Quantum Anomalous Hall Effect in Magnetic Doped Topological Insulators and Ferromagnetic Spin-Gapless Semiconductors-A Perspective Review

Spin Gapless Quantum Materials and Devices

Quantum materials, with nontrivial quantum phenomena and mechanisms, promise efficient quantum technologies with enhanced functionalities. Quantum technology is held back because a gap between fundamental science and its implementation is not fully understood yet. In order to capitalize the quantum advantage, a new perspective is required to figure out and close this gap. In this review, spin gapless quantum materials, featured by fully spin-polarized bands and the electron/hole transport, are discussed from the perspective of fundamental understanding and device applications. Spin gapless quantum materials can be simulated by minimal two-band models and could help to understand band structure engineering in various topological quantum materials discovered so far. It is explicitly highlighted that various types of spin gapless band dispersion are fundamental ingredients to understand quantum anomalous Hall effect. Based on conventional transport in the bulk and topological transport on the boundaries, various spintronic device aspects of spin gapless quantum materials as well as their advantages in different models for topological field effect transistors are reviewed.

Genuine Dirac Half-Metals in Two-Dimensions

When spin-orbit coupling (SOC) is absent, all proposed half-metals with twofold degenerate nodal points at the K (or K') point in 2D materials are classified as "Dirac half-metals" owing to the way graphene is utilized in the earliest studies. Actually, each band crossing point at the K or K' point is described by a 2D Weyl Hamiltonian with definite chirality; hence, it should be a Weyl point. To the best of its knowledge, there have not yet been any reports of a genuine (i.e., fourfold degenerate) 2D Dirac point half-metal. In this work, using first-principles calculations, it proposes for the first time that the 2D d0 -type ferromagnet Mg4 N4 is a genuine 2D Dirac half-metal candidate with a fourfold degenerate Dirac point at the S high-symmetry point, intrinsic magnetism, a high Curie temperature, 100% spin polarization, topology robust under the SOC and uniaxial and biaxial strains, and spin-polarized edge states. This work can serve as a starting point for future predictions of intrinsically magnetic materials with genuine 2D Dirac points, which will aid the frontier of topo-spintronics research in 2D systems.

Single-Atomic-Layer Stanene on Ferromagnetic Co Nanoislands with Topological Band Structures

Introducing magnetism to two-dimensional topological insulators is a central issue in the pursuit of magnetic topological materials in low dimensionality. By means of low-temperature growth at 80 K, we succeeded in fabricating a monolayer stanene on Co/Cu(111) and resolving ferromagnetic spin contrast by field-dependent spin-polarized scanning tunneling microscopy (SP-STM). Increases of both remanence to saturation magnetization ratio (M_r/M_s) and coercive field (H_c) due to an enhanced perpendicular magnetic anisotropy (PMA) are further identified by out-of-plane magneto-optical Kerr effect (MOKE). In addition to ultraflat stanene fully relaxed on bilayer Co/Cu(111) from density functional theory (DFT), characteristic topological properties including an in-plane s-p band inversion and a spin-orbit coupling (SOC) induced gap about 0.25 eV at the Γ̅ point have also been verified in the Sn-projected band structure. Interfacial coupling of single-atomic-layer stanene with ferromagnetic Co biatomic layers allows topological band features to coexist with ferromagnetism, facilitating a conceptual design of atomically thin magnetic topological heterostructures.

Engineering Second-Order Corner States in 2D Multiferroics

The understanding and manipulate of the second-order corner states are central to both fundamental physics and future topotronics applications. Despite the fact that numerous second-order topological insulators (SOTIs) are achieved, the efficient engineering in a given material remains elusive. Here, the emergence of 2D multiferroics SOTIs in SbAs and BP₅ monolayers is theoretically demonstrated, and an efficient and straightforward way for engineering the nontrivial corner states by ferroelasticity and ferroelectricity is remarkably proposed. With ferroelectric polarization of SbAs and BP₅ monolayers, the nontrivial corner states emerge in the mirror symmetric corners and are perpendicular to orientations of the in-plane spontaneous polarization. And remarkably the spatial distribution of the corner states can be effectively tuned by a ferroelastic switching. At the intermediate states of both ferroelectric and ferroelastic switchings, the corner states disappear. These finding not only combines exotic SOTIs with multiferroics but also pave the way for experimental discovery of 2D tunable SOTIs.

Electrical Manipulation of Topological Phases in a Quantum Anomalous Hall Insulator

Quantum anomalous Hall phases arising from the inverted band topology in magnetically doped topological insulators have emerged as an important subject of research for quantization at zero magnetic fields. Though necessary for practical implementation, sophisticated electrical control of molecular beam epitaxy (MBE)-grown quantum anomalous Hall matter have been stymied by growth and fabrication challenges. Here, a novel procedure is demonstrated, employing a combination of thin-film deposition and 2D material stacking techniques, to create dual-gated devices of the MBE-grown quantum anomalous Hall insulator, Cr-doped (Bi,Sb)₂ Te₃ . In these devices, orthogonal control over the field-induced charge density and the electric displacement field is demonstrated. A thorough examination of material responses to tuning along each control axis is presented, realizing magnetic property control along the former and a novel capability to manipulate the surface exchange gap along the latter. Through electrically addressing the exchange gap, the capabilities to either strengthen the quantum anomalous Hall state or suppress it entirely and drive a topological phase transition to a trivial state are demonstrated. The experimental result is explained using first principle theoretical calculations, and establishes a practical route for in situ control of quantum anomalous Hall states and topology.

Mini-review of interesting properties in Mn2CoAl bulk and films

Heusler compounds exhibit many interesting properties, such as high thermopower, magnetocaloric properties, and even topological insulator states. Heusler Mn2CoAl alloy has been experimentally and theoretically proposed as a promising spin-gapless semiconductor with novel electronic, magnetic, spintronic, transport, and topological properties. Furthermore, the spin-gapless semiconducting-like behaviors are also predicted in Mn2CoAl films by measuring the transport and magnetic properties. This mini-review systematically summarizes the interesting properties of Mn2CoAl bulk and Mn2CoAl-based films. This mini-review is hoped to guide further experimental investigations and applications in the particular scientific community.

Two-dimensional spin-gapless semiconductors: A mini-review

In the past decade, two-dimensional (2D) materials and spintronic materials have been rapidly developing in recent years. 2D spin-gapless semiconductors (SGSs) are a novel class of ferromagnetic 2D spintronic materials with possible high Curie temperature, 100% spin-polarization, possible one-dimensional or zero-dimensional topological signatures, and other exciting spin transport properties. In this mini-review, we summarize a series of ideal 2D SGSs in the last 3 years, including 2D oxalate-based metal-organic frameworks, 2D single-layer Fe2I2, 2D Cr2X3 (X = S, Se, and Te) monolayer with the honeycomb kagome (HK) lattice, 2D CrGa2Se4 monolayer, 2D HK Mn-cyanogen lattice, 2D MnNF monolayer, and 2D Fe4N2 pentagon crystal. The mini-review also discusses the unique magnetic, electronic, topological, and spin-transport properties and the possible application of these 2D SGSs. The mini-review can be regarded as an improved understanding of the current state of 2D SGSs in recent 3 years.

Robust topological one-way edge states in radius-fluctuated photonic Chern topological insulators

Recent developments in topological photonics have shown that the introduction of disorders can yield the innovative and striking transport phenomena. Here, we theoretically investigate topological one-way edge states in radius-fluctuated photonic Chern topological insulators (PCTIs), which are composed of two-dimensional gyromagnetic photonic crystals with cylinder site fixed but with cylinder radius fluctuated. We use a fluctuation index to characterize the degree of radius fluctuation, employ two empirical parameters to inspect the evolution of topological one-way edge states, and verify the stability of topological one-way edge states by calculating massive samples with various random numbers. We find that as the radius-fluctuation strength increases, there arises a competition between topological one-way edge state, Anderson localization state and trivial bulk state. We reveal that the Anderson localization state appears far more easily in the radius-fluctuation PCTI with even a weak strength compared with the position-perturbed PCTI with a strong randomness. We also demonstrate that the topological one-way edge states are protected against a strong fluctuation much larger than the fabrication errors in practical experiments. Our results show that the PCTIs consisting of gyromagnetic photonic crystals have a high-tolerance for the material and sample fabrication errors, and this would provide a deeper understanding of fundamental topology physics.

Understanding Signatures of Emergent Magnetism in Topological Insulator/Ferrite Bilayers

Magnetic insulator-topological insulator heterostructures have been studied in search of chiral edge states via proximity induced magnetism in the topological insulator, but these states have been elusive. We identified MgAl_{0.5}Fe_{1.5}O_{4}/Bi_{2}Se_{3} bilayers for a possible magnetic proximity effect. Electrical transport and polarized neutron reflectometry suggest a proximity effect, but structural data indicate a disordered interface as the origin of the magnetic response. Our results provide a strategy via correlation of microstructure with magnetic data to confirm a magnetic proximity effect.

Recent advances in two-dimensional ferromagnetism: strain-, doping-, structural- and electric field-engineering toward spintronic applications

Since the first report on truly two-dimensional (2D) magnetic materials in 2017, a wide variety of merging 2D magnetic materials with unusual physical characteristics have been discovered and thus provide an effective platform for exploring the associated novel 2D spintronic devices, which have been made significant progress in both theoretical and experimental studies. Herein, we make a comprehensive review on the recent scientific endeavors and advances on the various engineering strategies on 2D ferromagnets, such as strain-, doping-, structural- and electric field-engineering, toward practical spintronic applications, including spin tunneling junctions, spin field-effect transistors and spin logic gate, etc. In the last, we discuss on current challenges and future opportunities in this field, which may provide useful guidelines for scientists who are exploring the fundamental physical properties and practical spintronic devices of low-dimensional magnets.

Mn-Rich MnSb2 Te4 : A Topological Insulator with Magnetic Gap Closing at High Curie Temperatures of 45-50 K

Ferromagnetic topological insulators exhibit the quantum anomalous Hall effect, which is potentially useful for high-precision metrology, edge channel spintronics, and topological qubits.  The stable 2+ state of Mn enables intrinsic magnetic topological insulators. MnBi2 Te4 is, however, antiferromagnetic with 25 K Néel temperature and is strongly n-doped. In this work, p-type MnSb2 Te4 , previously considered topologically trivial, is shown to be a ferromagnetic topological insulator for a few percent Mn excess. i) Ferromagnetic hysteresis with record Curie temperature of 45-50 K, ii) out-of-plane magnetic anisotropy, iii) a 2D Dirac cone with the Dirac point close to the Fermi level, iv) out-of-plane spin polarization as revealed by photoelectron spectroscopy, and v) a magnetically induced bandgap closing at the Curie temperature, demonstrated by scanning tunneling spectroscopy (STS), are shown. Moreover, a critical exponent of the magnetization β ≈ 1 is found, indicating the vicinity of a quantum critical point. Ab initio calculations reveal that Mn-Sb site exchange provides the ferromagnetic interlayer coupling and the slight excess of Mn nearly doubles the Curie temperature. Remaining deviations from the ferromagnetic order open the inverted bulk bandgap and render MnSb2 Te4 a robust topological insulator and new benchmark for magnetic topological insulators.

Overcoming Boltzmann's Tyranny in a Transistor via the Topological Quantum Field Effect

The subthreshold swing is the critical parameter determining the operation of a transistor in low-power applications such as switches. It determines the fraction of dissipation due to the gate capacitance used for turning the device on and off, and in a conventional transistor it is limited by Boltzmann's tyranny to k_BT ln(10)/q. Here, we demonstrate that the subthreshold swing of a topological transistor in which conduction is enabled by a topological phase transition via electric field switching, can be sizably reduced in a noninteracting system by modulating the Rashba spin-orbit interaction. By developing a theoretical framework for quantum spin Hall materials with honeycomb lattices, we show that the Rashba interaction can reduce the subthreshold swing by more than 25% compared to Boltzmann's limit in currently available materials but without any fundamental lower bound, a discovery that can guide future material design and steer the engineering of topological quantum devices.