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For electrons living on a triangular lattice, the concept of "geometrical frustration" in the face of strong electric mutual repulsion is a crucial, decisive factor that shapes their behavior. In an insulating material, the coulomb repulsion force is relieved if each electron can point its spin anti-parallel to that of its nearest neighbors. On most lattices, this is readily implemented and leads to a state in which spins alternate up and down along each bond direction. On a triangular lattice, however, the geometric arrangement frustrates such ideal regularity.

In a Dirac semimetal, each Dirac node is resolved into two Weyl nodes with opposite "handedness" or chirality. The two chiral populations do not mix. However, in parallel electric and magnetic fields (E||B), charge is predicted to flow between the Weyl nodes, leading to negative magnetoresistance. This "axial" current is the chiral (Adler-Bell-Jackiw) anomaly investigated in quantum field theory. We report the observation of a large, negative longitudinal magnetoresistance in the Dirac semimetal Na3Bi. The negative magnetoresistance is acutely sensitive to deviations of the direction of B from E and is incompatible with conventional transport. By rotating E (as well as B), we show that it is consistent with the prediction of the chiral anomaly. [ABSTRACT FROM AUTHOR]

The recently discovered three-dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice, driving the system through a topological quantum phase transition. By directly measuring the topological quantum numbers and invariants, we report the observation of a phase transition in a tunable spin-orbit system, BiTL(S1-δSeδ)2, in which the topological state formation is visualized. In the topological state, vortex-like polarization states are observed to exhibit three-dimensional vectorial textures, which collectively feature a chirality transition as the spin momentum-locked electrons on the surface go through the zero carrier density point. Such phase transition and texture inversion can be the physical basis for observing fractional charge (±e/2) and other fractional topological phenomena. [ABSTRACT FROM AUTHOR]

Topological insulators are insulating materials that display massless, Dirac-like surface states in which the electrons have only one spin degree of freedom on each surface. These states have been imaged by photoemission, but little information on their transport parameters, for example, mobility, is available. We report the observation of Shubnikov-de Haas oscillations arising from the surface states in nonmetallic crystals of Bi2Te3. In addition, we uncovered a Hall anomaly in weak fields, which enables the surface current to be seen directly. Both experiments yield a surface mobility (9000 to 10,000 centimeter²per volt-second) that is substantially higher than in the bulk. The Fermi velocity of 4 x 105 meters per second obtained from these transport experiments agrees with angle-resolved photoemission experiments. [ABSTRACT FROM AUTHOR]

The Dirac Hamiltonian, which successfully describes relativistic fermions, applies equally well to electrons in solids with Linear energy dispersion, for example, in bismuth and graphene. A characteristic of these materials is that a magnetic field less than 10 tesla suffices to force the Dirac electrons into the lowest Landau Level, with resultant strong enhancement of the Coulomb interaction energy. Moreover, the Dirac electrons usually come with multiple favors or valley degeneracy. These ingredients favor transitions to a collective state with novel quantum properties in Large field. By using torque magnetometry, we have investigated the magnetization of bismuth to fields of 31 tesla. We report the observation of sharp field-induced phase transitions into a state with striking magnetic anisotropy, consistent with the breaking of the threefold valley degeneracy. [ABSTRACT FROM AUTHOR]

In a ferromagnet, an applied electric field E invariably produces an anomalous Hall current J[subH] that flows perpendicular to the plane defined by E and M (the magnetization). For decades, the question of whether J[subH] is dissipationless (independent of the scattering rate) has been debated without experimental resolution. In the ferromagnetic spinel CuCr[sub2]Se[sub4-x]Br[subx], the resistivity ρ (at low temperature) may be increased by several decades by varying x (Br) without degrading M. We show that J[subH]/E (normalized per carrier, at 5 kelvin) remains unchanged throughout. In addition to confirming the dissipationless nature of J[subH], our finding has implications for the generation and study of spin-Hall currents in bulk samples. [ABSTRACT FROM AUTHOR]