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1. Two-dimensional finite quantum Hall clusters of electrons with anisotropic features

   https://doi.org/10.1038/s41598-022-06093-y  

   Ciftja, Orion ( December 2022 , Scientific Reports)

   Abstract Low-dimensional nano and two-dimensional materials are of great interest to many disciplines and may have a lot of applications in fields such as electronics, optoelectronics, and photonics. One can create quantum Hall phases by applying a strong magnetic field perpendicular to a two-dimensional electron system. One characterizes the nature of the system by looking at magneto-transport data. There have been a few quantum phases seen in past experiments on GaAs/AlGaAs heterostructures that manifest anisotropic magnetoresistance, typically, in high Landau levels. In this work, we model the source of anisotropy as originating from an internal anisotropic interaction between electrons. We use this framework to study the possible anisotropic behavior of finite clusters of electrons at filling factor 1/6 of the lowest Landau level. 

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2. Deformation of the Fermi surface of a spinless two-dimensional electron gas in presence of an anisotropic Coulomb interaction potential

   https://doi.org/10.1038/s41598-021-82564-y  

   Ciftja, Orion ( February 2021 , Scientific Reports)

   We consider the stability of the circular Fermi surface of a two-dimensional electron gas system against an elliptical deformation induced by an anisotropic Coulomb interaction potential. We use the jellium approximation for the neutralizing background and treat the electrons as fully spin-polarized (spinless) particles with a constant isotropic (effective) mass. The anisotropic Coulomb interaction potential considered in this work is inspired from studies of two-dimensional electron gas systems in the quantum Hall regime. We use a Hartree–Fock procedure to obtain analytical results for two special Fermi liquid quantum electronic phases. The first one corresponds to a system with circular Fermi surface while the second one corresponds to a liquid anisotropic phase with a specific elliptical deformation of the Fermi surface that gives rise to the lowest possible potential energy of the system. The results obtained suggest that, for the most general situations, neither of these two Fermi liquid phases represent the lowest energy state of the system within the framework of the family of states considered in this work. The lowest energy phase is one with an optimal elliptical deformation whose specific value is determined by a complex interplay of many factors including the density of the system.

    

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3. Hunting for Majoranas

   https://doi.org/10.1126/science.ade0850  

   Yazdani, Ali ; von Oppen, Felix ; Halperin, Bertrand I. ; Yacoby, Amir ( June 2023 , Science)

   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. 

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4. Broken symmetries and excitation spectra of interacting electrons in partially filled Landau levels

   https://doi.org/10.1038/s41567-023-02126-z  

   Farahi, Gelareh ; Chiu, Cheng-Li ; Liu, Xiaomeng ; Papic, Zlatko ; Watanabe, Kenji ; Taniguchi, Takashi ; Zaletel, Michael P. ; Yazdani, Ali ( January 2023 , Nature Physics)

   Interacting electrons in flat bands give rise to a variety of quantum phases. One fundamental aspect of such states is the ordering of the various flavours—such as spin or valley—that the electrons can possess and the excitation spectrum of the broken-symmetry states that they form. These properties cannot be probed directly with electrical transport measurements. The zeroth Landau level of monolayer graphene with fourfold spin–valley degeneracy is a model system for such investigations, but the nature of its broken-symmetry states—particularly at partial fillings—is still not understood. Here we demonstrate a non-invasive spectroscopic technique with a scanning tunnelling microscope and use it to perform measurements of the valley polarization of the electronic wavefunctions and their excitation spectrum in the partially filled zeroth Landau level of graphene. We can extract information such as the strength of the Haldane pseudopotentials that characterize the repulsive interactions underlying the fractional quantum states. Our experiments also demonstrate that fractional quantum Hall phases are built upon broken-symmetry states that persist at partial filling. Our experimental approach quantifies the valley phase diagram of the partially filled Landau level as a model flat-band platform, which is applicable to other graphene-based electronic systems. 

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5. Next-generation even-denominator fractional quantum Hall states of interacting composite fermions

   https://doi.org/10.1073/pnas.2314212120  

   Wang, Chengyu ; Gupta, Adbhut ; Madathil, Pranav T. ; Singh, Siddharth K. ; Chung, Yoon Jang ; Pfeiffer, Loren N. ; Baldwin, Kirk W. ; Shayegan, Mansour ( December 2023 , Proceedings of the National Academy of Sciences)

   The discovery of the fractional quantum Hall state (FQHS) in 1982 ushered a new era of research in many-body condensed matter physics. Among the numerous FQHSs, those observed at even-denominator Landau level filling factors are of particular interest as they may host quasiparticles obeying non-Abelian statistics and be of potential use in topological quantum computing. The even-denominator FQHSs, however, are scarce and have been observed predominantly in low-disorder two-dimensional (2D) systems when an excited electron Landau level is half filled. An example is the well-studied FQHS at filling factor$\mathit{\nu }\mathbf{=}$5/2 which is believed to be a Bardeen-Cooper-Schrieffer-type, paired state of flux-particle composite fermions (CFs). Here, we report the observation of even-denominator FQHSs at$\mathit{\nu }\mathbf{=}$3/10, 3/8, and 3/4 in the lowest Landau level of an ultrahigh-quality GaAs 2D hole system, evinced by deep minima in longitudinal resistance and developing quantized Hall plateaus. Quite remarkably, these states can be interpreted as even-denominator FQHSs of CFs, emerging from pairing of higher-order CFs when a CF Landau level, rather than an electron or a hole Landau level, is half-filled. Our results affirm enhanced interaction between CFs in a hole system with significant Landau level mixing and, more generally, the pairing of CFs as a valid mechanism for even-denominator FQHSs, and suggest the realization of FQHSs with non-Abelian anyons.

    

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