The electric field induced quantum phase transition from topological to conventional insulator has been proposed as the basis of a topological field effect transistor [1-4]. In this scheme an electric field can switch 'on' the ballistic flow of charge and spin along dissipationless edges of the two-dimensional (2D) quantum spin Hall insulator [5-9], and when 'off' is a conventional insulator with no conductive channels. Such a topological transistor is promising for low-energy logic circuits [4], which would necessitate electric field-switched materials with conventional and topological bandgaps much greater than room temperature, significantly greater than proposed to date [6-8]. Topological Dirac semimetals (TDS) are promising systems in which to look for topological field-effect switching, as they lie at the boundary between conventional and topological phases [3,10-16]. Here we use scanning probe microscopy/spectroscopy (STM/STS) and angle-resolved photoelectron spectroscopy (ARPES) to show that mono-and bilayer films of TDS Na3Bi [3,17] are 2D topological insulators with bulk bandgaps >400 meV in the absence of electric field. Upon application of electric field by doping with potassium or by close approach of the STM tip, the bandgap can be completely closed then re-opened with conventional gap greater than 100 meV. The large bandgaps in both the conventional and quantum spin Hall phases, much

Spatially tailored pseudo-magnetic fields (PMFs) can give rise to pseudo-Landau levels and the valley Hall effect in graphene. At an experimental level, it is highly challenging to create the specific strain texture that can generate PMFs over large areas. Here, we report that superposing graphene on multilayer black phosphorus creates shear-strained superlattices that generate a PMF over an entire graphene-black phosphorus heterostructure with edge size of tens of micrometres. The PMF is intertwined with the spatial period of the moiré pattern, and its spatial distribution and intensity can be modified by changing the relative orientation of the two materials. We show that the emerging pseudo-Landau levels influence the transport properties of graphene-black phosphorus field-effect transistor devices with Hall bar geometry. The application of an external magnetic field allows us to enhance or reduce the effective field depending on the valley polarization with the prospect of developing a valley filter.

The role of electron-electron interactions in two-dimensional Dirac fermion systems remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction, we identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator and a semimetallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. We predict that experimental realizations of Dirac fermions span this crossover and that this determines whether the Fermi velocity is increased or decreased by interactions. We explain several long-standing mysteries, including why the observed Fermi velocity in graphene is consistently about 20% larger than values obtained from ab initio calculations and why graphene on different substrates shows different behaviors.

We study the low-energy electronic transport across periodic extended defects in graphene. In the continuum low-energy limit, such defects act as infinitesimally thin stripes separating two regions where Dirac Hamiltonian governs the low-energy phenomena. The behavior of these systems is defined by the boundary condition imposed by the defect on the massless Dirac fermions. We demonstrate how this low-energy boundary condition can be computed from the tight-binding model of the defect line. For simplicity we consider defect lines oriented along the zigzag direction, which requires the consideration of only one copy of Dirac equation. Three defect lines of this kind are studied and shown to be mappable between them: the pentagon-only, the zz(558) and the zz(5757) defect lines. In addition, in this same limit, we calculate the conductance across such defect lines with size L, and find it to be proportional to kF L at low temperatures.

The question of whether electron-electron interactions can drive a metal to insulator transition in graphene under realistic experimental conditions is addressed. Using three representative methods to calculate the effective long-range Coulomb interaction between π-electrons in graphene and solving for the ground state using quantum Monte Carlo methods, we argue that without strain, graphene remains metallic and changing the substrate from SiO2 to suspended samples hardly makes any difference. In contrast, applying a rather large -but experimentally realistic -uniform and isotropic strain of about 15% seems to be a promising route to making graphene an antiferromagnetic Mott insulator.PACS numbers: 71.27.+a,71.10.Fd,73.22.Pr,72.80.Vp Over the past decade graphene has established itself as a remarkable new material with superlative properties [1,2]. However, the early hopes to utilize it as a next generation transistor have been dashed mostly because graphene remains metallic -these prototypical Dirac fermions are immune to many of the conventional routes for driving two-dimensional electron gases into an insulating state, including, for example, Anderson localization and percolation transitions (see e.g. Ref.[3]). Other mechanisms for opening band-gaps including hydrogenation [4], application of uniaxial strain [5] and forming nanoribbons [6] severely degrade graphene's mobility. Very recently, moiré heterostuctures using graphene and hexagonal boron nitride have shown evidence of an insulating phase [7,8], although interpreting these results remains somewhat controversial [9][10][11][12].In this Letter, we explore a different avenue to make graphene insulating, namely, utilizing the electronelectron interactions. Despite much study on the effects of interactions in graphene [13] it is surprising how much still remains to be understood. While it is clear that without any electron-electron interactions, graphene should be a semi-metal (SM), and that for very strong interactions it should be an insulating anti-ferromagnet (AFM), it remains unclear what one should expect for the real graphene material. For example, there are distinct claims in the literature that suspended graphene should be insulating, strongly metallic and weakly metallic [14][15][16]. This discussion could have practical relevance as it could be the basis for a low power Mott-transistor [17].In this work we explore different ways of controlling the effective strength of electron-electron interactions in realistic graphene devices, and propose how one can move around its phase diagram. In particular (and in contrast to what is widely assumed to be true [2, 13]), we demonstrate that it is the non-universal, material-specific and short-range part of the electron-electron interactions that plays the dominant role in determining graphene's ground state. More interestingly, we conclude that application of isotropic strain is considerably more efficient in approaching the SM-AFM phase transition than substrate manipulation, providing a new route for...

In this article, we study zigzag graphene nanoribbons with edges reconstructed with Stone-Wales defects, by means of an empirical (first-neighbor) tight-binding method, with parameters determined by ab-initio calculations of very narrow ribbons. We explore the characteristics of the electronic band structure with a focus on the nature of edge states. Edge reconstruction allows the appearance of a new type of edge states. They are dispersive, with non-zero amplitudes in both sub-lattices; furthermore, the amplitudes have two components that decrease with different decay lengths with the distance from the edge; at the Dirac points one of these lengths diverges, whereas the other remains finite, of the order of the lattice parameter. We trace this curious effect to the doubling of the unit cell along the edge, brought about by the edge reconstruction. In the presence of a magnetic field, the zero-energy Landau level is no longer degenerate with edge states as in the case of pristine zigzag ribbon.Comment: 15 page

Small potential variations in 3D semimetal Na3Bi enable close approach to the Dirac point, allowing exploration of new physics.

In this paper we analyse the electronic properties of Dirac electrons in finite-size ribbons and in circular and hexagonal quantum dots. We show that due to the formation of sub-bands in the ribbons it is possible to spatially localize some of the electronic modes using a p-n-p junction. We also show that scattering of confined Dirac electrons in a narrow channel by an infinitely massive wall induces mode mixing, giving a qualitative reason for the fact that an analytical solution to the spectrum of Dirac electrons confined in a square box has not yet been found. A first attempt to solve this problem is presented. We find that only the trivial case k = 0 has a solution that does not require the existence of evanescent modes. We also study the spectrum of quantum dots of graphene in a perpendicular magnetic field. This problem is studied in the Dirac approximation, and its solution requires a numerical method whose details are given. The formation of Landau levels in the dot is discussed. The inclusion of the Coulomb interaction among the electrons is considered at the self-consistent Hartree level, taking into account the interaction with an image charge density necessary to keep the back-gate electrode at zero potential. The effect of a radial confining potential is discussed. The density of states of circular and hexagonal quantum dots, described by the full tight-binding model, is studied using the Lanczos algorithm. This is necessary to access the detailed shape of the density of states close to the Dirac point when one studies large systems. Our study reveals that zero-energy edge states are also present in graphene quantum dots. Our results are relevant for experimental research in graphene nanostructures. The style of writing is pedagogical, in the hope that newcomers to the subject will find this paper a good starting point for their research.