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      Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels

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          Abstract

          Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work we study the effect of a space dependent Weyl node separation, which we interpret as an emergent background axial vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or non-uniform magnetization and can also be engineered in cold-atomic systems. Using a semiclassical approach we show that the resulting axial magnetic field \(\mathbf{B}_{5}\) is observable through an enhancement of the conductivity as \(\sigma\sim \mathbf{B}_{5} ^{2}\) due to an underlying chiral pseudo magnetic effect. We then use two lattice models to analyze the effect of \(\mathbf{B}_5\) on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau level structure for different spatial profiles of \(\mathbf{B}_5\), revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as \(n=0\) pseudo-Landau levels resulting from a \(\mathbf{B}_5\) confined to the surface (ii) as a consequence of position-momentum locking a bulk \(\mathbf{B}_5\) creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces and (iii) there are equilibrium bound currents proportional to \(\mathbf{B}_{5}\) that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

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          Experimental realisation of the topological Haldane model

          The Haldane model on the honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band-structure, rather than being caused by an external magnetic field. Although an implementation in a material was considered unlikely, it has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors. Here we report on the experimental realisation of the Haldane model and the characterisation of its topological band-structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The model is based on breaking time-reversal symmetry as well as inversion symmetry. The former is achieved through the introduction of complex next-nearest-neighbour tunnelling terms, which we induce through circular modulation of the lattice position. For the latter, we create an energy offset between neighbouring sites. Breaking either of these symmetries opens a gap in the band-structure, which is probed using momentum-resolved interband transitions. We explore the resulting Berry-curvatures of the lowest band by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between both broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally and compare it to calculations using Floquet theory without free parameters. We verify that our approach, which allows for dynamically tuning topological properties, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realise spin-dependent topological Hamiltonians.
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            Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi

            Three-dimensional (3D) topological Dirac semimetals (TDSs) represent a novel state of quantum matter that can be viewed as '3D graphene'. In contrast to two-dimensional (2D) Dirac fermions in graphene or on the surface of 3D topological insulators, TDSs possess 3D Dirac fermions in the bulk. The TDS is also an important boundary state mediating numerous novel quantum states, such as topological insulators, Weyl semi-metals, Axion insulators and topological superconductors. By investigating the electronic structure of Na3Bi with angle resolved photoemission spectroscopy, we discovered 3D Dirac fermions with linear dispersions along all momentum directions for the first time. Furthermore, we demonstrated that the 3D Dirac fermions in Na3Bi were protected by the bulk crystal symmetry. Our results establish that Na3Bi is the first model system of 3D TDSs, which can also serve as an ideal platform for the systematic study of quantum phase transitions between rich novel topological quantum states.
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              Experimental discovery of Weyl semimetal TaAs

              , , (2015)
              Weyl semimetals are a class of materials that can be regarded as three-dimensional analogs of graphene breaking time reversal or inversion symmetry. Electrons in a Weyl semimetal behave as Weyl fermions, which have many exotic properties, such as chiral anomaly and magnetic monopoles in the crystal momentum space. The surface state of a Weyl semimetal displays pairs of entangled Fermi arcs at two opposite surfaces. However, the existence of Weyl semimetals has not yet been proved experimentally. Here we report the experimental realization of a Weyl semimetal in TaAs by observing Fermi arcs formed by its surface states using angle-resolved photoemission spectroscopy. Our first-principles calculations, matching remarkably well with the experimental results, further confirm that TaAs is a Weyl semimetal.
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                Author and article information

                Journal
                2016-07-14
                2016-07-21
                Article
                1607.04268
                a919c356-fb56-4dcf-93ab-0c156e4e297a

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                updated version with new references and additions, 19 pages, 8 figures. Typo in last author's name corrected
                cond-mat.mes-hall

                Nanophysics
                Nanophysics

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