Session B65: Topological Superconductivity in Josephson Junctions

Topological superconductivity in semiconductor-superconductor hybrid structures

Several proposals for inducing p-wave superconductivity in semiconductors proximitized by s-wave superconductors have been put forward. This includes systems where time-reversal symmetry is broken by either Zeeman energy or by phase differences in the proximitizing superconductors. In this talk, I discuss the detailed modeling of such structures and present results how for the comparison with experimental data for local and nonlocal conductance measurements. Finally, I discuss possible next steps in the search for nonabelian effects of Majorana zero modes.   

Towards Non-Abelian Statistics in Topological Planar Josephson Junctions

Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zero-energy emergent quasiparticles. With their non-Abelian statistics, they are suitable for implementing fault-tolerant topological quantum computing. While the main efforts to realize MBS have focused on 1D systems, the onset of topological superconductivity requires delicate parameter tuning and geometric constraints pose significant challenges for their control and demonstration of non-Abelian statistics. To overcome these challenges, building on recent advances in planar Josephson junctions (JJs) [1], we propose a novel platform of X-shaped JJs [2], where phase control can generate, exchange, and braid MBS. The underlying topological superconductivity exists over a large parameter space, consistent with our fabricated materials. With our experimental control of superconducting properties using five mini-gates in InAs/Al-based JJs, we show how such mini-gate control demonstrates non-Abelian statistics through MBS fusion [3], paving a promising way to topological quantum computing.

[1] M. Dartiailh, et. al, PRL 126, 036802 (2021).

[2] T. Zhou, et. al, PRL 124, 137001 (2020).

[3] T. Zhou, et. al, arXiv: 2101.09272 (2021).   

Robust topological superconductivity in spatially modulated planar Josephson junctions

Semiconductor-superconductor planar Josephson junctions are promising platforms for realizing topological superconductivity and Majorana zero modes. We purpose a spatially modulated structure consisting of a planar Josephson junction with periodically modulated width. Based on detailed numerical calculations for a low-energy effective model of the proposed device, we demonstrate that the topological gap characterizing the modulated structure is enhanced significantly, which, in turn, enhances the robustness of the associated Majorana zero modes. The enhancement of the topological gap is the result of a stronger effective spin-orbit coupling generated by the periodic potential induced by the spatial modulation of the junction. In addition, we find that the proposed structure supports a low-field topological superconducting phase within a significant range of electrostatic control parameters, in the absence of a superconducting phase difference across the junction. The optimal regime for operating the device can be achieved by tuning the electrostatic potential in the junction region.   

Visualizing Topological Phase Transitions in Planar Josephson Junctions

We investigate the signatures of topological superconductivity in the current-phase relation (CPR) of planar Josephson junctions (JJs). We show how the magnetic-field dependence of the CPR in phase-biased JJs can be used to obtain a good description and visualization of topological phase transitions. In particular, we propose a new method for obtaining the topological phase diagram in the phase and magnetic field space from CPR measurements. This allows to identify the superconducting phase difference and magnetic field at which the junction transits into the topological superconducting state. Furthermore, the magnetic-field dependence of the CPR in phase-biased JJs can also be used to predict the self-tuning of phase-unbiased JJs into the topological state. We discuss the reliability of the proposed method by comparing to direct numerical calculations of the topological phase diagram and to signatures provided by other physical quantities, like conductance and spin susceptibility.   

Enhancing topological superconductivity in phase-biased Josephson junctions

The manifestation of spin-orbit coupling in proximitized superconductivity is central to the formation of topological superconducting phases.  The most exciting property of topological superconductivity is its capacity to harbor non-Abelian excitations that could be the key to developing fault-tolerant quantum computers. Here we study planar Josephson junctions of highly transparent, epitaxial Al contacts on a near-surface InGaAs-InAs-InGaAs quantum well confinining a 2DEG with strong spin-orbit coupling and large g-factor.  This system has been predicted to support topological superconductivity and previous experimental work has yielded promising results consistent with theoretically derived signatures of nontrivial topology.  Our junction is embedded in a SQUID geometry with an integrated remote flux line, enabling phase-sensitive measurements and phase-control via magnetic flux applied far from the junction so as to preserve the superconducting gap.  We study the current-phase relation of the junction as a function of in-plane Zeeman field and gate voltage.  We further study the local density of states near the edge of the junction via tunneling spectroscopy with a quantum point contact while the junction is π-phase-biased, where the Zeeman condition for topology is relaxed.   

Tunneling spectroscopy in planar Josephson junctions

Planar Josephson junction based on two-dimensional electron gas (2DEG) with strong spin-orbit coupling, large g-factor and induced superconductivity is a promising platform to realize topological superconductivity and Majorana zero modes. Here we fabricate planar Josephson junctions on InAs 2DEG with epitaxial Al Contacts. Two tunneling probes are added to the ends of the junction to probe the density of states of edge modes. In a trivial regime, we show that we can screen devices and identify hard induced superconducting gaps in the junction. By application of an in-plane magnetic field the system is expected to make a transition to topological regime. We will present the induced gap and low-energy states measured at the two ends of the junction simultaneously as a function of the in-plane magnetic field,  the angle between the magnetic field and the junction.   

Local Control of Supercurrent Density in Epitaxial Al-InAs Josepshon Junctions

Gate tunable Josephson junctions (JJs) made from two dimensional electron gas can host topological superconductivity, a unique property that can be used for fault tolerant topological quantum computation. In planar Josephson junctions the carrier density and, therefore the overall current distribution could be modified electrostatically via metallic gates. In this work, by applying an out-of-plane magnetic field to an epitaxial Al-InAs JJ equipped with five mini-gates, we have extracted the spatial current distribution of our devices. We demonstrate that not only can the junction width be electrostatically defined and varied but also we can locally adjust the current profile to form superconducting quantum interference devices. Our studies show enhanced edge conduction in the junctions, which can be eliminated by mini-gates to create a uniform current distribution. The ability to locally tune the current distribution width of the junction could open a path for studying topological superconductivity in Josephson junctions.   

Microwave Driven Epitaxial Josephson Junctions with an In-plane Magnetic Field

The hunt for topological superconductivity has accelerated in recent years as it provides a suitable platform for fault-tolerant quantum computing. Planar epitaxial Al-InAs Josephson junctions (JJs) are a promising candidate to realize topological superconducting states due to their high transparency, strong spin-orbit coupling, and large g-factor. When a microwave drive is applied to a JJ, quantizied integer and possibly fractional constant voltage steps, Shapiro steps, appear in the Voltage-Current characteristic due to phase locking. The presence of the 4π-periodic Josephson effect, one of the signatures of topological superconductivity, results in missing odd Shapiro steps. However, highly transparent JJs in the topologically trivial regime, without a magnetic field, have also been shown to exhibit missing odd Shapiro. Theory predicts these JJs can be driven into a topological superconducting phase by applying an in-plane magnetic field. We study the effect of the Zeeman field on trivial and non-trivial signatures with and without microwave drive. We further consider the field angle and junction geometry on the observed signatures.   

Extracting strength of spin-orbit coupling in InAs-Al heterostructures: Implications for topological superconductivity

Topological superconductivity is expected to emerge in materials with a strong spin-orbit coupling. Beyond the realization of topological superconductivity it is important to control the topological-trivial phase transition as well. This can be achieved through a gate tunable spin-orbit coupling in epitaxially grown two-dimensional InAs-Al heterostrcutres. Here, we discuss extracting the strength of linear Dresselhaus and Rashba spin-orbit coupling terms from magnetoconductivity measurements which manifest as weak localization or antilocalization signatures. A fully quantum mechanical model is used to describe the electronic states and the interference effects resulting from scattering loops in the presence of an external out-of-plane magnetic field. The extracted experimental results are then compared with the solutions of the 8-band Kane model for Zinc blende crystals with a reduced symmetry in the growth direction. We then discuss the symmetry and the interplay of Dresselhaus and Rashba spin-orbit coupling terms as well as the effect of an in-plane magnetic field in realizing topological superconductivity.   

Topological superconductivity in the attractive Rashba-Hubbard model: A quantum Monte Carlo dynamical cluster approximation study

Fully gapped, spin singlet superconductors with antisymmetric spin-orbit coupling in a Zeeman magnetic field provide a promising route to realize superconducting states with non-Abelian topological order and therefore fault-tolerant quantum computation. Here we use a quantum Monte Carlo dynamical cluster approximation to study the superconducting properties of a doped two-dimensional attractive Hubbard model with Rashba spin orbit coupling in a Zeeman magnetic field. In the absence of spin orbit coupling, we find that the Zeeman field completely suppresses superconductivity in this model as expected from the Pauli depairing effect. When the Rashba spin orbit coupling is turned on, however, superconductivity is restored at finite temperatures. By inspecting the Fermi surface of the interacting model, we can draw conclusions about the topological character of the superconducting state.    

Observation of ​Phase Controllable Majorana​-like Bound States in Metamaterial-based Kitaev Chain Analogues

Motivated by the recent theoretical studies on a quasi-one-dimensional Su-Schrieffer-Heeger ladder model Hamiltonian [1], we experimentally demonstrate that the Majorana​-like Bound States (MBSs) can occur at the open edges of quasi-one-dimensional mechanical metamaterials, analogous to the Majorana Zero Modes at the edges of the Kitaev chain. Specifically, using mechanical systems made of magnetically coupled spinners, we demonstrate (1) the topological phase transition ​signaled by the emergence of the mid-gap MBSs, (2) the localization of MBS ​characterized by decay and oscillation (3) the hybridization of MBSs and ​control of relative phases of wave-function analogues by frequency tuning, and (4) the oscillation of the MBS hybridization splitting with varying the length of the ladder systems. ​We find strong agreement between experiments and theory. The implications to the Kitaev chain, qubits, and braidings, and the possibility of topologically protected mechanical memory are also discussed.   

Fermion parity switches in Majorana-Transmon qubits

Recent efforts have focused on replacing the weak link in the Josephson Junction (JJ) of a superconducting qubit by electrostatically-gateable technologies compatible with high magnetic fields [1]. Such alternatives are crucial in order to reach a regime relevant for readout of topological qubits based on Majorana zero modes (MZMs) [2]. In this talk, I will focus on JJs based on semiconducting nanowires that can be driven to a topological superconductor phase with MZMs. A fully microscopic theoretical description of such hybrid semiconductor-superconducting qubit allows to unveil new physics originated from the coherent interaction between the MZMs and the superconducting qubit degrees of freedom [3]. In the transmon regime, the microwave spectroscopy presents nontrivial features, including a full mapping of zero energy crossings and fermionic parity switches in the nanowire owing to Majorana oscillations [4].

[1] A perspective on semiconductor-based superconducting qubits, Applied Physics Letters, 117, 240501 (2020).

[2] Majorana qubits for topological quantum computing, R. Aguado and Leo Kouwenhoven, Physics Today 73, 6, 44 (2020)

[3]Superconducting islands with semiconductor-nanowire-based topological Josephson junctions, J. Avila, E. Prada, P. San-Jose and R. Aguado, Physical Review B, 102, 094518 (2020)

[4] Majorana oscillations and parity crossings in semiconductor nanowire-based transmon qubits, J. Avila, E. Prada, P. San-Jose and R. Aguado, Physical Review Research, 2, 033493 (2020).   

Local and non-local spectroscopy of phase-biased Josephson junctions in an InSbAs two-dimensional electron gas

Planar Josephson junctions (JJs) have been proposed as a route to creating phase-controllable Majorana zero-modes. We study such devices in a hybrid InSbAs/Al two-dimensional electron gas, which has previously shown promising electrical properties for the realization of topological superconductivity (i.e., strong spin-orbit coupling, a large g-factor and clean superconductor-semiconductor interfaces). Using simultaneous tunnelling spectroscopy at both ends of the junction, we observe Andreev bound states whose energies are modulated by the phase. The three-terminal nature of these devices also allows us to study the non-local conductance, giving additional insights into the bulk of the JJ. At finite in-plane magnetic fields, we see the onset of a phase-dependent inversion in the sign of the non-local conductance and the emergence of zero-bias peaks in local spectroscopy.