Bi2Te1.6S1.4 - a Topological Insulator in the Tetradymite Family

We describe the crystal growth, crystal structure, and basic electrical properties of Bi2Te1.6S1.4, which incorporates both S and Te in its Tetradymite quintuple layers in the motif -[Te0.8S0.2]-Bi-S-Bi-[Te0.8S0.2]-. This material differs from other Tetradymites studied as topological insulators due to the increased ionic character that arises from its significant S content. Bi2Te1.6S1.4 forms high quality crystals from the melt and is the S-rich limit of the ternary Bi-Te-S {\gamma}-Tetradymite phase at the melting point. The native material is n-type with a low resistivity; Sb substitution, with adjustment of the Te to S ratio, results in a crossover to p-type and resistive behavior at low temperatures. Angle resolved photoemission study shows that topological surface states are present, with the Dirac point more exposed than it is in Bi2Te3 and similar to that seen in Bi2Te2Se. Single crystal structure determination indicates that the S in the outer chalcogen layers is closer to the Bi than the Te, and therefore that the layers supporting the surface states are corrugated on the atomic scale.Comment: To be published in Physical Review B Rapid Communications 16 douuble spaced pages. 4 figures 1 tabl

Disorder-Induced Multiple Transition involving Z2 Topological Insulator

Effects of disorder on two-dimensional Z2 topological insulator are studied numerically by the transfer matrix method. Based on the scaling analysis, the phase diagram is derived for a model of HgTe quantum well as a function of disorder strength and magnitude of the energy gap. In the presence of sz non-conserving spin-orbit coupling, a finite metallic region is found that partitions the two topologically distinct insulating phases. As disorder increases, a narrow-gap topologically trivial insulator undergoes a series of transitions; first to metal, second to topological insulator, third to metal, and finally back to trivial insulator. We show that this multiple transition is a consequence of two disorder effects; renormalization of the band gap, and Anderson localization. The metallic region found in the scaling analysis corresponds roughly to the region of finite density of states at the Fermi level evaluated in the self-consistent Born approximation.Comment: 5 pages, 5 figure

Quasi-Topological Insulator and Trigonal Warping in Gated Bilayer Silicene

Bilayer silicene has richer physical properties than bilayer graphene due to its buckled structure together with its trigonal symmetric structure. The buckled structure arises from a large ionic radius of silicon, and the trigonal symmetry from a particular way of hopping between two silicenes. It is a topologically trivial insulator since it carries a trivial $\mathbb{Z}_{2}$ topological charge. Nevertheless, its physical properties are more akin to those of a topological insulator than those of a band insulator. Indeed, a bilayer silicene nanoribbon has edge modes which are almost gapless and helical. We may call it a quasi-topological insulator. An important observation is that the band structure is controllable by applying the electric field to a bilayer silicene sheet. We investigate the energy spectrum of bilayer silicene under electric field. Just as monolayer silicene undergoes a phase transition from a topological insulator to a band insulator at a certain electric field, bilayer silicene makes a transition from a quasi-topological insulator to a band insulator beyond a certain critical field. Bilayer silicene is a metal while monolayer silicene is a semimetal at the critical field. Furthermore we find that there are several critical electric fields where the gap closes due to the trigonal warping effect in bilayer silicene.Comment: 8 pages, 11 figures, to be published in J. Phys. Soc. Jp

Topological Insulators

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A 3D topological insulator supports novel spin polarized 2D Dirac fermions on its surface. In this Colloquium article we will review the theoretical foundation for these electronic states and describe recent experiments in which their signatures have been observed. We will describe transport experiments on HgCdTe quantum wells that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. We will then discuss experiments on Bi_{1-x}Sb_x, Bi_2 Se_3, Bi_2 Te_3 and Sb_2 Te_3 that establish these materials as 3D topological insulators and directly probe the topology of their surface states. We will then describe exotic states that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions, and may provide a new venue for realizing proposals for topological quantum computation. We will close by discussing prospects for observing these exotic states, a well as other potential device applications of topological insulators.Comment: 23 pages, 20 figures, Published versio

Magnetic Response in Quantized Spin Hall Phase of Correlated Electrons

We investigate the magnetic response in the quantized spin Hall (SH) phase of layered-honeycomb lattice system with intrinsic spin-orbit coupling lambda_SO and on-site Hubbard U. The response is characterized by a parameter g= 4 U a^2 d / 3, where a and d are the lattice constant and interlayer distance, respectively. When g< (sigma_{xy}^{s2} mu)^{-1}, where sigma_{xy}^{s} is the quantized spin Hall conductivity and mu is the magnetic permeability, the magnetic field inside the sample oscillates spatially. The oscillation vanishes in the non-interacting limit U -> 0. When g > (sigma_{xy}^{s2} mu)^{-1}, the system shows perfect diamagnetism, i.e., the Meissner effect occurs. We find that superlattice structure with large lattice constant is favorable to see these phenomena. We also point out that, as a result of Zeeman coupling, the topologically-protected helical edge states shows weak diamagnetism which is independent of the parameter g.Comment: 7 pages, the final version will be published in J. Phys. Soc. Jp

Valley Spin Sum Rule for Dirac Fermions: Topological Argument

We consider a two-dimensional bipartite lattice system. In such a system, the Bloch band spectrum can have some valley points, around which Dirac fermions appear as the low-energy excitations. Each valley point has a valley spin +1 or -1. In such a system, there are two topological numbers counting vortices and merons in the Brillouin zone, respectively. These numbers are equivalent, and this fact leads to a sum rule which states that the total sum of the valley spins is absent even in a system without time-reversal and parity symmetries. We can see some similarity between the valley spin and chirality in the Nielsen-Ninomiya no-go theorem in odd-spatial dimensions.Comment: 5 pages, 1 figure, some comments are added/revised, accepted for publication in J. Phys. Soc. Jp

Suspension and Measurement of Graphene and Bi2Se3 Atomic Membranes

Coupling high quality, suspended atomic membranes to specialized electrodes enables investigation of many novel phenomena, such as spin or Cooper pair transport in these two dimensional systems. However, many electrode materials are not stable in acids that are used to dissolve underlying substrates. Here we present a versatile and powerful multi-level lithographical technique to suspend atomic membranes, which can be applied to the vast majority of substrate, membrane and electrode materials. Using this technique, we fabricated suspended graphene devices with Al electrodes and mobility of 5500 cm^2/Vs. We also demonstrate, for the first time, fabrication and measurement of a free-standing thin Bi2Se3 membrane, which has low contact resistance to electrodes and a mobility of >~500 cm^2/Vs

Quantum corrections in the Boltzmann conductivity of graphene and their sensitivity to the choice of formalism

Semiclassical spin-coherent kinetic equations can be derived from quantum theory with many different approaches (Liouville equation based approaches, nonequilibrium Green's functions techniques, etc.). The collision integrals turn out to be formally different, but coincide in textbook examples as well as for systems where the spin-orbit coupling is only a small part of the kinetic energy like in related studies on the spin Hall effect. In Dirac cone physics (graphene, surface states of topological insulators like Bi_{1-x}Sb_x, Bi_2Te_3 etc.), where this coupling constitutes the entire kinetic energy, the difference manifests itself in the precise value of the electron-hole coherence originated quantum correction to the Drude conductivity $\sim e^2/h * \ell k_F$. The leading correction is derived analytically for single and multilayer graphene with general scalar impurities. The often neglected principal value terms in the collision integral are important. Neglecting them yields a leading correction of order $(\ell k_F)^{-1}$, whereas including them can give a correction of order $(\ell k_F)^0$. The latter opens up a counterintuitive scenario with finite electron-hole coherent effects at Fermi energies arbitrarily far above the neutrality point regime, for example in the form of a shift $\sim e^2/h$ that only depends on the dielectric constant. This residual conductivity, possibly related to the one observed in recent experiments, depends crucially on the approach and could offer a setting for experimentally singling out one of the candidates. Concerning the different formalisms we notice that the discrepancy between a density matrix approach and a Green's function approach is removed if the Generalized Kadanoff-Baym Ansatz in the latter is replaced by an anti-ordered version.Comment: 31 pages, 1 figure. An important sign error has been rectified in the principal value terms in equation (52) in the vN & NSO expression. It has no implications for the results on the leading quantum correction studied in this paper. However, for the higher quantum corrections studied in arXiv:1304.3929 (see comment in the latter) the implications are crucia

New Family of Robust 2D Topological Insulators in van der Waals Heterostructures

We predict a new family of robust two-dimensional (2D) topological insulators in van der Waals heterostructures comprising graphene and chalcogenides BiTeX (X=Cl, Br and I). The layered structures of both constituent materials produce a naturally smooth interface that is conducive to proximity induced new topological states. First principles calculations reveal intrinsic topologically nontrivial bulk energy gaps as large as 70-80 meV, which can be further enhanced up to 120 meV by compression. The strong spin-orbit coupling in BiTeX has a significant influence on the graphene Dirac states, resulting in the topologically nontrivial band structure, which is confirmed by calculated nontrivial Z2 index and an explicit demonstration of metallic edge states. Such heterostructures offer an unique Dirac transport system that combines the 2D Dirac states from graphene and 1D Dirac edge states from the topological insulator, and it offers new ideas for innovative device designs