Session S60: Topological Superconductivity Induced in Spin-Orbit-Coupled Materials

Topological superconductivity in superconductor–semiconductor heterostructures

Superconductor–semiconductor heterostructures represent a versatile platform for realizing Majorana zero-energy modes. In this talk, I will explain how to engineer topological superconductivity at the interface of a conventional (s-wave) superconductor and a semiconductor with spin-orbit interaction. I will discuss state-of-the-art numerical approaches for modeling realistic devices which take into account proximity-induced superconductivity, orbital and Zeeman effect of an applied magnetic field, spin-orbit coupling as well as the electrostatic environment on equal footing. Finally, I will review recent materials science progress in growing superconductor–semiconductor heterostructures and discuss promising new directions.   

Josephson controlled topological superconductivity

In this talk I will describe how the Josephson effect may be employed to realize one dimensional topological superconductivity, with the Josephson phase difference being a "user-friendly" knob to drive the system to become topological. I will describe the basic idea, the experimental observations, the relation to topological superconductivity based on quantum wires, a surprising effect of disorder, and a scheme for braiding Majorana zero modes in Josephson junctions. I will also describe how this system manifests a first order phase transition into a topological phase.   

Nature of the insulating and superconducting states of monolayer WTe2

Although in the bulk WTe₂ is a semimetal, exfoliated to a monolayer it becomes a topological insulator that undergoes a transition to a metallic state on electron doping of 5x10¹² cm^-2, and furthermore this metallic state becomes superconducting at temperatures below about 1 K. This proximity, in terms of doping, of a small-gap insulator to a superconductor is surprising, and the insulator exhibits a number of other unusual properties. We will summarize and compare these properties and assess the possibility that the insulating state has a many-body character akin to an excitonic insulator. In addition, we will present and evaluate evidence that the helical edge states remain throughout the insulator to superconductor transition.   

Phase control of zero energy modes in topological Josephson junctions

Recent works have realized Majorana zero modes in planar Josephson junctions consisting of a semiconductor with strong spin-orbit coupling proximitized by two superconducting leads. Such systems offer the tantalizing possibility of using the phase difference Φ across the two superconductors as a new experimental knob to tune into and out of the topological regime, possibly at ultra-fast timescales, apart from having advantages such as reduced sensitivity to chemical potential tuning and appearance of Majorana bound states at zero magnetic field. Here, we demonstrate strong phase control of Andreev bound states that emerge from the gap at Φ~0 and coalesce at zero energy at Φ~π. The zero energy modes at Φ~π appear at in-plane magnetic fields as low as ~220 mT and persist robustly with variations of in-plane Zeeman field and gate voltages in a wide range. At larger in-plane magnetic fields, the zero energy modes become phase independent and stick for all values of Φ. We also study the behavior of the zero energy states with respect to large out-of-plane magnetic fields that can tune the phase texture within the Josephson junction, and possibly result in motion of Majorana zero modes.   

Phase signature of topological transition in Josephson junctions

Topological transition transforms common superconductivity into an exotic phase of matter, which holds promise for fault-tolerant quantum computing. A hallmark of this transition is the emergence of Majorana states. While two-dimensional semiconductor/superconductor heterostructures are desirable platforms for topological superconductivity, direct phase-measurements as the fingerprint of the underlying topological transition have been missing.
On gate tunable Josephson junctions made on epitaxial Al/InAs, we observe a closing and a reopening of the superconducting gap with increasing in-plane magnetic field. Since our junctions are embedded into a phase-sensitive SQUID, we are able to measure a π-jump in the superconducting phase across the junction coincident with the closing and reopening of the superconducting gap. Theoretical simulations confirm this transition is topological and compatible with the emergence of Majorana states while the magnetic field angle dependence of the transition further constrain this scenario. Remarkably, in each junction, this topological transition can be controlled by changing the gate voltage. These findings reveal versatile two-dimensional platforms for scalable topological quantum computing.   

Signatures of topological superconductivity in Josephson junctions

Topological superconductivity is a phase of matter supporting Majorana bound states, quasiparticles that store information in a nonlocal manner and can be used as qubits that are robust against local perturbations. We theoretically investigate the emergence of topological superconductivity in Josephson junctions with tunable chemical potential and Rashba spin-orbit coupling, subjected to an in-plane magnetic field. As the magnetic field along the junction increases above some critical value the system experiences a transition from the trivial to the topological superconducting phase. Theoretical simulations show that such a transition is accompanied by a minimum in the critical current and a corresponding jump in the phase difference across the junction. The sensitivity of the topological transition to the in-plane magnetization direction provides and additional fingerprint for the emergence of topological superconductivity. The theoretical simulations are in good agreement with the recent experimental detection of topological phase transitions in gate-tunable JJs built on epitaxial Al/InAs [1].

[1] M. C. Dartiailh et al., arXiv: 1906.01179   

In-vacuo growth and fabrication of superconductor-semiconductor hybrid heterostructures for topological quantum computation

Superconductor-semiconductor heterostructures are the backbone of Majorana Zero Mode (MZM) based topological quantum computing. Magneto-transport in nanowires of InSb with partial shells of aluminum has highlighted the significance of abrupt and epitaxial, in-vacuo growth of superconductors on semiconductors. Going forward, two key challenges need to be addressed. Firstly, the demonstration of in-vacuo, selective area growth of superconductors on wafer-scale semiconductors and, secondly, in-vacuo fabrication of proposed topological qubit devices. This work reports on the Molecular Beam Epitaxy (MBE) of selective area hybrid heterostructures using various approaches with the aim of creating a versatile platform for fabrication of topological qubits in vacuo.   

Accessing different topological classes and types of Majorana edge states in 1D p-wave superconductors using perturbations

Classification and realization of various classes of topological superconductors with different types of Majorana bound states (MBS) is of ongoing interest. The standard platform of these studies have been the conventional 1D Kitaev wire and its realizations. Here, we present the edge states of different types of p-wave SC in 1D in the presence of an additional Zeeman field and s-wave SC component. Within the framework of the tenfold classification scheme, we study the transition between different topological classes caused by such perturbations and analyze the nature of the corresponding MBS. Further, we study the junctions between different classes of topological superconductors and explore transport properties to probe the mid-gap states.   

Phase Control of Majorana Bound States in a Topological X Junction

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 [1]. 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 experiments in planar Josephson junctions (JJs) [2-4], we propose a MBS platform of X-shaped JJs. This versatile implementation reveals how external flux control of the superconducting phase difference can generate and manipulate multiple MBS pairs to probe non-Abelian statistics. The underlying topological superconductivity exists over a large parameter space, consistent with materials used in our fabrication of such X junctions, as an important step towards topological quantum computing.
[1] C. Nayak, et. al, Rev. Mod. Phys. 80, 1083 (2008).
[2] A. Fornieri, et. al, Nature 569, 89 (2019).
[3] H. Ren, et. al, Nature 569, 93 (2019).
[4] W. Mayer, et. al, arXiv:1906.01179 (2019).