Equilibrium First-Order Melting and Second-Order Glass Transitions of the Vortex Matter in Bi2_2Sr2_2CaCu2_2O8_8

The thermodynamic $H-T$ phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_8$ was mapped by measuring local \emph{equilibrium} magnetization $M(H,T)$ in presence of vortex `shaking'. Two equally sharp first-order magnetization steps are revealed in a single temperature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium $M(T)$ slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid at higher fields.Comment: 5 pages, 4 figures. To be published in Phys. Rev. Let

Interplay of Anisotropy and Disorder in the Doping-Dependent Melting and Glass Transitions of Vortices in Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}

We study the oxygen doping dependence of the equilibrium first-order melting and second-order glass transitions of vortices in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Doping affects both anisotropy and disorder. Anisotropy scaling is shown to collapse the melting lines only where thermal fluctuations are dominant. Yet, in the region where disorder breaks that scaling, the glass lines are still collapsed. A quantitative fit to melting and replica symmetry breaking lines of a 2D Ginzburg-Landau model further reveals that disorder amplitude weakens with doping, but to a lesser degree than thermal fluctuations, enhancing the relative role of disorder.Comment: 4 pages, 4 figure

Multiple Changes of Order of the Vortex Melting Transition in BSCCO with Dilute Columnar Defects

A low concentration of columnar defects is reported to transform a first-order vortex lattice melting line in BSCCO crystals into alternating segments of first-order and second-order transitions separated by two critical points. As the density of CDs is increased, the critical points shift apart and the range of the intermediate second-order transition expands. A third, low temperature critical point was also observed in one sample. The measurement of equilibrium magnetization and the mapping of the melting line down to 27K was made possible by employment of the shaking technique.Comment: 5 pages, 3 figure

Termination dependent topological surface states of the natural superlattice phase Bi4_4Se3_3

We describe the topological surface states of Bi$_4$Se$_3$, a compound in the infinitely adaptive Bi$_2$-Bi$_2$Se$_3$ natural superlattice phase series, determined by a combination of experimental and theoretical methods. Two observable cleavage surfaces, terminating at Bi or Se, are characterized by angle resolved photoelectron spectroscopy and scanning tunneling microscopy, and modeled by ab-initio density functional theory calculations. Topological surface states are observed on both surfaces, but with markedly different dispersions and Kramers point energies. Bi$_4$Se$_3$ therefore represents the only known compound with different topological states on differently terminated surfaces.Comment: 5 figures references added Published in PRB: http://link.aps.org/doi/10.1103/PhysRevB.88.08110

Transport Properties of Vortex Matter Governed by the Edge Inductance of Superconducting Bi2_{2}Sr2_{2}CaCu2_{2}O8_{8} Single Crystals

We study the distribution of transport current across superconducting Bi$_2$Sr$_2$CaCu$_2$O$_8$ crystals and the vortex flow through the sample edges. We show that the $T_x$ transition is of electrodynamic rather than thermodynamic nature, below which vortex dynamics is governed by the edge inductance instead of the resistance. This allows measurement of the resistance down to two orders of magnitude below the transport noise. By irradiating the current contacts the resistive step at vortex melting is shown to be due to loss of c-axis correlations rather than breakdown of quasi-long-range order within the a-b planes

Evidence for one-dimensional chiral edge states in a magnetic Weyl semimetal Co₃Sn₂S₂

The physical realization of Chern insulators is of fundamental and practical interest, as they are predicted to host the quantum anomalous Hall (QAH) effect and topologically protected chiral edge states which can carry dissipationless current. Current realizations of the QAH state often require complex heterostructures and sub-Kelvin temperatures, making the discovery of intrinsic, high temperature QAH systems of significant interest. In this work we show that time-reversal symmetry breaking Weyl semimetals, being essentially stacks of Chern insulators with inter-layer coupling, may provide a new platform for the higher temperature realization of robust chiral edge states. We present combined scanning tunneling spectroscopy and theoretical investigations of the magnetic Weyl semimetal, Co3Sn2S2. Using modeling and numerical simulations we find that depending on the strength of the interlayer coupling, chiral edge states can be localized on partially exposed kagome planes on the surfaces of a Weyl semimetal. Correspondingly, our dI/dV maps on the kagome Co3Sn terraces show topological states confined to the edges which display linear dispersion. This work provides a new paradigm for realizing chiral edge modes and provides a pathway for the realization of higher temperature QAH effect in magnetic Weyl systems in the two-dimensional limit. © 2021, The Author(s)

Ripple modulated electronic structure of a 3D topological insulator

3D topological insulators, similar to the Dirac material graphene, host linearly dispersing states with unique properties and a strong potential for applications. A key, missing element in realizing some of the more exotic states in topological insulators is the ability to manipulate local electronic properties. Analogy with graphene suggests a possible avenue via a topographic route by the formation of superlattice structures such as a moir\'e patterns or ripples, which can induce controlled potential variations. However, while the charge and lattice degrees of freedom are intimately coupled in graphene, it is not clear a priori how a physical buckling or ripples might influence the electronic structure of topological insulators. Here we use Fourier transform scanning tunneling spectroscopy to determine the effects of a one-dimensional periodic buckling on the electronic properties of Bi2Te3. By tracking the spatial variations of the scattering vector of the interference patterns as well as features associated with bulk density of states, we show that the buckling creates a periodic potential modulation, which in turn modulates the surface and the bulk states. The strong correlation between the topographic ripples and electronic structure indicates that while doping alone is insufficient to create predetermined potential landscapes, creating ripples provides a path to controlling the potential seen by the Dirac electrons on a local scale. Such rippled features may be engineered by strain in thin films and may find use in future applications of topological insulators.Comment: Nature Communications (accepted

The development of ferromagnetism in the doped topological insulator Bi2-xMnxTe3

The development of ferromagnetism in Mn-doped Bi2Te3 is characterized through measurements on a series of single crystals with different Mn content. Scanning tunneling microscopy analysis shows that the Mn substitutes on the Bi sites, forming compounds of the type Bi2-xMnxTe3, and that the Mn substitutions are randomly distributed, not clustered. Mn doping first gives rise to local magnetic moments with Curie-like behavior, but by the compositions Bi1.96Mn0.04Te3 and Bi1.91Mn0.09Te3 a second order ferromagnetic transition is observed, with Tc ~ 9-12 K. The easy axis of magnetization in the ferromagnetic phase is perpendicular to the Bi2Te3 basal plane. Thermoelectric power and Hall effect measurements show that the Mn-doped Bi2Te3 crystals are p-type. Angle resolved photoemission spectroscopy measurements show that the topological surface states that are present in pristine Bi2Te3 are also present in ferromagnetic Mn-doped Bi2-xMnxTe3, and that the dispersion relations of the surface states are changed in a subtle fashion

One-dimensional Topological Edge States of Bismuth Bilayers

The hallmark of a time-reversal symmetry protected topologically insulating state of matter in two-dimensions (2D) is the existence of chiral edge modes propagating along the perimeter of the system. To date, evidence for such electronic modes has come from experiments on semiconducting heterostructures in the topological phase which showed approximately quantized values of the overall conductance as well as edge-dominated current flow. However, there have not been any spectroscopic measurements to demonstrate the one-dimensional (1D) nature of the edge modes. Among the first systems predicted to be a 2D topological insulator are bilayers of bismuth (Bi) and there have been recent experimental indications of possible topological boundary states at their edges. However, the experiments on such bilayers suffered from irregular structure of their edges or the coupling of the edge states to substrate's bulk states. Here we report scanning tunneling microscopy (STM) experiments which show that a subset of the predicted Bi-bilayers' edge states are decoupled from states of Bi substrate and provide direct spectroscopic evidence of their 1D nature. Moreover, by visualizing the quantum interference of edge mode quasi-particles in confined geometries, we demonstrate their remarkable coherent propagation along the edge with scattering properties that are consistent with strong suppression of backscattering as predicted for the propagating topological edge states.Comment: 15 pages, 5 figures, and supplementary materia