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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.

The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the topological Chern invariants. In magnets, the internal magnetization allows Hall conductivity in the absence of external magnetic field. This anomalous Hall effect (AHE) has become an important tool to study quantum magnets. 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. The Hall effect in the nonlinear response regime, on the other hand, may not be subject to such symmetry constraints. Here, we report the observation of the nonlinear Hall effect (NLHE) in the electrical transport of the nonmagnetic 2D quantum material, bilayer WTe2. Specifically, flowing an electrical current in bilayer WTe2 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 about 90 degree. We further show that the NLHE directly measures the "dipole moment" of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. 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.

The charge density wave (CDW) in 1T-TiSe2 accompanied by the periodic lattice distortion has a nontrivial symmetry configuration. The symmetry is important as an indication of the mechanism and a cue for experimental probes. We examine the symmetry of the system and clear up the connection of electronic structures between the normal and the CDW states. Especially, we unravel the consequential irreducible representations (IRs) of electronic states and, more ahead, those of gap functions among bands when the CDW occurs. Normally symmetry-related topology will be achieved directly, so we assert that the theory is valuable and practical for the search of topological CDW insulators., Comment: 13 pages, 5 figures

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

The Weyl semimetal WTe2 and MoTe2 show great potential in generating large spin currents since they possess topologically-protected spin-polarized states and can carry a very large current density. In addition, the intrinsic noncentrosymmetry of WTe2 and MoTe2 endows with a unique property of crystal symmetry-controlled spin-orbit torques. An important question to be answered for developing spintronic devices is how spins relax in WTe2 and MoTe2. Here, we report a room-temperature spin relaxation time of 1.2 ns (0.4 ns) in WTe2 (MoTe2) thin film using the time-resolved Kerr rotation (TRKR). Based on ab initio calculation, we identify a mechanism of long-lived spin polarization resulting from a large spin splitting around the bottom of the conduction band, low electron-hole recombination rate and suppression of backscattering required by time-reversal and lattice symmetry operation. In addition, we find the spin polarization is firmly pinned along the strong internal out-of-plane magnetic field induced by large spin splitting. Our work provides an insight into the physical origin of long-lived spin polarization in Weyl semimetals which could be useful to manipulate spins for a long time at room temperature.

We propose that the quasi-one-dimensional molybdenum selenide compound Tl2-xMo6Se6 is a time-reversal-invariant topological superconductor induced by inter-sublattice pairing, even in the absence of spin-orbit coupling (SOC). No noticeable change in superconductivity is observed in Tl-deficient (0<=x<=0.1) compounds. At weak SOC, the superconductor prefers the triplet d vector lying perpendicular to the chain direction and two-dimensional E2u symmetry, which is driven to a nematic order by spontaneous rotation symmetry breaking. The locking energy of the d vector is estimated to be weak and hence the proof of its direction would rely on tunnelling or phase-sensitive measurements., Comment: 6 pages, 3 figures, 1 table

Charge density wave (CDW) phases are symmetry-reduced states of matter in which a periodic modulation of the electronic charge frequently leads to drastic changes of the electronic spectrum, including the emergence of energy gaps. We analyze the CDW state in a 1T-TiSe$_2$ monolayer within a density functional theory framework and show that, similarly to its bulk counterpart, the monolayer is unstable towards a commensurate $2{\times}2$ periodic lattice distortion (PLD) and CDW at low temperatures. Analysis of the electron and phonon spectrum establishes the PLD as the stable $T=0$ K configuration with a narrow bandgap, whereas the undistorted and semi-metalic state is stable only above a threshold temperature. The lattice distortions as well as the unfolded and reconstructed band structure in the CDW phase agree well with experimental results. We also address evidence in our results for the role of electron-electron interactions in the CDW instability of 1T-TiSe$_2$ monolayers., Comment: 5 pages, 4 figures

We introduce the first multiorbital effective tight-binding model to describe the effect of electron-electron interactions in this system. Upon fixing all the effective hopping parameters in the normal state against an ab initio band structure, and with only the overall scale of the interactions as the sole adjustable parameter, we find that a self-consistent Hartree-Fock solution reproduces extremely well the experimental behavior of the charge density wave (CDW) order parameter in the full range $0

The discoveries of Dirac and Weyl semimetal states in spin-orbit compounds led to the realizations of elementary particle analogs in table-top experiments. In this paper, we propose the concept of a three-dimensional type-II Dirac fermion and identify a new topological semimetal state in the large family of transition-metal icosagenides, MA3 (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl3 family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node consists of four type-II Weyl nodes with chiral charge +/-1 via symmetry breaking. Furthermore, we predict the Landau level spectrum arising from the type-II Dirac fermions in VAl3 that is distinct from that of known Dirac semimetals. We also show a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions. The new type-II Dirac fermions, their novel magneto-transport response, the topological tunability and the large number of compounds make VAl3 an exciting platform to explore the wide-ranging topological phenomena associated with Lorentz-violating Dirac fermions in electrical and optical transport, spectroscopic and device-based experiments., Comment: 28 pages, 7 Figures

Atomically thin transitional metal ditellurides like WTe2 and MoTe2 have triggered tremendous research interests because of their intrinsic nontrivial band structure. They are also predicted to be 2D topological insulators and type-II Weyl semimetals. However, most of the studies on ditelluride atomic layers so far rely on the low-yield and time-consuming mechanical exfoliation method. Direct synthesis of large-scale monolayer ditellurides has not yet been achieved. Here, using the chemical vapor deposition (CVD) method, we demonstrate controlled synthesis of high-quality and atom-thin tellurides with lateral size over 300 {\mu}m. We found that the as-grown WTe2 maintains two different stacking sequences in the bilayer, where the atomic structure of the stacking boundary is revealed by scanning transmission electron microscope (STEM). The low-temperature transport measurements revealed a novel semimetal-to-insulator transition in WTe2 layers and an enhanced superconductivity in few-layer MoTe2. This work paves the way to the synthesis of atom-thin tellurides and also quantum spin Hall devices.

Topological metals and semimetals (TMs) have recently drawn significant interest. These materials give rise to condensed matter realizations of many important concepts in high-energy physics, leading to wide-ranging protected properties in transport and spectroscopic experiments. The most studied TMs, i.e., Weyl and Dirac semimetals, feature quasiparticles that are direct analogues of the textbook elementary particles. Moreover, the TMs known so far can be characterized based on the dimensionality of the band crossing. While Weyl and Dirac semimetals feature zero-dimensional points, the band crossing of nodal-line semimetals forms a one-dimensional closed loop. In this paper, we identify a TM which breaks the above paradigms. Firstly, the TM features triply-degenerate band crossing in a symmorphic lattice, hence realizing emergent fermionic quasiparticles not present in quantum field theory. Secondly, the band crossing is neither 0D nor 1D. Instead, it consists of two isolated triply-degenerate nodes interconnected by multi-segments of lines with two-fold degeneracy. We present materials candidates. We further show that triplydegenerate band crossings in symmorphic crystals give rise to a Landau level spectrum distinct from the known TMs, suggesting novel magneto-transport responses. Our results open the door for realizing new topological phenomena and fermions including transport anomalies and spectroscopic responses in metallic crystals with nontrivial topology beyond the Weyl/Dirac paradigm., Comment: 24 pages, 4 figures, and 1 table

Weyl semimetals are novel topological conductors that host Weyl fermions as emergent quasiparticles. While the Weyl fermions in high-energy physics are strictly defined as the massless solution of the Dirac equation and uniquely fixed by Lorentz symmetry, there is no such constraint for a topological metal in general. Specifically, the Weyl quasiparticles can arise by breaking either the space-inversion ($\mathcal{I}$) or time-reversal ($\mathcal{T}$) symmetry. They can either respect Lorentz symmetry (type-I) or strongly violate it (type-II). To date, different types of Weyl fermions have been predicted to occur only in different classes of materials. In this paper, we present a significant materials breakthrough by identifying a large class of Weyl materials in the RAlX (R=Rare earth, Al, X=Ge, Si) family that can realize all different types of emergent Weyl fermions ($\mathcal{I}$-breaking, $\mathcal{T}$-breaking, type-I or type-II), depending on a suitable choice of the rare earth elements. Specifically, RAlX can be ferromagnetic, nonmagnetic or antiferromagnetic and the electronic band topology and topological nature of the Weyl fermions can be tuned. The unparalleled tunability and the large number of compounds make the RAlX family of compounds a unique Weyl semimetal class for exploring the wide-ranging topological phenomena associated with different types of emergent Weyl fermions in transport, spectroscopic and device-based experiments., Comment: This paper reports theoretical prediction of Weyl semimetal (type-I and type-II) states in the R-Al-X family. For the experimental discovery, see our earlier paper at http://arxiv.org/abs/1603.07318

We theoretically investigate the development of unconventional superconductivity in the Sb(111) thin film when its Fermi level is tuned to near type-II Van Hove singularities (VHS), which locate at non-time-reversal invariant momenta. Via patch renormalization group analysis, we show that the leading instability is a chiral p + ip-wave superconducting order. The origin of such pairing relies on the hexagonal structure of the VHS and strong spin-orbit coupling, resulting in the anisotropy of the electron-electron scattering to provide an attractive channel. Our study hence suggests that superconducting Sb thin films originated from VHS physics may host Majorana zero modes in the magnetic vortices and provides another application perspective to such material., Comment: 7 pages, 5 figures, accepted by Physical Review B

We report theoretical and experimental discovery of Lorentz-violating Weyl fermion semimetal type-II state in the LaAlGe class of materials. Previously type-II Weyl state was predicted in WTe2 materials which remains unrealized in surface experiments. We show theoretically and experimentally that LaAlGe class of materials are the robust platforms for the study of type-II Weyl physics., Comment: This paper reports theoretical prediction and experimental discovery together. A detailed theoretical paper describing the topology of the full family of X(Lanthanides)AlGe materials will follow. Other related papers can be found at http://physics.princeton.edu/zahidhasangroup/index_WS.html

Topological semimetals (TSMs) including Weyl semimetals and nodal-line semimetals are expected to open the next frontier of condensed matter and materials science. Although the first inversion breaking Weyl semimetal was recently discovered in TaAs, its magnetic counterparts, i.e., the time-reversal breaking Weyl and nodal line semimetals, remain elusive. They are predicted to exhibit exotic properties distinct from the inversion breaking TSMs including TaAs. In this paper, we identify the magnetic topological semimetal state in the ferromagnetic half-metal compounds Co$_2$TiX (X=Si, Ge, or Sn) with Curie temperatures higher than 350 K. Our first-principles band structure calculations show that, in the absence of spin-orbit coupling, Co$_2$TiX features three topological nodal lines. The inclusion of spin-orbit coupling gives rise to Weyl nodes, whose momentum space locations can be controlled as a function of the magnetization direction. Our results not only open the door for the experimental realization of topological semimetal states in magnetic materials at room temperatures, but also suggest potential applications such as unusual anomalous Hall effects in engineered monolayers of the Co$_2$TiX compounds at high temperatures., Comment: 16 pages, 4 figures, and 1 table

The recent discovery of the first Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature. Such a topological semimetal features a novel type of anomalous surface state, the Fermi arc, which connects a pair of Weyl nodes through the boundary of the crystal. Here, we present theoretical calculations of the quasi-particle interference (QPI) patterns that arise from the surface states including the topological Fermi arcs in the Weyl semimetals TaAs and NbP. Most importantly, we discover that the QPI exhibits termination-points that are fingerprints of the Weyl nodes in the interference pattern. Our results, for the first time, propose an interference signature of the topological Fermi arcs in TaAs, which provides important guidelines for STM measurements on this prototypical Weyl semimetal compound. The scattering channels presented here is relevant to transport phenomena on the surface of the TaAs class of Weyl semimetals. Our work is also the first systematic calculation of the quantum interferences from the Fermi arc surface states, which is in general useful for future STM studies on other Weyl semimetals., Comment: 15pages, 6 figures

A Weyl semimetal is a new state of matter that host Weyl fermions as quasiparticle excitations. The Weyl fermions at zero energy correspond to points of bulk band degeneracy, Weyl nodes, which are separated in momentum space and are connected only through the crystal's boundary by an exotic Fermi arc surface state. We experimentally measure the spin polarization of the Fermi arcs in the first experimentally discovered Weyl semimetal TaAs. Our spin data, for the first time, reveal that the Fermi arcs' spin polarization magnitude is as large as 80% and possesses a spin texture that is completely in-plane. Moreover, we demonstrate that the chirality of the Weyl nodes in TaAs cannot be inferred by the spin texture of the Fermi arcs. The observed non-degenerate property of the Fermi arcs is important for the establishment of its exact topological nature, which reveal that spins on the arc form a novel type of 2D matter. Additionally, the nearly full spin polarization we observed (~80%) may be useful in spintronic applications., Comment: 4 figures, 15 pages

Weyl semimetals are expected to open up new horizons in physics and materials science because they provide the first realization of Weyl fermions and exhibit protected Fermi arc surface states. However, they had been found to be extremely rare in nature. Recently, a family of compounds, consisting of TaAs, TaP, NbAs and NbP was predicted as Weyl semimetal candidates. Here, we experimentally realize a Weyl semimetal state in TaP. Using photoemission spectroscopy, we directly observe the Weyl fermion cones and nodes in the bulk and the Fermi arcs on the surface. Moreover, we find that the surface states show an unexpectedly rich structure, including both topological Fermi arcs and several topologically-trivial closed contours in the vicinity of the Weyl points, which provides a promising platform to study the interplay between topological and trivial surface states on a Weyl semimetal's surface. We directly demonstrate the bulk-boundary correspondence and hence establish the topologically nontrivial nature of the Weyl semimetal state in TaP, by resolving the net number of chiral edge modes on a closed path that encloses the Weyl node. This also provides, for the first time, an experimentally practical approach to demonstrating a bulk Weyl fermion from a surface state dispersion measured in photoemission., Comment: Theoretical discovery of TaP as a Weyl Fermion material (November 2014) was made in http://www.nature.com/ncomms/2015/150612/ncomms8373/full/ncomms8373.html

Weyl nodes are topological objects in three-dimensional metals. Their topological property can be revealed by studying the high-field transport properties of a Weyl semimetal. While the energy of the lowest Landau band (LLB) of a conventional Fermi pocket always increases with magnetic field due to the zero point energy, the LLB of Weyl cones remains at zero energy unless a strong magnetic field couples the Weyl fermions of opposite chirality. In the Weyl semimetal TaP, we achieve such a magnetic coupling between the electron-like Fermi pockets arising from the W1 Weyl fermions. As a result, their LLBs move above chemical potential, leading to a sharp sign reversal in the Hall resistivity at a specific magnetic field corresponding to the W1 Weyl node separation. By contrast, despite having almost identical carrier density, the annihilation is unobserved for the hole-like pockets because the W2 Weyl nodes are much further separated. These key findings, corroborated by other systematic analyses, reveal the nontrivial topology of Weyl fermions in high-field measurements., Comment: the Fig2 and Fig 3 are not compatible with this version