Integer quantum Hall effect on a six-valley hydrogen-passivated silicon (111) surface

Microscopic Model for Fractional Quantum Hall Nematics

Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give rise to a nematic FQH phase, a topological state with a spontaneously broken rotational symmetry. While experiments on FQH states in the second Landau level have reported signatures of putative FQH nematics in anisotropic transport, a realistic model for this state has been lacking. We show that the standard model of particles in the lowest Landau level interacting via the Coulomb potential realizes the FQH nematic transition, which is reached by a progressive reduction of the strength of the shortest-range Haldane pseudopotential. Using exact diagonalization and variational wave functions, we demonstrate that the FQH nematic transition occurs when the system's neutral gap closes in the long-wavelength limit while the charge gap remains open. We confirm the symmetry-breaking nature of the transition by demonstrating the existence of a "circular moat" potential in the manifold of states with broken rotational symmetry, while its geometric character is revealed through the strong fluctuations of the nematic susceptibility and Hall viscosity.

Valley-Polarized Quantum Hall Phase in a Strain-Controlled Dirac System

In multivalley systems, the valley pseudospin offers rich physics going from encoding of information by its polarization (valleytronics), to exploring novel phases of matter when its degeneracy is changed. Here, by strain engineering, we reveal fully valley-polarized quantum Hall phases in the Pb_{1-x}Sn_{x}Se Dirac system. Remarkably, when the valley energy splitting exceeds the fundamental band gap, we observe a "bipolar quantum Hall phase," heralded by the coexistence of hole and electron chiral edge states at distinct valleys in the same quantum well. This suggests that spatially overlaid counterpropagating chiral edge states emerging at different valleys do not interfere with each other.

Atomically Precise Manufacturing of Silicon Electronics

Atomically precise manufacturing (APM) is a key technique that involves the direct control of atoms in order to manufacture products or components of products. It has been developed most successfully using scanning probe methods and has received particular attention for developing atom scale electronics with a focus on silicon-based systems. This review captures the development of silicon atom-based electronics and is divided into several sections that will cover characterization and atom manipulation of silicon surfaces with scanning tunneling microscopy and atomic force microscopy, development of silicon dangling bonds as atomic quantum dots, creation of atom scale devices, and the wiring and packaging of those circuits. The review will also cover the advance of silicon dangling bond logic design and the progress of silicon quantum atomic designer (SiQAD) simulators. Finally, an outlook of APM and silicon atom electronics will be provided.

Quantum Hall valley nematics

Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states: quantum Hall valley nematics. These phases of matter emerge when the formation of a topologically insulating quantum Hall state is accompanied by the spontaneous breaking of a point-group symmetry that combines a spatial rotation with a permutation of valley indices. The resulting orientational order is particularly sensitive to quenched disorder, while quantum Hall physics links charge conduction to topological defects. We discuss how these combine to yield a rich phase structure, and their implications for transport and spectroscopy measurements. In parallel, we discuss relevant experimental systems. We close with an outlook on future directions.

Electrically tunable valley polarization in Weyl semimetals with tilted energy dispersion

Tunneling transport across electrical potential barriers in Weyl semimetals with tilted energy dispersion is investigated. We report that the electrons around different valleys experience opposite direction refractions at the barrier interface when the energy dispersion is tilted along one of the transverse directions. Chirality dependent refractions at the barrier interface polarize the Weyl fermions in angle-space according to their valley index. A real magnetic barrier configuration is used to select allowed transmission angles, which results in electrically controllable and switchable valley polarization. Our findings may pave the way for experimental investigation of valley polarization, as well as valleytronic and electron optic applications in Weyl semimetals.

Surface Landau levels and spin states in bismuth (111) ultrathin films

The development of next-generation electronics is much dependent on the discovery of materials with exceptional surface-state spin and valley properties. Because of that, bismuth has attracted a renewed interest in recent years. However, despite extensive studies, the intrinsic electronic transport properties of Bi surfaces are largely undetermined due to the strong interference from the bulk. Here we report the unambiguous determination of the surface-state Landau levels in Bi (111) ultrathin films using scanning tunnelling microscopy under magnetic fields perpendicular to the surface. The Landau levels of the electron-like and the hole-like carriers are accurately characterized and well described by the band structure of the Bi (111) surface from density functional theory calculations. Some specific surface spin states with a large g-factor are identified. Our findings shed light on the exploiting surface-state properties of Bi for their applications in spintronics and valleytronics.

SU(3) Quantum Hall Ferromagnetism in SnTe

The (111) surface of SnTe hosts one isotropic Γ[over ¯]-centered and three degenerate anisotropic M[over ¯]-centered Dirac surface states. We predict that a nematic phase with spontaneously broken C_{3} symmetry will occur in the presence of a perpendicular magnetic field when the N=0 M[over ¯] Landau levels are 1/3 or 2/3 filled. The nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions that favor a valley-polarized state and weaker intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the threefold M[over ¯] Landau-level degeneracy, yielding a ground state energy with 2π/3 periodicity as a function of Zeeman-field orientation angle.

Screening and transport in 2D semiconductor systems at low temperatures

Low temperature carrier transport properties in 2D semiconductor systems can be theoretically well-understood within RPA-Boltzmann theory as being limited by scattering from screened Coulomb disorder arising from random quenched charged impurities in the environment. In this work, we derive a number of analytical formula, supported by realistic numerical calculations, for the relevant density, mobility, and temperature range where 2D transport should manifest strong intrinsic (i.e., arising purely from electronic effects) metallic temperature dependence in different semiconductor materials arising entirely from the 2D screening properties, thus providing an explanation for why the strong temperature dependence of the 2D resistivity can only be observed in high-quality and low-disorder 2D samples and also why some high-quality 2D materials manifest much weaker metallicity than other materials. We also discuss effects of interaction and disorder on the 2D screening properties in this context as well as compare 2D and 3D screening functions to comment why such a strong intrinsic temperature dependence arising from screening cannot occur in 3D metallic carrier transport. Experimentally verifiable predictions are made about the quantitative magnitude of the maximum possible low-temperature metallicity in 2D systems and the scaling behavior of the temperature scale controlling the quantum to classical crossover.

Strongly Metallic Electron and Hole 2D Transport in an Ambipolar Si-Vacuum Field Effect Transistor

We report experiment and theory on an ambipolar gate-controlled Si(111)-vacuum field effect transistor where we study electron and hole (low-temperature 2D) transport in the same device simply by changing the external gate voltage to tune the system from being a 2D electron system at positive gate voltage to a 2D hole system at negative gate voltage. The electron (hole) conductivity manifests strong (moderate) metallic temperature dependence with the conductivity decreasing by a factor of 8 (2) between 0.3 K and 4.2 K with the peak electron mobility (∼18  m2/V s) being roughly 20 times larger than the peak hole mobility (in the same sample). Our theory explains the data well using random phase approximation screening of background Coulomb disorder, establishing that the observed metallicity is a direct consequence of the strong temperature dependence of the effective screened disorder.

Multicomponent Skyrmion lattices and their excitations

We study quantum Hall ferromagnets with a finite density of topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrized by a d-component spinor field. In the absence of anisotropies we find a hexagonal Skyrmion lattice that completely breaks the underlying SU(d) symmetry with the low-lying excitation spectrum separating into d(2) - 1 gapless acoustic magnetic modes and a magnetophonon. The ground state charge density modulations, which inevitably exist in these lattices, vanish exponentially in d. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant to experiments with AlAs quantum wells. Here we find a transition which breaks a sixfold rotational symmetry of the triangular lattice, followed by the formation of a square lattice at large values of anisotropy strength.

Coupling the valley degree of freedom to antiferromagnetic order

Conventional electronics are based invariably on the intrinsic degrees of freedom of an electron, namely its charge and spin. The exploration of novel electronic degrees of freedom has important implications in both basic quantum physics and advanced information technology. Valley, as a new electronic degree of freedom, has received considerable attention in recent years. In this paper, we develop the theory of spin and valley physics of an antiferromagnetic honeycomb lattice. We show that by coupling the valley degree of freedom to antiferromagnetic order, there is an emergent electronic degree of freedom characterized by the product of spin and valley indices, which leads to spin-valley-dependent optical selection rule and Berry curvature-induced topological quantum transport. These properties will enable optical polarization in the spin-valley space, and electrical detection/manipulation through the induced spin, valley, and charge fluxes. The domain walls of an antiferromagnetic honeycomb lattice harbors valley-protected edge states that support spin-dependent transport. Finally, we use first-principles calculations to show that the proposed optoelectronic properties may be realized in antiferromagnetic manganese chalcogenophosphates (MnPX3, X = S, Se) in monolayer form.

Control of valley polarization in monolayer MoS2 by optical helicity

Electronic and spintronic devices rely on the fact that free charge carriers in solids carry electric charge and spin. There are, however, other properties of charge carriers that might be exploited in new families of devices. In particular, if there are two or more minima in the conduction band (or maxima in the valence band) in momentum space, and if it is possible to confine charge carriers in one of these valleys, then it should be possible to make a valleytronic device. Valley polarization, as the selective population of one valley is designated, has been demonstrated using strain and magnetic fields, but neither of these approaches allows dynamic control. Here, we demonstrate that optical pumping with circularly polarized light can achieve complete dynamic valley polarization in monolayer MoS(2) (refs 11, 12), a two-dimensional non-centrosymmetric crystal with direct energy gaps at two valleys. Moreover, this polarization is retained for longer than 1 ns. Our results, and similar results by Zeng et al., demonstrate the viability of optical valley control and suggest the possibility of valley-based electronic and optoelectronic applications in MoS(2) monolayers.

Valley-selective circular dichroism of monolayer molybdenum disulphide

A two-dimensional honeycomb lattice harbours a pair of inequivalent valleys in the k-space electronic structure, in the vicinities of the vertices of a hexagonal Brillouin zone, K_±. It is particularly appealing to exploit this emergent degree of freedom of charge carriers, in what is termed 'valleytronics'. The physics of valleys mimics that of spin, and will make possible devices, analogous to spintronics, such as valley filter and valve, and optoelectronic Hall devices, all very promising for next-generation electronics. The key challenge lies with achieving valley polarization, of which a convincing demonstration in a two-dimensional honeycomb structure remains evasive. Here we show, using first principles calculations, that monolayer molybdenum disulphide is an ideal material for valleytronics, for which valley polarization is achievable via valley-selective circular dichroism arising from its unique symmetry. We also provide experimental evidence by measuring the circularly polarized photoluminescence on monolayer molybdenum disulphide, which shows up to 50% polarization.

The monolayer transition-metal dichalcogenide molybdenum disulphide has recently attracted attention owing to its distinctive electronic properties. Cao and co-workers present numerical evidence suggesting that circularly polarized light can preferentially excite a single valley in the band structure of this system.

Spin polarized electron transport near the Si/SiO2 interface

Using long-distance lateral devices, spin transport near the interface of Si and its native oxide (SiO(2)) is studied by spin-valve measurements in an in-plane magnetic field and spin precession measurements in a perpendicular magnetic field at 60 K. As electrons are attracted to the interface by an electrostatic gate, we observe shorter average spin transit times and an increase in spin coherence, despite a reduction in total spin polarization. This behavior, which is in contrast with the expected exponential depolarization seen in bulk transport devices, is explained using a transform method to recover the empirical spin current transit-time distribution and a simple two-stage drift-diffusion model. We identify strong interface-induced spin depolarization (reducing the spin lifetime by over 2 orders of magnitude from its bulk transport value) as the consistent cause of these phenomena.