Resolving the Topological Classification of Bismuth with Topological Defects

Bulk boundary correspondence in topological materials allows to study their bulk topology through the investigation of their topological boundary modes. However, for classes that share similar boundary phenomenology, the growing diversity of topological phases may lead to ambiguity in the topological classification of materials. Such is the current status of bulk bismuth. While some theoretical models indicate that bismuth possesses a trivial topological nature, other theoretical and experimental studies suggest non-trivial topological classifications such as a strong or a higher order topological insulator, both of which hosts helical modes on their boundaries. Here we use a novel approach to resolve the topological classification of bismuth by spectroscopically mapping the response of its boundary modes to a topological defect in the form of a screw dislocation (SD). We find that the edge mode extends over a wide energy range, and withstands crystallographic irregularities, without showing any signs of backscattering. It seems to bind to the bulk SD, as expected for a topological insulator (TI) with non-vanishing weak indices. We argue that the small scale of the bulk energy gap, at the time reversal symmetric momentum $L$, positions bismuth within the critical region of a topological phase transition to a strong TI with non-vanishing weak indices. We show that the observed boundary modes are approximately helical already on the $\mathbb{Z}_2$ trivial side of the topological phase transition. This work opens the door for further possibilities to examine the response of topological phases to crystallographic topological defects, and to uniquely explore their associated bulk boundary phenomena

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

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

Hot Electrons Regain Coherence in Semiconducting Nanowires

The higher the energy of a particle is above equilibrium the faster it relaxes due to the growing phase-space of available electronic states it can interact with. In the relaxation process phase coherence is lost, thus limiting high energy quantum control and manipulation. In one-dimensional systems high relaxation rates are expected to destabilize electronic quasiparticles. We show here that the decoherence induced by relaxation of hot electrons in one-dimensional semiconducting nanowires evolves non-monotonically with energy such that above a certain threshold hot-electrons regain stability with increasing energy. We directly observe this phenomenon by visualizing for the first time the interference patterns of the quasi-one-dimensional electrons using scanning tunneling microscopy. We visualize both the phase coherence length of the one-dimensional electrons, as well as their phase coherence time, captured by crystallographic Fabry-Perot resonators. A remarkable agreement with a theoretical model reveals that the non-monotonic behavior is driven by the unique manner in which one dimensional hot-electrons interact with the cold electrons occupying the Fermi-sea. This newly discovered relaxation profile suggests a high-energy regime for operating quantum applications that necessitate extended coherence or long thermalization times, and may stabilize electronic quasiparticles in one dimension

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

Interplay between ferromagnetism, surface states, and quantum corrections in a magnetically doped topological insulator

The breaking of time-reversal symmetry by ferromagnetism is predicted to yield profound changes to the electronic surface states of a topological insulator. Here, we report on a concerted set of structural, magnetic, electrical and spectroscopic measurements of \MBS thin films wherein photoemission and x-ray magnetic circular dichroism studies have recently shown surface ferromagnetism in the temperature range 15 K $\leq T \leq 100$ K, accompanied by a suppressed density of surface states at the Dirac point. Secondary ion mass spectroscopy and scanning tunneling microscopy reveal an inhomogeneous distribution of Mn atoms, with a tendency to segregate towards the sample surface. Magnetometry and anisotropic magnetoresistance measurements are insensitive to the high temperature ferromagnetism seen in surface studies, revealing instead a low temperature ferromagnetic phase at $T \lesssim 5$ K. The absence of both a magneto-optical Kerr effect and anomalous Hall effect suggests that this low temperature ferromagnetism is unlikely to be a homogeneous bulk phase but likely originates in nanoscale near-surface regions of the bulk where magnetic atoms segregate during sample growth. Although the samples are not ideal, with both bulk and surface contributions to electron transport, we measure a magnetoconductance whose behavior is qualitatively consistent with predictions that the opening of a gap in the Dirac spectrum drives quantum corrections to the conductance in topological insulators from the symplectic to the orthogonal class.Comment: To appear in Phys. Rev.