Session H35: Topological Insulators: General

Topological Insulators as Substrates for CO Oxidation Catalysis by Ultrathin Au Films

We propose a novel application of three dimensional topological insulators (3DTIs) in heterogeneous catalysis based on first- principles calculations within density functional theory. We use a Bi$_2$Se$_3$ substrate as the support of an ultrathin Au film, and show that the Au adatoms are strongly bound to and able to wet the surface of Bi$_2$Se$_3$. More importantly, we find the topological surface states of Bi$_2$Se$_3$ are robust against Au deposition, and it can enhance the interaction between Au and CO, O$_2$ molecules by acting as an $``$electron bath$"$. The present study may broaden the potential technological applications of 3DTIs, and shine some new light on the understanding of the role of surface states in heterogeneous catalysis.   

Topological insulators on the ruby lattice

We study a tight-binding model on the two-dimensional ruby lattice. This lattice supports two types of second neighbor spin-dependent hopping parameters in an s-band model that preserves time-reversal symmetry. We discuss the phase diagram of this model for various values of the hopping parameters, and note an interesting interplay between the two spin-orbit terms that individually would drive the system to a Z2 topological insulating phase. The fidelity of each phase is also calculated.   

Extension of the Kitaev model on the square lattice

We study an extension of the Kitaev model [1] on the square lattice, where two types of Gamma matrices on neighboring sites have interaction that respects time reversal symmetry. A family of Kitaev models can be classified as the topological insulator/superconductor when described by Majorana fermions [2]. Our model is in class DIII in Altland-Zirnbauer classification, and thus a Z$_{2}$ invariant characterizes two distinct phases. There appear helical Majorana edge modes in the topological phase. The same model on the one-dimensional ladder is also studied. \\[4pt] [1] A. Kitaev, Annals of Physics 321, 2 (2006).\\[0pt] [2] S. Ryu, Phys. Rev. B 79, 075124 (2009).   

Electrical manipulation and measurement of spin properties of quantum spin Hall edge states

The existence of the quantum spin Hall state has been confirmed in a series of experiments performed in HgTe quantum wells but a quantitative observation of the helical edge structure is still lacking. We study an electrical manipulation and measurement of helicity properties of the edge states by employing the Rashba spin-orbit interaction (SOI). Specifically, we show that a spatially uniform Rashba SOI, controllable by the gate voltage, can be utilized in tuning the spin orientation of the edge modes (J. I. V\"ayrynen and T. Ojanen, arXiv:1010.1353). We introduce a point-contact geometry where helicity of the edge modes can be accessed by two- terminal conductance measurements.   

Electronic Transport in Exfoliated Bismuth Selenide

Recent theoretical and experimental work has identified bismuth selenide as a promising candidate for studies of three-dimensional topological insulators due to its large bulk semiconducting gap crossed by topological Dirac surface states. We report on the fabrication and measurement of mesoscale exfoliated bismuth selenide devices, including the effects of electric-field-effect gating and magnetic field on transport and possible signatures of topological states. We will also discuss fabrication strategies to mitigate surface disorder and doping   

Approaching the insulating state in Ca-doped Bi$_{2}$Se$_{3}$ nanodevices

We report a systematic tuning of the carrier density in Ca-doped Bi$_{2}$Se$_{3}$ nanodevices. A clear transition from the metallic to insulating state is observed as both the Ca-concentration and the gate voltage are tuned. At high temperatures, the devices behave metallic as indicated by the linear temperature dependence of the electrical resistivity as the devices are initially cooled. As the temperature is lowered, the resistivity shows a minimum then increases. This insulating behavior can be modeled by a thermal activated conductivity, which is taken over by saturation at the lowest temperatures. At 1.5 K, the resistivity undergoes a $\sim $5-fold increase as a gate voltage is swept from -60 V to 60 V. The field-effect mobility is found to be about $\sim $ 5000 cm2/Vs. We have also observed a systematic evolution of the magnetoresistance as the chemical potential is tuned via the gate voltage. The combination of the chemical and electronic dopings provides an effective way to access the low carrier density gap states in Bi2Se3 topological insulator nanodevices. This work was supported in part by DOE and NSF.   

Topological Response Theory of Doped Topological Insulators

We generalize the topological response theory of three-dimensional topological insulators (TI) to metallic systems -- specifically, doped TI with finite bulk carrier density and a time-reversal symmetry breaking field near the surface. We show that there is an inhomogeneity-induced Berry phase contribution to the surface Hall conductivity that is completely determined by the occupied states and is independent of other details such as band dispersion and impurities. In the limit of zero bulk carrier density, this intrinsic surface Hall conductivity reduces to the half-integer quantized surface Hall conductivity of TI. Our theory is directly related to the TI materials currently under experimental investigation, which have finite residual bulk carrier densities.   

Topological states in one dimensional solids and photonic crystals

We show that the band structure of a one-dimensional solid with particle-hole symmetry may be characterized by a topological index that owes its existence to the non-trivial homotopy of the space of non-degenerate real symmetric matrices. Moreover we explicitly demonstrate a theorem linking the topological index to the existence of bound states on the surface of a semi-infinite one dimensional solid. Our analysis is a one-dimensional analogue of the analysis of topological insulators in two and three dimensions by Balents and Moore; our results may be relevant to long molecules that are the one dimensional analogue of topological insulators. We propose the realization of this physics in a one-dimensional photonic crystal. In this case the topology of the bandstructure reveals itself not as a bound surface state but as a Lorentzian feature in the time delay of light that is otherwise perfectly reflected by the photonic crystal.   

Robustness of topologically protected surface states in layering of Bi$_2$Te$_3$ thin films

Recently, topological insulators with time-reversal symmetry have drawn great attention due to their topologically protected states. Topological insulators differ from band insulators in that a bulk energy gap opens up due to strong spin-orbit coupling and that metallic surface states reside in the energy gap. The surface states of topological insulators are topologically protected in that impurities preserving time-reversal symmetry neither destroy the surface states nor impact the topological nature of the surface states. Recently, bulk bismuth-based alloys were shown to be topological insulators. Thin films offer valuable probes of topological insulators as well as device applications. Additionally, bismuth-based thin films of a thickness of a few nanometers were fabricated on substrates or suspended across trenches. We investigate surface states of Bi$_2$Te$_3$(111) thin films of one to six quintuple layers using density-functional theory including spin-orbit coupling. We construct a method to identify topologically protected surface states of thin film topological insulators. Applying this method to Bi$_2$Te$_3$ thin films, we examine the topological nature of the surface states as a function of the film thickness and compare our results with experimental data and other theoretical reports.   

Spin and Charge Transport on the Surface of a Topological Insulator

We derive diffusion equations, which describe spin-charge coupled transport on the helical metal surface of a three-dimensional topological insulator. The main feature of these equations is a large magnitude of the spin-charge coupling, which leads to interesting and observable effects. In particular, we predict a new magnetoresistance effect, which manifests in a nonohmic correction to a voltage drop between a ferromagnetic spin-polarized electrode and a nonmagnetic electrode, placed on top of the helical metal. This correction is proportional to the cross-product of the spin polarization of the ferromagnetic electrode and the charge current between the two electrodes. We also demonstrate tunability of this effect by applying a gate voltage, which makes it possible to operate the proposed device as a transistor.   

Spin and Charge Transport in Thin Films of Topological Insulators

We develop a theory of spin-charge coupled transport in thin films of topological insulator materials, when the top and bottom surfaces of the sample hybridize. We find significant differences from the case of transport on unhybridized surfaces. In particular, we find significant reduction of the spin relaxation rates, which enhances all the spin-related transport effects, compared to the case of a single surface. We also find that the out-of-plane component of the spin, which is absent from the hydrodynamic transport equations in the single surface case, reappears when the surfaces are hybridized.   

Conductance of a helical edge liquid coupled to a magnetic impurity

In a quantum spin Hall system, which can be realized in HeTe/(Hg,Cd)Te semiconductor quantum wells [1], helical edge states carry a current and the conductance takes the universal value of $2e^2/h$. This is because an impurity without internal degrees of freedom cannot backscatter an electron at the edge in the presence of time-reversal symmetry [2]. On the other hand, backscattering by a magnetic impurity is allowed. We study the effect of backscattering from a magnetic impurity on the conductance of a quantum spin Hall system [3], and obtain the correction $\delta G(\omega)$ to the electrical conductance as a function of frequency $\omega$. We find that the correction $\delta G(\omega)$ vanishes in the dc limit ($\omega \to 0$), when our model conserves the total spin $S_z$. Another interesting transport property is the thermal conductance, which is affected by the coupling to the magnetic impurity even at $\omega\to 0$. We find that the temperature dependence of the thermal conductance shows a non-monotonic behavior with a minimum occurring at the Kondo temperature. \\[4pt] [1] M. Konig {\it et al.}, Science 318, 766 (2007). \\[0pt] [2] C. Wu, B. A. Bernevig and S. C. Zhang, Phys. Rev. Lett. 96, 106401 (2006); C. Xu and J. E. Moore, Phys. Rev. B 73, 045322 (2006). \\[0pt] [3] J. Maciejko {\it et al.}, Phys. Rev. Lett. 102, 256803 (2009).   

Design Principles and Coupling Mechanisms in the 2D Quantum-Well Topological Insulator HgTe/CdTe

We present atomistic band structure calculations revealing a different mechanism than recently surmised via {$\bf k\cdot p$} calculations about the evolution of the topological state (TS) in HgTe/CdTe. We show that {\it 2D interface} (not {\it 1D edge}) TS are possible. We find that the transitions from a topological insulator at critical HgTe thickness of $n= 23$ ML (62.5 {\AA}) to a normal insulator at smaller $n$ is due to the crossing between two interface localized states: one derived from the S-like $\Gamma_{6c}$ and one derived from the P-like $\Gamma_{8v}$ light-hole, not because of the crossing of an interface state and an extended QW state. These atomistic calculations suggest that a 2D TS can exist in a 2D system, even without truncating its symmetry to 1D, thus explaining the otherwise surprising similarity between the 2D dispersion curves of the TS in HgTe/CdTe with those of the TS in 3D bulk materials such as Bi$_2$Se$_3$. Ref: J.W. Luo and A. Zunger, Phys. Rev. Lett. {\bf 105}, 176805 (2010).   

Towards Quantum Spin Hall Effect in InAs/GaSb Quantum Wells

Recently, it has been proposed that inverted InAs/GaSb composite quantum wells (CQWs) should exhibit the Quantum Spin Hall Effect (QSHE), characterized by the energy gap in the bulk and gapless edge modes which are protected from backscattering by time reversal symmetry. We have successfully fabricated a double-gated device on high-quality MBE-grown InAs/GaAs CQWs in the inverted regime, in which we were able to vary the band structure via an electrical field, and tune the Fermi level into mini-gap regime. We observed clear evidence for an energy gap in the inverted regime, with values of the gap consistent with those theoretically predicted; however, the mini-gap exhibits residual conductivity of non-trivial origin, which complicates transport investigation of proposed edge channels. We note that the InAs surface states around the sample edges may play a role in the observed resistivity features. In ongoing work, we pursue Cooper pair injection experiments by proximity to an s-wave superconductor, which should provide a novel probe of the proposed helical edge modes. We will discuss our progress towards observing QSHE in this unique material system. The work at Rice was supported by grants from NSF, Keck Foundation, and Hackerman Advanced Research Program.