Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session S10: Topological Insulators - Mainly Transport Properties (Theory) |
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Sponsoring Units: DCMP Chair: Hsin-Hua Lai, National High Magnetic Field Laboratory Room: 007A |
Thursday, March 5, 2015 8:00AM - 8:12AM |
S10.00001: Distorted signal transport in topological insulators and its applications Xiao Zhang, Chinghua Lee We develop a theoretical approach for studying the distorted signal transport in topological insulators. It works for arbitrarily applied electric fields and relaxation time. Exact analytic results are obtained for generic driving fields, with a particularly elegant expression for the trigonometric function case. We analytically and numerically study the effects of temperature, relaxation time etc for topological insulators in real conditions and its applications. [Preview Abstract] |
Thursday, March 5, 2015 8:12AM - 8:24AM |
S10.00002: Current distribution in a two-dimensional topological insulator Xiaoqian Dang, John Burton, Evgeny Tsymbal Topological insulator (TI) is a bulk insulator with spin-dependent surface (edge) states that are protected by time-reversal symmetry. This property makes TIs very interesting for potential application in electronic devices. Here we report on theoretical investigations of transport properties of a model two-dimensional (2D) TI where the conductance is controlled by the topologically protected edge states. We utilize the tight-binding form of the Bernevig-Hughes-Zhang model [1] and employ the Landauer-B\"{u}ttiker formalism to explore the transport properties in the presence of impurities. Using the Green's function technique we calculate the current distribution for states within the bulk band gap of the 2D TI. Interestingly, in absence of impurities we find that the current density decays into the bulk in an oscillatory fashion reflecting an oscillatory decay pattern of the local density of states as predicted from the complex band structure. [2] Non-magnetic impurities disturb this picture and lead to a complex spatial distribution of current; however, the net transmission along the edge is conserved and remains a spin conductance quantum as expected from general considerations.\\[4pt] [1] B. A. Bernevig \textit{et al}., \textit{Science}, \textbf{314}, 1757 (2006).\\[0pt] [2] X. Dang \textit{et al}., Phys. Rev. B \textbf{90},155370 (2014). [Preview Abstract] |
Thursday, March 5, 2015 8:24AM - 8:36AM |
S10.00003: Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model David Bauer, Thomas Jackson, Rahul Roy We study the correlation between the band geometry of the Hofstadter model in the limit of small flux and the stability of fractional quantum Hall states in this system. We develop a perturbative calculation of the quantum metric that agrees well with numerical calculations. In contrast to most models studied so far where the fluctuations of the Berry curvature seem to dictate the stability of any fractionalized topological phases, we find that in the Hofstadter model, the trace of the quantum metric seems to be the predominant factor. [Preview Abstract] |
Thursday, March 5, 2015 8:36AM - 8:48AM |
S10.00004: High-field charge transport on the surface of Bi$_2$Se$_3$ M.Q. Weng, M.W. Wu We present a theoretical study on the high-field charge transport on the surface of Bi$_2$Se$_3$ and reproduce all the main features of the recent experimental results, i.e., the incomplete current saturation and the finite residual conductance in the high applied field regime [Costache {\it et al.}, Phys. Rev. Lett. {\bf 112}, 086601 (2014)]. Due to the hot-electron effect, the conductance decreases and the current shows a tendency of saturation with the increase of the applied electric field. Moreover, the electric field can excite carriers within the surface bands through interband precession and leads to a higher conductance. As a joint effect of the hot-electron transport and the carrier excitation, the conductance approaches a finite residual value in the high-field regime and the current saturation becomes incomplete. We thus demonstrate that, contrary to the conjecture in the literature, the observed transport phenomena can be understood qualitatively in the framework of surface transport alone. Furthermore, if a constant bulk conductance which is insensitive to the field is introduced, one can obtain a good quantitative agreement between the theoretical results and the experimental data [M. Q. Weng and M. W. Wu, Phys. B {\bf 90}, 125306, (2014)]. [Preview Abstract] |
Thursday, March 5, 2015 8:48AM - 9:00AM |
S10.00005: Dimensional crossover of transport characteristics in topological insulator nanofilms Ken-Ichiro Imura, Yukinori Yoshimura, Koji Kobayashi, Tomi Ohtsuki Recently, much effort has been made to grow thin films of a topological insulator. Naturally, its primary purpose was to reduce the contribution of the bulk to transport quantities. Here, we propose that searching for quantized transport in such TI thin films is an efficient way for probing non-trivial topological features encoded in the 3D bulk band structure. In a recent work (Kobayashi, KI, Yoshimura {\&} Ohtsuki, arXiv:1409.1707), we have highlighted the following issues: 1) Transport characteristics of TI thin films is well understood by studying the conductance both in the edge and slab geometries. 2) We introduce ``conductance maps'' for revealing the dimensional crossover in such TI thin films. Quantization of the conductance occurs both in the edge and in the slab geometries, but not at the same time. 3) We focus on the even-odd feature in transport with respect to the number of stacked layers. We found parameter regimes in which the even-odd feature is broken by inversion of the finite-size gap associated with hybridization of the top and bottom surface wave functions. We propose that tuning the hybridization gap of a TI thin film and make it inverted is an effective way of realizing a 2D quantum spin Hall state. [Preview Abstract] |
Thursday, March 5, 2015 9:00AM - 9:12AM |
S10.00006: Extrinsic spin-orbit coupling and density dependent weak antilocalization in three-dimensional topological insulators Weizhe Liu, Pierre Adroguer, Xintao Bi, Ewelina Hankiewicz, Dimitrie Culcer Topological insulators (TIs) have revolutionized our understanding of insulating behaviour. Three-dimensional TIs are insulators in the bulk but conducting along their surfaces. Much of recent researches on 3D TIs focus on overcoming the \textit{transport bottleneck}, namely the fact that surface transport is overwhelmed by bulk transport stemming from unintentional doping. The key to overcoming this bottleneck is identifying unambiguous signatures of surface state transport. We will discuss one such signature: weak antilocalization, meaning that coherent backscattering increases the electrical conductivity. The features of this effect, however, are rather subtle, because in TI the impurities have also strong spin-orbit coupling. I will show that spin-orbit coupled impurities introduce an additional time scale, which is expected to be shorter than the dephasing time, and the resulting conductivity has a distinguished part with linear dependent on the carrier number density. The result we predict is directly observable experimentally. [Preview Abstract] |
Thursday, March 5, 2015 9:12AM - 9:24AM |
S10.00007: Topological suppression of quantum tunneling Jia-Hua Gu, Kai Sun In this talk, we prove that if we bring together two band insulators with different topology, described by arbitrary topological indices, there must exist specific momentum points in the Brillouin zone where the wavefunctions of the two insulators are orthogonal and cannot hybridize. For 2D insulators, this conclusion implies that topology will prohibit tunneling of electrons between the two insulators at this momentum. This conclusion can also be generalized to some strongly-correlated topological systems. Explicit demonstration and proof will be provided for topological band insulators and fractional quantum Hall states. [Preview Abstract] |
Thursday, March 5, 2015 9:24AM - 9:36AM |
S10.00008: Charge Transport in 3D topological insulators in the presence of surface potential fluctuation Xingyue Peng, Yiming Yang, Rajiv Singh, Sergey Savrasov, Dong Yu Field effect measurements on the surface of a 3D topological insulator (TI) have often shown a high minimum conductivity as the Fermi level is shifted to Dirac point. Not only does this minimum conductivity vary from 5 to 50 e$^{2}$/h strongly dependent on sample details but the gate dependent conductivity also exhibits anomalous non-monotonic behavior which is not yet understood. Understanding the nature of this minimum conductivity is crucial for the design and fabrication of novel spintronic devices based on 3D TIs. We propose a theoretic model to explain this anomalous behavior, considering the existence of surface potential fluctuations as indicated by scanning tunneling spectroscopy (STS) and scanning photocurrent microscopy (SPCM) measurements on the surface of a 3D TI. Our model agrees well with preexisting experiments and our own transport measurements in field effect transistors (FETs) incorporating Sb-doped single Bi$_{2}$Se$_{3}$ nanoribbons. [Preview Abstract] |
Thursday, March 5, 2015 9:36AM - 9:48AM |
S10.00009: Effects of the boundary geometry on the edge current in the two dimensional topological insulator Hyeonjin Doh, Hyoung Joon Choi We study the effects of the boundary shape on the edge transport of the two dimensional topological insulator described by Kane-Mele model. The edge state is robust against all time-reversal invariant defects. However, when we consider an arbitrary sample, the edge is not straight and consists of various types of boundaries. Actually, the transport property of the edge-state in the Kane-Mele model depends on the boundary type of the edge such as zigzag and armchair edges. Therefore, the edge-transport can be affected by a corner connecting two different types of edges. Here, we investigate the energy spectrum of the various shapes of finite-size honeycomb lattice with corners along the edge. We also calculate the transport properties on the edges by applying an artificial gauge field which drives a persistent current along the edges. Although the corner of the edge seems a geometrical defects and is expected to have a little effect on the transport, our results show that the geometrical defects strongly affect the edge current depending on the corner types. [Preview Abstract] |
Thursday, March 5, 2015 9:48AM - 10:00AM |
S10.00010: Distinctive features of transport in topological insulators Vincent Sacksteder, Quansheng Wu, Kristin Arnardottir, Ivan Shelykh, Stefan Kettemann The surface states of a topological insulator in a fine-tuned magnetic field are ideal candidates for realizing a topological metal which is protected against disorder. Its signatures are (1) a conductance plateau in long wires and (2) a conductivity which always increases with sample size. We numerically show that the bulk substantially accelerates the conductance plateaus's decay in a magnetic field. It also reduces the effects of surface disorder and causes the magnitude of the surface conductivity and the magnetoconductivity to depend systematically on sample details such as doping and disorder strength. In addition, we predict a new signature of the topological state: at low temperatures the magnetoresistance will deviate strongly from the Hikami-Larkin-Nagaoka (HLN) formula. In this regime the magnetoresistance is dominated by scattering processes which wrap around the TI sample. The HLN formula's shoulder is replaced by a feature with a larger critical field magnetic strength that is caused by wrapping. Inside the wrapping regime the magnetoconductance will lose its dependence on temperature. This new topological signature should be visible in the same samples and temperatures where the Altshuler-Aronov-Spivak (AAS) effect has already been observed. [Preview Abstract] |
Thursday, March 5, 2015 10:00AM - 10:12AM |
S10.00011: Berry-phase description of Topological Crystalline Insulators Aris Alexandradinata, B. Andrei Bernevig, Xi Dai We study a class of translationally-invariant insulators protected by crystalline symmetries. Some of these insulators have no spin-orbit coupling, and may be realized in intrinsically spinless systems such as photonic crystals and ultra-cold atoms. Some of these insulators have no time-reversal symmetry as well, i.e., the relevant symmetries are purely crystalline. Nevertheless, topological phases exist which are distinguished by their robust surface modes. Their band topology is unveiled by the crystalline analog of Berry phases, i.e., parallel transport across certain non-contractible loops in the Brillouin zone. We also identify certain topological phases without any robust surface modes - they are uniquely distinguished by parallel transport along bent loops, whose shapes are determined by the symmetry group. Finally, we highlight recent interferometry experiments which demonstrate that these Berry phases are measurable. [Preview Abstract] |
Thursday, March 5, 2015 10:12AM - 10:24AM |
S10.00012: Majorana zero modes choose Euler numbers - revealed by full counting statistics Dong E. Liu, Alex Levchenko, Roman M. Lutchyn We consider a quantum dot (QD) coupled to a Majorana zero mode and two normal leads and study transport properties of the system. We investigate the full counting statistics of charge tunneling events which allows one to extract information about current fluctuations in the system. Using Keldysh path-integral approach, we compute the cumulant generating function for the quantum dot with Majorana and normal lead couplings. We first consider a non-interacting spinless QD, and find that for the symmetric dot-lead couplings, the zero-frequency cumulants exhibit a universal pattern (Euler polynomial), independent of the microscopic parameters. For a spinful QD, the Coulomb interaction effects are discussed for both strong interaction (single-electron occupancy regime) and weak interactions (perturbative regime). In the latter case, the interactions do not change the universal pattern at small voltage bias. Compared to the case without Majorana coupling, we show that, while the tunneling conductance might exhibit zero-bias anomaly due to Majorana or Kondo physics, the full counting statistics are qualitatively different in the presence of the Majorana coupling. [Preview Abstract] |
Thursday, March 5, 2015 10:24AM - 10:36AM |
S10.00013: Simple examples of Symmetry-Protected Topological phases and Symmetry-Enriched Topological phases of quantum lines Olexei Motrunich, Scott Geraedts We construct models realizing distinct confining phases of lattice gauge theories envisioned in a formal classification of gapped phases of gauge theories by Kapustin and Thorngreen, arXiv:1309.4721. This generalizes ideas of Symmetry-Protected Topological (SPT) phases in Condensed Matter to systems where fundamental microscopic objects are quantum lines, which is of interest in High Energy Theory. Specifically, in (3+1)D, we consider discrete $Z_N$ lattice gauge theory models, with two copies of $Z_N$, and construct N distinct confining phases by engineering condensation of bound states of magnetic fluxes (which are quantum lines in 3d) and $Z_N$ electric field lines. In (4+1)D, we consider compact quantum electrodynamics (CQED) models, with two copies of CQED, and engineer condensation of bound states of monopoles (which are quantum lines in 4d) and U(1) electric field lines. When the bound states contain a single monopole, we find SPT-like phases of the lattice gauge theory, while when the bound states contain multiple monopoles, we find analogs of Symmetry-Enriched Topological phases, where in the present case we also have fractionalization of Faraday lines. The distinct character of these topological phases of quantum lines is revealed by unusual physics at a boundary. [Preview Abstract] |
Thursday, March 5, 2015 10:36AM - 10:48AM |
S10.00014: Interacting surface states of three-dimensional topological insulators Titus Neupert, Stephan Rachel, Ronny Thomale, Martin Greiter We numerically investigate the surface states of a strong topological insulator in the presence of strong electron-electron interactions. We choose a spherical topological insulator geometry to make the surface amenable to a finite size analysis. The single-particle problem maps to that of Landau orbitals on the sphere with a magnetic monopole at the center that has unit strength and opposite sign for electrons with opposite spin. Assuming density-density contact interactions, we find superconducting and anomalous (quantum) Hall phases for attractive and repulsive interactions, respectively, as well as chiral fermion and chiral Majorana fermion boundary modes between different phases. Our setup is preeminently adapted to the search for topologically ordered surface terminations that could be microscopically stabilized by tailored surface interaction profiles. [Preview Abstract] |
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