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.     

Spin-dependent quasiparticle reflection and bound States at interfaces with itinerant antiferromagnets

We find a novel channel of quasiparticle reflection from the simplest two-sublattice antiferromagnet (AF) on a bipartite lattice. Low-energy quasiparticles in a normal metal (N) experience spin-dependent retroreflection at AF/N interfaces. As a combined effect of antiferromagnetic and Andreev reflections, subgap Andreev states arise at an AF/superconductor (SC) interface. When the antiferromagnetic reflection dominates the specular one, Andreev bound states have almost zero energy on AF/s-wave superconductor (sSC) interfaces, whereas there are no low-energy subgap states on AF/d-wave superconductor (dSC) boundaries. For an sSC/AF/sSC junction, the bound states are found to split, due to the finite width of the AF interlayer, and carry the supercurrent. The theory developed in the present Letter is based on a novel quasiclassical approach, which applies to interfaces involving itinerant antiferromagnets.     

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.     

Spin transport properties in ferromagnet/superconductor junctions on topological insulator

The spin-dependent Andreev reflection is investigated theoretically by analyzing the electronic transport in a thin-film topological insulator (TI) ferromagnet/superconductor (FM/SC) junction. The tunneling conductance and shot noise are calculated based on the Dirac-Bogoliubov-de Gennes equation and Blonder-Tinkham-Klapwijk theory. It is found that the magnetic gap in ferromagnet can enhance the Andreev retro-reflection but suppress the specular Andreev reflection. The gate potential applied to the electrode on top of superconductor can enhance the two types of reflections. There is a transition between the two types of reflections at which both the tunneling conductance and differential shot noise become zero. These results provide a method to realize and detect experimentally the intra-band specular Andreev reflection in thin film TI-based FM/SC structures.     

Effect of spin-dependent phases of tunneling electrons on the conductance of a point ferromagnet/isolator/superconductor contact

The Andreev reflection probability for a ferromagnet/isolator/superconductor (FIS) contact at the arbitrary spin-dependent amplitudes of the electron waves transmitted through and reflected from the potential barrier is found. It is shown that the Andreev reflection probabilities of electron and hole excitations in the FIS contact are different. The energy levels of the Andreev bound states are found. The ballistic conductance of the point FIS contact is calculated. The text was submitted by the author in English.     

Dominant Majorana bound energy and critical current enhancement in ferromagnetic-superconducting topological insulator

Among the potential applications of topological insulators, we theoretically study the coexistence of proximity-induced ferromagnetic and superconducting orders in the surface states of a 3-dimensional topological insulator. The superconducting electron-hole excitations can be significantly affected by the magnetic order induced by a ferromagnet. In one hand, the surface state of the topological insulator, protected by the time-reversal symmetry, creates a spin-triplet and, on the other hand, magnetic order causes to renormalize the effective superconducting gap. We find Majorana mode energy along the ferromagnet/superconductor interface to sensitively depend on the magnitude of magnetization m _zfs from superconductor region, and its slope around perpendicular incidence is steep with very low dependency on m _zfs . The superconducting effective gap is renormalized by a factor η(m _zfs ), and Andreev bound state in ferromagnet-superconductor/ferromagnet/ferromagnet-superconductor (FS/F/FS) Josephson junction is more sensitive to the magnitude of magnetizations of FS and F regions. In particular, we show that the presence of m _zfs has a noticeable impact on the gap opening in Andreev bound state, which occurs in finite angle of incidence. This directly results in zero-energy Andreev state being dominant. By introducing the proper form of corresponding Dirac spinors for FS electron-hole states, we find that via the inclusion of m _zfs , the Josephson supercurrent is enhanced and exhibits almost abrupt crossover curve, featuring the dominant zero-energy Majorana bound states.     

Conductance of SIN and SIS junctions with chiral superconductors

Low-temperature conductance peaks due to the surface Andreev bound states in SIN and SIS junctions with chiral superconductors are considered. It is shown that, in SIN junctions, the conductance as a function of voltage, G(V), is highly sensitive to the dependence of the barrier transparency on the direction of the quasiparticle momentum. A weak magnetic field applied to the junction shifts the conductance peaks. In symmetric SIS junctions, the presence of chiral levels of Andreev bound states on both sides of the barrier gives rise to a conductance peak at V=0.     

Quasiparticle cooling using a topological insulator–superconductor hybrid junction

In this work, we investigate the thermoelectric properties of a hybrid junction realised coupling surface states of a three-dimensional topological insulator with a conventional s-wave superconductor. We focus on the ballistic devices and study the quasiparticle flow, carrying both electric and thermal currents, adopting a scattering matrix approach based on conventional Blonder–Tinkham–Klapwijk formalism. We calculate the cooling efficiency of the junction as a function of the microscopic parameters of the normal region (i.e. the chemical potential, etc.). The cooling power increases when moving from a regime of Andreev specular-reflection to a regime where Andreev retro-reflection dominates. Differently from the case of a conventional N/S interface, we can achieve efficient cooling of the normal region, without including any explicit impurity scattering at the interface, to increase normal reflection.     

Andreev reflection between a normal metal and the FFLO superconductor II: A self-consistent approach

We consider Andreev reflection in a two dimensional junction between a normal metal and a heavy fermion superconductor in the Fulde–Ferrell (FF) type of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state. We assume s-wave symmetry of the superconducting gap. The parameters of the superconductor: the gap magnitude, the chemical potential, and the Cooper pair center-of-mass-momentum Q, are all determined self-consistently within a mean-field (BCS) scheme. The Cooper pair momentum Q is chosen as perpendicular to the junction interface. We calculate the junction conductance for a series of barrier strengths. In the case of incoming electron with spin σ = ↑ only for magnetic fields close to the upper critical field H_c2, we obtain the so-called Andreev window, i.e. the energy interval in which the reflection probability is maximal, which in turn is indicated by a peak in the conductance. The last result differs with other non-self-consistent calculations existing in the literature.     

Multiple andreev reflections in topological insulator nanoribbons

Superconducting proximity junctions made of topological insulator (TI) nanoribbons (NRs) provide a useful platform for studying topological superconductivity. We report on the fabrication and measurement of Josephson junctions (JJs) using Sb-doped Bi₂Se₃ NRs in contact with Al electrodes. Aharonov–Bohm and Altshuler–Aronov–Spivak oscillations of the axial magneto-conductance of TI NR were observed, indicating the existence of metallic surface states along the circumference of the TI NR. We observed the supercurrent in the TI NR JJ and subharmonic gap structures of the differential conductance due to multiple Andreev reflections. The interface transparency of the TI NR JJs estimated based on the excess current reaches τ = 0.83, which is among the highest values reported for TI JJs. The temperature dependence of critical current is consistent with the short and ballistic junction model confirming the formation of highly transparent superconducting contacts on the TI NR. Our observations would be useful for exploring topological Josephson effects in TI NRs.     

Tunneling conductance in topological insulator ferromagnet/p-wave superconductor junctions

The tunneling conductance in topological insulator (TI) ferromagnet/p-wave superconductor (FM/pS) junction is studied based on the Blonder–Tinkham–Klapwijk (BTK) theory. The Fermi energy mismatch between FM and pS as well as the finite quasiparticle lifetime are considered. Three kinds of pairings p_x, p_y, and p_x+ip_y-waves for pS are chosen. It is found that the spectrum strongly depend on the magnetic gap, the gate potential, the quasiparticle lifetime as well as the type of the pair potential symmetry. The pair potential symmetry drastically affects the formation of the zero-energy bound states dependent on the magneto effect or the Fermi energy mismatch effect. The finite quasiparticle lifetime effect can suppress the Andreev resonant scattering process at eV=Δ₀ and smear the dips in the conductance.     

Effect of surface Andreev bound states on the Bean-Livingston barrier in d-wave superconductors

We study the influence of surface Andreev bound states in d-wave superconductors on the Bean-Livingston surface barrier for entry of a vortex line into a strongly type-II superconductor. Starting from Eilenberger theory, we derive a generalization of London theory to incorporate the anomalous surface currents arising from the Andreev bound states. This allows us to find an analytical expression for the modification of the Bean-Livingston barrier in terms of a single parameter describing the influence of the Andreev bound states. We find that the field of first vortex entry is significantly enhanced. Also, the depinning field for vortices near the surface is renormalized. Both effects are temperature dependent and depend on the orientation of the surface relative to the d-wave gap.     

Spectrum of Andreev bound states in a molecule embedded inside a microwave-excited superconducting junction

Nondissipative Josephson current through nanoscale superconducting constrictions is carried by spectroscopically sharp energy states, the so-called Andreev states. Although theoretically predicted almost 40 years ago, no direct spectroscopic evidence of these Andreev bound states exists to date. We propose a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single-level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy, and a superconducting-phase-dependent ac Stark shift of the cavity frequency. Dispersive measurement of this frequency shift can be used for Andreev bound state spectroscopy.     

Coherent multiple charge transfer in a superconducting NbN tunnel junction

We measured shot noise and submillimeter-wave response in a superconducting NbN tunnel junction that had a subharmonic gap structure on the current-voltage (I-V) curve. We found that the observed effective charge, defined from the noise-current ratio, tends to a steplike function of voltage. In the presence of submillimeter-wave radiation of frequency v, novel step structures spaced by hv/2e below and above the half-gap voltage clearly appeared on the I-V curve, overlapping the ordinary photon-assisted tunneling steps spaced by hv/e. Observation of these features provides clear evidence that coherent multiple Andreev reflection processes occur in the NbN tunnel junction with low barrier transparency.     

Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the 0-<Emphasis Type="Italic">π</Emphasis> transition

Behavior of Andreev gap states in a quantum dot with Coulomb repulsion symmetricallyattached to superconducting leads is studied via the perturbation expansion in theinteraction strength. We find the exact asymptotic form of the spin-symmetric solution forthe Andreev states continuously approaching the Fermi level. We thereby derive a criticalinteraction at which the Andreev states at zero temperature merge at the Fermi energy,being the upper bound for the 0-π transition. We show that the spin-symmetricsolution becomes degenerate beyond this interaction, in the π phase, and the Andreevstates do not split unless the degeneracy is lifted. We further demonstrate that thedegeneracy of the spin-symmetric state extends also into the 0 phase in which the solutions with zero andnon-zero frequencies of the Andreev states may coexist.     

Splitting of a Cooper pair by a pair of Majorana bound states

We propose a method to probe the nonlocality of a pair of Majorana bound states by crossed Andreev reflection, which is the injection of an electron into one bound state followed by the emission of a hole by the other (equivalent to the splitting of a Cooper pair). We find that, at sufficiently low excitation energies, this nonlocal scattering process dominates over local Andreev reflection involving a single bound state. As a consequence, the low-temperature and low-frequency fluctuations deltaI(i) of currents into the two bound states i=1, 2 are maximally correlated: deltaI_1deltaI_2[over ]=deltaI_i(2).[over ].     

Strain-modulated anisotropic Andreev reflection in a graphene-based superconducting junction

We investigate the Andreev reflection across a uniaxial strained graphene-based superconducting junction. Compared with pristine graphene-based superconducting junction, three opposite properties are found. Firstly, in the regime of the interband conversion of electron-hole, the Andreev retro-reflection happens. Secondly, in the regime of the intraband conversion of electron-hole, the specular Andreev reflection happens. Thirdly, the perfect Andreev reflection, electron-hole conversion with unit efficiency, happens at a nonzero incident angle of electron. These three exotic properties arise from the strain-induced anisotropic band structure of graphene, which breaks up the original relation between the direction of velocity of particle and the direction of the corresponding wavevector. Our finding gives an insight into the understanding of Andreev reflection and provides an alternative method to modulate the Andreev reflection.     

Andreev states and shot noise in bicrystal junctions of cuprate superconductors

Experimentally observed features of the electrical and noise characteristics of bicrystal junctions of cuprate superconductors, such as linearity of the critical current density versus square root of the junction transparency and increase in the spectral density of shot noise for small bias voltages (below the superconducting gap), indicate that the superconducting current in cuprate bicrystal junctions is determined by the passage of quasi-particles through a potential barrier at the superconductor boundaries. This process involves bound states appearing as a result of multiple Andreev reflections in superconductors with dominant wavefunction components of the d _x ² ? _y ² symmetry type. At the same time, interpretation of the experimental current-phase and current-magnetic field curves requires that the character of faceting at the bicrystal junctions would be also taken into account.     

Majorana fermions and exotic surface Andreev bound states in topological superconductors: application to Cu(x)Bi2Se3

The recently discovered superconductor Cu(x)Bi2Se3 is a candidate for three-dimensional time-reversal-invariant topological superconductors, which are predicted to have robust surface Andreev bound states hosting massless Majorana fermions. In this work, we analytically and numerically find the linearly dispersing Majorana fermions at k=0, which smoothly evolve into a new branch of gapless surface Andreev bound states near the Fermi momentum. The latter is a new type of Andreev bound states resulting from both the nontrivial band structure and the odd-parity pairing symmetry. The tunneling spectra of these surface Andreev bound states agree well with a recent point-contact spectroscopy experiment [S. Sasaki et al., Phys. Rev. Lett. 107, 217001 (2011)] and yield additional predictions for low temperature tunneling and photoemission experiments.     

Andreev tunneling and Josephson current in light irradiated graphene

We investigate the Andreev tunneling and Josephson current in graphene irradiated with high-frequency linearly polarized light. The corresponding stroboscopic dynamics can be solved using Floquet mechanism which results in an effective stationary theory to the problem exhibiting an anisotropic Dirac spectrum and modified pseudospin-momentum locking. When applied to an irradiated normal graphene - superconductor (NS) interface, such analysis reveal Andreev reflection (AR) to become an oscillatory function of the optical strength. Specifically we find that, by varying the polarization direction we can both suppress AR considerably or cause the Andreev transport to remain maximum at sub-gap excitation energies even in the presence of Fermi level mismatch. Furthermore, we study the optical effect on the Andreev bound states (ABS) within a short normal-graphene sheet, sandwiched between two s-wave superconductors. It shows redistribution of the low energy regime in the ABS spectrum, which in turn, has major effect in shaping the Josephson super-current. Subjected to efficient tuning, such current can be sufficiently altered even at the charge neutrality point. Our observations provide useful feedback in regulating the quantum transport in Dirac-like systems, achieved via controlled off-resonant optical irradiation on them.