Session N13: Focus Session: Topological Materials - Topological Superconductivity

Zero bias conductance peak anomaly in topological insulator - superconductor junctions

We have fabricated planar junctions between topological insulator Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ and superconducting Pb with MgO barrier and studied the conductance spectra of the junctions under different temperatures and magnetic fields. Two types of Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ thin films, grown by hybrid physical-chemical vapor deposition (HPCVD) and molecular beam epitaxy (MBE), were used. A few nanometers thick MgO layer made by RF sputtering was used as the barrier. We observed a zero bias conductance peak (ZBCP) anomaly in the spectra. The peak width ranges from 1 mV to 17 mV in different samples. The ZBCP height decreases with increasing temperature and disappears when the temperature is above the $T_{c}$ of Pb. The ZBCP is also suppressed by both perpendicular and parallel magnetic fields and vanishes above the critical field of Pb. We will discuss the possible origins of the ZBCP in the junctions.   

Superconducting-Tip STM on Cobaltates as a Platform for Exploring Topological Superconductivity

In recent years, Na$_{x}$CoO$_{2}$ has attracted much attention for its unconventional superconductivity and antiferromagnetic phases. More recently it has been proposed that inducing superconductivity into the stoichiometric compound through the proximity effect could lead to topological superconductivity where Majorana physics might be accessed. We first explore this surface state with standard scanning tunneling spectroscopy and tuning fork-based atomic force microscopy, and then investigate the proximity effect scenario by introducing a superconducting tip to probe the superconductor-vacuum-topological junction.   

Dynamics of Josephson vortex interacting with Majorana bound modes in Long Josephson Junctions

We investigate the effects of Majorana bound modes on Josephson vortex (i.e., fluxon) dynamics by examining a long Josephson junction deposited on a topological insulator. Majorana bound states are represented as two counterpropagating edge modes along either superconducting side, which couples to the local Josephson phase difference. A fluxon (a 2$\pi$ phase configuration) interacts with Majorana bound states via the Jackiw-Rebbi mechanism [1] as pointed out by Grosfeld and Stern [2]. We find the effective equation of motion for the fluxon by integrating out the Majorana modes. This motion can be described by the double sine-Gordon equation. As a consequence, there may be fractional Shapiro steps in the I-V characteristics. In addition, the fluxon may have internal modes. We study the criteria for these effects to occur and to be detectable. \\[4pt] [1] R. Jackiw and C. Rebbi, Phys. Rev. D \textbf{13}, 3398 (1976).\\[0pt] [2] E. Grosfeld and A. Stern, PNAS \textbf{108}, 11810 (2011).   

Edge superconducting correlation in attractive-U-Kane-Mele Hubbard model

The two-dimensional Kane-Mele model with attractive Hubbard interaction $U$ is studied by using a self-consistent mean-field theory. At $U=0$, the ground state is a topological insulator. At $U$ larger than a critical value $U_c$, the ground state is a bulk superconductor. At $0 [Preview Abstract]

Strong and weak 2D topological superconductors with spin-orbit coupling

We study pairing symmetries of superconducting states in a centrosymmetric system with quasi-one dimensional bands and spin-orbit coupling. When the spin-orbit coupling is weak, we mainly find even-parity pairing which is topologically trivial. When the spin-orbit coupling is (moderately) strong, the paring is dominantly p-wave, which is an odd-parity pairing. Depending on the interaction parameters, we find two different odd-parity pairing states. One has p+ip pairing with nonzero strong topological invariants, which breaks time reversal symmetry and possesses gapless chiral Majorana modes. The other has p+ip pairing for spin-up electrons but p-ip pairing for spin-down electrons, which preserves time reversal symmetry and hosts nontrivial weak Z$_2$ topological invariants. In the weak topological superconductors, there are gapless modes associated with lattice dislocations. Possible applications to the recent discovered BiS-based superconductors will be discussed.   

Majorana bound states and non-local spin correlations in a quantum wire on a topological superconductor

We theoretically study the proximity effect of the one-dimensional quantum wire of usual metal without the spin-orbit interaction on the substrate of unconventional superconductor. Three cases are considered for the substrate, i.e., (i) chiral superconductor in class D with broken time reversal symmetry, and class DIII superconductor (ii) with and (iii) without the nontrivial $Z_2$ number. The Cooper pairs are induced into the wire, resulting effective one dimensional superconducting system. We found the degenerate zero energy Majorana bound states at both ends of the wire for all the cases, unlike single Majorana state in spin-orbit coupled system with $s$-wave superconductor, which might have been experimentally observed. The degenerate Majorana bound states are unstable against the spin-orbit interaction in case (i) while are protected by time reversal symmetry in cases (ii) and (iii). These degenerate Majorana bound states constitute the spin 1/2 degrees of freedom at each end of the wire. It is also shown that the non-locally correlated two spins at the two ends of the wire can be controlled by the gating potential on the wire.   

Josephson supercurrent through a topological insulator surface state

The long-sought yet elusive Majorana fermion is predicted to arise from a combination of a superconductor and a topological insulator. We present direct evidence for a Josephson supercurrent in superconductor (Nb) - topological insulator (Bi$_2$Te$_3$) - superconductor e-beam fabricated junctions by the observation of clear Shapiro steps under microwave irradiation, and a critical current modulation by magnetic field. The dependence of the critical current on temperature and electrode spacing shows that the junctions are in the ballistic limit on a length scale of 100 nm. Shubnikov-de Haas oscillations in magnetic fields up to 30 T reveal a topologically non-trivial two-dimensional surface state. We argue that the ballistic Josephson current is hosted by this surface state despite the fact that the normal state transport is dominated by diffusive bulk conductivity. Nanostructured SQUIDs containing topological Josephson junctions are realized experimentally. Clear critical current modulation of both the junctions and the SQUID with applied magnetic fields have been observed. We show that the SQUIDs have a periodicity in the voltage-flux characteristic of $\Phi_0$ consistent with numerical expectations. We propose several strategies towards realizing a doubled periodicity, belonging to the presence of Majorana fermions.   

Microscopic theory for a ferromagnetic nanowire/superconductor heterostructure: Transport, fluctuations, and topological superconductivity

Motivated by the recent experiment of Wang et al. [Nat. Phys. {\bf 6}, 389 (2010)], who observed a highly unusual transport behavior of ferromagnetic cobalt nanowires proximity-coupled to superconducting electrodes, we study the proximity effect and temperature-dependent transport in such a mesoscopic hybrid structure. It is assumed that the asymmetry in the tunneling barrier gives rise to the Rashba spin-orbit coupling in the barrier that enables induced p-wave superconductivity in the ferromagnet to exist. We first develop a microscopic theory of Andreev scattering at the spin-orbit-coupled interface, derive a set of self-consistent boundary conditions, and find an expression for the p-wave minigap in terms of the microscopic parameters of the contact. Second, we study the temperature dependence of the resistance near the superconducting transition, and we find that it should generally feature a fluctuation-induced peak. The upturn in resistance is related to the suppression of the single-particle density of states due to the formation of fluctuating pairs, whose tunneling is suppressed. In conclusion, we discuss this and related setups involving ferromagnetic nanowires in the context of one-dimensional topological superconductors.   

Odd-frequency superconducting pairing in topological insulators

We discuss the appearance of odd-frequency spin-triplet $s$-wave superconductivity, first proposed by Berezinskii [J. Exp. Theor. Phys. 20 287 (1974)], on the surface of a topological insulator proximity coupled to a conventional spin-singlet $s$-wave superconductor. Using both analytical and numerical methods, we show that this disorder robust odd-frequency state is present whenever there is an in-surface gradient in the proximity induced gap. Such a gradient exists in both superconductor-normal state junctions as well as when an in-surface supercurrent is present. The time-independent order parameter for the odd-frequency superconductor is proportional to the in-surface gap gradient. The induced odd-frequency component does not produce any low-energy states.   

Detection of one-dimensional helical mode in topological insulator nanowire interferometer

In topological insulators (TIs), the spin-momentum locking together with time reversal symmetry (TRS) protects surface electrons from localization, which is the defining signature of TIs and the key property to realize exotic physics and applications. In quasi-one-dimensional (1D) TI nanowires, the surface electrons form 1D quantum modes of different topological natures, allowing us to observe topological protection via quantum interference modulated by magnetic flux[1,2]. We report low-temperature transport of bismuth selenide (Bi2Se3)-Se core-shell nanowire devices in parallel magnetic fields. Magneto-oscillations of different physical origins are studied systematically in ballistic regime and diffusive regime. Especially at strongly disordered limit, we observe a topologically-protected helical 1D mode at half magnetic flux quantum (h/2e). The quantum interference under TRS breaking magnetic field will be discussed as well. \newline [1] J.H. Bardarson, P.W. Brouwer, and J. E. Moore, Phys. Rev. Lett. \textbf{105}, 156803 (2010). \newline [2] Y. Zhang, A. Vishwanath, Phys. Rev. Lett. \textbf{105}, 206601 (2010).   

Superconducting Proximity Effect in Topological Insulators

Superconductor-topological insulator interfaces are prime candidates in the search for Majorana fermions in the solid state. We report on recent transport measurements of proximity-induced superconductivity through topological insulators with varying chemical compositions and growth methods. We will discuss the Josephson effect, tunneling spectroscopy, and measurement of normal-state conduction channels as means to detect Majorana states.   

Transport study on tunnel junction structures based on In2Se3/Bi2Se3 heterostructures

Bi2Se3 is a 3D Topological Insulator (TI) candidate material with structural similarity to In2Se3, which is a band insulator with large band gap. This compatibility leads to possibility of epitaxial growth of In2Se3/Bi2Se3 heterostructure, which has various application potential. For example, by depositing Superconducting or Ferromagnetic materials on top of this heterostructure, tunnel junctions can be fabricated. We have studied device structures made up of such tunnel junctions. In2Se3 was grown on top of Bi2Se3 using molecular beam epitaxy on Al2O3(0001) substrates. Superconductor (Nb) or Ferromagnet (CoFe, Gd) was then sputtered on top of In2Se3 and photolithography was used to make the tunnel junctions. Transport measurement data obtained from such structures will be presented.