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We report an unconventional quantum spin Hall phase in the monolayer T$_\text{d}$-WTe$_2$, which exhibits hitherto unknown features in other topological materials. The low-symmetry of the structure induces a canted spin texture in the $yz$ plane, which dictates the spin polarization of topologically protected boundary states. Additionally, the spin Hall conductivity gets quantized ($2e^2/h$) with a spin quantization axis parallel to the canting direction. These findings are based on large-scale quantum simulations of the spin Hall conductivity tensor and nonlocal resistances in multi-probe geometries using a realistic tight-binding model elaborated from first-principle methods. The observation of this canted quantum spin Hall effect, related to the formation of topological edge states with nontrivial spin polarization, demands for specific experimental design and suggests interesting alternatives for manipulating spin information in topological materials., Comment: For comments please contact josehugo.garcia@icn2.cat

The ability to switch magnetic elements by spin-orbit-induced torques has recently attracted much attention for a path towards high-performance, non-volatile memories with low power consumption. Realizing efficient spin-orbit-based switching requires harnessing both new materials and novel physics to obtain high charge-to-spin conversion efficiencies, thus making the choice of spin source crucial. Here we report the observation of spin-orbit torque switching in bilayers consisting of a semimetallic film of 1T'-MoTe2 adjacent to permalloy. Deterministic switching is achieved without external magnetic fields at room temperature, and the switching occurs with currents one order of magnitude smaller than those typical in devices using the best-performing heavy metals. The thickness dependence can be understood if the interfacial spin-orbit contribution is considered in addition to the bulk spin Hall effect. Further threefold reduction in the switching current is demonstrated with resort to dumbbell-shaped magnetic elements. These findings foretell exciting prospects of using MoTe2 for low-power semimetal material based spin devices.

We adapted a recently proposed framework to characterize the optical response of interacting electrons in solids in order to expedite its computation without compromise in accuracy at the microscopic level. Our formulation is based on reliable parameterizations of Hamiltonians and Coulomb interactions, which allows economy and flexibility in obtaining response functions. It is suited to computing the optical response to fields of arbitrary temporal shape and strength, to arbitrary order in the field, and natively accounts for excitonic effects. We demonstrate the approach by computing the frequency-dependent susceptibilities of MoS2 and hexagonal BN monolayers up to the third-harmonic. Grounded on a generic non-equilibrium many-body perturbation theory, this framework allows extensions to handle generic interaction models or to describe electronic processes taking place at ultrafast time scales., Comment: This update contains the published version. 20 pages, 9 figures

Recent theoretical advances have proposed a new class of topological crystalline insulator (TCI) phases protected by rotational symmetries. Distinct from topological insulators (TIs), rotational symmetry-protected TCIs are expected to show unique topologically protected boundary modes: First, the surface normal to the rotational axis features unpinned Dirac surface states whose Dirac points are located at generic k points. Second, due to the higher-order bulk boundary correspondence, a 3D TCI also supports 1D helical edge states. Despite the unique topological electronic properties, to date, purely rotational symmetry-protected TCIs remain elusive in real materials. Using first-principles band calculations and theoretical modeling, we identify the van der Waals material $\alpha$-Bi4Br4 as a TCI purely protected by rotation symmetry. We show that the Bi4Br4's (010) surface exhibits a pair of unpinned topological Dirac fermions protected by the two-fold rotational axis. These unpinned Dirac fermions show an exotic spin texture highly favorable for spin transport and a band structure consisting of van Hove singularities due to Lifshitz transition. We also identify 1D topological hinge states along the edges of an $\alpha$-Bi4Br4 rod. We further discuss how the proposed topological electronic properties in $\alpha$-Bi4Br4 can be observed by various experimental techniques.

The nature of Fermi surface defines the physical properties of conductors and many physical phenomena can be traced to its shape. Although the recent discovery of a current-dependent nonlinear magnetoresistance in spin-polarized non-magnetic materials has attracted considerable attention in spintronics, correlations between this phenomenon and the underlying fermiology remain unexplored. Here, we report the observation of nonlinear magnetoresistance at room temperature in a semimetal WTe2, with an interesting temperature-driven inversion. Theoretical calculations reproduce the nonlinear transport measurements and allow us to attribute the inversion to temperature-induced changes in Fermi surface convexity. We also report a large anisotropy of nonlinear magnetoresistance in WTe2, due to its low symmetry of Fermi surfaces. The good agreement between experiments and theoretical modeling reveals the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These results lay a new path to explore ramifications of distinct fermiology for nonlinear transport in condensed-matter.

A population imbalance at different valleys of an electronic system lowers its effective rotational symmetry. We introduce a technique to measure such imbalance - a valley polarization - that exploits the unique fingerprints of this symmetry reduction in the polarization-dependent second-harmonic generation (SHG). We present the principle and detection scheme in the context of hexagonal two-dimensional crystals, which include graphene-based systems and the family of transition metal dichalcogenides, and provide a direct experimental demonstration using a 2H-MoSe$_{2}$ monolayer at room temperature. We deliberately use the simplest possible setup, where a single pulsed laser beam simultaneously controls the valley imbalance and tracks the SHG process. We further developed a model of the transient population dynamics which analytically describes the valley-induced SHG rotation in very good agreement with the experiment. In addition to providing the first experimental demonstration of the effect, this work establishes a conceptually simple, com-pact and transferable way of measuring instantaneous valley polarization, with direct applicability in the nascent field of valleytronics.

Topological crystalline insulators (TCI) are insulating electronic phases of matter with nontrivial topology originating from crystalline symmetries. Recent theoretical advances have provided powerful guidelines to search for TCIs in real materials. Using density functional theory, we identify a class of new TCI states in the tetragonal lattice of the Ca$_2$As material family. On both top and side surfaces, we observe topological surface states protected independently by rotational and mirror symmetries. We show that a particular lattice distortion can single out the newly proposed topological protection by the rotational symmetry. As a result, the Dirac points of the topological surface states are moved to generic locations in momentum space away from any high symmetry lines. Such topological surface states have not been seen before. Moreover, the other family members, including Ca$_2$Sb, Ca$_2$Bi and Sr$_2$Sb, feature different topological surface states due to their distinct topological invariants. We thus further propose topological phase transitions in the pseudo-binary systems such as (Ca$_{1-x}$Sr$_x$)$_2$As and Ca$_2$As$_x$Sb$_{1-x}$. Our work reveals rich and exotic TCI physics across the Ca$_2$As family of materials, and suggests the feasibility of materials database search methods to discover new TCIs., Comment: 5 pages, 4 figures

We report the first detailed characterization of the sheet third-harmonic optical susceptibility, $\chi_{s}^{(3)}$, of tungsten diselenide (WSe$_{2}$). With a home-built confocal microscope setup developed to study harmonics generation, we map the second- and third-harmonic intensities as a function of position in the sample, pump power and polarization angle, for single and few layers flakes of WSe$_{2}$. We register a value of $|\chi_{s}^{(3)}| \approx$ 0.91 $\times$ 10$^{-28}$ m$^{3}$ V$^{-2}$ at a fundamental excitation frequency of $\hbar\omega$ = 0.8 eV, which is comparable in magnitude to the third-harmonic susceptibility of other group-VI transition metal dichalcogenides. The simultaneously recorded second-harmonic susceptibility is found to be $|\chi_{s}^{(2)}| \approx$ 0.70 $\times$ 10$^{-19}$ m$^{2}$ V$^{-1}$ in very good agreement on the order of magnitude with recent reports for WSe$_{2}$, which asserts the robustness of our values for $|\chi_{s}^{(3)}|$., Comment: 20 pages, 8 figures, 1 table

We investigate the excitonic spectrum of MoS$_2$ monolayers and calculate its optical absorption properties over a wide range of energies. Our approach takes into account the anomalous screening in two dimensions and the presence of a substrate, both cast by a suitable effective Keldysh potential. We solve the Bethe-Salpeter equation using as a basis a Slater-Koster tight-binding model parameterized to fit ab initio MoS$_2$ band structure calculations. The resulting optical conductivity is in good quantitative agreement with existing measurements up to ultraviolet energies. We establish that the electronic contributions to the C excitons arise not from states in the vicinity of the $\Gamma$ point, but from a set of $k$-points over extended portions of the Brillouin zone. Our results reinforce the advantages of approaches based on effective models to expeditiously explore the properties and tunability of excitons in TMD systems., Comment: Published version, 16 pages, 10 figures

Recent experiments suggest that excitonic degrees of freedom play an important role in precipitating the charge density wave (CDW) transition in $1T$-$\mathrm{TiSe}_2$. Through systematic calculations of the electronic and phonon spectrum based on density functional perturbation theory, we show that the predicted critical doping of the CDW phase overshoots the experimental value by 1 order of magnitude. In contrast, an independent self-consistent many-body calculation of the excitonic order parameter and renormalized band structure is able to capture the experimental phase diagram in extremely good qualitative and quantitative agreement. This demonstrates that electron-electron interactions and the excitonic instability arising from direct electron-hole coupling are pivotal to accurately describe the nature of the CDW in this system. This has important implications to understand the emergence of superconductivity within the CDW phase of this and related systems.

One of the enticing features common to most of the two-dimensional electronic systems that are currently at the forefront of materials science research is the ability to easily introduce a combination of planar deformations and bending in the system. Since the electronic properties are ultimately determined by the details of atomic orbital overlap, such mechanical manipulations translate into modified electronic properties. Here, we present a general-purpose optimization framework for tailoring physical properties of two-dimensional electronic systems by manipulating the state of local strain, allowing a one-step route from their design to experimental implementation. A definite example, chosen for its relevance in light of current experiments in graphene nanostructures, is the optimization of the experimental parameters that generate a prescribed spatial profile of pseudomagnetic fields in graphene. But the method is general enough to accommodate a multitude of possible experimental parameters and conditions whereby deformations can be imparted to the graphene lattice, and complies, by design, with graphene's elastic equilibrium and elastic compatibility constraints. As a result, it efficiently answers the inverse problem of determining the optimal values of a set of external or control parameters that result in a graphene deformation whose associated pseudomagnetic field profile best matches a prescribed target. The ability to address this inverse problem in an expedited way is one key step for practical implementations of the concept of two-dimensional systems with electronic properties strain-engineered to order. The general-purpose nature of this calculation strategy means that it can be easily applied to the optimization of other relevant physical quantities which directly depend on the local strain field, not just in graphene but in other two-dimensional electronic membranes., Comment: 37 pages, 9 figures. This submission contains low-resolution bitmap images; high-resolution images can be found in version 1, which is ~13.5 MB

The electronic implications of strain in graphene can be captured at low energies by means of pseudovector potentials which can give rise to pseudomagnetic fields. These strain-induced vector potentials arise from the local perturbation to the electronic hopping amplitudes in a tight-binding framework. Here we complete the standard description of the strain-induced vector potential, which accounts only for the hopping perturbation, with the explicit inclusion of the lattice deformations or, equivalently, the deformation of the Brillouin zone. These corrections are linear in strain and are different at each of the strained, inequivalent Dirac points, and hence are equally necessary to identify the precise magnitude of the vector potential. This effect can be relevant in scenarios of inhomogeneous strain profiles, where electronic motion depends on the amount of overlap among the local Fermi surfaces. In particular, it affects the pseudomagnetic field distribution induced by inhomogeneous strain configurations, and can lead to new opportunities in tailoring the optimal strain fields for certain desired functionalities., Comment: Errata for version 2

As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity and electronics at the limits of their validity. The availability of reliable atomistic potentials for graphene allows unprecedented precise simulations of the mechanical response of atomic membranes. Here we describe the transport and electronic structure in the neighbourhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene that occur in non-epitaxial suspended samples where shear stresses are unavoidable. We use a combination of atomistic mechanical simulations, analytical geometry and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport and mobility in suspended samples. We also point out how the geometry-generated pseudo-magnetic/electric fields might disrupt Landau quantization under a magnetic field.

We study the magnetization of square and hexagonal graphene dots. It is shown that two classes of hexagonal dots have a second order phase transition at a critical Hubbard energy $U$, whoose value is similar to the one in bulk graphene, albeit the dots do not have a density of states proportional to the absolute value of the energy, relatively to the Dirac point. Furthermore, we show that a particular class of hexagonal dots having zig-zag edges, does not exhibit zero energy edge states. We also study the effect of uniaxial strain on the evolution of the magnetization of square dots, and find that the overall effect is an enhancement of magnetization with strain. The enhancement can be as large as 100% for strain of the order of 20%. Additionaly, stress induces a spatial displacement of the magnetization over the dot, moving it from the zig-zag to the armchair edges., Comment: Figure and references added. Conclusions section enlarged; http://link.aps.org/doi/10.1103/PhysRevB.80.245436

We review the problem of adatoms in graphene under two complementary points of view, scattering theory and strong correlations. We show that in both cases impurity atoms on the graphene surface present effects that are absent in the physics of impurities in ordinary metals. We discuss how to observe these unusual effects with standard experimental probes such as scanning tunneling microscopes, and spin susceptibility., Comment: For the Proceedings of the "Graphene Week 2008" at the ICTP in Trieste, Italy. 8 pages, 8 figures

We analyze the effect of tensional strain in the electronic structure of graphene. In the absence of electron-electron interactions, within linear elasticity theory, and a tight-binding approach, we observe that strain can generate a bulk spectral gap. However this gap is critical, requiring threshold deformations in excess of 20%, and only along preferred directions with respect to the underlying lattice. The gapless Dirac spectrum is robust for small and moderate deformations, and the gap appears as a consequence of the merging of the two inequivalent Dirac points, only under considerable deformations of the lattice. We discuss how strain-induced anisotropy and local deformations can be used as a means to affect transport characteristics and pinch off current flow in graphene devices., Comment: Expanded version of the original paper

We propose a route to all-graphene integrated electronic devices by exploring the influence of strain on the electronic structure of graphene. We show that strain can be easily tailored to generate electron beam collimation, 1D channels, surface states and confinement, the basic elements for all-graphene electronics. In addition this proposal has the advantage that patterning can be made on substrates rather than on the graphene sheet, thereby protecting the integrity of the latter., Comment: Minor changes

We study the problem of Coulomb field-induced charging of the ground state in a system of 2D massive Dirac particles (gapped graphene). As in its 3D QED counterpart, the critical Coulomb coupling is renormalized to higher values, compared to the massless case. We find that in gapped graphene a novel supercritical regime is possible, where the screening charge is comparable to the impurity charge, thus leading to suppression of the Coulomb field at nanometer scales. We corroborate this with numerical solution of the tight-binding problem in the honeycomb lattice., Comment: Revised and extended version

We present a study of different models of local disorder in graphene. Our focus is on the main effects that vacancies -- random, compensated and uncompensated --, local impurities and substitutional impurities bring into the electronic structure of graphene. By exploring these types of disorder and their connections, we show that they introduce dramatic changes in the low energy spectrum of graphene, viz. localized zero modes, strong resonances, gap and pseudogap behavior, and non-dispersive midgap zero modes., Comment: 16 pages, lower resolution figures

We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results also have relevance for the problem of disorder in d-wave superconductors., Comment: Replaced with published version. 4 pages, 4 figures. Fig. 1 was revised