We address an outstanding problem that represents a critical roadblock in the development of the
Majorana-based topological qubit using semiconductor-superconductor hybrid structures: the quantitative
characterization of disorder effects generated by the unintentional presence of charge impurities within
the hybrid device. Given that disorder can have far-reaching consequences for the Majorana physics but
is intrinsically difficult to probe experimentally in a hybrid structure, providing a quantitative theoretical
description of disorder effects becomes essential. To accomplish this task, we develop a microscopic theory
that (i) provides a quantitative characterization of the effective potential generated by a charge impurity
embedded inside a semiconductor wire proximity coupled to a superconductor layer by solving selfconsistently
the associated three-dimensional Schrödinger-Poisson problem, (ii) describes the low-energy
physics of the hybrid structure in the presence of s-wave superconductivity, spin-orbit coupling, Zeeman
splitting, and disorder arising from multiple charge impurities by using the results of (i) within a standard
free-fermion approach, and (iii) links the microscopic results to experimentally observable features by
generating tunneling differential-conductance maps as a function of the control parameters (e.g., Zeeman
field and chemical potential). We find that charge impurities lead to serious complications regarding the
realization and observation of Majorana zero modes, which have direct implications for the development
of Majorana-based qubits. More importantly, our work provides a clear direction regarding what needs to
be done for progress in the field, including specific materials-quality and semiconductor-purity targets that
must be achieved to create a topological qubit.
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Enhanced topological superconductivity in spatially modulated planar Josephson junctions
We propose a semiconductor-superconductor hybrid device for realizing topological superconductivity and
Majorana zero modes consisting of a planar Josephson junction structure with periodically modulated junction
width. By performing a numerical analysis of the effective model describing the low-energy physics of the hybrid
structure, we demonstrate that the modulation of the junction width results in a substantial enhancement of the
topological gap and, consequently, of the robustness of the topological superconducting phase and associated
Majorana zero modes. This enhancement is due to the formation of minibands with strongly renormalized
effective parameters, including stronger spin-orbit coupling, generated by the effective periodic potential induced
by the modulated structure. In addition to a larger topological gap, the proposed device supports a topological
superconducting phase that covers a significant fraction of the parameter space, including the low Zeeman field
regime, in the absence of a superconducting phase difference across the junction. Furthermore, the optimal
regime for operating the device can be conveniently accessed by tuning the potential in the junction region
using, for example, a top gate.
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- Award ID(s):
- 2014156
- NSF-PAR ID:
- 10476247
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 104
- Issue:
- 15
- ISSN:
- 2469-9950
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Hybrid semiconductor-superconductor nanowires have emerged as a promising platform for realizing topological superconductivity (TSC). Here, we present a route to TSC using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core. Tunneling into the core reveals a hard induced gap near zero applied flux, corresponding to zero phase winding, and a gapped region with a discrete zero-energy state around one applied flux quantum, corresponding to 2π phase winding. Theoretical analysis indicates that the winding of the superconducting phase can induce a transition to a topological phase supporting Majorana zero modes. Measured Coulomb blockade peak spacing around one flux quantum shows a length dependence that is consistent with the existence of Majorana modes at the ends of the nanowire.
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We consider theoretically the physics of bulk topological superconductivity accompanied by boundary non- Abelian Majorana zero modes in semiconductor-superconductor (SM-SC) hybrid systems consisting of finite wires in the presence of correlated disorder arising from random charged impurities. We find the system to manifest a highly complex behavior due to the subtle interplay between finite wire length and finite disorder, leading to copious low-energy in-gap states throughout the wire and considerably complicating the interpretation of tunneling spectroscopic transport measurements used extensively to search forMajorana modes. The presence of disorder-induced low-energy states may lead to the nonexistence of end Majorana zero modes even when tunneling spectroscopy manifests zero-bias conductance peaks in local tunneling and signatures of bulk gap closing/reopening in the nonlocal transport. In short wires within the intermediate disorder regime, apparent topology may manifest in small ranges (“patches”) of parameter values, which may or may not survive the longwire limit depending on various details. Because of the dominance of disorder-induced in-gap states, the system may even occasionally have an appropriate topological invariant without manifesting isolated end Majorana zero modes. We discuss our findings in the context of a recent breakthrough experiment from Microsoft reporting the simultaneous observations of zero-bias conductance peaks in local tunneling and gap opening in nonlocal transport within small patches of parameter space. Based on our analysis, we believe that the disorder strength to SC-gap ratio must decrease further for the definitive realization of non-Abelian Majorana zero modes in SM-SC devices.more » « less
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BACKGROUND The past decade has witnessed considerable progress toward the creation of new quantum technologies. Substantial advances in present leading qubit technologies, which are based on superconductors, semiconductors, trapped ions, or neutral atoms, will undoubtedly be made in the years ahead. Beyond these present technologies, there exist blueprints for topological qubits, which leverage fundamentally different physics for improved qubit performance. These qubits exploit the fact that quasiparticles of topological quantum states allow quantum information to be encoded and processed in a nonlocal manner, providing inherent protection against decoherence and potentially overcoming a major challenge of the present generation of qubits. Although still far from being experimentally realized, the potential benefits of this approach are evident. The inherent protection against decoherence implies better scalability, promising a considerable reduction in the number of qubits needed for error correction. Transcending possible technological applications, the underlying physics is rife with exciting concepts and challenges, including topological superconductors, non-abelian anyons such as Majorana zero modes (MZMs), and non-abelian quantum statistics. ADVANCES In a wide-ranging and ongoing effort, numerous potential material platforms are being explored that may realize the required topological quantum states. Non-abelian anyons were first predicted as quasiparticles of topological states known as fractional quantum Hall states, which are formed when electrons move in a plane subject to a strong perpendicular magnetic field. The prediction that hybrid materials that combine topological insulators and conventional superconductors can support localized MZMs, the simplest type of non-abelian anyon, brought entirely new material platforms into view. These include, among others, semiconductor-superconductor hybrids, magnetic adatoms on superconducting substrates, and Fe-based superconductors. One-dimensional systems are playing a particularly prominent role, with blueprints for quantum information applications being most developed for hybrid semiconductor-superconductor systems. There have been numerous attempts to observe non-abelian anyons in the laboratory. Several experimental efforts observed signatures that are consistent with some of the theoretical predictions for MZMs. A few extensively studied platforms were subjected to intense scrutiny and in-depth analyses of alternative interpretations, revealing a more complex reality than anticipated, with multiple possible interpretations of the data. Because advances in our understanding of a physical system often rely on discrepancies between experiment and theory, this has already led to an improved understanding of Majorana signatures; however, our ability to detect and manipulate non-abelian anyons such as MZMs remains in its infancy. Future work can build on improved materials in some of the existing platforms but may also exploit new materials such as van der Waals heterostructures, including twisted layers, which promise many new options for engineering topological phases of matter. OUTLOOK Experimentally establishing the existence of non-abelian anyons constitutes an outstandingly worthwhile goal, not only from the point of view of fundamental physics but also because of their potential applications. Future progress will be accelerated if claims of Majorana discoveries are based on experimental tests that go substantially beyond indicators such as zero-bias peaks that, at best, suggest consistency with a Majorana interpretation. It will be equally important that these discoveries build on an excellent understanding of the underlying material systems. Most likely, further material improvements of existing platforms and the exploration of new material platforms will both be important avenues for progress toward obtaining solid evidence for MZMs. Once that has been achieved, we can hope to explore—and harness—the fascinating physics of non-abelian anyons such as the topologically protected ground state manifold and non-abelian statistics. Proposed topological platforms. (Left) Proposed state of electrons in a high magnetic field (even-denominator fractional quantum Hall states) are predicted to host Majorana quasiparticles. (Right) Hybrid structures of superconductors and other materials have also been proposed to host such quasiparticles and can be tailored to create topological quantum bits based on Majoranas.more » « less
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Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu–Shiba–Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay among Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction, spin–orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin–spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevB.104.155428
