Session H45: Topological Josephson Junction

Magnetic field induced 4$\pi$ periodic Josephson effect in InAs nanowires

Majorana zero modes (MZM) are leading candidates to implement \emph{topological} quantum computing, owing to their predicted non-Abelian properties and their non-local protection against decoherence. While the observation of a zero-bias conductance peak in tunneling spectroscopy of nanowires strongly suggests the onset of these zero-energy states, additional proof of their existence has remained elusive. Here, we report measurements of Josephson radiation in Josephson junctions formed in a proximity-induced superconducting InAs nanowire with an epitaxially-grown Al shell. The emitted radiation is directly measured \emph{on-chip}, using photon-assisted tunneling across nearby capacitively-coupled superconducting tunnel junctions. The frequency of the detected signal evolves from a 2$\pi$ to a 4$\pi$ periodicity as the magnetic field is increased. The evolution of this transition is studied as a function of chemical potential and of transmission across the nanowire junctions. These results are interpreted using both topological and non-topological models.   

Signatures of Majorana assisted tunneling in 1D Josephson junction rings.

Majorana zero modes in condensed matter settings have drawn immense attention recently and the search for unequivocal signatures of Majorana modes is underway. In this respect the presence of 4$\pi$ periodic tunneling between topological superconductors, which is assisted by the Majorana modes is a promising candidate. In this work, we study how the inclusion of Majorana assisted tunneling modifies physics in a ring of Josephson junction coupled islands. In addition, we study parity breaking processes in a controlled manner by coupling the ring to a two-level electronic system, such as found in quantum dots. For the ring alone, we find that the effects of the 2$\pi$ periodic terms are suppressed by increasing the number of islands in the ring. This allows a clearer distinction of the 4$\pi$ periodicity. In the combined system, we find that the periodicity can be tuned by controlling the occupation energy of the two level system. We also discuss the signatures of Majoranas that remain after parity breaking effects restore the $2\pi$ periodicity.   

Detecting topological superconductivity using doubled Shapiro steps

The fractional Josephson effect has been observed in many instances as a signature of a topological superconducting state containing zero-energy Majorana modes. However, it has been suggested that such a fractional Josephson effect might occur in non-topological systems. Here, we apply a scattering matrix-based noise formalism to calculate the fractional ac Josephson effect in one such non-topological scenario that may occur generically in semiconductor-based Josephson junctions. We find that the presence of a weakly coupled resonant impurity bound state in a semiconductor in the vicinity of a highly transparent channel produces a nearly topological fractional Josephson effect similar to Majorana modes. The Josephson effect signature for Majorana modes become distinct from this non-topological scenario only at low frequency. We argue that a variant of the fractional Josephson effect, namely the doubled Shapiro step, which can be performed at lower frequency and will generically appear in topological superconductors, can provide a more reliable signature of the topological superconducting state.   

Conductance spectroscopy of nontopological-topological superconductor junctions

We calculate the zero-temperature differential conductance $dI/dV$ of a voltage-biased one-dimensional junction between a nontopological and a topological superconductor for arbitrary junction transparency using the scattering matrix formalism. We consider two models for the topological superconductors: (i) spinful $p$-wave and (ii) $s$-wave with spin-orbit coupling and spin splitting. In the tunneling limit (small junction transparencies) where only single Andreev reflections contribute to the current, the conductance for voltages below the nontopological superconductor gap $\Delta_s$ is zero and there are two conductance peaks at $eV = \pm \Delta_s$ with the quantized value $(4-\pi)2e^2/h$ due to resonant Andreev reflection from the Majorana zero mode. However, when the junction transparency is not small, there is a finite conductance for $e|V| < \Delta_s$ arising from multiple Andreev reflections. The conductance at $eV = \pm \Delta_s$ in this case is no longer quantized. In general, the conductance is particle-hole asymmetric except for sufficiently small transparencies. We further show that, for certain values of parameters, the tunneling conductance of a zero-energy conventional Andreev bound state can resemble that of Majorana. Ref: Setiawan et. al. arXiv:1609.09086   

Magnetic field and gate tunable supercurrent fluctuations in multimode semiconductor nanowires

Semiconducting nanowires coupled to superconductors are crucial in proposals for inducing, detecting, and controlling topological superconductivity and Majorana fermion bound states. Using NbTiN-InSb-NbTiN Josephson junctions, we study supercurrents flowing in quasi-ballistic nanowires with strong spin-orbit interaction and in high magnetic fields, thus combining the essential ingredients required for Majorana fermions. Operating in a multimode regime, we observe aperiodic supercurrent fluctuations with several nodes at a finite magnetic field. The node fields are gate tunable. By numerically calculating the supercurrent in a realistic, three dimensional device geometry, we analyze the possible causes of these fluctuations: Zeeman splitting, spin-orbit interaction, and interference between modes. We find that interference dominates over the other effects in the investigated magnetic field range of 0-2 T. Demonstrating and controlling supercurrent interference effects is crucial to understanding the signatures of Majorana fermions in Josephson junctions, and it will benefit the future construction of topological quantum circuits.   

Josephson currents induced by the Witten effect

We reveal the existence of a new type of topological Josephson effect involving type II superconductors and three-dimensional topological insulators as tunnel junctions. We predict that vortex lines induce a variant of the Witten effect that is the consequence of the axion electromagnetic response of the topological insulator: at the interface of the junction each flux quantum attains a fractional electrical charge of e/4. As a consequence, if an external magnetic field is applied perpendicular to the junction, the Witten effect induces an AC Josephson effect in absence of any external voltage. We derive a number of further experimental consequences and propose potential setups where these quantized, flux induced, Witten effects may be observed. \\F. S. Nogueira, Z. Nussinov, and J. van den Brink, Phys. Rev. Lett. {\bf 117}, 167002 (2016). \newline F. S. Nogueira, Z. Nussinov, and J. van den Brink, Phys. Rev. D {\bf 94}, 085003 (2016).   

Electrical Transport in Bi2Te3 Thin Film Devices: Effective Band Structure, Charge Carrier Distribution and Josephson Coupling

Engineering of topological states in Josephson junctions requires understanding of the effective band structure of the topological insulator (TI) material that forms the weak link. Previous work has focused on optimizing materials aspects to boost the effective Josephson coupling while providing little insight into underlying mechanisms. We present transport measurements on back-gated Bi$_2$Te$_3$ thin film devices with low levels of bulk doping. Carrier densities are obtained from a two-carrier model fit to the Hall effect data. To validate the fits, we calculate the band structure of a thin film using a tight-binding model and find excellent agreement in the number of transport carriers. We conclude that the bottom region of the film changes from a deep quantum well to a depletion zone as the back-gate voltage is lowered, which explains a change in the observed weak-antilocalization signal with gate bias. For our Nb/Bi$_2$Te$_3$/Nb Josephson junctions, we observe that the Josephson coupling energy scales according to the theory of long diffusive SNS contacts with a smaller, effective value for the Thouless energy of the weak link that takes into account the longer dwell time in the junction area due to interface barriers and the conductivity mismatch between the materials.   

Experimental studies on hybrid superconductor-topological insulator nanoribbon Josephson devices

The spin-helical topological surface states (TSS) of topological insulators in proximity with an s-wave superconductor are predicted to demonstrate signatures of topological superconductivity and host Majorana fermions. Here, we report on the observation of gate-tunable proximity-induced superconductivity in an intrinsic BiSbTeSe$_{\mathrm{2}}$ topological insulator nanoribbon (TINR) based Josephson junction (JJ) with Nb contacts. We observe a gate-tunable critical current (I$_{\mathrm{C}})$ with an anomalous behavior in the temperature (T) dependence of I$_{\mathrm{C}}$. We discuss various possible scenarios that could be relevant to this anomalous behavior, such as (i) the different temperature dependence of supercurrent generated by in-gap, where phase slip plays an important role, and out-of-gap Andreev bound states or (ii) the different critical temperatures associated with the top and bottom topological surface states. Our modeling of I$_{\mathrm{C}}$ vs. T suggests the possible existence of one pair of in-gap Andreev bound states in our TINR. We have also studied the effects of magnetic fields on the critical current in our TINR Josephson junctions.   

Josephson Tunneling between Superconducting Topological Surface States

Proximity at the interface of a 3D topological insulator (TI) and a conventional s-wave superconductor can induce a 2D topological superconducting state. We grew s-wave superconductor (Nb)/TI (Bi-Sb-Te)/s-wave superconductor(Nb) heterostructures using molecular beam epitaxy (MBE) and fabricated sandwich typed Josephson junctions. Through the superconducting proximity effect, we realized topological superconducting surface states on both the top and bottom surfaces of the topological insulator film. Transport measurements showed an anomalous zero-bias conductance peak (ZBCP) at 135mK, in addition to the conventional Josephson effect between the two superconductor leads. This suggests Josephson tunneling occurs between the two proximity-driven topological surface states.   

Detecting Topological Superconductivity with $\varphi_{0}$ Josephson Junctions

Topological superconductivity can emerge in conventional superconductors in the presence of spin-orbit interaction and magnetic fields. Remarkably, the recent experimental discovery of $\varphi_{0}$ Josephson junctions by Szombati et al., characterized by a finite phase offset in the supercurrent, require the same ingredients as topological superconductors, which suggests a profound connection between these two distinct phenomena. Here, we theoretically show that a quantum dot $\varphi_{0}$ Josephson junction can serve as a new qualitative indicator for topological superconductivity: Microscopically, we find that the phase shift in a junction of $s-$wave superconductors is due to the spin-orbit induced mixing of singly occupied states on the qantum dot, while for a topological superconductor junction it is due to singlet-triplet mixing. Because of this important difference, when the spin-orbit vector of the quantum dot and the external Zeeman field are orthogonal, the $s$-wave superconductors form a $\pi$ Josephson junction while the topological superconductors have a finite offset $\varphi_{0}$ by which topological superconductivity can be distinguished from conventional superconductivity. Our prediction can be immediately tested in nanowire   

Controlling Majorana bound states in a Josephson junction on a topological insulator

We theoretically study a Josephson junction on a topological insulator under a magnetic field such that the number of flux quanta inside the Josephson junction is larger than one. Majorana bound states emerge along the junction where the superconducting phase difference of the junction equals to $\pi $. We find that the fermionic state composed of the Majorana bound states can be manipulated and controlled by a bias voltage between the two superconductors. The features of Majorana bound states such as exchange can be detected by measuring the Josephson current.   

Ten-fold way of topological Josephson effects in superconductors

We obtain the ten-fold way classification of topological Josephson effects in superconductors using the K-theory. We show how the ten Altland-Zirnbauer symmetry classes can be realized in singlet or triplet superconductors with or without spin-orbit couplings and/or coexisting magnetic orders. In particular, we show that in three spatial dimensions there always exists a topological Josephson effect in each symmetry class, and that in one spatial dimension there are novel topological pumps mediated by paired or unpaired Majorana bound states.