Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session R03: Topological Phases |
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Sponsoring Units: DCMP Chair: Haruki Watanabe Room: BCEC 107B |
Thursday, March 7, 2019 8:00AM - 8:12AM |
R03.00001: Controlling topologically protected states by external fields and doping Alvaro Diaz Fernandez, Francisco Domínguez-Adame, Elena Díaz Topological materials often display topologically protected surface states with Dirac-like dispersions. Controlling their properties is desirable for their foreseen applications and a number of proposals have been put forward to this respect (e.g. [1,2,3,4]). In this contribution, the system I will consider is a topological boundary. I will discuss how applying uniform electric and magnetic fields that preserve the symmetries lead to an anisotropic reduction of the Fermi velocity as the fields are increased. [5,6]. I will also show how a δ-layer of donor atoms at the boundary can lead to a coexistence of a two-dimensional electron gas with the topological surface states. Moreover, the linear optical response is markedly reshaped by the presence of the topological state [7]. |
Thursday, March 7, 2019 8:12AM - 8:24AM |
R03.00002: Topological phases of the rainbow chain German Sierra Inhomegenous quantum many body systems exhibit novel phenomena such as the breaking of the area law of entanglement entropy. A notable example is the so called rainbow model which consists of a XX spin chain where the exchange coupling constants decrease exponentially from the center towards the edges. This system has been analyzed in great detail using the strong disorder renormalization group method and conformal field theory. These methods explain the appearance of long range valence bonds across the spin chain, having the shape of a rainbow. In this talk, we shall explain another feature which is the appearance of topological order in the rainbow chain with an odd number of sites. In the particular case when there is rotational symmetry one obtains the Haldane phase. This result indicates that the short range entanglement characteristic of the SPT phases can be related to the long range entanglement of the critical phases by considering the inhomogenous deformation of the latters. |
Thursday, March 7, 2019 8:24AM - 8:36AM |
R03.00003: Topology and localization in the Kondo lattice model Ying Su, Shizeng Lin The Kondo lattice model describing the coupling between conduction electrons and localized magnetic moments is relevant for a large family of physical systems. Here we reveal that the one-dimensional Kondo lattice model with a magnetic elliptical spiral is a topological insulator with a Chern number 2Z in the two-dimensional space with one physical dimension and one ancillary dimension spanned by the Goldstone mode of the spiral. The 2Z topological classification can be reduced to Z if certain spin rotation symmetry is broken. Moreover, when the elliptical spiral is incommensurate, the electronic states can be localized for a strong local exchange coupling. The topological protected edge states are responsible for the pumping of electron charge, and give rise to multiferroic response. The coexistence of nontrivial band topology and Anderson localization results in a unique charge pumping. Our work uncovers hitherto undiscovered nontrivial topology and Anderson localization in the Kondo lattice model. |
Thursday, March 7, 2019 8:36AM - 8:48AM |
R03.00004: Topology of Quantum Systems Out of Equilibrium Max McGinley, Nigel R Cooper We investigate the topological properties of many-body quantum systems undergoing unitary time-evolution. We find that it is possible for the topology of the wavefunction to change out of equilibrium, and accordingly establish the existence of a robust nonequilibrium topological classification which generally differs from equilibrium [1]. The classification naturally inherits phenomenology familiar from equilibrium – it is robust against disorder and interactions, and exhibits a nonequilibrium bulk-boundary correspondence, which we probe using the entanglement spectrum. We explicitly construct a nonequilibrium generalisation of the `ten-fold way', which applies to non-interacting fermionic systems with non-spatial symmetries in all dimensions [2]. The differences between equilibrium and nonequilibrium topology are shown to have directly observable consequences, in both bulk and boundary physics. In particular, we show that non-equilibrium topological effects have important ramifications for various Majorana fermion-based implementations of quantum memories. |
Thursday, March 7, 2019 8:48AM - 9:00AM |
R03.00005: Self-assembled Bismuth Selenide (Bi_{2}Se_{3}) quantum dots grown by molecular beam epitaxy Marcel Claro, Abhinandan Gangopadhyay, David Smith, Maria Tamargo Three-dimensional topological insulators (TIs) are insulators in the bulk with surface states that have spins locked with momentum and are protected by time-reversal symmetry. Control of these states can be useful for novel applications in quantum computing and spintronics. Some properties of these materials can be enhanced by electronic confinement in quantum dots (QDs)^{1,2}. Bi_{2}Se_{3} is particularly interesting since its band gap is relatively large and the experimentally verified Dirac cone is in the Γ-point. Bi_{2}Se_{3 }has been grown successfully by molecular beam epitaxy (MBE) on different substrates, and a lithographically defined QD with quantum confinement was previously demonstrated^{3}. We report the growth of self-assembled Bi_{2}Se_{3} QDs by MBE using the droplet epitaxy technique. The QDs form after anneal of Bi droplets under a Se flux. They are crystalline and have average dimensions of 12-nm height (12 quintuple layers) and 46-nm width, and a density of 8.5x10^{9} cm^{-2}. The QD formation process developed is simple, reproducible and tunable. |
Thursday, March 7, 2019 9:00AM - 9:12AM |
R03.00006: Quantization of Fractional Corner Charge in C_{n}-symmetric Topological Crystalline Insulators Wladimir Benalcazar, Tianhe Li, Taylor Hughes We show that C_{n} symmetries quantize the corner charge in crystalline topological insulators. |
Thursday, March 7, 2019 9:12AM - 9:24AM |
R03.00007: Topological Phase Transitions Induced by Giant Strains Produced by Chemical Pressure Rajdeep Banerjee, Manish Jain, Shobhana Narasimhan Monolayer germanene has to be chemically functionalized to be stable. Though -CH_{3} functionalized germanene has been predicted to undergo a topological phase transition when subjected to an external biaxial strain, achieving the requisite large values of strain by mechanical means is essentially impossible. We show that instead, chemical functionalization using -CX_{3} groups (X = F, Cl, Br, I) induces giant chemical strains (of 9.5%, 37.4%, 48.9% and 62.8%, respectively) on the germanene lattice, relative to GeCH_{3}. For X = F and Cl, this causes the topological insulating phase to become stable at either a small or zero strain (with respect to the ground state geometry of GeCX_{3}), respectively. When X = Cl, the system undergoes a symmetry-lowering distortion that shifts the valence band maximum and conduction band minimum away from the zone center, while preserving the topological insulator phase. For X = Br, we obtain a trivial insulator, and for X = I, the system is unstable. Our finding that monolayer GeCCl_{3} is a topological insulator under ambient conditions is of interest for possible applications in future devices. |
Thursday, March 7, 2019 9:24AM - 9:36AM |
R03.00008: Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial Wang You, Li-Jun Lang, Ching Hua Lee, Baile Zhang, Yidong Chong We demonstrate that harmonic generation in a left-handed NLTL can be greatly increased by the presence of a topological edge state. Our NLTL is a nonlinear analogue of the Su-Schrieffer-Heeger (SSH) lattice. Recent studies of nonlinear SSH circuits have investigated the solitonic and self-focusing behaviors of modes at the fundamental harmonic. We find, however, that frequency-mixing processes in an SSH NLTL have important effects that have previously been neglected. The presence of a topological edge mode at the first harmonic can produce strong higher-harmonic signals that propagate into the lattice, acting as an effectively nonlocal cross-phase nonlinearity. We observe maximum third-harmonic signal intensities that are 5 times that of a comparable left-handed NLTL of a conventional design, and a 250-fold intensity contrast between the topologically nontrivial and trivial lattice configurations. Our work may have applications for compact electronic frequency generators, as well as for advancing the fundamental understanding of the effects of nonlinearities on topological states. |
Thursday, March 7, 2019 9:36AM - 9:48AM |
R03.00009: Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice Huaqing Huang, Feng Liu Despite the rapid progress in the field of the quantum spin Hall (QSH) effect, most of the QSH systems studied up to now are based on crystalline materials. Here we propose that the QSH effect can be realized in quasicrystal lattices (QLs). We show that the electronic topology of aperiodic and amorphous insulators can be characterized by a spin Bott index Bs. The nontrivial QSH state in a QL is identified by a nonzero spin Bott index Bs=1, associated with robust edge states and quantized conductance. We also map out a topological phase diagram in which the QSH state lies in between a normal insulator and a weak metal phase due to the unique wave functions of QLs. Our findings not only provide a better understanding of electronic properties of quasicrystals but also extend the search of the QSH phase to aperiodic and amorphous materials that are experimentally feasible. |
Thursday, March 7, 2019 9:48AM - 10:00AM |
R03.00010: Connecting higher-order topological insulators to lower-dimensional topological insulators Akishi Matsugatani, Haruki Watanabe In recent years, the role of crystal symmetries in enriching the variety of TIs have been actively investigated. Higher-order TIs are a new type of topological crystalline insulators that exhibit gapless boundary states whose dimensionality is lower than those on the surface of conventional TIs. In this paper, relying on a concrete tight-binding model, we show that higher-order TIs can be smoothly connected to conventional TIs in a lower dimension without the bulk-gap closing or symmetry breaking. Our result supports the understanding of higher- order TIs as a stacking of lower-dimensional TIs in a way respecting all the crystalline symmetry. |
Thursday, March 7, 2019 10:00AM - 10:12AM |
R03.00011: Inequivalent Berry Phases for the Bulk Polarization Haruki Watanabe, Masaki Oshikawa We discuss the characterization of the polarization for insulators under the periodic boundary condition in terms of the Berry phase, clarifying confusing subtleties. For band insulators, the Berry phase can be formulated in terms of the Bloch function in momentum space. More generally, in the presence of interactions or disorders, one can instead use the many-body ground state as a function of the flux piercing the ring. However, the definition of the Bloch function and the way of describing the flux are not unique. As a result, the value of the Berry phase and its behavior depend on how precisely it is defined. In particular, identifying the Berry phase as a polarization, its change represents a polarization current, which also depends on the definition. We demonstrate this by elucidating mutual relations among different definitions of the Berry phase and showing that they correspond to currents measured differently in real space. Despite the nonuniqueness of the polarization current, the total charge transported during a Thouless pumping process is independent of the definition, reflecting its topological nature. |
Thursday, March 7, 2019 10:12AM - 10:24AM |
R03.00012: Magic-Angle Physics in Two-Dimensional Topological Insulators Yixing Fu, Justin Wilson, Jed Pixley The Bernevig-Hughes-Zhang (BHZ) model is a quintessential model for a two-dimensional Z_{2} topological insulator with topological and trivial insulator phases separated from each other by semimetallic critical points. We study the fate of the BHZ model in the presence of a quasiperiodic potential by using the kernel polynomial method to calculate the density of states and conductivity to determine the zero temperature phase diagram. The semimetal undergoes magic-angle transitions driven by the quasiperiodic potential, which generates flat bands at the transition to a metallic phase similar to other two-dimensional systems with Dirac nodes. Additionally, the topological insulating phases undergo quantum phase transitions into a metallic phase due to the quasiperiodic potential closing the insulating band gap. Lastly, we also study how the surface states strongly renormalize due to these unique quasiperiodic driven transitions. |
Thursday, March 7, 2019 10:24AM - 10:36AM |
R03.00013: Disentangling interacting symmetry protected phases of fermions in two dimensions Tyler Ellison, Lukasz Fidkowski We explicitly construct the ground states of certain 2+1D fermionic symmetry protected topological (SPT) phases using finite depth circuits of local unitaries. We recover the classification of the so called supercohomology SPT phases and demonstrate that the composition of our unitaries captures the corresponding SPT group structure. Our strategy is to first build an auxiliary bosonic model from group supercohomology data and then employ the recently developed lattice-level fermionization duality to obtain the fermionic SPT. This construction both yields fixed point lattice Hamiltonians that can be defined on arbitrary triangulations and disentangles the roles of supercohomology data and spin structure in fermionic SPT phases. Further, the global symmetry of our circuits implies that these SPT phases can be many-body localized. |
Thursday, March 7, 2019 10:36AM - 10:48AM |
R03.00014: Symmetry and Topology in Non-Hermitian Systems Hengyun Zhou, Jong Yeon Lee, Shang Liu, Bo Zhen The ideas of topology have found great success in Hermitian physical systems, but the incorporation of non-Hermitian effects may lead to even richer possibilities. Here, we present two results regarding the roles of symmetry and topology in non-Hermitian physical systems. First, we provide a systematic classification of non-Hermitian symmetry protected topological phases in arbitrary spatial dimension, based on the Bernard-LeClair symmetry classes. We discuss the physical insights provided by such a classification, and how it can serve as an important guide for future searches of non-Hermitian topological systems. We then discuss how symmetries can protect the existence of a surface of exceptional points, which are a natural generalization of Hermitian topological nodal phases. |
Thursday, March 7, 2019 10:48AM - 11:00AM |
R03.00015: Topological crystalline insulator states in the Ca_{2}As family XIAOTING ZHOU, Chuang-Han Hsu, Tay-Rong Chang, Qiong Ma, Pablo Jarillo-Herrero, Nuh Gedik, Arun Bansil, Vitor Pereira, Suyang Xu, Hsin Lin, Liang Fu Topological crystalline insulators (TCIs) are insulating electronic phases of matter with nontrivial topology originating from crystalline symmetries. Recent theoretical advances have proposed new TCI states protected by rotational symmetries and provided powerful guidelines to search for TCIs in real materials. Building upon recent theoretical works, we demonstrate a feasible method to identify new TCI states based on first-principles calculations.We systematically unveil the topological properties of the TCI states in Ca_{2}As. On both top and side surfaces, we observe topological surface states protected independently by rotational and mirror symmetries.We show that a particular lattice distortion can single out the newly proposed topological protection by the rotational symmetry. As a result, the Dirac points of the topological surface states are moved to generic locations in momentum space away from any high-symmetry lines. Such topological surface states have not been seen before. Our work reveals rich and exotic TCI physics across the Ca_{2}As family of materials and demonstrates a complete roadmap for uncovering TCIs topological nature based on first-principles calculations. Such a method can be broadly applied in searching for new TCIs. |
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