Magnetoresistance is the change in a material's electrical resistance in response to an applied magnetic field. Materials with large magnetoresistance have found use as magnetic sensors, in magnetic memory, and in hard drives at room temperature, and their rarity has motivated many fundamental studies in materials physics at low temperatures. Here we report the observation of an extremely large positive magnetoresistance at low temperatures in the non-magnetic layered transition-metal dichalcogenide WTe2: 452,700 per cent at 4.5 kelvins in a magnetic field of 14.7 teslas, and 13 million per cent at 0.53 kelvins in a magnetic field of 60 teslas. In contrast with other materials, there is no saturation of the magnetoresistance value even at very high applied fields. Determination of the origin and consequences of this effect, and the fabrication of thin films, nanostructures and devices based on the extremely large positive magnetoresistance of WTe2, will represent a significant new direction in the study of magnetoresistivity.

Dirac semimetals and Weyl semimetals are 3D analogs of graphene in which crystalline symmetry protects the nodes against gap formation [1-3]. Na3Bi and Cd3As2 were predicted to be Dirac semimetals [4, 5], and recently confirmed to be so by photoemission [6-8]. Several novel transport properties in a magnetic field H have been proposed for Dirac semimetals [2, 10, 11, 16]. Here we report an interesting property in Cd3As2 that was unpredicted, namely a remarkable protection mechanism that strongly suppresses back-scattering in zero H. In single crystals, the protection results in ultrahigh mobility, 9 × 10 6 cm 2 /Vs at 5 K. Suppression of backscattering results in a transport lifetime 10 4 × longer than the quantum lifetime. The lifting of this protection by H leads to a very large magnetoresistance. We discuss how this may relate to changes to the Fermi surface induced by H.

The three dimensional (3D) Dirac semimetal, which has been predicted theoretically [1], is a new electronic state of matter. It can be viewed as 3D generalization of graphene, with a unique electronic structure in which conduction and valence band energies touch each other only at isolated points in momentum space (i.e. the 3D Dirac points), and thus it cannot be classified either as a metal or a semiconductor. In contrast to graphene [2], the Dirac points of such a semimetal are not gapped by the spin-orbit interaction and the crossing of the linear dispersions is protected by crystal symmetry [1]. In combination with broken time-reversal or inversion symmetries, 3D Dirac points may result in a variety of topologically non-trivial phases with unique physical properties [1, 3-5]. They have, however, escaped detection in real solids so far. Here we report the direct observation of such an exotic electronic structure in cadmium arsenide (Cd 3 As 2 ) by means of angle-resolved photoemission spectroscopy (ARPES). We identify two momentum regions where electronic states that strongly disperse in all directions form narrow cone-like structures, and thus prove the existence of the long sought 3D Dirac points. This electronic structure naturally explains why Cd 3 As 2 has one of the highest known bulk electron mobilities [6]. This realization of a 3D Dirac semimetal in Cd 3 As 2 not only opens a direct path to a wide spectrum of applications, but also offers a robust platform for engineering topologically-nontrivial phases including Weyl semimetals and Quantum Spin Hall systems.Without considering any aspects of topology, electronic band theory classifies materials as insulators, semiconductors and metals depending on the presence and the size of the energy gap between the valence and conduction bands. Semimetals belong to a "buffer zone" between semiconductors and metals and are characterized by a small energy overlap between the conduction and valence bands. This overlap is vaguely defined, partly because the notion of momentum is traditionally not included in the simple classification. In contrast, 3D Dirac semimetals are precisely defined in terms of the momentum dependent band structure: the mentioned overlap occurs only at a set of isolated points in momentum space where linear energy vs. wavevector dispersions cross at the Fermi level. Such an anomalous Fermi surface in three dimensions would obviously be a source of intriguing physical properties, as is the case with its 2D analog -graphene. Considering a 3D Dirac point as an overlapping of two Weyl points [1,[3][4][5] immediately promotes 3D Dirac semimetals to one of the most wanted new materials from a theoretical point of view: apart from being natively topologically non-trivial, in some cases they can also be viewed as parent materials for accessing the Weyl semimetal state [7].In order to identify a 3D Dirac semimetal experimentally, one needs to locate a Dirac point in a 3D momentum space and measure the corresponding dispersions of the electronic states....

A variety of monolayer crystals have been proposed to be two-dimensional topological insulators exhibiting the quantum spin Hall effect (QSHE), possibly even at high temperatures. Here we report the observation of the QSHE in monolayer tungsten ditelluride (WTe) at temperatures up to 100 kelvin. In the short-edge limit, the monolayer exhibits the hallmark transport conductance, ~/ per edge, where is the electron charge and is Planck's constant. Moreover, a magnetic field suppresses the conductance, and the observed Zeeman-type gap indicates the existence of a Kramers degenerate point and the importance of time-reversal symmetry for protection from elastic backscattering. Our results establish the QSHE at temperatures much higher than in semiconductor heterostructures and allow for exploring topological phases in atomically thin crystals.

Condensed-matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations as well as the possibility to manipulate them for potential applications. It has recently been proposed that chiral, massless particles known as Weyl fermions can emerge in certain bulk materials or in topological insulator multilayers and give rise to unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry effectively forming a massless Dirac fermion has been predicted to appear as low-energy excitations in a number of materials termed three-dimensional Dirac semimetals. Here we report scanning tunnelling microscopy measurements at sub-kelvin temperatures and high magnetic fields on the II-V semiconductor Cd3As2. We probe this system down to atomic length scales, and show that defects mostly influence the valence band, consistent with the observation of ultrahigh-mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference, we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a magnetic field applied along the axis of the Dirac points, Weyl fermions are the low-energy excitations in Cd3As2.

A topological insulator protected by time-reversal symmetry is realized via spinorbit interaction driven band inversion. The topological phase in the Bi 1−x Sb x system is due to an odd number of band inversions. A related spin-orbit system, the Pb 1−x Sn x Te, has long been known to contain an even number of inversions based on band theory. Here we experimentally investigate the possibility of a mirror symmetry protected topological crystalline insulator phase in the Pb 1−x Sn x Te class of materials which has been theoretically predicted to exist in its end compound SnTe. Our experimental results show that at a finite-Pb composition above the topological inversion phase transition, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order distinct from that observed in Bi 1−x Sb x . Our observation of the spin-polarized Dirac surface states in the inverted Pb 1−x Sn x Te and their absence in the non-inverted compounds related via a topological phase transition provide the experimental groundwork for opening the research on novel topological order in quantum devices.

The Dirac and Weyl semimetals are unusual materials in which the nodes of the bulk states are protected against gap formation by crystalline symmetry. The chiral anomaly, predicted to occur in both systems, was recently observed as a negative longitudinal magnetoresistance (LMR) in NaBi (ref. ) and in TaAs (ref. ). An important issue is whether Weyl physics appears in a broader class of materials. We report evidence for the chiral anomaly in the half-Heusler GdPtBi. In zero field, GdPtBi is a zero-gap semiconductor with quadratic bands. In a magnetic field, the Zeeman energy leads to Weyl nodes. We have observed a large negative LMR with the field-steering properties specific to the chiral anomaly. The chiral anomaly also induces strong suppression of the thermopower. We report a detailed study of the thermoelectric response function α of Weyl fermions. The scheme of creating Weyl nodes from quadratic bands suggests that the chiral anomaly may be observable in a broad class of semimetals.

2The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field [1]. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the topological Chern invariants [2, 3]. In magnets, the internal magnetization allows Hall conductivity in the absence of external magnetic field [3]. This anomalous Hall effect (AHE) has become an important tool to study quantum magnets [3][4][5][6][7][8]. In nonmagnetic materials without external magnetic fields, the electrical Hall effect is rarely explored because of the constraint by time-reversal symmetry.However, strictly speaking, only the Hall effect in the linear response regime, i.e., the Hall voltage linearly proportional to the external electric field, identically vanishes due to time-reversal symmetry [9]. The Hall effect in the nonlinear response regime, on the other hand, may not be subject to such symmetry constraints [10][11][12]. Here, we report the observation of the nonlinear Hall effect (NLHE) [12] in the electrical transport of the nonmagnetic 2D quantum material, bilayer WTe 2 . Specifically, flowing an electrical current in bilayer WTe 2 leads to a nonlinear Hall voltage in the absence of magnetic field. The NLHE exhibits unusual properties sharply distinct from the AHE in metals: The NLHE shows a quadratic I -V characteristic; It strongly dominates the nonlinear longitudinal response, leading to a Hall angle of ∼ 90 • . We further show that the NLHE directly measures the "dipole moment" [12] of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe 2 . Our results demonstrate a new Hall effect and provide a powerful methodology to detect Berry curvature in a wide range of nonmagnetic quantum materials in an energy-resolved way.In 1879 Edwin H. Hall observed that, when an electrical current passes through a gold film under a magnetic field, a transverse voltage develops [1]. This effect, known as the Hall effect, forms the basis of both fundamental research and practical applications such as magnetic field measurements and motion detectors. In contrast to the classical Hall effect where the Lorentz force bends the trajectory of the charge carriers, quantum mechanics describes the "bending" by the intrinsic geometry of the quantum electron wavefunctions under time-reversal symmetry breaking. This crucial theoretical understanding eventually led to the seminal discoveries of the Berry curvature and the topological Chern number, which have become pillars of modern condensed matter physics [2, 3]. One important cur-3 rent frontier is to identify AHE with quantized or topological character in unconventional magnetic quantum materials, where spin-orbit coupling (SOC), geometrical frustration and electronic correlations coexist [3][4][5][6][7][8]. These extensive studies [1,[3][4][5][6][7][8] have established a paradigm for the electrical Hall effect: (1) A non-vanishing Hall conductivity arises from the momentum-integrated Berry curva...