Session R4: Topologocal insulators: Nanostructures and Possible Applications: Transport phenomena

Thermoelectric power factor of topological insulator Bi$_{\mathrm{2-x}}$Sb$_{\mathrm{x}}$Te$_{\mathrm{3-y}}$Se$_{\mathrm{y}}$

Topological insulator (TI) is a new quantum material. The surface states of TIs are protected by time-reversal symmetry which allows charge carrier to propagate on the edge of surface conducting channel without scattering. Bi$_{1.5}$Sb$_{0.5}$Te$_{1.7}$Se$_{1.3}$ is a well-known TI [1] and thermoelectric material because of its promising thermoelectric performances at room temperature. The conversion efficiency of~thermoelectric material is characterized by the dimensionless figure of merit ZT.~Decades of effort were devoted to ZT optimization either through composition alteration or nanostructure fabrication. In this study, the temperature dependence of resistance of bulk (exfoliated specimen with 140 $\mu $m thickness) shows semiconductor behavior (0.04 $\Omega $ cm at 300 K) without saturating regime in lower temperatures. In contrast, its nanoflake counterpart (100-500 nm) [2] shows a transition from semiconductor to metallic behavior near 100 -- 150 K with decreasing temperature and saturation at 10 K. Surface contribution to the total conductance of exfoliated specimens was acquired through Hall effect measurements in the magnetic field ranging from -9 to 9 Tesla. Surface contribution of BSTS samples increases from 3{\%} to 70{\%} as thickness decreases from 140 to 7~$\mu $m. In this work, we report a systematic study of thermoelectric power factor for various thicknesses of BSTS specimens to examine the thermoelectric power factor of their surfaces.\\[4pt] [1] Zhi Ren et al., Phys. Rev. B 84, 165311 (2011).\\[0pt] [2] Bin Xia et al., e-print arXiv1203.2997   

Spin-dependent Peltier effect in 3D topological insulators

The Peltier effect represents the heat carrying capacity of a certain material when current passes through it. When two materials with different Peltier coefficients are placed together, the Peltier effect causes heat to flow either towards or away from the interface between them. This work utilizes the spin-polarized property of 3D topological insulator (TI) surface states to describe the transport of heat through the spin-up and spin-down channels. It has been observed that the spin channels are able to carry heat independently of each other. Spin currents can therefore be employed to supply or extract heat from an interface between materials with spin-dependent Peltier coefficients. The device is composed of a thin film of Bi2Se3 sandwiched between two layers of Bi2Te3. The thin film of Bi2Se3$_{\mathrm{\thinspace }}$serves both as a normal and topological insulator. It is a normal insulator when its surfaces overlap to produce a finite band-gap. Using an external gate, Bi2Se3 film can be again tuned in to a TI. Sufficiently thick Bi2Te3 always retain TI behavior. Spin-dependent Peltier coefficients are obtained and the spin Nernst effect in TIs is shown by controlling the temperature gradient to convert charge current to spin current.   

Surface-to-surface scattering in three-dimensional (3D) topological insulator (TI) thin films

When the thickness of a 3D TI material is reduced below approximately 6nm, hybridization of the opposite surfaces states can result in inter-surface tunneling. Due to the rotational symmetry of the thin film, the k-s locking relation on opposite surfaces also has opposite chirality. Thus, in this inter-surface scattering mechanism, back-scattering is allowed without the flip of the spin. This effect breaks the protection of TI surface states against back-scattering. To~investigate the influence of the inter-surface scattering mechanism, we study different near-elastic scattering mechanisms in the surface state transport using Boltzmann transport equations within the relaxation time approximation. The effect of~screened Coulomb~impurities, low-energy acoustic phonons and surface magnetic~impurities on the TI surface states will be discussed. The response of the inter-surface scattering of TI states to various external stimuli such as a Rashba-like splitting and the orientation of the impurity magnetic moments will also be presented. Using our simulation results, we propose possible experimental methods to modulate the back-scatter protection of TI surface states in thin film TI materials.   

Realization of Negative Capacitance with Topological Insulator Based MOS Capacitor

Negative capacitance is one of way to achieve steep subthreshold slope exceeding its thermal limit in metal-oxide-semiconductor field effect transistor (MOSFET). The common materials under study for negative capacitance are ferroelectric thin films. However, the integration of regular ferroelectric materials (e.g., PZT) into semiconductor based devices is usually difficult due to the high temperature required for crystallization and precise control of oxygen percentage in ferroelectric materials. In this work, we found that negative capacitance can be achieved by introducing a topological insulator interlayer into a conventional MOS capacitor. Three-dimensional topological insulators inherently contain a insulator/semiconductor bulk and a gapless conducting surface. When an electric field is added to topological insulator interlayer, imbalanced charge carriers (electrons and holes) would be generated and then accumulate on either surface of the film, resulting in a temporary residual polarization. As a result, a ferroelectric-like hysteresis and negative capacitance are achieved. We believe this approach will be very attractive to achieve steep subthreshold using negative capacitance.   

Transport measurements of the topological surface states in Bi$_2$Te$_3$ nanoribbon field effect devices

We have grown nanoribbons (NRs) of Bi$_2$Te$_3$, a prototype topological insulator, by CVD and characterized them by TEM, Raman Spectroscopy and EDS. We fabricate backgated field effect devices where the chemical potential can be tuned and ambipolar field effect has been observed. The as-grown NRs are n-type and the 4-terminal resistance (R4p) versus temperature (T) shows a metallic behavior. Applying a sufficiently negative Vg, the R4p vs T displays an insulating behavior that saturates in a plateau at T $<$ 100K, suggesting a metallic surface conduction dominant at low temperatures. Aharonov-Bohm (AB) oscillations of surface conducting carriers are observed in the magneto-resistance (MR) with a magnetic (B) field parallel to the NR axis. We have also measured the Shubnikov de Haas (SdH) oscillations with the B-field perpendicular to the NR axis at different carrier densities (n). The extrapolated Landau level crossing at 1/B = 0 is $\sim$0.5 and the extracted cyclotron mass from the T-dependence of the SdH oscillations is proportional to $\sqrt{n}$, providing direct evidence of the Dirac fermion nature of the topological surface state. Gate-tunable weak anti-localization is observed and the extracted number of decoupled coherent conduction channels is 2 at the charge neutrality point.   

Majorana qubit rotations in microwave cavities

Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states. These oscillations can be used to implement an additional single-qubit gate. Supplemented with one braiding operation, this gate allows to perform arbitrary single-qubit operations.   

Electrical transport studies of Topological Insulator Bi$_{2}$Te$_{3}$ Nanotubes

We have studied electrical transport properties of candidate topological insulator Bismuth Telluride (Bi$_{2}$Te$_{3})$ nanotubes. Bi$_{2}$Te$_{3}$ nanotube samples were synthesized by solution phase method, with the outer diameters in the range of 70$\pm $5 nm and inner diameter 50$\pm $5 nm and the length of 3 to 10 um. Platinum contact leads were fabricated on the nanotubes by focusing ion beam assisted deposition. Electrical transport measurements were conducted at low temperatures and high magnetic fields (up to 9T). The nanotubes showed good insulating behavior in comparison with the thin films which are often metallic. Resistance oscillation as a function of magnetic field was observed when the magnetic field is applied parallel to the nanotubes. The periods range from 6000 Oe to 8350 Oe, which correspond to the diameter of 80 to 100 nm according to Aharonov-Bohm oscillation formula. This is close but slightly larger than the outer diameter of the nanotubes. The amplitude of the oscillations decays rapidly as field increases, possibly due to scattering. When the magnetic field was applied perpendicular to the nanotube, no resistance oscillation was observed. The possible origins of the oscillation effect will be discussed.   

Surface state transport in MBE-grown topological insulator (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_3$ thin films and field effect transistors

Topological insulators feature spin-helical, Dirac fermion surface states, promising potential applications in both nanoelectronics and spintronics. However, experimental identification of a clear transport signal of the surface state conduction is still challenging. Here, we report a systematical study of the gate tunable magneto-transport in MBE grown (Bi$_{1-x}$Sb$_{x})_{2}$Te$_{3}$ (x$=$0.96) thin film on SrTiO$_{3}$ substrate. We observed an ambipolar field effect and a sign change in the Hall resistance as the gate voltage (V$_{g})$ crosses the Dirac point (V$_{D})$. Temperature (T) dependence of the resistance at different V$_{g}$ shows a transition from a metallic to an insulating bulk with 100{\%} surface conduction at low T. Weak antilocalization measurements indicate a $\pi $ Berry phase near V$_{D}$. We also performed spin valve measurements and observed a resistance asymmetry (which reverses with reversing current direction) between the positive and negative in-plane magnetic fields, demonstrating the predicted locking between spin and momentum for the surface state. We also studied the thermal-electric transport, demonstrating a sign change of the thermoelectric power across the V$_{D}$ as the carrier type switches from electron to hole.   

Detection of Majorana Fermions in circuit QED

Superconducting quantum circuits, such as the flux and the transmon qubits, have been proposed to measure and control the quantum state of topological qubits based on pairs of Majorana fermions [1-4]. This is possible by making the superconducting qubit transition frequencies sensitive to the fermionic parity representing the topological qubit state. In this talk, we propose to measure the fermionic parity using a flux qubit integrated in a microwave resonator. In this proposal, the flux qubit always remains in its ground state and is used as a passive circuit element which modifies the resonance frequency of the resonator depending on the charge state of a nearby pair of Majorana fermions. Since it is always in its ground state, the requirements on the qubit coherence properties and fabrication parameters are less stringent than in other proposals. \newline [1] F. Hassler et al., New Journ. Phys. 12 125002 (2010) \newline [2] F. Hassler et al., New Journ. Phys. 13 095004 (2011) \newline [3] L. Jiang et al., Phys. Rev. Lett. 106 130504 (2011) \newline [4] P. Bonderson and R. Lutchyn, Phys. Rev. Lett. 106 130505 (2011)   

Antimony arsenide: Chemical ordering and order-disorder transition in SbAs

The A7 structure of the Group V elements can display chemical ordering of Sb and As, which were previously thought to mix randomly. Our structural characterization of the compound SbAs is performed by single-crystal and high-resolution synchrotron x-ray diffraction, and neutron and x-ray pair distribution function analysis. All least-squares refinements indicate ordering of Sb and As, resulting in a GeTe-type structure without inversion symmetry. This lowering of symmetry does not result in any new Bragg reflections, so high-quality scattering data are required. High-temperature diffraction studies reveal an ordering transition around 550 K. Transport and infrared reflectivity measurements, along with first-principles calculations, find that SbAs has a direct band separation larger than that of Sb or As. Because even subtle substitutions in the semimetals, notably Bi$_{1-x}$Sb$_x$, can open semiconducting energy gaps, a further investigation of the interplay between chemical ordering and electronic structure on the A7 lattice is warranted.   

Probing Topological Superconductors with Elastic Strain Fields

We introduce a model for superconductivity in a topological insulator. The response of this system is probed by applying an external stress. We find that the stain field introduces connections in the superconductor and the response of the superconductor is given by the chiral anomaly which is proportional to the disclination density (for s-wave) or dislocations density (for the p-wave) superconductor. This result modifies the sound wave equations. In particular, we find that the core of the disclinations contains the normal matter in a superconductor. The presence of the long-range field induced by the topological response modifies the elastic properties of the solid which can be probed experimentally. The effect of rotating magnetic fields is also considered. Due to the Larmor theorem it is shown that the rotations replace the magnetic field by an effective magnetic field.   

High resolution spin- and angle-resolved photoelectron spectroscopy for 3D spin vectorial analysis

Spin- and angle-resolved photoelectron spectroscopy (SARPES) is the excellent tool which can directly observe the band structure of crystals with separating spin-up and -down states. Recent findings of new class of materials possessing strong spin orbit interaction such as Rashba spin splitting systems or topological insulators stimulate to develop new SARPES apparatuses and many sophisticated techniques have been reported recently[1-3]. Here we report our newly developed a SARPES apparatus for spin vectorial analysis with high precision at Hiroshima Synchrotron Radiation Center. Highly efficient spin polarimeter utilizing very low energy electron diffraction (VLEED) makes high resolution ($\Delta E<$ 10 meV, $\Delta \theta \sim \pm$ 0.2 $^{\circ}$) compatible with the SARPES measurement[4]. By placing two VLEED spin detectors orthogonally we have realized the polarization measurement of all spin components (x, y and z) with the high resolution. Some examples of the three-dimensional spin observation will be presented. [1] M. Hoesch et al., J. Electron Spectrosc. Relat. Phenom. 124, 263 (2002). [2] T. Okuda, et al., Rev. Sci. Instrum. 79, 123117 (2008). [3] S. Souma, et al., Rev. Sci. Instrum. 81, 095101 (2010). [4] T. Okuda, et al., Rev. Sci. Instrum. 82, 103302 (2011).   

Transport Measurements on Topological Insulators with Superconductor Electrodes

Interplay between topological insulators (TIs) and superconductors (SCs) is interesting to study novel physics such as Majorana fermions. Here we report transport measurements on bulk TI interfaced with superconducting electrodes, including indium (In) and niobium (Nb). The TI crystals are high quality $Bi_2Te_3, Bi_2Se_3, Bi_2Te_2Se$ grown by the Bridgman method. Multiple superconducting transitions have been observed in $Bi_2Te_3$/In systems, possibly due to the superconducting alloys formed by In and Bi. Below the superconducting temperature of In (or Nb), the resistance of TI/Sc structure shows a pronounced upturn which may be a probe of spin-polarized surface states in TI and the interplay with SC.