Session D65: Topological Superconductivity in Nanowires

Disorder and topological superconductivity

Topological superconductors have the potential to be one of the simplest platforms to demonstrate topologically protected degeneracy because they are effectively non-interacting phases. Proposals such as those based on semiconductor-superconductor hybrids, topological superconductors, quantum Hall gases and iron superconductors provide a range of options to engineer such platforms. Unfortunately, despite the nominal stability of topological superconductors to weak disorder, realizing a topological phase often requires an effective one dimensional scattering rate below the induced superconducting gap. In this talk I will review how this principle restricts various platforms such as those based on semiconductor nanowires, quantum Hall systems and line Josephson junctions. I will also discuss transport experiment proposals to identify device issues from disorder and device imperfections.   

Withdrawn

Hybrid superconductor-semiconductor nanowires are being intensively studied in an effort to detect and manipulate Majorana bound states. Traditionally, a superconductor is deposited or grown epitaxially over some of the facets of the semiconducting wire and a Zeeman field is applied to drive the system into the topological regime. One of the main drawbacks of this platform is the need to subject the wire to strong magnetic fields that degrade the superconducting state of the parent superconductor. In the last couple of years, new nanowire configurations are being explored that could present some advantages with respect to previous designs. In this talk, I will discuss theoretical and experimental progress on one the most promising proposals: the so-called full-shell nanowires, where the semiconducting nanowire is fully coated with a superconducting shell. These wires could develop Majorana modes in the presence of small external magnetic fields not driven by the Zeeman effect, but by the winding of the superconducting phase around the semiconducting core.   

Steering Majorana braiding via skyrmion-vortex pairs: a scalable platform

Majorana zero modes are quasiparticles that hold promise as building blocks for topological quantum computing. However, the litmus test for their detection, the observation of exotic non-abelian statistics revealed by braiding, has so far eluded experimental efforts. Here we take advantage of the fact that skyrmion-vortex pairs in superconductor-ferromagnet heterostructures harboring Majorana zero modes can be easily manipulated in two spatial dimensions. We adiabatically braid the hybrid topological structures and explicitly confirm the non-abelian statistics of the Majorana zero modes numerically using a self-consistent calculation of the superconducting order parameter. Our proposal of controlling skyrmion-vortex pairs provides the necessary leeway toward a scalable topological quantum computing platform.

[1] J. Nothhelfer, K. M. D. Hals, K. Everschor-Sitte, and M. Rizzi, European Patent Application EP3751472A1 / International Patent Application WO2020EP66120 (2019).   

Manipulation of Majorana bound states in proximity to a quantum ring with Rashba coupling

The quest for Majorana zero modes in the laboratory is an active field of research in condensed matter physics. In this regard, there have been many theoretical proposals; however, their experimental detection remains elusive. In this article, we present a realistic setting by considering a quantum ring with Rashba spin-orbit coupling and threaded by a magnetic flux, in contact with a topological superconducting nanowire. We focus on spin-polarized persistent currents to assess the existence of Majorana zero modes. We find that the Rashba spin-orbit coupling allows for tuning the position of the zero modes in flux space and has sizable effects on spin-polarized persistent currents. Our results pave the way towards probing the existence of Majorana zero modes.

[1] A. Y. Kitaev, Physics-Uspekhi 44, 131 (2001).

[2] E. Prada, P. San-Jose, M. W. A. de Moor, A. Geresdi, E. J. H. Lee, J. Klinovaja, D. Loss, J. Nygård, R. Aguado and L. P. Kouwenhoven, Nat. Rev. Phys. 2, 575 (2020).

[3] E. Prada, R. Aguado and P. San José, Phys. Rev. B 96, 085418 (2017).

[4] J. P. Ramos-Andrade, P. A. Orellana and S. E. Ulloa J. Phys. Condens. Matter 30, 045301 (2018).

[5] S. K. Maiti, M. Dey and S. N. Karmakar, Physica E 64, 169 (2014).   

Tunable interdot coupling via Andreev levels

Quantum dot-superconductor-quantum dot is a widely used mesoscopic system for studying fundamental physics, such as Cooper pair splitting, spin qubit coupling via superconductor among others. However, when the superconductor is of metallic nature, the interdot tunneling strength decays with $k_F L$ in a power law and is difficult to fine-tune by system parameters. In this work we consider a short semiconductor-superconductor hybrid nanowire for which the low-energy physics is a pair of Andreev levels. We find that the Andreev-level-mediated interdot tunneling strength is tunable and has a universal dependence on the nanowire parameters, such as chemical potential, spin-orbit interaction and induced Zeeman spin splitting. Moreover, we show that in tunnel spectroscopy resonant current flowing through the system is proportional to the square of interdot tunneling strength when dots are connected to external normal leads.  Our findings will facilitate the device characterization and optimization in related experiments.    

Extended quantum-mechanical supersymmetry in Majorana nanowires

Extended supersymmetry (SUSY) with central charges has been one of the most important notions in quantum field theory and string theory since the second string revolution in the 90s and the revolution of quantum field theory by Seiberg and Witten. In spite of its great importance in formal aspects of quantum field theory and string theory, all high energy theorists regard it as a useful tool which is not directly related to reality, because the extended N=2 SUSY does not allow chiral fermions relevant for elementary particles such as quarks and leptons. In high energy phenomenology, only N=1 SUSY and its breaking are considered.

In our recent works[1,2], we provide the first experimentally accessible example of extended SUSY with central charges and partial spontaneous SUSY breaking in condensed matter. Specifically, we describe the realization of a periodic chain of partially-overlapping 0D Majorana modes in 1D Majorana nanowires, by applying periodically and spatially modulated potentials or magnetic fields. This system realizes a 1D Majorana dispersive fermion which we identify with the Nambu-Goldstone mode (Goldstino) of the spontaneously and partially broken SUSY. Notice that the famous Witten's no-go theorem prohibiting partial SUSY breaking can be evaded only by the presence of a central extension in the extended SUSY algebra, and our model indeed includes a central extension. Despite the several proposals to realize SUSY in condensed matter, our proposal gives the first condensed matter realization of an extended SUSY with central extensions.

[1] Marra, Inotani, Nitta, arXiv:2106.09039;

[2] Marra, Inotani, Nitta, arXiv:2106.09047.   

Gate-controlled Elastic Co-Tunneling and Crossed Andreev Reflection mediated by Andreev Bound States

Elastic co-tunneling (ECT) and crossed Andreev reflection (CAR) are complementary processes that take place when two normal leads are separated by a thin superconductor. In the former, an electron hops from one lead to another, and in the latter, two correlated electrons from both sides enter or leave the superconducting segment. Controlling the ECT and CAR amplitudes and extending the range over which they can occur is desirable to couple spin qubits and form artificial topological structures such as the Kitaev chain. We fabricate and measure CAR and ECT in an InSb nanowire device, where two quantum dots are separated by a superconducting segment. We show by comparison to a theoretical model that both ECT and CAR are mediated by an Andreev bound state (ABS) residing under the superconducting segment. Since ECT and CAR are mediated by the ABS, we show that they extend beyond the superconducting coherence length, and their amplitudes are tuned by external plunger gate and magnetic field. This tunability is an essential tool for the future engineering of topological superconductivity in meta-materials.   

Delocalized Andreev bound states and non-topological Majorana excitations in InSb nanowiresc

Majorana bound states are zero-energy modes that are created and annihilated by the same operator. They are highly sought after mainly due to their non-abelian statistics, a property desirable both for fundamental research and possible applications in the field of quantum computing. Majorana zero-modes are necessarily spin-less, which directed the attention of their pursuit on the boundary of topological superconductors. Andreev bound states (ABS), however, are spin-full excitations formed when a quantum level is coupled to a superconductor and thus cannot create Majorana modes. A recent proposal showed that it is possible to create a non-local ABS when two spin-less quantum dots are coupled via a superconductor. Following this proposal, we fabricate an InSb nanowire device, in which a short Al strip separates two spin-split quantum dots. 

By measuring the spectrum of the system, we show that we can precisely control the relevant parameters of the system. Finally, by comparing with a theoretical model, we tune the system into a sweet spot where the zero-energy modes are expected to be Majorana excitations.    

Tunneling spectroscopy in InSbAs-Al multi-probe devices

Majorana zero modes can emerge as edge states in a one-dimensional topological superconductor.The primary experimental approach for identification is an emerging zero-bias peaks (ZBPs) in tunneing spectroscopy at the edge of the system, which, however, can also be due to many trivial origins. A more unique (and thus strong) accompanying signature is the re-opening of the bulk superconducting gap. Some initial attempts have been done on the mostly studied nanowire platform, where it requires some sophisticated fabrication steps .Here we study the electron transport of the quasi-1D structures made from the new InSbAs2DEGs-Al system, where the semiconductor shows very strong spin-orbit interaction. In addition, the inherent design flexibility allows for a straightforward realization of multiple tunnel junctions along the 1D strip. By using tunneling spectroscopy, we study both the local energy spectra simultaneously at different positions, and also the non-local responses of individual sections. At zero magnetic field, locally we have observed the hard superconducting gap with same gap size along the wire, indicating a uniform proximity over μm-long length scale. The superconducting gap becomes smaller and eventually close at in-plane field B≈1.1 T, after which zero bias peaks emerge at tunnel probes located at the edges, while this is less prominent for probes in the bulk. At similar magnetic field, a sign flip of the non-local conductance has also been repeatedly observed.   

Vortex-induced pairing suppression and near-zero modes in quantum dots coupled to full-shell nanowires

We analyze the subgap excitations and phase diagram of a quantum dot (QD) coupled to a semiconducting nanowire fully wrapped by a superconducting (S) shell. We take into account how a Little-Parks (LP) pairing vortex in the shell influences the proximity effect on the dot. We find that under axially symmetric QD-S coupling, shell vortices cause the induced pairing to vanish, producing instead a level renormalization that pushes subgap levels closer to zero energy and flattens parity crossings as the coupling strength increases. This vortex-induced stabilization mechanism has analogues in symmetric S-QD-S Josephson junctions at phase π, and can naturally lead to patterns of near-zero modes weakly dispersing with parameters in all but the zero-th lobe of the LP spectrum. We also show that, under certain conditions, this mechanism could give rise to states that mimic some of the features of Majorana bound states in full-shell wires, despite of the fact that they are topologically trivial.   

Structural investigation of cryogenic-grown Sn thin films on InSb substrates

Superconductor-semiconductor hybrid structures fabricated by optimizing interface formation recipes contribute to better topological superconducting devices. Lately, we measured superconductivity and 2e parity charging in crystalline tin islands grown at cryogenic temperatures on InSb nanowire facets. To further understand the structural properties of those heterostructures, we deposited tin layers on InSb (110) and (001) substrates using different growth recipes, including the one used for nanowires. First of all, X-ray diffraction spectroscopy performed at room temperature shows that tin thin films grown on InSb are epitaxial and in the cubic alpha phase. Depending on the capping strategy to prevent thin film dewetting, some films may contain beta tin grains that are superconducting. We finally propose a mechanism responsible for the formation of the beta grains in the thin films.   

Distinguishing topological Majorana zero modes: non-local conductance versus the von Neumann entropy

The topological origin of the zero bias conductance signatures of Majorana zero modes has been a topic of intense debate. We propose to differentiate between true Majorana bound states and trivial Andreev bound states using the von Neumann entanglement entropy. The topological von Neumann entropy provides a distinct signature of non-local correlations of topological origin. We also establish its connection with recently proposed ideas on the lines of the non-local conductance spectra in a three-terminal normal-topological superconductor-normal hybrid system. We show that both entanglement entropy and non-local conductance exhibit a clear topological phase transition signature for long enough system sizes. However, we observe that the non-local conductance fails to signal a topological phase transition for small system sizes. Moreover, we demonstrate the robustness of entanglement entropy to system parameters as well as its size, establishing it as an ideal metric for distinguishing topological phases.

[1] A. Kejriwal and B. Muralidharan, ArXiv:2112.02235, (2021).