We report electrical conductance measurements of Bi nanocontacts created by repeated tip-surface indentation using a scanning tunneling microscope at temperatures of 4 K and 300 K. As a function of the elongation of the nanocontact we measure robust, tens of nanometers long plateaus of conductance G0 = 2e2 /h at room temperature. This observation can be accounted for by the mechanical exfoliation of a Bi(111) bilayer, a predicted QSH insulator, in the retracing process following a tipsurface contact. The formation of the bilayer is further supported by the additional observation of conductance steps below G0 before break-up at both temperatures. Our finding provides the first experimental evidence of the possibility of mechanical exfoliation of Bi bilayers, of the existence of the QSH phase in a two-dimensional crystal, and, most importantly, of the observation of the QSH phase at room temperature.Topological insulators present a gap in the bulk, but host surface states protected against backscattering by time reversal symmetry [1]. This implies that they are immune to non-magnetic disorder-induced localization, i.e., they are able to carry electrical current on the surface regardless of imperfections. 2D TIs[2], actually predicted before their three-dimensional (3D) counterparts [3], are expected to exhibit the so-called quantum spin Hall (QSH) phase, a spin filtered version of the integer quantum Hall effect [4]. While the most exotic experimental manifestation of this phase is through a nearly universal spin Hall conductivity of ≈ e/2π, a truly universal charge transport is expected to manifest, e.g., as a two-terminal conductance G 0 = 2e 2 /h.To date, two types of 2D systems have been predicted to be QSH insulators: two-dimensional crystals such as graphene [2] or Bi(111) bilayers [5] and semiconductor heterojunctions such as CdTe/HgTe[6] or, more recently, InAs/GaSb quantum wells [7]. Transport measurements in CdTe/HgTe [6] and InAs/GaSb[8] quantum wells have revealed the presence of protected edge states and provided the first experimental evidence of the QSH phase to date. The QSH state in 2D crystals, on the other hand, has not been experimentally confirmed to date. The fact that spin-orbit coupling (SOC) in graphene is so weak precludes the observation of the QSH phase in this material. Bismuth, on the contrary, presents a naturally large SOC, its mechanical and electronic properties are well characterized for bulk and surface [9], in nanowire form [10], and, recently, the existence of edge states in Bi(111) bilayers has been reported [11]. Other proposals stay, at this moment, at a more speculative level [12].Cleavage techniques are becoming common in the quest for 2D crystals [13]. With a few exceptions [14], they remain largely unexplored in the field of topological in- sulators (TI's). We report here, using scanning tunneling microscope (STM) based mechanical and electrical characterization techniques, the first evidence of the QSH phase in a two-dimensional crystal such as an exfoliated Bi(111) bi...

The degeneracies in the spinor bandstructure of bcc Fe are studied from first principles. We find numerous isolated band touchings carrying chiral charges of magnitude one (Weyl points) or two (double-Weyl nodes), as well as nonchiral degeneracy loops (nodal rings). Some degeneracies are located on symmetry lines or planes in the Brillouin zone and others at generic low-symmetry points, realizing all possible scenarios consistent with the magnetic point group. We clarify the general theory relating the chiral band touchings to the Chern numbers of the Fermi sheets enclosing them, and use this approach to determine the Chern numbers on the Fermi surface of bcc Fe. Although most Fermi sheets enclose Weyl nodes, in almost all cases the net enclosed charge vanishes for symmetry reasons, resulting in a vanishing Chern number. The exceptions are two inversionsymmetric electron pockets along the symmetry line ∆ parallel to the magnetization. Each of them surrounds a single Weyl point, leading to Chern numbers of ±1. These small topological pockets contribute a sizable amount to the nonquantized part of the intrinsic anomalous Hall conductivity, proportional to their reciprocal-space separation. Variation of the Fermi level (or other system parameters) may lead to a touching event between Fermi sheets, accompanied by a transfer of Chern number between them.

We propose an intrinsic spin scattering mechanism in graphene originated by the interplay of atomic spinorbit interaction and the local curvature induced by flexural distortions of the atomic lattice. Starting from a multiorbital tight-binding Hamiltonian with spin-orbit coupling considered nonperturbatively, we derive an effective Hamiltonian for the spin scattering of the Dirac electrons due to flexural distortions. We compute the spin lifetime due to both flexural phonons and ripples and we find values in the microsecond range at room temperature. Interestingly, this mechanism is anisotropic on two counts. First, the relaxation rate is different for off-plane and in-plane spin quantization axis. Second, the spin relaxation rate depends on the angle formed by the crystal momentum with the carbon-carbon bond. In addition, the spin lifetime is also valley dependent. The proposed mechanism sets an upper limit for spin lifetimes in graphene and will be relevant when samples of high quality can be fabricated free of extrinsic sources of spin relaxation.