 1+1 dimensional descendant of the 2+1 dimensional Chern–Simons theory is presented. Field strength of the Berry gauge field corresponding to the 4+1 dimensional Dirac theory is explicitly derived through the Foldy–Wouthuysen transformation. Acquainted with it, the second Chern numbers are calculated for specific choices of the integration domain. A method is proposed to obtain 3+1 and 2+1 dimensional descendants of the effective field theory of the 4+1 dimensional time reversal invariant topological insulator theory. Inspired by the spin Hall effect in graphene, a hypothetical model of the time reversal invariant spin Hall insulator in 3+1 dimensions is proposed.     

Properties of superconductor–Luttinger-liquid hybrid systems

In this paper, we review some recent results concerning the physics of superconductor–Luttinger-liquid proximity systems. We discuss both equilibrium (the pair amplitude, Josephson current, and the local density of states) and nonequilibrium (the subgap current) properties.     

The Andreev conductance in superconductor–insulator–normal metal structures

The Andreev subgap conductance at 0.08–0.2 K in thin-film superconductor (aluminum)–insulator–normal metal (copper, hafnium, or aluminum with iron-sublayer-suppressed superconductivity) structures is studied. The measurements are performed in a magnetic field oriented either along the normal or in the plane of the structure. The dc current–voltage (I–U) characteristics of samples are described using a sum of the Andreev subgap current dominating in the absence of the field at bias voltages U < (0.2–0.4)Δ_c/e (where Δ_c is the energy gap of the superconductor) and the single-carrier tunneling current that predominates at large voltages. To within the measurement accuracy of 1–2%, the Andreev current corresponds to the formula \({I_n} + {I_s} = {K_n}\tanh \left( {{{eU} \mathord{\left/ {\vphantom {{eU} {2k{T_{eff}}}}} \right. \kern-\nulldelimiterspace} {2k{T_{eff}}}}} \right) + {K_s}{{\left( {{{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} \right)} {\sqrt {1 - {{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} }}} \right. \kern-\nulldelimiterspace} {\sqrt {1 - {{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} }}\) following from a theory that takes into account mesoscopic phenomena with properly selected effective temperature T _eff and the temperature- and fieldindependent parameters K _n and K _s (characterizing the diffusion of electrons in the normal metal and superconductor, respectively). The experimental value of K _n agrees in order of magnitude with the theoretical prediction, while K _s is several dozen times larger than the theoretical value. The values of T _eff in the absence of the field for the structures with copper and hafnium are close to the sample temperature, while the value for aluminum with an iron sublayer is several times greater than this temperature. For the structure with copper at T = 0.08–0.1 K in the magnetic field B_|| = 200–300 G oriented in the plane of the sample, the effective temperature T _eff increases to 0.4 K, while that in the perpendicular (normal) field B _⊥ ≈ 30 G increases to 0.17 K. In large fields, the Andreev conductance cannot be reliably recognized against the background of single- carrier tunneling current. In the structures with hafnium and in those with aluminum on an iron sublayer, the influence of the magnetic field is not observed.     

Electric flow through an ideal ferromagnet–superconductor junction

It is investigated the possibility of controlling the electric flow through a ferromagnet–superconductor junction by spin polarization, within a simple, ideal model of a perfect ferromagnetic–superconductor junction. The ferromagnetic and superconducting properties as well as the Andreev reflection are briefly reviewed and the electrical resistance of the junction is computed both in the diffusive and ballistic regime for the ferromagnetic sample. It is shown that the resistance of the junction increases with increasing magnetization, including both positive or negative jumps on passing from the ballistic to the diffusive regime.     

Tunneling conductance oscillations in spin–orbit coupled metal–insulator–superconductor junctions

The tunneling conductance for a device consisting of a metal–insulator–superconductor (MIS) junction is studied in presence of Rashba spin–orbit coupling (RSOC) via an extended Blonder–Tinkham–Klapwijk formalism. We find that the tunneling conductance as a function of an effective barrier potential that defines the insulating layer and lies intermediate to the metallic and superconducting electrodes, displays an oscillatory behavior. The tunneling conductance shows high sensitivity to the RSOC for certain ranges of this potential, while it is insensitive to the RSOC for others. Additionally, when the period of oscillations is an odd multiple of a certain value of the effective potential, the conductance spectrum as a function of the biasing energy demonstrates a contrasting trend with RSOC, compared to when it is not an odd multiple. The explanations for the observation can be found in terms of a competition between the normal and Andreev reflections. Similar oscillatory behavior of the conductance spectrum is also seen for other superconducting pairing symmetries, thereby emphasizing that the insulating layer plays a decisive role in the conductance oscillations of a MIS junction. For a tunable Rashba coupling, the current flowing through the junction can be controlled with precision.     

Influence of the in-plane magnetic field on the Andreev conductance of a superconductor–insulator–normal metal structure

Pronounced conductance due to electrons experiencing Andreev reflection from a superconducting condensate has been observed in superconductor (aluminum)–insulator (aluminum oxide)–normal metal (copper) tunnel junctions at low voltages, along with single-electron tunneling. It has been discovered experimentally that the collective current is suppressed in the magnetic field parallel to the tunnel junction plane and the Andreev conductance decreases nearly twofold in a field of ～20–30 mT.     

Screening properties of multiply connected ferromagnet–superconductor hybrid structures

Superconducting phase transition temperature T _c of a ferromagnet/superconductor (SF) hybrid structure consisting of a hollow superconducting (S) cylinder (shell) with the central part (core) filled with a ferromagnetic (F) metal has been analyzed on the basis of linearized Usadel equations. It has been shown that the proximity effect between the S and F metals, as well as the exchange interaction, may induce an inhomogeneous superconducting state with Δ ~ exp(iLθ + ipz), which is characterized by nonzero circulation of phase L and wavenumber p describing the Larkin–Ovchinnikov–Fulde–Ferrell (LOFF) instability along the cylinder axis. The transitions between the states with different values of L and p, which are accompanied by a nonmonotonic dependence of superconducting transition temperature T _c and effective magnetic field penetration depth Λ into the SF structure on the characteristic size of the ferromagnetic region, have been investigated.     

Experimental realization of a three-dimensional topological insulator phase in ternary chalcogenide TlBiSe₂

We report the first observation of a topological surface state on the (111) surface of the ternary chalcogenide TlBiSe? by angle-resolved photoemission spectroscopy. By tuning the synchrotron radiation energy we reveal that it features an almost ideal Dirac cone with the Dirac point well isolated from bulk continuum states. This suggests that TlBiSe? is a promising material for realizing quantum topological transport.     

Zero-energy states bound to a magnetic π-flux vortex in a two-dimensional topological insulator

We show that the existence of a pair of zero-energy modes bound to a vortex carrying a π-flux is a generic feature of the topologically non-trivial phase of the M–B model, which was introduced to describe the topological band insulator in HgTe quantum wells. We explicitly find the form of the zero-energy states of the corresponding Dirac equation, which contains a novel momentum-dependent mass term and describes a generic topological transition in a band insulator. The obtained modes are exponentially localized in the vortex-core, with the dependence of characteristic length on the parameters of the model matching the dependence extracted from a lattice version of the model. We consider in full generality the short-distance regularization of the vector potential of the vortex, and show that a particular choice yields the modes localized and simultaneously regular at the origin. Finally, we also discuss a realization of two-dimensional spin-charge separation through the vortex zero-modes.     

Magnetic field enhanced single particle tunneling in MoS_2–superconductor vertical Josephson junction

As a prototypical transition-metal dichalcogenide semiconductor, MoS_2 possesses strong spin–orbit coupling, which provides an ideal platform for the realization of interesting physical phenomena. Here, we report the magnetotransport properties in NbN–MoS_2–NbN sandwich junctions at low temperatures. Above the critical temperature around ～11 K, the junction resistance shows weak temperature dependence, indicating a tunneling behavior. While below ～11 K, nearly zero junction resistance is observed, indicating the superconducting state in the MoS_2 layer induced by the superconducting proximity effect. When a perpendicular magnetic field ～1 T is applied, such proximity effect is suppressed, accompanying with insulator-like temperature-dependence of the junction resistance. Intriguingly, when further increasing the magnetic field, the junction conductance is significantly enhanced, which is related to the enhanced single particle tunneling induced by the decrease of the superconducting energy gap with increasing magnetic fields. In addition, the possible Majorana zero mode on the surface of MoS_2 can further lead to the enhancement of the junction conductance.     

Rapid preparation of Mg（B1-xCx）2 superconductor using hybrid microwave method

The crystal structure and the superconductivity for samples Mg（B1-xCx）2 （0〈 x 〈0.09） prepared by a hybrid microwave synthesis have been investigated. The starting material B10C is also obtained by using the microwave method. The carbon can distribute uniformly in the Mg（B1-xCx）2 samples because boron and carbon are mixed on an atomic scale in the staring material B10C. The dependences of both lattice parameters and superconducting transition temperature Tc on carbon content accord with those reported in the literature. The upper critical field He2 at 20 K can be enhanced from about 4.3 T for x = 0 to 10 T for x = 0.05. The critical current density Jc of Mg（B0.95 C0.05）2 is 1.05×10^4 A/cm^2 at 20 K and 1 T.     

Electron–phonon coupling in topological insulator Bi_2Se_3 thin films with different substrates

Broadband transient reflectivity traces were measured for Bi_2 Se_3 thin films with various substrates via a 400 nm pump–white-light-probe setup. We have verified the existence of a second Dirac surface state in Bi_2 Se_3 and qualitatively located it by properly analyzing the traces acquired at different probe wavelengths. Referring to the band structure of Bi_2 Se_3, the relaxation mechanisms for photo-excited electrons with different energies are also revealed and studied. Our results show a second rise of the transient reflection signal at the time scale of several picoseconds. The types of substrate can also significantly affect the dynamics of the rising signal. This phenomenon is attributed to the effect of lattice heating and coherent phonon processes. The mechanism study in this work will benefit the fabrication of high-performance photonic devices based on topological insulators.     

Computation of effective electron–phonon relaxation times in a high-Tc superconductor using the measured track radii

Energy relaxation processes after fast heavy ions passage through YBa₂Cu₃O_7−δ single crystal have been calculated. Effective times τ of electron–atom energy relaxation have been determined as fitting parameters for each pair of the measured track radius and the value of dE/dx. The latter quantity has been chosen over the interval of 20–40 keV/nm. The calculated results are compared with short pulse laser experiments and with Allen's theory, which predicts almost a linear dependence of τ on electron temperature.     

Quantum critical properties in the topological Ginzburg–Landau theory of self-dual Josephson junction arrays

This paper examines the multicritical behavior of a generalized U(_N1)×U(_N2)$U\left(N_1\right)\times U\left(N_2\right)$ Ginzburg–Landau theory containing two multicomponent complex fields which couple differently to two gauge fields described by two Maxwell terms and one mixed-Chern–Simons term. This model is relevant to the dynamics of Cooper pairs and vortices in a self-dual Josephson junction array system near its superconductor–insulator transition. We develop a renormalization group flow at fixed dimension and obtain the beta functions at one loop when both disorder fields are critical. Two sets of infrared-stable charged fixed points solutions are found for N>_Nc$N>N_c$: partially charged solutions with respect to the gauge fields exist with _Nc=35.6$N_c=35.6$, and fully charged solutions exist with _Nc=12.16$N_c=12.16$. We show that fine tuning the ratio of the two energy scales in the model has the effect of reducing the critical number _Nc$N_c$ and thus enlarges the region where the quantum phase transition is continuous. It is also found that the decoupled fixed point which is stable in the neutral case is no longer attainable in the presence of fluctuating gauge fields. We probe the conductivity at the critical point and show that it has a universal character determined by the renormalization group infrared-stable fixed-point values of the gauge couplings.     

A surface-plasmon-polariton wavelength splitter based on a metal–insulator–metal waveguide

A surface-plasmon-polariton (SPP) wavelength splitter based on a metal–insulator–metal waveguide with multiple teeth is proposed. Using the transfer-matrix method, a plasmonic band gap is identified in the multiple-toothed structure, and the splitting wavelength of the SPP splitter can be easily adapted by adjusting the widths of the teeth and the gaps. The proposed wavelength splitter is further verified through finite-difference time-domain (FDTD) simulations, in which SPPs with incident wavelengths of 756 nm and 892 nm are successfully split and guided in opposite directions in the waveguide, with extinction ratios of 30 dB and 29 dB, respectively.