Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Y41: Topological Insulators Under Extreme Conditions - Theory |
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Sponsoring Units: DCMP Chair: Xinjiang Zhou, Institute of Physics, Chinese Academy of Sciences Room: Mile High Ballroom 3C |
Friday, March 7, 2014 8:00AM - 8:12AM |
Y41.00001: Bulk-surface Correspondence and the Hofstadter Problem of SU(2) Landau Levels in 3D Lattices Yi Li We show that the continuum description of topological states in three-dimensional SU(2) Landau levels can be connected to topological Bloch states in three dimensions. We consider SU(2) Landau levels in a cubic lattice, which exhibits spin-orbit coupled surface states protected by the time-reversal symmetry. We show that the bulk topological properties can be obtained from the topology in the surface states. We also show a generalized Hofstadter problem in three dimensions. [Preview Abstract] |
Friday, March 7, 2014 8:12AM - 8:24AM |
Y41.00002: Low-temperature conductivity and magnetoconductivity of two-dimensional Dirac fermions in topological insulators Hai-Zhou Lu Low-temperature electronic transport in topological insulators exhibits a dilemma. A negative cusp in weak-field magnetoconductivity is widely believed to be the signature of weak antilocalization (WAL) from the topological surface states. WAL is a quantum interference effect that enhances the conductivity with decreasing temperature at very low temperatures. A magnetic field can destroy WAL as well as the enhanced conductivity, giving rise to the negative magnetoconductivity showing that WAL used to be there. However, the conductivity in most experiments was observed to drop logarithmically with decreasing temperature, a behavior opposite to WAL. We model the surface and bulk states in topological insulators as massless and massive Dirac fermions, and derive the conductivity formula as a function of magnetic field and temperature, by taking into account the quantum interference and electron-electron interaction simultaneously. The formula reconciles the dilemma by explicitly clarifying that the WL-like temperature dependence of the conductivity is dominated by the interaction while the WAL-like magnetoconductivity is mainly contributed by the quantum interference. [Preview Abstract] |
Friday, March 7, 2014 8:24AM - 8:36AM |
Y41.00003: Dyon condensation: an effective way to construct topological phases with symmetry Peng Ye, Xiao-Gang Wen In this work, we construct three-dimensional exotic phases of bosons with time-reversal symmetry and boson number conservation U(1) symmetry by means of \emph{fermionic projective construction}. We first construct an \emph{algebraic bosonic insulator} which is a symmetric bosonic state with an emergent U(1) gapless gauge field. We then obtain many gapped bosonic states that do not break the time-reversal symmetry and boson number conservation via proper \emph{dyon condensations}. We identify the constructed states by calculating the allowed electric and magnetic charges of their excitations, as well as the statistics and the symmetric transformation properties of those excitations. This allows us to show that our constructed states can be trivial SPT states (\emph{i.e.} trivial Mott insulators of bosons with symmetry), non-trivial SPT states (\emph{i.e.} bosonic topological insulators) and SET states (\emph{i.e.} fractional bosonic topological insulators). In non-trivial SPT states, the elementary monopole (carrying zero electric charge but unit magnetic charge) and elementary dyon (carrying both unit electric charge and unit magnetic charge) are fermionic and bosonic, respectively. In SET states, intrinsic excitations may carry fractional charge. [Preview Abstract] |
Friday, March 7, 2014 8:36AM - 8:48AM |
Y41.00004: Melting transitions of quantum liquid crystalline order coexisting with electronic topological Chern insulators or other topological phases Onkar Parrikar, Gil Young Cho, Robert Leigh, Taylor Hughes Motivated by recent progress in understanding the interplay between the lattice and electronic topological phases, we consider quantum-melting transitions of liquid crystalline order that coexists with electronic topological phases. In certain classes of Chern band insulators, it has been previously demonstrated that there are topological Chern-Simons terms for local lattice deformations such as a Hall viscosity term. The Chern-Simons terms can induce non-trivial statistics for the topological lattice defects and furthermore dress the defects with certain symmetry quantum numbers. On the other hand, the melting transitions of such liquid-crystalline orders are driven by the condensation of lattice defects. Based on these observations, we show how the topological terms can change the nature of the proximate phases of the quantum liquid crystalline phases. We derive and study the effective field theories for the quantum phase transitions, and demonstrate some concrete examples. [Preview Abstract] |
Friday, March 7, 2014 8:48AM - 9:00AM |
Y41.00005: Magnetoelectric Effect in Topological Insulator Films Beyond Linear Response Regime Oleg Tretiakov, Dashdeleg Baasanjav, Kentaro Nomura We study the response of topological insulator films to strong magnetic and electric fields beyond the linear response theory. As a model, we use three-dimensional lattice Wilson-Dirac Hamiltonian where we simultaneously introduce both magnetic field as Aharonov Bohm phase and electric field as potential energy depending on lattice coordinate. We compute the energy spectrum by numerically diagonalizing this Hamiltonian for electrons and obtain the quantized magnetoelectric polarizability. In addition, we find that the magnetoelectric effect vanishes as width of the film decreases, due to the hybridization of surface wavefunctions. Furthermore, by applying a gate voltage between the surfaces, we observe multiple quantized plateaus of $\theta$-term. We explain that the multiple quantization rule of $\theta$ is mainly determined by the physics of Landau level structures on the top and bottom surfaces of topological insulator, whereas the small deviations from the exact quantization are coming from the asymmetry of the surface wavefunctions in the bulk. We also show that the magnetoelectric effect persists even for strong bulk interactions with magnetic field or magnetic impurities. [Preview Abstract] |
Friday, March 7, 2014 9:00AM - 9:12AM |
Y41.00006: Stability of surface states of general weak Z2 topological insulators and superconductors Takahiro Morimoto, Akira Furusaki A three-dimensional weak topological insulator (TI) is adiabatically connected to stacked layers of two-dimensional strong topological insulators and typically possesses two surface Dirac cones that can be gapped out without breaking the time-reversal symmetry. Unexpected strength of weak TIs has been pointed out by recent theoretical studies, showing that the surface Dirac fermions of weak TIs are not localized when the mean of the random potential is zero, as a consequence of the uniqueness of the dimerization mass term gapping out the surface Dirac cones. Motivated by these, we study the surface stability of weak $Z_2$ topological insulators and superconductors (TIs/TSCs) in the general Altland-Zirnbauer symmetry classes, considering representative Dirac Hamiltonians in various spatial dimensions. We show that we can always find a unique Dirac mass term that dimerizes stacked layers and gaps out surface Dirac fermions. The two dimerized gapped phases with different signs of the mass are distinguished by a $Z_2$ index. If we impose spatial uniformity of the randomness of the surface on average, then the gapless surface states are not localized because they are connected with the quantum critical point between the two $Z_2$-distinct dimerized phases. [Preview Abstract] |
Friday, March 7, 2014 9:12AM - 9:24AM |
Y41.00007: A self-consistent study of the ferromagnetic ordering of magnetic adatoms on the surface of topological insulator Wei Qin, Zhenyu Zhang Ferromagnetically coupled magnetic adatoms on the surface of a three-dimensional topological insulator (TI) will induce a band gap by breaking time-reversal symmetry. The opened gap not only causes a lowering of the total energy of the band electrons, but also influences the magnetic coupling between the magnetic adatoms; in turn, variations in the magnetic coupling will affect the original collective magnetic states of the adatoms on the TI surface. We study \textit{self-consistently} the RKKY interactions between magnetic adatoms on a TI surface, mediated by massive Dirac electrons. Analytical expressions of RKKY interactions are presented, which contain the widely known Heisenberg-like, Ising-like, and DM-like terms [1]. Our results show that the self-consistent band gap will weaken the ferromagnetic couplings between the magnetic adatoms. Finally, we expand our study to the case that magnetic adatoms interact with the surface electrons of TI via anisotropic exchange couplings. [Preview Abstract] |
Friday, March 7, 2014 9:24AM - 9:36AM |
Y41.00008: Weak-field Hall conductivity in a single Dirac cone Masaki Noro, Shuichi Murakami Weak-field Hall conductivity is calculated in a single Dirac cone within a self-consistent Born approximation. In this system, electronic orbital motion and Zeeman splitting term contribute to the Hall conductivity. The contribution from the electronic orbital motion agrees with the Hall conductivity in graphene apart from the factor of four coming from spin and valley degeneracy, where the electronic structure forms pseudo-spin Dirac cones. On the other hand, the contribution from the Zeeman splitting term, which is seen only in a single Dirac cone, shows unique behavior. The contribution from Zeeman splitting term is symmetric with respect to the Dirac point as a function of the Fermi energy, in contrast to the antisymmetric behavior of the orbital contribution. It does not depend so much on energy for high Fermi energy region, while it shows a dip around the Dirac point. Besides its singular behavior, we note that the size of this contribution is comparable with that of the electronic orbital motion when we apply experimentally reasonable parameters. Consequently, the total weak-field Hall conductivity is neither symmetric nor antisymmetric with respect to the Dirac point, We compare this result with experimental results on surfaces of topological insulators. [Preview Abstract] |
Friday, March 7, 2014 9:36AM - 9:48AM |
Y41.00009: Calculation of Magnetoresistance of an Ideal Topological Insulator Using Boltzmann Transport Teoman Ozturk, Richard Field III, Yun Suk Eo, Steven Wolgast, Kai Sun, Cagliyan Kurdak The electrical conductivity of a topological surface state is expected to be enhanced due to the suppression of backscattering resulting from spin-momentum locking. We will present numerical calculation of this enhancement factor using Boltzmann transport for an ideal topological insulator with a single Dirac cone in an arbitrary magnetic field and discuss the manifestations of this for a Corbino sample placed in a tilted magnetic field. [Preview Abstract] |
Friday, March 7, 2014 9:48AM - 10:00AM |
Y41.00010: Theoretical studies of surface states in three-dimensional topological-insulator thin films in a strong magnetic field. Anna Pertsova, Carlo M. Canali, Allan H. MacDonald The peculiar structure of the Landau levels (LLs) in topological insulators (TIs), in particular the existence of a field-independent (zeroth) LL, is a characteristic signature of the Dirac surface states. However, recently it has been shown that the hybridization between top and bottom surfaces in a 3D TI thin film may lead to a splitting of the zeroth LL and even to its absence in the ultra-thin film limit. We report on microscopic tight-binding modelling of Bi$_{2}$Se$_{3}$ thin films [1] in the presence of a strong magnetic field. We find that the zeroth LL is absent for thicknesses below 4QLs, in agreement with experiments. Calculations of the LL spectrum of a 5QL-thick slab reveal a strong asymmetry with respect to the Dirac point and a clear signature of the first LL, in good agreement with Dirac-Hamiltonian model calculations. The latter feature persists in a wide range of magnetic fields and involves an extended window of energies, including bulk states away from the Dirac point. We use our results to predict an interplay between the external magnetic field and gate-voltage dependence of the anomalous Hall effect that is characteristic of topological magnetic states.\\[4pt] [1] A.Pertsova and C.M.Canali, arXiv:1311.0691. [Preview Abstract] |
Friday, March 7, 2014 10:00AM - 10:12AM |
Y41.00011: Magnetization fluctuations on the surface of a magnetically-doped topological insulator Dmitry Efimkin, Victor Galitski Ordering of magnetic impurities on the surface of a topological insulator gaps out the surface states and gives rise to anomalous quantum Hall effect, as demonstrated in recent experiments [1, 2]. Here we study theoretically fluctuation phenomena that occur in the vicinity of the ferromagnetic transition in such magnetically-doped topological insulators. We calculate the density of states of the electronic excitations and study transport properties in the fluctuation region. \\[4pt] [1] S.Y. Xu et al., Nature Phys. 8, 616 (2012). \\[0pt] [2] Y. L. Chen et al., Science 329, 659 (2010). [Preview Abstract] |
Friday, March 7, 2014 10:12AM - 10:24AM |
Y41.00012: Interplay between Mn-acceptor state and Dirac surface states in Mn-doped Bi$_{2}$Se$_{3}$ topological insulator M.R. Mahani, A. Pertsova, F. Islam, C.M. Canali Bi$_{2}$Se$_{3}$ is a 3D topological insulator (TI) exhibiting a single Dirac cone of surface states localized on the (111) surface. Magnetic impurities embedded in the surface of a TI may cause a breaking of time-reversal symmetry, opening a gap at the Dirac point that changes the topological character of the surface states. Substitutional Mn also introduces acceptor states in the bulk gap of the host material. These acceptor levels can be directly probed by scanning tunneling spectroscopy. However, the nature of these states and their interplay with the Dirac surface states has not been analyzed theoretically. Here we present results of DFT calculations investigating the properties of a single substitutional Mn and its associated acceptor state in Bi$_{2}$Se$_{3}$TI. In agreement with experiment we find that Mn impurities are in Mn$^{2+}$ valence state, with a magnetic moment close to 5 $\mu_{\mathrm{B}}$. The Mn-acceptor is predominantly of $p$ character and is localized mainly on the Mn and the nearest-neighbor Se atoms. Its electronic structure and spin-polarization are determined by the hybridization with the Mn $d$ levels, which is strongly affected by lattice relaxation and electronic correlations at the Mn site. We argue that magnetism and the topological character of Mn-doped Bi$_{2}$Se$_{3}$ is the result of this non-trivial interplay between acceptor and Dirac electron spins, and their coupling with the localized Mn magnetic moment. [Preview Abstract] |
Friday, March 7, 2014 10:24AM - 10:36AM |
Y41.00013: Fractionalization of Faraday lines in generalized compact quantum electrodynamics models in three dimensions Olexei Motrunich, Scott Geraedts Motivated by ideas of fractionalization and topological order in bosonic models with short-range interactions, we consider similar phenomena in formal lattice gauge theory models. Specifically, we show that a compact quantum electrodynamics (CQED) in (3+1)D can have, besides familiar Coulomb and confined phases, additional unusual confined phases where excitations are quantum lines carrying fractions of the elementary unit of electric field strength. We construct a model that has $N$-tupled monopole condensation and realizes 1/N fractionalization of the quantum Faraday lines; this phase has another excitation which is a $Z_N$ particle that picks up a phase of $e^{i 2\pi/N}$ when going around the fractionalized electric field line excitation. Alternatively, we can introduce a conventional bosonic field and condense bound states of monopoles and bosons. This can lead to fractionalization of both Faraday lines and bosons, as well as a quantized transverse response. We compare and contrast with bosonic topological insulators in (3+1)D. [Preview Abstract] |
Friday, March 7, 2014 10:36AM - 10:48AM |
Y41.00014: Physical observables in a model with topological structure and time-dependent perturbations Benjamin M. Fregoso, Jan P. Dahlhaus, Joel E. Moore, James K. Freericks We study a model of spin-full fermions on a lattice in a finite geometry that is acted upon by a time-dependent perturbation, e.g., an intense laser pulse, which induces non-trivial topological band structure. While it is possible for such time-dependent perturbations to modify the band structure, e.g, creating edge states or modifying the Chern number, it is far less clear under what conditions such topological effects can be observed in experimental settings. Two regimes are studied, the transient regime and the non-equilibrium steady state regime. We provide conditions under which physical observables carry signatures of the induced topological structure. [Preview Abstract] |
Friday, March 7, 2014 10:48AM - 11:00AM |
Y41.00015: Chern and Majorana modes of quasiperiodic systems Gerardo Naumis, Indubala Satija In this work, we investigate the self-similar states found in quasiperiodic systems characterized by topological invariants--the Chern numbers. We show that the topology introduces a competing length in the self-similar band edge states transforming peaks into doublets of size equal to the Chern number [1]. This length intertwines with quasiperiodicity and introduces an intrinsic scale, producing Chern beats related to Friedel oscillations. An explanation based on Thouless equations for band edge modes of the Harper equation is provided to understand the Chern dressing of the fractal spectrum. Chern numbers also influence the zero-energy mode that, for quasiperiodic systems, is related to the Majorana modes: the remnant of the edge localized topological state that delocalizes at the onset to a topological transition. In superconducting wires, the exponentially decaying profile of the edge localized Majorana modes also encode fingerprints of the Chern states that reside in close proximity to zero energy. \\[4pt] [1] I. Satija, G.G. Naumis, ``Chern and Majorana modes in Quasicrystals,'' Phys. Rev. B 88, 054204 (2013). [Preview Abstract] |
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