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The family of transition metal dipnictides (TMDs) has been of theoretical and experimental interest because this family hosts topological states and extremely large magnetoresistance (MR). Recently, TaAs2, a member of this family, has been predicted to support a topological crystalline insulating state. Here, by using high resolution. Angle resolved photoemission spectroscopy (ARPES), we reveal both closed and open pockets in the metallic Fermi surface and linearly dispersive bands on the (201) surface, along with the presence of extreme MR observed from magneto-transport measurements. A comparison of the ARPES results with first-principles computations show that the linearly dispersive bands on the measured surface of TaAs2 are trivial bulk bands. The absence of symmetry-protected surface state on the (201) surface indicates its topologically dark nature. The presence of open Fermi surface features suggests that the open orbit fermiology could contribute to the extremely large MR of TaAs., Comment: 13 pages, 5 figures

Flat bands coupled with magnetism and topological orders near or at the Fermi level are well known to drive exotic correlation physics and unconventional superconductivity. Here, based on first-principles modeling combined with an in-depth symmetry analysis, we reveal the presence of topological flat bands involving low-energy Ni-$3d_{z^2}$ states in the recently discovered superconductor LaNiO$_{2}$. Our analysis demonstrates that LaNiO$_2$ is an Axion insulator with $\mathbb{Z}_{4} = 2$ and that it supports topological crystalline insulating states protected by the glide mirror symmetries. The topological flat bands in LaNiO$_{2}$ are also shown to host odd-parity superconductivity. Our study indicates that the nickelates would provide an interesting materials platform for exploring the interplay of flat bands, topological states, and superconductivity., Comment: 8, 3 figures, 1 table

We report the magnetic and electronic transport properties of the inversion and time-reversal symmetry breaking Weyl semimetal NdAlGe. This material is analogous to NdAlSi, whose helical magnetism presents a rare example of a Weyl-mediated collective phenomenon, but with a larger spin-orbit coupling. Our neutron diffraction experiments revealed that NdAlGe, similar to NdAlSi, supports an incommensurate Ising spin density wave ($T_{\text{inc}}=6.8$ K) with a small helical spin canting of 3$^\circ$ and a long-wavelength of $\sim$ 35 nm, which transitions to a commensurate ferrimagnetic state below $T_{\text{com}}=5.1$ K. Using small-angle neutron scattering, we showed that the zero-field cooled ferrimagnetic domains form stripes in real space with characteristic length scales of 18 nm and 72 nm parallel and perpendicular to the [110] direction, respectively. Interestingly, for the transport properties, NdAlSi does not exhibit an anomalous Hall effect (AHE) that is commonly observed in magnetic Weyl semimetals. In contrast to NdAlSi, we identify two different AHE regimes in NdAlGe that are respectively governed by intrinsic Berry curvature and extrinsic disorders/spin fluctuations. Our study suggests that Weyl-mediated magnetism prevails in this group of noncentrosymmetric magnetic Weyl semimetals NdAl$X$, but transport properties including AHE are affected by material-specific extrinsic effects such as disorders, despite the presence of prominent Berry curvature., Comment: Preprint, 16 pages, 6 main figures, 6 supplementary figures

The Su, Schrieffer and Heeger (SSH) model, describing the soliton excitations in polyacetylene due to the formation of antiphase domain walls (DW) from the alternating bond pattern, has served as a paradigmatic example of one-dimensional (1D) chiral topological insulators. While the SSH model has been realized in photonic and plasmonic systems, there have been limited analogues in three-dimensional (3D) electronic systems, especially regarding the formation of antiphase DWs. Here, we propose that pristine bulk Bi, in which the dimerization of $(111)$ atomic layers renders alternating covalent and van der Waals bonding within and between successive $(111)$ bilayers, respectively, serves as a 3D analogue of the SSH model. First, we confirm that the two dimerized Bi structures belong to different Zak phases of 0 and $\pi$ by considering the parity eigenvalues and Wannier charge centers, while the previously reported bulk topological phases of Bi remain invariant under the dimerization reversal. Next, we demonstrate the existence of topologically non-trivial $(111)$ and trivial $(11\bar{2})$ DWs in which the number of in-gap DW states (ignoring spin) is odd and even respectively, and show how this controls the interlinking of the Zak phases of the two adjacent domains. Finally, we derive general criteria specifying when a DW of arbitrary orientation exhibits a $\pi$ Zak phase based on the flip of parity eigenvalues. An experimental realization of dimerization in Bi and the formation of DWs may be achieved via intense femtosecond laser excitations that can alter the interatomic forces and bond lengths.

Large intrinsic anomalous Hall effect (AHE) due to the Berry curvature in magnetic topological semimetals is attracting enormous interest due to its fundamental importance and technological relevance. Mechanisms resulting in large intrinsic AHE include diverging Berry curvature in Weyl semimetals, anticrossing nodal rings or points of non-trivial bands, and noncollinear spin structures. Here we show that a half-topological semimetal (HTS) state near a topological critical point can provide a new mechanism for driving an exceptionally large AHE. We reveal this through a systematic experimental and theoretical study of the antiferromagnetic (AFM) half-Heusler compound TbPdBi. We not only observed an unusual AHE with a surprisingly large anomalous Hall angle {\Theta}H (tan {\Theta}H ~ 2, the largest among the antiferromagnets) in its field-driven ferromagnetic (FM) phase, but also found a distinct Hall resistivity peak in the canted AFM phase within a low field range, where its isothermal magnetization is nearly linearly dependent on the field. Moreover, we observed a nearly isotropic, giant negative magnetoresistance with a magnitude of ~98%. Our in-depth theoretical modelling demonstrates that these exotic transport properties originate from the HTS state. A minimal Berry curvature cancellation between the trivial spin-up and nontrivial spin-down bands results not only in an extremely large AHE, but it also enhances the spin polarization of the spin-down bands substantially and thus leads to a giant negative magnetoresistance. Our study advances the understanding of the interplay between band topology and magnetism and offers new clues for materials design for spintronics and other applications.

In one-dimensional (1D) systems, electronic interactions lead to a breakdown of Fermi liquid theory and the formation of a Tomonaga-Luttinger Liquid (TLL). The strength of its many-body correlations can be quantified by a single dimensionless parameter, the Luttinger parameter $K$, characterising the competition between the electrons' kinetic and electrostatic energies. Recently, signatures of a TLL have been reported for the topological edge states of quantum spin Hall (QSH) insulators, strictly 1D electronic structures with linear (Dirac) dispersion and spin-momentum locking. Here we show that the many-body interactions in such helical Luttinger Liquid can be effectively controlled by the edge state's dielectric environment. This is reflected in a tunability of the Luttinger parameter $K$, distinct on different edges of the crystal, and extracted to high accuracy from the statistics of tunnelling spectra at tens of tunneling points. The interplay of topology and many-body correlations in 1D helical systems has been suggested as a potential avenue towards realising non-Abelian parafermions.

Nontrivial band topologies in semimetals lead to robust surface states that can contribute dominantly to the total conduction. This may result in reduced resistivity with decreasing feature size contrary to conventional metals, which may highly impact the semiconductor industry. Here we study the resistivity scaling of a representative topological semimetal CoSi using realistic band structures and Green's function methods. We show that there exists a critical thickness d_c dividing different scaling trends. Above d_c, when the defect density is low such that surface conduction dominates, resistivity reduces with decreasing thickness; when the defect density is high such that bulk conduction dominates, resistivity increases in as conventional metals. Below d_c, the persistent remnants of the surface states give rise to decreasing resistivity down to the ultrathin limit, unlike in topological insulators. The observed CoSi scaling can apply to broad classes of topological semimetals, providing guidelines for materials screening and engineering. Our study shows that topological semimetals bear the potential of overcoming the resistivity scaling challenges in back-end-of-line interconnect applications.

p x n-type materials refer to materials with a p-type Seebeck coefficient in one direction and a n-type coefficient in the orthogonal direction. This type of materials allows for a transverse thermoelectric response, which is highly desirable for energy applications. Here, we report the observation of p x n-type behavior in TaIrTe4, a type-II Weyl semimetal, with an in-plane thermopower anisotropy S$_{xx}$-S$_{yy}$ reaches a maximum value 40${\mu}$V/K at 200K. Intriguingly. we found that such a p x n-type behavior is absent in the similar compound NbIrTe4. The presence and absence of p x n-type behavior in these two materials are consistent with density functional theory calculations, which further predict that the thermopower anisotropy in both compounds can be enhanced up to 130${\mu}$V/K by electron doping. Such a strong thermopower anisotropy originates from the presence of both p-type and n-type carriers, each with high mobility in one direction. These results suggest that although type-II Weyl semimetal phase does not guarantee the existence of p x n-type behavior, its unique band structure provides the ingredient to engineer and optimize this phenomenon., Comment: 9 pages, 3 figures

Recent classification efforts encompassing crystalline symmetries have revealed rich possibilities for solid-state systems to support a tapestry of exotic topological states. However, finding materials that realize such states remains a daunting challenge. Here we show how the interplay of topology, symmetry, and magnetism combined with doping and external electric and magnetic field controls can be used to drive the previously unreported SrIn$_2$As$_2$ materials family into a variety of topological phases. Our first-principles calculations and symmetry analysis reveal that SrIn$_2$As$_2$ is a dual topological insulator with $Z_2=(1;000)$ and mirror Chern number $C_M= -1$. Its isostructural and isovalent antiferromagnetic cousin EuIn$_2$As$_2$ is found to be an axion insulator with $Z_4= 2$. The broken time-reversal symmetry via Eu doping in Sr$_{1-x}$Eu$_x$In$_2$As$_2$ results in a higher-order or topological crystalline insulator state depending on the orientation of the magnetic easy axis. We also find that antiferromagnetic EuIn$_2$P$_2$ is a trivial insulator with $Z_4= 0$, and that it undergoes a magnetic field-driven transition to an ideal Weyl fermion or nodal fermion state with $Z_4= 1$ with applied magnetic field. Our study identifies Sr$_{1-x}$Eu$_x$In$_2$(As, P)$_2$ as a new tunable materials platform for investigating the physics and applications of Weyl and nodal fermions in the scaffolding of crystalline and axion insulator states., Comment: 8 Pages, 4 Figures, SM not included

The rare-earth monopnictide (REM) family, which hosts magnetic ground states with extreme magnetoresistance, has established itself as a fruitful playground for the discovery of interesting topological phases. Here, by using high-resolution angle-resolved photoemission spectroscopy complemented by first-principles density functional-theory based modeling, we examine the evolution of the electronic structure of the candidate REM Dirac semimetal NdSb across the magnetic transition. A complex angel-wing-like band structure near the zone center and three arc-like features at the zone corner have been observed. This dramatic reconstruction of the itinerant bands around the zone center is shown to be driven by the magnetic transition: Specifically,, the Nd 5d electron band backfolds at the Gamma point and hybridizes with the Sb 5p hole bands in the antiferromagnetic phase. Our study indicates that antiferromagnetism plays an intricate role in the electronic structure of the REM family., Comment: 13 pages, 13 figures; Supplemental Materials included

Weyl semimetal (WSM), a novel state of quantum matter, hosts Weyl fermions as emergent quasiparticles resulting from the breaking of either inversion or time-reversal symmetry. Magnetic WSMs that arise from broken time-reversal symmetry provide an exceptional platform to understand the interplay between magnetic order and Weyl physics, but few WSMs have been realized. Here, we identify CeAlSi as a new non-centrosymmetric magnetic WSM via angle-resolved photoemission spectroscopy (ARPES) and first-principles, density-functional theory based calculations. Our surface-sensitive vacuum ultraviolet ARPES data confirms the presence of surface Fermi arcs as, the smoking gun evidence for the existence of the Weyl semimetallic state in CeAlSi. We also observe bulk Weyl cones in CeAlSi using bulk-sensitive soft-X-ray ARPES measurements. In addition, Ce 4f at bands are found near the Fermi level, indicating that CeAlSi is a unique platform for investigating exotic quantum phenomena resulting from the interaction of topology, magnetism and electronic correlations., Comment: 12 pages, 4 figures; supplementary information included

A van der Waals coupled Weyl semimetal material NbIrTe4 is investigated by combining scanning tunneling microscopy/spectroscopy and first principles calculations. We observe a sharp peak in the tunneling conductance near the zero bias energy, and its origin is ascribed to a van Hove singularity associated with a Lifshitz transition of the topologically none trivial Fermi arc states. Furthermore, tunneling spectroscopy measurements show a surprisingly large signature of electron boson coupling, which presumably represents anomalously enhanced electron phonon coupling through the enhanced charge susceptibility. Our finding in van der Waals coupled material is particularly invaluable due to applicable exfoliation technology for searching exotic topological states by further manipulating near Fermi energy van Hove singularity in nanometer scale flakes and their devices.

A developing frontier in condensed matter physics is the emergence of novel electromagnetic responses, such as topological and anomalous Hall effect (AHE), in ferromagnetic Weyl semimetals (FM-WSMs). Candidates of FM-WSM are limited to materials that preserve inversion symmetry and generate Weyl crossings by breaking time-reversal symmetry. These materials share three common features: a centrosymmetric lattice, a collinear FM ordering, and a large AHE observed when the field is parallel to the magnetic easy-axis. Here, we present CeAlSi as a new type of FM-WSM, where the Weyl nodes are stabilized by breaking inversion symmetry, but their positions are tuned by breaking time-reversal symmetry. Unlike the other FM-WSMs, CeAlSi has a noncentrosymmetric lattice, a noncollinear FM ordering, and a novel AHE that is anisotropic between the easy- and hard-axes. It also exhibits large FM domains that are promising for both device applications and an interplay between the Weyl nodes and FM domain walls., Comment: Preprint, 20 pages, 4 figures

The tetragonal ferrimagnetic Mn$_3$Ga exhibits a wide range of intriguing magnetic properties. Here, we report the emergence of topologically nontrivial nodal lines in the absence of spin orbit coupling (SOC) which are protected by both mirror and $C_{4z}$ rotational symmetries. In the presence of SOC we demonstrate that the doubly degenerate nontrivial crossing points evolve into $C_{4z}$-protected Weyl nodes with chiral charge of $\pm$2. Furthermore, we have considered the experimentally reported noncollinear ferrimagnetic structure, where the magnetic moment of the Mn$_I$ atom (on the Mn-Ga plane) is tilted by an angle $\theta$ with respect to the crystallographic $c$ axis. The evolution of the Weyl nodes with $\theta$ reveals that the double Weyl nodes split into a pair of charge-1 Weyl nodes whose separation can be tuned by the magnetic orientation in the noncollinear ferrimagnetic structure., Comment: 5 pages, 4 figures

Most topological insulators discovered today in spinful systems can be transformed from topological semimetals (TSMs) with vanishing bulk gap via introducing the spin-orbit coupling (SOC), which manifests the intrinsic links between the gapped TI phases and the gapless TSMs. Recently, we have proposed a new family of TSMs in time-reversal invariant {\it spinless} systems, which host butterfly-like nodal-lines (NLs) consisting of a pair of identical concentric intersecting coplanar ellipses (CICE). In this Communication, we unveil the intrinsic link between this exotic class of nodal-line semimetals (NLSMs) and a $\mathbb{Z}_{4}$ = 2 topological crystalline insulator (TCI), by including substantial SOC. We demonstrate that in three space groups ({\it i.e.} $Pbam$ (No.55), $P4/mbm$ (No.127) and $P4_2/mbc$ (No.135)), the TCI supports a fourfold Dirac fermion on the (001) surface protected by two glide symmetries, which originates from the intertwined drumhead surface states of the CICE NLs. The higher order topology is further demonstrated by the emergence of one-dimensional helical hinge states, indicating a new higher order topological insulator protected by a glide symmetry., Comment: 6 pages, 3 figures

In recent years, the exotic properties of topological semimetals (TSMs) have attracted great attention and significant efforts have been made in seeking for new topological phases and material realization. In this work, we propose a new family of TSMs which harbors an unprecedented nodal line (NL) landscape consisting of a pair of concentric intersecting coplanar ellipses (CICE) at half-filling. Meanwhile, the CICE at half-filling guarantees the presence of a second pair of CICE beyond half-filling. Both CICEs are linked at four-fold degenerate points (FDPs) at zone boundaries. In addition, we identify the generic criteria for the existence of the CICE in a time reversal invariant {\it spinless} fermion system or a spinfull system with negligible spin-orbital coupling (SOC). Consequently, 9 out of 230 space groups (SGs) are feasible for hosting CICE whose location centers in the first Brillouin zone (BZ) are identified. We provide a simplest model with SG $Pbam$ (No. 55) which exhibits CICE, and the exotic intertwined drumhead surface states, induced by double-band-inversions. Finally, we propose a series of material candidates that host butterfly-like CICE NLs, such as, ZrX$_2$ (X=P,As), GeTe$_5$Tl$_2$, CYB$_2$ and Al$_2$Y$_3$., Comment: 6 pages, 3 figures

We have investigated magnetotransport properties and the topological electronic structure of the half-Heusler compound TbPtBi. Our experiments reveal an exceptionally large anomalous Hall effect (AHE) in the canted antiferromagnetic state of TbPtBi with the anomalous Hall angle (AHA) reaching ~0.68-0.76, which is a few times larger than the previously reported record in GdPtBi. First-principles electronic structure and the associated anomalous Hall conductivity were computed in order to interpret the experimental results. Our analysis shows that the AHE in TbPtBi does not originate from the Weyl points but that it is driven by the large net Berry curvature produced by the anticrossing of spin-split bands near the Fermi level in TbPtBi.

The interplay between topology and magnetism is essential for realizing novel topological states including the axion insulator, the magnetic Weyl semimetal, etc. An intrinsically ferromagnetic topological material with only the topological bands at the charge neutrality energy has so far remained elusive. By rationally designing the natural heterostructure consisting of [MnBi2Te4] septuple layers and [Bi2Te3] quintuple layers, we report MnBi8Te13 as the first intrinsic ferromagnetic topological material with clean low-energy band structure. Based on the thermodynamic, transport and neutron diffraction measurements, our data show that despite the adjacent [MnBi2Te4] being 44.1 {\AA} apart, MnBi8Te13 manifests long-range ferromagnetism below 10.5 K with strong coupling between magnetism and charge carriers. Our first-principles calculations and angle-resolved photoemission spectroscopy measurements further demonstrate that MnBi8Te13 is an intrinsic ferromagnetic axion state. Therefore, MnBi8Te13 serves as an ideal system to investigate rich emergent phenomena, including the quantized anomalous Hall effect and quantized topological magnetoelectric effect., Comment: 6 figs

Recent reports of a large anomalous Hall effect (AHE) in ferromagnetic Weyl semimetals (FM WSM) have led to a resurgence of interest in this enigmatic phenomenon. However, due to a lack of tunable materials, the interplay between the intrinsic mechanism caused by Berry curvature and extrinsic mechanisms due to scattering remains unclear in FM WSMs. In this contribution, we present a thorough investigation of both the extrinsic and intrinsic AHE in a new family of FM WSMs, PrAlGe$_{1-x}$Si$_x$, where $x$ can be tuned continuously. From DFT calculations, we show that the two end members, PrAlGe and PrAlSi, have different Fermi surfaces but similar Weyl node structures. Experimentally, we observe moderate changes in the anomalous Hall coefficient ($R_S$) but significant changes in the ordinary Hall coefficient ($R_0$) in PrAlGe$_{1-x}$Si$_x$ as a function of $x$, confirming a change of Fermi surface. By comparing the magnitude of $R_0$ and $R_S$, we identify two regimes; $|R_0|<|R_S|$ when $x\le0.5$ and $|R_0|>|R_S|$ when $x>0.5$. Through a detailed scaling analysis, we discover a universal anomalous Hall conductivity (AHC) from intrinsic contribution when $x\le0.5$. Such universal AHC is absent when $x>0.5$. Thus, we point out the significance of the extrinsic mechanisms in FM WSMs and report the first observation of a transition from intrinsic to extrinsic AHE in PrAlGe$_{1-x}$Si$_x$., Comment: 11 pages, 11 figure, 3 tables

Symmetry plays a major role in all disciplines of physics. Within the field of topological materials there is a great interest in understanding how the mechanics of crystalline and internal symmetries protect crossings between the conduction and valence bands. Additionally, exploring this direction can lead to a deeper understanding on the topological properties of crystals hosting a variety of symmetries. For the first time, we report the experimental observation of topological surface states in the nodal loop semimetal HfP2 using angle resolved photoemission spectroscopy (ARPES) which is supported by our first principles calculations. Our study shows termination dependent surface states in this compound. Our experimental data reveal surface states linked to three unique nodal loops confirmed by theoretical calculation to be topologically non-trivial. This work demonstrates that transition metal dipnictides provide a good platform to study non-trivial topological states protected by nonsymmorphic symmetry., Comment: 7 pages, 4 figures

The quantum behaviour of electrons in materials lays the foundation for modern electronic and information technology. Quantum materials with novel electronic and optical properties have been proposed as the next frontier, but much remains to be discovered to actualize the promise. Here we report the first observation of topological quantum properties of chiral crystals in the RhSi family. We demonsrate that this material hosts novel phase of matter exhibiting nearly ideal topological surface properties that emerge as a consequence of the crystals' structural chirality or handedness. We also demonstrate that the electrons on the surface of this crystal show a highly unusual helicoid structure that spirals around two high-symmetry momenta signalling its topological electronic chirality. Such helicoid Fermi arcs on the surface experimentally characterize the topological charges of $\pm{2}$, which arise from the bulk chiral fermions. The existence of bulk high-fold degenerate fermions are guaranteed by the crystal symmetries, however, in order to determine the topological charge in the chiral crystals it is essential to identify and study the helical arc states. Remarkably, these topological conductors we discovered exhibit helical Fermi arcs which are of length $\pi$, stretching across the entire Brillouin zone and orders of magnitude larger than those found in all known Weyl semimetals. Our results demonstrate novel electronic topological state of matter on a structurally chiral crystal featuring helicoid Fermi arc surface states. The exotic electronic chiral fermion state realised in these materials can be used to detect a quantised photogalvanic optical response or the chiral magnetic effect and its optical version in future devices as described by G. Chang \textit{et.al.,} `Topological quantum properties of chiral crystals' Nature Mat. 17, 978-985 (2018)., Comment: 28 pages, 12 figures

Young and Kane have given a great insight for 2D Dirac semimetals with nontrivial topology in the presence of nonsymmorphic crystalline symmetry. Based on one of 2D nonsymmorphic square lattice structures they proposed, we further construct a set of 3D minimal tight-binding models via vertically stacking the 2D nonsymmorphic lattice. Specifically, our model provides a platform to generate three topologically semimetallic phases such as Dirac nodal line semimetals, Weyl nodal line semimetals and Weyl semimetals. The off-centered mirror symmetry sufficiently protects nodal lines emerging within mirror-invariant plane with a nontrivial mirror invariant $n_{M\mathbb{Z}}$, whereas twofold screw rotational symmetry protects nontrivial Weyl nodal points with topological charge $C=2$. Interestingly, Weyl nodal loops are generated without mirror symmetry protection, where nontrivial "drumhead" surface states emerge within loops. In the presence of both time-reversal and inversion symmetries, the emergence of weak topological insulator phases is discussed as well., Comment: 8 pages, 6 figures and 1 table

3D Dirac semimetals are an emerging class of materials that possess topological electronic states with a Dirac dispersion in their bulk. In nodal-line Dirac semimetals, the conductance and valence bands connect along a closed path in momentum space, leading to the prediction of pseudospin vortex rings and pseudospin skyrmions. Here, we use Fourier transform scanning tunneling spectroscopy (FT-STS) at 4.5 K to resolve quasiparticle interference (QPI) patterns at single defect centers on the surface of the line nodal semimetal zirconium silicon sulfide (ZrSiS). Our QPI measurements show pseudospin conservation at energies close to the line node. In addition, we determine the Fermi velocity to be $\hbar v_F = 2.65 \pm 0.10$ eV {\AA} in the {\Gamma}-M direction ~300 meV above the Fermi energy $E_F$, and the line node to be ~140 meV above $E_F$. More importantly, we find that certain scatterers can introduce energy-dependent non-preservation of pseudospins, giving rise to effective scattering between states with opposite valley pseudospin deep inside valence and conduction bands. Further investigations of quasiparticle interference at the atomic level will aid defect engineering at the synthesis level, needed for the development of lower-power electronics via dissipationless electronic transport in the future.

We have investigated spin reorientation phenomena and interaction driven effects under the presence of applied strains on the (001) surface of Pb$_{1-x}$Sn$_x$(Te, Se) topological crystalline insulators, which host multiple Dirac cones. Our analysis is based on a four-band $k\cdot p$ model, which captures the spin and orbital textures of the surface states at low energies around the $\bar{X}$ and $\bar{Y}$ points, including the Lifshitz transition. Even without breaking the time-reversal symmetry, we find that certain strains which break the mirror symmetry can induce hedgehog-like spin texture associated with gap formation at the Dirac points. The Chern number of the gapped surface ground state is shown to be tunable through the interplay of strains and a perpendicular Zeeman field. We also consider effects of strain in the presence of interactions in driving competing orders, and obtain the associated phase diagram at the mean-field level. Potential applications of our results for low power consuming electronics are discussed., Comment: 11 pages, 9 figures, and two tables

In a topological insulator, it is the electrons on the surface or edge that carry the signature of topology. Recently, a novel topological state has been proposed in metals or semimetals (gapless) whose band-structure is similar to that of a three-dimensional analog of graphene. However, to this date the signature of its topology remains an open question. We report the experimental discovery of a pair of polarized Fermi arc surface state modes in the form of a new type of two-dimensional polarized electron gas on the surfaces of Dirac semimetals. These Fermi arc surface states (FASS) are observed to connect across an even number of bulk band gapless nodes and found to have their spin uniquely locked to their momentum. We show that these states are distinctly different from the topological surface states (TSS) seen in all known topological insulators. Our observed exotic two-dimensional states not only uncover the novel topology of gapless Dirac metals (such as sodium tribismuth Na$_3$Bi) but also opens new research frontiers for the utilization of topological Fermi arc electron gases for a wide range of fundamental physics and spintronic studies., Comment: ScienceExpress (2014) adv.online, 18-Dec-2014; Related papers on the discovery of topological Fermi arcs and Weyl Semimetals (WSMs) are at http://physics.princeton.edu/zahidhasangroup/index_Lists.html