This content will become publicly available on May 11, 2024
 Award ID(s):
 2118310
 NSFPAR ID:
 10419476
 Author(s) / Creator(s):
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 Date Published:
 Journal Name:
 Nature
 ISSN:
 00280836
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract The proposal of faulttolerant quantum computations, which promise to dramatically improve the operation of quantum computers and to accelerate the development of the compact hardware for them, is based on topological quantum field theories, which rely on the existence in Nature of physical systems described by a Lagrangian containing a nonAbelian (NA) topological term. These are solidstate systems having twodimensional electrons, which are coupled to magneticfluxquanta vortexes, forming complex particles, known as anyons. Topological quantum computing (TQC) operations thus represent a physical realization of the mathematical operations involving NA representations of a braid group B n , generated by a set of n localized anyons, which can be braided and fused using a “tweezer” and controlled by a detector. For most of the potential TQC material systems known so far, which are 2Delectron–gas semiconductor structure at high magnetic field and a variety of hybrid superconductor/topologicalmaterial heterostructures, the realization of anyon localization versus tweezing and detecting meets serious obstacles, chief among which are the necessity of using current control, i.e., mobile particles, of the TQC operations and high density electron puddles (containing thousands of electrons) to generate a single vortex. Here we demonstrate a novel system, in which these obstacles can be overcome, and in which vortexes are generated by a single electron. This is a ~ 150 nm size many electron InP/GaInP 2 selforganized quantum dot, in which molecules, consisting of a few localized anyons, are naturally formed and exist at zero external magnetic field. We used highspatialresolution scanning magnetophotoluminescence spectroscopy measurements of a set of the dots having five and six electrons, together with manybody quantum mechanical calculations to demonstrate spontaneous formation of the anyon magnetoelectron particles ( e ν ) having fractional charge ν = n / k, where n = 1–4 and k = 3–15 are the number of electrons and vortexes, respectively, arranged in molecular structures having a builtin (internal) magnetic field of 6–12 T. Using direct imaging of the molecular configurations we observed fusion and braiding of e ν  anyons under photoexcitation and revealed the possibility of using charge sensing for their control. Our investigations show that InP/GaInP 2 anyonmolecule QDs, which have intrinsic transformations of localized e ν  anyons compatible with TQC operations and capable of being probed by charge sensing, are very promising for the realization of TQC.more » « less

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, nonabelian anyons such as Majorana zero modes (MZMs), and nonabelian quantum statistics. ADVANCES In a wideranging and ongoing effort, numerous potential material platforms are being explored that may realize the required topological quantum states. Nonabelian 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 nonabelian anyon, brought entirely new material platforms into view. These include, among others, semiconductorsuperconductor hybrids, magnetic adatoms on superconducting substrates, and Febased superconductors. Onedimensional systems are playing a particularly prominent role, with blueprints for quantum information applications being most developed for hybrid semiconductorsuperconductor systems. There have been numerous attempts to observe nonabelian 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 indepth 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 nonabelian 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 nonabelian 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 zerobias 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 nonabelian anyons such as the topologically protected ground state manifold and nonabelian statistics. Proposed topological platforms. (Left) Proposed state of electrons in a high magnetic field (evendenominator 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

We present microscopic, multiple Landau level, (frustrationfree and positive semidefinite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are partonlike and whose excitations display either Abelian or nonAbelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate Sduality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing partonlike states, specifically at filling factor
. The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closedshell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zeroenergy mode is a unique parton state. We conjecture that partonlike states generally span the subspace of manybody wave functions with the twobody\nu=2/3 $\nu =2/3$ clustering property within any given number of Landau levels, that is, wave functions withM $M$ thorder coincidence plane zeroes and both holomorphic and antiholomorphic dependence on variables. General arguments are supplemented by rigorous considerations for theM $M$ case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for partonlike states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.M=3 $M=3$ 
null (Ed.)One of the most exciting areas of research in quantum condensed matter physics is the push to create topologically protected qubits using nonAbelian anyons. The focus of these efforts has been Majorana zero modes (MZMs), which are predicted to emerge as localized zeroenergy states at the ends of 1D topological superconductors. A key role in the search for experimental signatures of these quasiparticles has been played by the scanning tunnelling microscope (STM). The power of highresolution STM techniques is perhaps best illustrated by their application in identifying MZMs in 1D chains of magnetic atoms on the surface of a superconductor. In this platform, STM spectroscopic mapping has demonstrated the localized nature of MZM zeroenergy excitations at the ends of such chains, and experiments with superconducting and magnetic STM tips have been used to uniquely distinguish them from trivial edge modes. Beyond the atomic chains, STM has also uncovered signatures of MZMs in 2D materials and topological surface and boundary states, when they are subjected to the superconducting proximity effect. Looking ahead, future STM experiments may be able to demonstrate the nonAbelian statistics of MZMs.more » « less

BACKGROUND Landau’s Fermi liquid theory provides the bedrock on which our understanding of metals has developed over the past 65 years. Its basic premise is that the electrons transporting a current can be treated as “quasiparticles”—electronlike particles whose effective mass has been modified, typically through interactions with the atomic lattice and/or other electrons. For a long time, it seemed as though Landau’s theory could account for all the manybody interactions that exist inside a metal, even in the socalled heavy fermion systems whose quasiparticle mass can be up to three orders of magnitude heavier than the electron’s mass. Fermi liquid theory also lay the foundation for the first successful microscopic theory of superconductivity. In the past few decades, a number of new metallic systems have been discovered that violate this paradigm. The violation is most evident in the way that the electrical resistivity changes with temperature or magnetic field. In normal metals in which electrons are the charge carriers, the resistivity increases with increasing temperature but saturates, both at low temperatures (because the quantized lattice vibrations are frozen out) and at high temperatures (because the electron mean free path dips below the smallest scattering pathway defined by the lattice spacing). In “strange metals,” by contrast, no saturation occurs, implying that the quasiparticle description breaks down and electrons are no longer the primary charge carriers. When the particle picture breaks down, no local entity carries the current. ADVANCES A new classification of metallicity is not a purely academic exercise, however, as strange metals tend to be the hightemperature phase of some of the best superconductors available. Understanding hightemperature superconductivity stands as a grand challenge because its resolution is fundamentally rooted in the physics of strong interactions, a regime where electrons no longer move independently. Precisely what new emergent phenomena one obtains from the interactions that drive the electron dynamics above the temperature where they superconduct is one of the most urgent problems in physics, attracting the attention of condensed matter physicists as well as string theorists. One thing is clear in this regime: The particle picture breaks down. As particles and locality are typically related, the strange metal raises the distinct possibility that its resolution must abandon the basic building blocks of quantum theory. We review the experimental and theoretical studies that have shaped our current understanding of the emergent strongly interacting physics realized in a host of strange metals, with a special focus on their posterchild: the copper oxide hightemperature superconductors. Experiments are highlighted that attempt to link the phenomenon of nonsaturating resistivity to parameterfree universal physics. A key experimental observation in such materials is that removing a single electron affects the spectrum at all energy scales, not just the lowenergy sector as in a Fermi liquid. It is observations of this sort that reinforce the breakdown of the singleparticle concept. On the theoretical side, the modern accounts that borrow from the conjecture that strongly interacting physics is really about gravity are discussed extensively, as they have been the most successful thus far in describing the range of physics displayed by strange metals. The foray into gravity models is not just a pipe dream because in such constructions, no particle interpretation is given to the charge density. As the breakdown of the independentparticle picture is central to the strange metal, the gravity constructions are a natural tool to make progress on this problem. Possible experimental tests of this conjecture are also outlined. OUTLOOK As more strange metals emerge and their physical properties come under the scrutiny of the vast array of experimental probes now at our disposal, their mysteries will be revealed and their commonalities and differences cataloged. In so doing, we should be able to understand the universality of strange metal physics. At the same time, the anomalous nature of their superconducting state will become apparent, offering us hope that a new paradigm of pairing of nonquasiparticles will also be formalized. The correlation between the strength of the linearintemperature resistivity in cuprate strange metals and their corresponding superfluid density, as revealed here, certainly hints at a fundamental link between the nature of strange metallicity and superconductivity in the cuprates. And as the gravityinspired theories mature and overcome the challenge of projecting their powerful mathematical machinery onto the appropriate crystallographic lattice, so too will we hope to build with confidence a complete theory of strange metals as they emerge from the horizon of a black hole. Curved spacetime with a black hole in its interior and the strange metal arising on the boundary. This picture is based on the string theory gaugegravity duality conjecture by J. Maldacena, which states that some strongly interacting quantum mechanical systems can be studied by replacing them with classical gravity in a spacetime in one higher dimension. The conjecture was made possible by thinking about some of the fundamental components of string theory, namely Dbranes (the horseshoeshaped object terminating on a flat surface in the interior of the spacetime). A key surprise of this conjecture is that aspects of condensed matter systems in which the electrons interact strongly—such as strange metals—can be studied using gravity.more » « less