Session Q38: Topological Insulators: Theory and Experiment

Three Dimensional Topological Insulators on the Half-Heusler Lattice

Using both tight-binding model and first-principles density functional theory, it is shown that a class of materials in the half-Heusler structure are topological insulators. Specifically, the Z2 topological index is evaluated based on the bulk magnetoelectric polarizability calculation and the surface-band structure is also obtained explicitly. We find there is a metal to topological insulator phase transition upon the application of pressure.   

Band Topology of Insulators via Entanglement Spectrum

The entanglement spectrum has been proposed as a ground state property that captures characteristic edge excitations. Here we study the entanglement spectrum of topological insulators. We first show that insulators with topological surface states will necessarily also have protected modes in the entanglement spectrum. However, surprisingly, the converse is not true. Protected entanglement modes can also appear for insulators without physical surface states, in which case they capture a more elusive topological property. This occurs in insulators with only inversion symmetry. The entanglement spectrum remains gapless, because inversion acts in a counterintuitive way on the entanglement states. A many-body characterization of the topological phase via the entanglement spectrum is helpful for understanding the interacting case.   

Persistent current and $\varphi$-junction induced by Topological Insulator

We predict the persistent current and the anomalous current-phase relation of the Josephson current in the superconductor/two dimensional Topological Insulator/superconductor (S/TI/S) junction. Both of these two effects originate from breaking the Fermion doubling. We find that the exchange field can induce a persistent current in the edge of the topological insulator which usually only happen as the flux effect. The persistent current is linearly dependent on the exchange field. On the other hand, in a S/TI/S junction, the phase shift $\varphi$ is controlled linearly by either an exchange field or a magnetic field which are perpendicular to the surface of the two-dimensional topological insulator. An experiment based on the radio-frequency (rf) method is proposed to realize our theory.   

Topological insulators in the presence of interactions

We study the behavior of topological insulators in the presence of interactions. As a paradigm, we consider the Haldane model subject to a standard Hubbard onsite term. The Haldane model consists of a nearest neighbor tight binding model on a honeycomb lattice plus second neighbor hopping accounting for intrinsic spin-orbit interaction. For strong interactions, the system develops a Mott gap and we derive an effective spin model by including the intrinsic spin-orbit interaction. In the weak-coupling limit, we thoroughly investigate the competition between the Dirac liquid phase and the topological insulator phase which is favored by the Haldane term. The stability of the topological insulator phase in the presence of the Hubbard term is discussed.   

Topological Kondo Insulators

We explore the possibility for the Ce-based topological Kondo insulators. Kondo insulators are specific type of materials where Kondo lattice effect andleads to a formation of a band insulator. We describe the insulating phase within the large-N mean field approximation for the Kondo lattice model and classify the possible topological insulating states with respect to the symmetry of the lowest lying Kramers doublet of the cerium ion. We discuss possible experimental implications of our theory for the Ce-based Kondo insulators CeNiSn and CeRhSb.   

Electrical transport study of Bi$_{2}$Se$_{3}$ and Bi$_{1-x}$Sb$_{x}$ crystals

Bi$_{2}$Se$_{3}$ and Bi$_{1-x}$Sb$_{x}$ are predicted and recently confirmed by ARPES experiments to be 3D topological insulators. We have successfully grown Bi$_{2}$Se$_{3}$ and Bi$_{1-x}$Sb$_{x}$ single crystals using a two-step melting method. Both X-ray diffraction (XRD) and electron back-scatter diffraction (EBSD) show excellent structural quality of the crystals on the micro- and macro-scales. The undoped Bi$_{2}$Se$_{3}$ is metallic, but Bi$_{1-x}$Sb$_{x}$ is insulating for x=0.09 and 0.10. We have also fabricated devices with a wide range of thicknesses and measured the electrical transport properties. The longitudinal resistance R$_{xx}$ and Hall resistance R$_{xy}$ measurements are conducted from 1.5K to room temperature in a magnetic field up to 8 Tesla. The sample thickness dependence of the 2D carrier density indicates that there is a large surface carrier density contributing to the transport properties. The devices are then exposed to several dilute gases (e.g. H2, Cl2, etc.), and the effect of the chemical treatment is studied by comparing to the transport properties measured before the gas exposure. We will discuss the correlation between the surface carrier density and the chemical treatment.   

Tuning the Fermi Level in the Topological Insulator Bi$_{2}$Se$_{3}$ by Gate Voltage

We have fabricated field-effect devices using cleaved, few-monolayer Bi$_{2}$Se$_{3}$ for electrical transport measurements. By varying the applied gate potential $V_{G}$, we can shift the chemical potential $\mu$ through the bulk electronic bands. In as-grown crystals $\mu$ is pinned to the bulk conduction band due to carriers donated by Se vacancies. In these crystals the density of electrons can be varied continuously with $V_{G}$ and mobilities ~ 2000 cm$^{2}$ / Vs realized. In crystals chemically doped with Ca to suppress the density from the remnant bulk electron pocket, we can tune $\mu$ below the conduction band edge. From the behavior of the resistance and Hall resistivity vs. $V_{G}$, we show that we can access states inside the energy gap. A finite conductance is observed for all $V_{G}$ consistent with conducting surface states or impurity bands in the bulk band gap. Transport measurements are performed down to $T$ = 0.3 K and up to magnetic field $H$ = 14 T. We measure the Hall resistivity to extract the carrier density $n_{Hall}$ and observe suppression of conductance $\sigma_{xx}$ in large $H$.   

Unusual Linear Magnetoresistance in Non-Metallic Topological Insulator Bi$_{2}$Te$_{3}$

ARPES experiments have shown that, in both Be$_{2}$Se$_{3}$ and Bi$_{2}$Te$_{3}$, the energy gap is crossed by a single surface state (SS) with Dirac-like dispersion [1,2]. Spin-resolved ARPES [1] shows that the spin of the SS has a Rashba-like coupling, consistent with the identification of these materials as topological insulators. To explore the surface-state transport properties in Bi$_{2}$Te$_{3}$, we have examined in detail the low-temperature ($T)$ transport properties in crystals with non-metallic \textit{$\rho $} vs. $T$ profiles. At 0.3 K, we observe an unusual $H$-linear magnetoresistance (MR) that extends in field $H$ from 0.05 T to 14 T. The $H$-linear dependence is observed with \textbf{H} $\vert \vert $ \textbf{c} and \textbf{H} in-plane. We discuss a scenario in which the $H$-linear MR arises from the effect of \textbf{H} on the spins of the carriers in the topological SS. We also discuss a comparison with $H$-linear MR in Bi$_{1-x}$Sb$_{x}$. \\[4pt] [1] Y. Xia \textit{et al}., Nat. Phys. \textbf{5}, 398 (2009). \\[0pt] [2] Y. L. Chen \textit{et al}., Science, \textbf{325}, 178 (2009).   

Doping effects in Bi$_{2}$Se$_{3}$ and Bi$_{2}$Te$_{3}$ topological insulators

Topological insulators are found to have a bulk electronic gap and a gapless surface state. The surface state has been observed in Bi$_{2}$Se$_{3}$ and Bi$_{2}$Te$_{3}$ by ARPES and STM, but is still considered a challenging problem for transport measurements due to the dominant bulk conductance. By chemical doping, the Fermi level can be tuned to fall inside the band gap\footnote{Hor \textit{et al.} PRB \textbf{79} 195208 (09)} and therefore suppress the bulk conductivity. Non-metallic conducting Bi$_{2}$Se$_{3}$ crystals are obtained. Previously unobserved $p$-type behavior has been induced\footnote{Ibid.} and a novel magnetofingerprint signal\footnote{Checkelsky \textit{et al.} arXiv:0909.1840} is seen through low level Ca-doping in Bi$_{2}$Se$_{3}$. Bi$_{2}$Se$_{3}$ can also be tuned to a bulk superconductor, with $T_{c}\sim $3.8 K, by Cu-intercalation in the van der Waals gaps.\footnote{Hor \textit{et al}. arXiv:0909.2890.} This shows that Cooper pairing is possible in Bi$_{2}$Se$_{3}$ with implications for Majorana fermion physics study and potential quantum computing devices. Mn-doped Bi$_{2}$Te$_{3}$ has ferromagnetic transition at $\sim $15 K, suggesting a possible magnetic topological insulator.   

The Large-Gap Topological Insulator Class Bi$_2$Se$_3$ with a Single Dirac Cone on the Surface

According to recent theories and experiments, strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can exhibit macroscopic entanglement effects. It has been suggested that a topological insulator with a single spin-textured Dirac cone interfaced with a superconductor can form the most elementary unit for performing fault-tolerant quantum computation. Here we present an angle-resolved photoemission spectroscopy study and first- principle theoretical calculation which reveal Bi$_2$Se$_3$ as the first observation of such a topological state of matter featuring a single surface Dirac cone. Our results, supported by our theoretical predictions and calculations, demonstrate that undoped compound of this class of materials can serve as the parent matrix compound for the long-sought topological device where in-plane surface carrier transport would have a purely quantum topological origin. Furthermore, our study suggests that the undoped compound reached via n-to-p doping should show topological transport phenomena even at room temperature.   

Dynamical Axion Field in Topological Magnetic Insulators

Axions are very light, very weakly interacting particles postulated more than 30 years ago in the context of the Standard Model of particle physics. Their existence could explain the missing dark matter of the universe. However, despite intensive searches, they have yet to be detected. In this work, we show that magnetic fluctuations of topological insulators couple to the electromagnetic fields exactly like the axions, and propose several experiments to detect this dynamical axion field. In particular, we show that the axion coupling enables a nonlinear modulation of the electromagnetic field, leading to attenuated total reflection. We propose a novel optical modulators device based on this principle.   

Exciton Condensation and Charge Fractionalization in a Topological Insulator Film

An odd number of gapless Dirac fermions is guaranteed to exist at a surface of a strong topological insulator such as Bi$_2$Se$_3$ and Bi$_2$Te$_3$. We show that in a thin-film geometry and under external bias, electron-hole pairs that reside in these surface states can condense to form a novel exotic quantum state which we propose to call ``topological exciton condensate'' (TEC). The TEC is similar in general terms to the exciton condensate recently argued to exist in a biased graphene bilayer, but with different topological properties. It exhibits a host of unusual properties including a stable zero mode and a fractional charge $\pm e/2$ carried by a singly quantized vortex in the TEC order parameter.   

Impurity-induced states on the surface of 3D topological insulators

We have investigated the modifications to local electronic structure on the surface of strong topological insulators (3D), due to local impurities and step edges. We find that in the case of a local impurity that is magnetic or non-magnetic in nature, prominent resonances can form near the Dirac point of the surface band. However, we find that the Dirac point itself is left unaffected by both types of impurity. We conjecture that increasing concentrations of local magnetic impurities or a mix of local potential impurities with both attractive and repulsive characters can contribute to opening a gap in the (originally) gapless spectrum of surface states by the gradual depletion of extended states around the Dirac point. We also find that these surface magnetic impurities should interact via an RKKY interaction that is antiferromagnetic in character (sign of the first oscillation; opposite in sign to the usually-obtained ferromagnetic interaction). Finally, we also present a general calculation of scattering at step edges on the surface consistent with the various symmetries and thus deduce the character of LDOS modulation near the step. Ref: Rudro R. Biswas and Alexander V. Balatsky, arXiv:0910.4604, Nov 2009.   

Hybridization of surface states in thin films of topological insulators

Recent theory and experiments have shown that 3D topological insulators have an odd number of Dirac fermions on their surfaces. The single Dirac cone in the simplest case is topologically protected and robust to impurities for a single surface. Here we consider the hybridization of surface states in a thin film due to their proximity, which opens a gap in the surface modes. We construct a low energy effective Hamiltonian in various cases to compute the surface structure. These thin films have recently been synthesized using molecular-beam epitaxy, and we use the effective Hamiltonian to discuss their possible applications.   

Fermion transfer by vortex tunneling

We study a Fabry-Perot interferometer made out of magnetic and superconducting regions on the surface state of a 3D topological insulator. In particular we investigate the possibility of transferring a chiral edge Majorana fermion between two counter-propagating edges by the tunneling of two superconducting vortices across the superconducting region. This process is potentially useful for topological charge measurement.