Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session Q35: Topological Insulators: Interactions |
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Sponsoring Units: DCMP Chair: Christopher Varney, Georgetown University / University of Maryland Room: C140 |
Wednesday, March 23, 2011 11:15AM - 11:27AM |
Q35.00001: Fragile Mott Insulators Steven Kivelson, Hong Yao We prove that there exists a class of crystalline insulators, which we call ``fragile Mott insulators'' which are not adiabatically connected to any sort of band insulator provided time-reversal and certain point-group symmetries are respected, but which are otherwise unspectacular in that they exhibit no topological order nor any form of fractionalized quasiparticles. Different fragile Mott insulators are characterized by different nontrivial one-dimensional representations of the crystal point group. We illustrate this new type of insulators with two examples: the d-Mott insulator discovered in the checkerboard Hubbard model at half-filling and the Affleck-Kennedy-Lieb-Tasaki insulator on the square lattice. [Preview Abstract] |
Wednesday, March 23, 2011 11:27AM - 11:39AM |
Q35.00002: Correlation effects in quantum spin Hall states: a Quantum Monte Carlo study Thomas C. Lang, Martin Hohenadler, Fakher F. Assaad We consider a quantum spin hall insulator as realized by the Kane-Mele model with spin orbit coupling $\lambda$ supplemented by a Hubbard $U$ term. On the basis of projective auxiliary field quantum Monte Carlo simulations on lattice sizes up to $ 12 \times 12 $, we map out the magnetic phase diagram. Beyond a critical value of $U> U_c$ the quantum spin Hall insulating state is unstable towards magnetic ordering. At $U < U_c$ we study the spin, charge and single particle dyanmics of the helical edge state by retaining the Hubbard interactions only on the edge of a ribbon. As $U_c$ is approached we observe a substantial depletion of low-lying spectral weight in the dynamical charge structure factor, and a robust signature of the helical edge state in the single particle spectral function. [Preview Abstract] |
Wednesday, March 23, 2011 11:39AM - 11:51AM |
Q35.00003: Quantum Monte Carlo simulations on interaction effects in the 2D Kane-Mele-Hubbard model Dong Zheng, Congjun Wu, Guang-Ming Zhang Interaction effects in topological insulators remain an open question. We have proved that the determinant quantum Monte-Carlo simulation on the two dimensional Kane-Mele model augmented by the Hubbard interaction is free of the sign-problem. Consequentially, the interplay between band topology and strong interaction can be studied at a high numeric precision. The process how the topological band insulator evolves into the antiferromagnetic Mott insulator as increasing interaction strength is studied by calculating both the bulk and edge electronic properties. The possibility of an exotic topological Mott-insulator is examined. [Preview Abstract] |
Wednesday, March 23, 2011 11:51AM - 12:03PM |
Q35.00004: Interactions and doping effects in a topological insulator Stephan Rachel, Karyn Le Hur We investigate the effect of repulsive and attractive onsite interactions on a Quantum Spin Hall Insulator (QSHI). For repulsive interactions, we show that the topological phase is stable up to quite large interactions $U\sim t$ before the system reaches a magnetically ordered phase\,[1]. For attractive interactions, we discuss superconductivity in a doped QSHI and compare it with a doped trivial band insulator. We also consider the effect of spin orbit coupling to zero--mode bound states at vortex cores.\\[10pt] [1] S.Rachel and K.Le Hur, Phys.\,Rev.\,B 82, 075106 (2010). [Preview Abstract] |
Wednesday, March 23, 2011 12:03PM - 12:15PM |
Q35.00005: Mott Physics at the Boundaries of Topological Insulators Amal Medhi, Pramod Kumar Verma, Vijay Shenoy, H. R. Krishnamurthy We address how the nature of linearly dispersing edge states of a topological insulating solid evolves with increasing electron-electron correlation engendered by a Hubbard like on-site repulsion. We report studies on strips (2D) and slabs (3D) of varying widths and thicknesses of topological insulators described by model Hamiltonians using an inhomogeneous slave rotor mean-field theory. Motivated by these studies, we construct variational wavefunctions with approriate Gutzwiller-Jastrow correlations and study them using the Monte-Carlo method. These studies reveal the width/thickness dependence of the critical on-site repulsion that obtains an edge Mott insulating state, and uncover the mechanism of the Mott transition in such systems. [Preview Abstract] |
Wednesday, March 23, 2011 12:15PM - 12:27PM |
Q35.00006: Interaction and distortion driven topological phases in multi-band lattices Jun Wen, Mehdi Kargarian, Gregory Fiete In this work we investigate the phase diagram of $5d$ transition metal oxides on the pyrochlore lattice. In particular, the competition between Coulomb interaction, spin-orbit coupling and distortion are discussed. Spin-orbit coupling entangles the spin and $t_{2g}$ orbitals giving rise to doublet $j=1/2$ and quadruplet $j=3/2$ states. While most pervious works discussed the doublet manifold, we focus on the quadruplet manifold which is relevant for several perovskites. Coulomb interaction is taken into account using the slave-rotor mean field theory and we obtain a phase diagram for this model, which includes exotic phases. We extend the model by including lattice distortion which further splits the quadruplet $j=3/2$ manifold. Under a variety of distortions a topological phase is stabilized, and we discuss how the overall phase diagram is altered with lattice distortions. [Preview Abstract] |
Wednesday, March 23, 2011 12:27PM - 12:39PM |
Q35.00007: Magnetic responce in the quantized spin Hall system with electron correlation Jun Goryo, Nobuki Maeda We investigate the magnetic response in the quantized spin Hall (SH) phase of layered-honeycomb lattice system with intrinsic spin-orbit coupling $\lambda_{\rm SO}$ and on-site Hubbard $U$. The response is characterized by a parameter $g= 4 U a^2 d / 3$, where $a$ and $d$ are the lattice constant and interlayer distance, respectively. When $g< (\sigma_{xy}^{s2} \mu)^{-1}$, where $\sigma_{xy}^{s}$ is the quantized spin Hall conductivity and $\mu$ is the magnetic permeability, the magnetic field inside the sample oscillates spatially. The oscillation vanishes in the non-interacting limit $U \rightarrow 0$. When $g > (\sigma_{xy}^{s2} \mu)^{-1}$, the system shows perfect diamagnetism, i.e., the Meissner effect occurs. We find that superlattice structure with large $a$ is favorable to see these phenomena. We also point out that, as a result of Zeeman coupling, the topologically-protected helical edge states shows weak diamagnetism which is independent of $g$. [Preview Abstract] |
Wednesday, March 23, 2011 12:39PM - 12:51PM |
Q35.00008: Electrostatic Effects in Topological Insulators Dimitris Galanakis, Tudor Stanescu We study electrostatic effects in topological insulators generated by non-uniform charge distributions and by external electric fields. The system is modeled using a tight-binding model and the Coulomb interaction is included at a mean-field level within a self-consistent calculation. The self-consistent charge profiles are calculated numerically for both insulating and low density metallic systems. Using this approach, we investigate the bending of the bulk bands due to the presence of surface states and of charged surface impurities and the effect of applying gate voltages to topological insulator films of variable thickness. Our results shed new light on the potential differences between surface- and bulk-sensitive measurements of topological insulators. [Preview Abstract] |
Wednesday, March 23, 2011 12:51PM - 1:03PM |
Q35.00009: Coulomb drag between helical edge states Vladimir Zyuzin, Gregory Fiete We theoretically investigate the Coulomb drag between the edge states of two quantum spin Hall systems. Using an interacting theory of the one-dimensional helical edge modes, we show that the drag vanishes at second order in the inter-edge interaction, where it is typically finite in other systems, due to the absence of backscattering within the edges. However, in the presence of a small external magnetic field, the drag is finite and scales as the fourth power of the magnetic field, a behavior that sharply distinguishes it from other systems. We obtain the temperature dependence of the drag for regimes of both linear and quadratic edge dispersion in the presence of a finite field. This work was financially supported by ARO under Grant No. W911NF-09-1-0527. V. A. Zyuzin and G. A. Fiete, Phys. Rev. B 82, 113305 (2010). [Preview Abstract] |
Wednesday, March 23, 2011 1:03PM - 1:15PM |
Q35.00010: Effect of electron-electron interaction on surface transport in three-dimensional topological insulators Hridis Pal, Dmitrii Maslov We study the effect of electron-electron interaction on the temperature dependence of surface charge transport in three dimensional topological insulators. In conventional two dimensional materials at small temperatures, the presence or absence of $T^2$ dependence in the resistivity is found to depend on the Fermi surface geometry- whether it is concave or convex and whether it is simply connected or multiply connected. In the recently discovered three-dimensional topological insulators such as Bi$_2$Te$_3$, Bi$_2$Se$_3$, and Sb$_2$Te$_3$ the Fermi surface of the two dimensional surface states, owing to the underlying lattice symmetry, changes curvature from convex to concave as a function of energy. The contribution from electron-electron interaction is therefore expected to affect the resistivity in these materials which we investigate in this study. [Preview Abstract] |
Wednesday, March 23, 2011 1:15PM - 1:27PM |
Q35.00011: Cooper Pair Injection into Topological Insulators Koji Sato We theoretically study tunneling of Cooper pairs (CP's) from a superconductor spanning a two-dimensional topological insulator strip into its helical edge states. The coherent low-energy electron-pair tunneling sets off positive nonlocal current cross-correlations along the edges, which reflect an interplay of two quantum-entanglement mechanisms. First of all, superconducting spin pairing dictates a CP partitioning into the helical edge liquids, which transport electrons in the opposite directions for opposite spin orientations. Luttinger-liquid (LL) correlations for the electron-density fluctuations are, furthermore, forcing paired electrons to enter into opposite insulator-strip edges, revealing CP spin entanglement in the inter-edge current correlations. At the same time, the LL behavior, in the absence of Fermi-liquid leads, fractionalizes electrons injected at a given edge into counter-propagating charge pulses carrying definite fractions of the elementary electron charge. The superconductivity as well as LL correlations thus introduce positive current cross-correlations, which reveal a wealth of information about both subsystems. Sato, Loss, Tserkovnyak, arXiv:1003.4316v1. To be published in Physical Review Letters [Preview Abstract] |
Wednesday, March 23, 2011 1:27PM - 1:39PM |
Q35.00012: Instabilities of quadratic band crossing points Stefan Uebelacker, Carsten Honerkamp The variation of the orbital composition of bands around band crossing points near the Fermi level can generate interesting effects. In particular, rather simple interactions can give rise to the spontaneous formation of topological insulating phases (S. Raghu et al., Phys. Rev. Lett. 100, 156401 (2008)). In contrast with Dirac points, quadratic band crossing points offer the advantage of a nonzero density of states at the crossing point, and instabilities occur already at small interaction strengths. Here, we present results of functional renormalization group calculations for models with a quadratic band crossing point and discuss the possibilities for nontrivial insulating phases induced by local interactions. [Preview Abstract] |
Wednesday, March 23, 2011 1:39PM - 1:51PM |
Q35.00013: Fractionalization and topological point defects in the charge-ordered kagome lattice Andreas Ruegg, Gregory A. Fiete The charge-ordered state on the kagome lattice shows some features which are closely related to two-dimensional topological insulators. This motivated us to study a two-dimensional system of spin-polarized fermions on the kagome lattice at filling fraction $f=1/3$ interacting through a nearest-neighbor interaction $V$ using the unrestricted mean-field approach. Above a critical interaction strength $V_c$, a charge-density wave is stabilized. We find that topological point defects in the charge order bind a fractional charge. The value of the bound charge is 1/2 as long as an effective sublattice symmetry is preserved but changes continuously with the strength of the symmetry-breaking field. Moreover, we compute the confinement potential between two fractionally charged defects and argue that the polaron state, formed upon doping the charge-density wave, can be viewed as a bound state of two defects. [Preview Abstract] |
Wednesday, March 23, 2011 1:51PM - 2:03PM |
Q35.00014: Stability of spontaneous quantum Hall state in the Triangular Kondo-lattice model Yasuyuki Kato, Ivar Martin, Cristian Batista We study the behavior of the quarter-filled Kondo lattice model on a triangular lattice by combining a zero-temperature variational approach and finite-temperature Monte-Carlo simulations. For intermediate coupling between itinerant electrons and classical moments ${\bf S}_j$, we find a thermodynamic phase transition into an exotic spin ordering with uniform scalar spin chirality and $\langle {\bf S}_j \rangle=0$. The state exhibits spontaneous quantum Hall effect. We also study how its properties are affected by the application of an external magnetic field. [Preview Abstract] |
Wednesday, March 23, 2011 2:03PM - 2:15PM |
Q35.00015: Quantum corrections to conductivity in topological insulator thin films: Weak localization and electron-electron interaction Ashley DaSilva, Jian Wang, Cui-Zu Chang, Ke He, Xu-Cun Ma, Qi-Kun Xue, Jainendra Jain, Nitin Samarth, Moses Chan We study quantum corrections to transport in topological insulator candidate Bi$_2$Se$_3$, with and without doping with Pb. We study thin films with the expectation that the topological surface states will have substantial contribution to transport. Our observations are not consistent with the theory of diffusive transport of noninteracting electrons, because while the temperature dependence is consistent with weak localization, the magnetoresistance is positive, suggestive of weak anti-localization. We show that the theory including quantum corrections from both electron-electron interaction and disorder is qualitatively correct in all magnetic field directions that we have studied. We mention the implications of our results to the possibility of conducting surface states. [Preview Abstract] |
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