Engineering Dirac electrons emergent on the surface of a topological insulator

Abstract

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid ³He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.     

Observation of Quantum Anomalous Hall Effect and Exchange Interaction in Topological Insulator/Antiferromagnet Heterostructure

Integration of a quantum anomalous Hall insulator with a magnetically ordered material provides an additional degree of freedom through which the resulting exotic quantum states can be controlled. Here, an experimental observation is reported of the quantum anomalous Hall effect in a magnetically-doped topological insulator grown on the antiferromagnetic insulator Cr₂O₃. The exchange coupling between the two materials is investigated using field-cooling-dependent magnetometry and polarized neutron reflectometry. Both techniques reveal strong interfacial interaction between the antiferromagnetic order of the Cr₂O₃ and the magnetic topological insulator, manifested as an exchange bias when the sample is field-cooled under an out-of-plane magnetic field, and an exchange spring-like magnetic depth profile when the system is magnetized within the film plane. These results identify antiferromagnetic insulators as suitable candidates for the manipulation of magnetic and topological order in topological insulator films.     

A short guide to topological terms in the effective theories of condensed matter

This article is meant as a gentle introduction to the topological terms that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples, mainly from the area of quantum magnetism and superfluids/superconductors. We then briefly discuss how these ideas are now finding incarnations in the studies of symmetry-protected topological phases, which are in a sense a generalization of the concept of topological insulators to a wider range of materials, including magnets and cold atoms.     

A Single‐Electron Transistor Made of a 3D Topological Insulator Nanoplate

Quantum confined devices of 3D topological insulators are proposed to be promising and of great importance for studies of confined topological states and for applications in low‐energy‐dissipative spintronics and quantum information processing. The absence of energy gap on the topological insulator surface limits the experimental realization of a quantum confined system in 3D topological insulators. Here, the successful realization of single‐electron transistor devices in Bi₂Te₃ nanoplates using state‐of‐the‐art nanofabrication techniques is reported. Each device consists of a confined central island, two narrow constrictions that connect the central island to the source and drain, and surrounding gates. Low‐temperature transport measurements demonstrate that the two narrow constrictions function as tunneling junctions and the device shows well‐defined Coulomb current oscillations and Coulomb‐diamond‐shaped charge‐stability diagrams. This work provides a controllable and reproducible way to form quantum confined systems in 3D topological insulators, which should greatly stimulate research toward confined topological states, low‐energy‐dissipative devices, and quantum information processing.     

Quantum Topological Boundary States in Quasi‐Crystals

Topological phases play a novel and fundamental role in matter and display extraordinary robustness to smooth changes in material parameters or disorder. A crossover between topological material and quantum information may lead to inherent fault‐tolerant quantum simulations and quantum computing. Quantum features may be preserved by being encoded among topological structures of physical evolution systems. This requires stimulation, manipulation, and observation of topological phenomena at the single quantum particle level, which has not, however, yet been realized. It is asked whether the quantum features of single photons can be preserved in topological structures. The boundary states are experimentally observed at the genuine single‐photon level and the performance of the topological phase is demonstrated to protect the quantum features against diffusion‐induced decoherence in coupled waveguides and noise decoherence from the ambient environment. Compatibility between macroscopic topological states and microscopic single photons in the ambient environment is thus confirmed, leading to a new avenue to “quantum topological photonics” and providing more new possibilities for quantum materials and quantum technologies.     

A topological sorting algorithm for three‐layer channel routing

Abstract

Three‐layer channel routing is an important problem in VLSI layout. In this paper, we present a topological sorting algorithm to determine the topological order on nets depending on the operations of the vertical constraint graph (VCG) and the horizontal constraint graph (HCG). According to the order, the base router can finish the connections of all nets. In the algorithm, the HVH mode is assumed, and some examples including Deutsch's difficult example are used as test problems.     

On‐Chip Andreev Devices: Hard Superconducting Gap and Quantum Transport in Ballistic Nb–In0.75Ga0.25As‐Quantum‐Well–Nb Josephson Junctions

A superconducting hard gap in hybrid superconductor–semiconductor devices has been found to be necessary to access topological superconductivity that hosts Majorana modes (non‐Abelian excitation). This requires the formation of homogeneous and barrier‐free interfaces between the superconductor and semiconductor. Here, a new platform is reported for topological superconductivity based on hybrid Nb–In_0.75Ga_0.25As‐quantum‐well–Nb that results in hard superconducting gap detection in symmetric, planar, and ballistic Josephson junctions. It is shown that with careful etching, sputtered Nb films can make high‐quality and transparent contacts to the In_0.75Ga_0.25As quantum well, and the differential resistance and critical current measurements of these devices are discussed as a function of temperature and magnetic field. It is demonstrated that proximity‐induced superconductivity in the In_0.75Ga_0.25As‐quantum‐well 2D electron gas results in the detection of a hard gap in four out of seven junctions on a chip with critical current values of up to 0.2 µA and transmission probabilities of >0.96. The results, together with the large g ‐factor and Rashba spin–orbit coupling in In_0.75Ga_0.25As quantum wells, which indeed can be tuned by the indium composition, suggest that the Nb–In_0.75Ga_0.25As–Nb system can be an excellent candidate to achieve topological phase and to realize hybrid topological superconducting devices.     

Josephson Effect and Charge Distribution in Thin Bi2Te3 Topological Insulators

Thin layers of topological insulator materials are quasi-2D systems featuring a complex interplay between quantum confinement and topological band structure. To understand the role of the spatial distribution of carriers in electrical transport, the Josephson effect, magnetotransport, and weak anti-localization are studied in bottom-gated thin Bi₂Te₃ topological insulator films. The experimental carrier densities are compared to a model based on the solutions of the self-consistent Schrödinger–Poisson equations and they are in excellent agreement. The modeling allows for a quantitative interpretation of the weak antilocalization correction to the conduction and of the critical current of Josephson junctions with weak links made from such films without any ad hoc assumptions.     

Topological Quantum Phase Transition and Superconductivity Induced by Pressure in the Bismuth Tellurohalide BiTeI

A pressure‐induced topological quantum phase transition has been theoretically predicted for the semiconductor bismuth tellurohalide BiTeI with giant Rashba spin splitting. In this work, evolution of the electrical transport properties in BiTeI and BiTeBr is investigated under high pressure. The pressure‐dependent resistivity in a wide temperature range passes through a minimum at around 3 GPa, indicating the predicted topological quantum phase transition in BiTeI. Superconductivity is observed in both BiTeI and BiTeBr, while resistivity at higher temperatures still exhibits semiconducting behavior. Theoretical calculations suggest that superconductivity may develop from the multivalley semiconductor phase. The superconducting transition temperature, T_c, increases with applied pressure and reaches a maximum value of 5.2 K at 23.5 GPa for BiTeI (4.8 K at 31.7 GPa for BiTeBr), followed by a slow decrease. The results demonstrate that BiTeX (X = I, Br) compounds with nontrivial topology of electronic states display new ground states upon compression.     

Synthesis and characterization of 3D topological insulators: a case TlBi(S1?xSex)2

In this article, practical methods for synthesizing Tl-based ternary III-V-VI₂ chalcogenide TlBi(SSe_x)₂ are described in detail, along with characterization by x-ray diffraction and charge transport properties. The TlBi(SSe_x)₂ system is interesting because it shows a topological phase transition, where a topologically nontrivial phase changes to a trivial phase without changing the crystal structure qualitatively. In addition, Dirac semimetals whose bulk band structure shows a Dirac-like dispersion are considered to exist near the topological phase transition. The technique shown here is also generally applicable for other chalcogenide topological insulators, and will be useful for studying topological insulators and related materials.     

Van der Waals heterostructures based on three-dimensional topological insulators

Three-dimensional (3D) topological insulators (TIs) have generated tremendous research interest over the past decade due to their topologically-protected surface states with linear dispersion and helical spin texture. The topological surface states offer an important platform to realize topological phase transitions, topological magnetoelectric effects and topological superconductivity via 3D TI-based heterostructures. In this review, we summarize the key findings of magneto and quantum transport properties in 3D TIs and their related heterostructures with normal insulators, ferromagnets and superconductors. For intrinsic 3D TIs, the experimental evidences of the topological surface states and their coupling effects are reviewed. Whereas for 3D TI related heterostructures, we focus on some important phenomenological magnetotransport activities and provide explanations for the proximity-induced topological and quantum effects.     

Quantum‐Hall to Insulator Transition in Ultra‐Low‐Carrier‐Density Topological Insulator Films and a Hidden Phase of the Zeroth Landau Level

A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it is challenging to probe the zeroth Landau level due to large electron–hole puddles smearing its energy landscape. Here, by developing ultra‐low‐carrier density topological insulator Sb₂Te₃ films, an extreme quantum limit of the topological surface state is reached and a hidden phase at the zeroth Landau level is uncovered. First, an unexpected quantum‐Hall‐to‐insulator‐transition near the zeroth Landau level is discovered. Then, through a detailed scaling analysis, it is found that this quantum‐Hall‐to‐insulator‐transition belongs to a new universality class, implying that the insulating phase discovered here has a fundamentally different origin from those in nontopological systems.     

Mechanical Analogue of a Majorana Bound State

The discovery of topologically nontrivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., quantum Hall or anomalous quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. Here, a topologically bound mechanical state, a different class of nonpropagating protected state that cannot be destroyed by local perturbations, is demonstrated. It is in particular a mechanical analogue of the well‐known Majorana bound states (MBSs) of electronic topological superconductor systems. The topological binding is implemented by creating a Kekulé distortion vortex on a 2D mechanical honeycomb superlattice that can be mapped to a magnetic flux vortex in a topological superconductor.     

Generalized topological efficiency – case study with C84 fullerene

Abstract

A pure topological mechanism able to explain fullerenes stability is presented here. The non-trivial case of the C₈₄ fullerene isomers with isolated Pentagons Is in fact analyzed. This original computational approach is based on the generalization of the topological efficiency potentials which may be used to study all types of carbon allotropes.     

Engineering Dirac electrons emergent on the surface of a topological insulator

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid ³He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.     

Criteria for Realizing Room-Temperature Electrical Transport Applications of Topological Materials

The unusual electronic states found in topological materials can enable a new generation of devices and technologies, yet a long-standing challenge has been finding materials without deleterious parallel bulk conduction. This can arise either from defects or thermally activated carriers. Here, the criteria that materials need to meet to realize transport properties dominated by the topological states, a necessity for a topological device, are clarified. This is demonstrated for 3D topological insulators, 3D Dirac materials, and 1D quantum anomalous Hall insulators, though this can be applied to similar systems. The key parameters are electronic bandgap, dielectric constant, and carrier effective mass, which dictate under what circumstances (defect density, temperature, etc.) the unwanted bulk state will conduct in parallel to the topological states. As these are fundamentally determined by the basic atomic properties, simple chemical arguments can be used to navigate the phase space to ultimately find improved materials. This will enable rapid identification of new systems with improved properties, which is crucial to designing new material systems and push a new generation of topological technologies.     

Strain and carrier-induced coexistence of topologically insulating and superconducting phase in iodized Si(111) films

The importance of silicon in modern electronic devices has led to considerable interest in exploring the unconventional electronic properties of Si-based materials for future applications in spintronics and quantum computing. Here, using density functional theory, we present the results of a systematic study of the effect of strain on Si(111) thin films whose surfaces are functionalized with iodine. Films with an odd number of layers under biaxial strain are found to undergo a phase transition from a normal insulator to a topological insulator and ultimately to a metal. The spin-orbit coupling-induced topologically nontrivial band gap at the Γ point is found to be as large as 0.50 eV, which not only surpasses that of other Si-based topological materials, it is also large enough for practical realization of quantum spin Hall states at room temperature. No such nontrivial states are found in films with an even number of layers. Mechanisms for such a strain-induced transition are illustrated by a tight-binding model composed of s, p_x, and p_y orbitals. Equally important, we predict that iodized silicene, when stretched and hole-doped, would be a phonon-mediated superconductor with a critical temperature of 9.2 K. This coexistence of a topological insulator and a superconducting phase in a single material is unusual; it has the potential for applications in electronic circuits and for the realization of Majorana fermions in quantum computations.

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Adiabatic photo-steering theory in topological insulators

Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane–Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed.     

The dynamics of three-mode coupling in a trapped Bose gas

ABSTRACT

Multiple mode couplings in topological coherent modes of Bose–Einstein condensate are considered, by introducing an external alternating (resonating) field in the system. This analysis is based on the analytical solutions of nonlinear Gross–Pitaevskii equation for a trapped Bose gas at nearly absolute zero temperature. The dynamics of fractional populations of the generated coherent modes are analysed, particularly for a three-level system in the limit of small to large detuning of the intermediate state. These coupled topological modes, though nonlinear, are analogous to a resonant atom and exhibit a variety of significant non-trivial phenomena (effects), like: dynamic phase transitions, interference patterns, critical phenomena, mode-locking and chaotic motion.