Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session P44: Topological Protection in Correlated Electron Systems 2 |
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Sponsoring Units: DCMP Chair: Saurabh Maiti, University of Massachusetts Amherst Room: LACC 504 |
Wednesday, March 7, 2018 2:30PM - 2:42PM |
P44.00001: Gapless Symmetry Protected Topological Order Thomas Scaffidi, Daniel Parker, Romain Vasseur We introduce exactly solvable gapless quantum systems in d dimensions that support symmetry protected topological (SPT) edge modes. Our construction leads to bosonic, long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls "decorated" with dimension (d−1) SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry-broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, these edge modes are robust against arbitrary symmetry-preserving local perturbations near the edges. In two dimensions, we construct wavefunctions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics. |
Wednesday, March 7, 2018 2:42PM - 2:54PM |
P44.00002: Interface Symmetry-Protected Topological States Luiz Santos, Jennifer Cano, Michael Mulligan, Taylor Hughes Bosonic Symmetry-Protected Topological (SPT) states are entangled gapped phases of matter fundamentally different than trivial product states. I will discuss a mechanism whereby local interactions give rise to one-dimensional SPT states at the gapped interface between two dimensional systems. I shall approach this interface problem using a one-dimensional Luttinger liquid theory whose instability towards a gapped state is driven by local interactions that respect a set of discrete symmetries responsible for the stable properties of the emergent SPT state. I will discuss the entanglement properties as well as zero mode excitations supported by domain walls along these SPT interfaces. |
Wednesday, March 7, 2018 2:54PM - 3:06PM |
P44.00003: Kondo Effect with Weyl Semimetal Fermi Arcs Da Ma, Hua Chen, Haiwen Liu, Xincheng Xie We investigate the Kondo effect of the Fermi arcs in a time-reversal-invariant Weyl semimetal with the variational method. To show the consequence brought out by the nontrivial spin texture, we calculate the spatial spin-spin correlation functions. The correlation functions exhibit high anisotropy. The diagonal correlation functions are dominated by the antiferromagnetic correlation while the off-diagonal part has more complicated pattern. The correlation functions obey the same symmetry as the spin texture. Tuning chemical potential changes the pattern of the correlation functions and the correlation length. The correlation functions of the Weyl semimetal Fermi arcs and that from a Dirac semimetal show discrepancy. |
Wednesday, March 7, 2018 3:06PM - 3:18PM |
P44.00004: Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point Vladyslav Kozii, Liang Fu We introduce a topological theory to study quasiparticles in interacting and/or disordered many-body systems, which have a finite lifetime due to inelastic and/or elastic scattering. The one-body quasiparticle Hamiltonian includes both the Bloch Hamiltonian of band theory and the self-energy due to interactions, which is non-Hermitian when quasiparticle lifetime is finite. We study the topology of non-Hermitian quasiparticle Hamiltonians in momentum space, whose energy spectrum is complex. The interplay of band structure and quasiparticle lifetime is found to have remarkable consequences in zero- and small-gap systems. In particular, we predict the existence of topological exceptional point and bulk Fermi arc in Dirac materials with two distinct quasiparticle lifetimes. |
Wednesday, March 7, 2018 3:18PM - 3:30PM |
P44.00005: Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions Chenjie Wang, Nat Tantivasadakarn, Meng Cheng We study Abelian braiding statistics of loop excitations in three-dimensional (3D) gauge theories with fermionic particles and the closely related problem of classifying 3D fermionic symmetry-protected topological (FSPT) phases with unitary symmetries. It is known that the two problems are related by turning FSPT phases into gauge theories through gauging the global symmetry of the former. We show that there exist certain types of Abelian loop braiding statistics that are allowed only in the the presence of fermionic particles, which correspond to 3D ``intrinsic'' FSPT phases, i.e., those that do not stem from bosonic SPT phases. We show that the simplest unitary symmetry to support 3D intrinsic FSPT phases is $\mathbb{Z}_2\times\mathbb{Z}_4$. To establish the results, we first derive a complete set of physical constraints on Abelian loop braiding statistics. Solving the constraints, we obtain all possible Abelian loop braiding statistics in 3D gauge theories, including those that correspond to intrinsic FSPT phases. Then, we construct exactly soluble state-sum models to realize the loop braiding statistics. These state-sum models generalize the well-known Crane-Yetter and Dijkgraaf-Witten models. |
Wednesday, March 7, 2018 3:30PM - 3:42PM |
P44.00006: Symmetry breaking and fermionic fractional Chern insulator in topologically trivial bands Stefanos Kourtis We describe a mechanism by which fermions in topologically trivial bands can form correlated states exhibiting a fractional quantum Hall (FQH) effect upon introduction of strong repulsive interactions. These states are solid-liquid composites, in which a FQH liquid is induced by the formation of charge order (CO), following a recently proposed paradigm of symmetry-breaking topological (SBT) order [Phys. Rev. Lett. 113, 216404 (2014)]. We devise a spinless fermion model on a triangular lattice, featuring a topologically trivial phase when interactions are omitted. Adding strong short-range repulsion, we first establish a repulsion-driven CO phase at density ρ_{CO} = 2/3 particles per site, then dope the model to higher densities ρ = ρ_{CO} + ν/6. At ν=1/3,2/5 (ρ=13/18,11/15), we observe definitive signatures of both CO and the FQH effect --- sharply peaked static structure factor, gapped and degenerate energy spectrum and fractionally quantized Hall conductivity σ_{H} = 1/3,2/5 in units of e^{2}/h --- over a range of all model parameters. We thus obtain the first strong evidence for fermionic SBT order in topologically trivial bands. |
Wednesday, March 7, 2018 3:42PM - 3:54PM |
P44.00007: Partial transpose and many-body invariants in fermionic symmetry protected topological phases Ken Shiozaki, Hassan Shapourian, Shinsei Ryu We developed a fully many-body formulation of non-local order parameters which detect various topological phases of fermions protected by antiunitary symmetry. Our formulation does not refer to single particle wave functions. An important ingredient for the construction of non-local order parameters is a fermionic counter part of partial transpose, which I give the detail in this talk. As an application, I present the many-body extension of the Kane-Mele Z2 topological invariant for time-reversal symmetric topological insulators in two spatial dimensions. |
Wednesday, March 7, 2018 3:54PM - 4:06PM |
P44.00008: Higgs mechanism of rank-2 gauge theory and fracton topological order Han Ma, Michael Hermele, Xie Chen Fractons are quasiparticle excitations in d = 3 gapped topological ordered phases whose motion is constrained. Their physical mechanism for generating them is still missing. It has been noticed that in the higher rank U(1) gauge theories, charges cannot move freely due to the extra conservation laws. To make connection to the gapped fracton models, we study what happens when the higher rank gauge theories are Higgsed. Surprisingly, all the higher rank Z_N gauge theories obtained through Higgsing do not contain fractons. In particular, we show that the rank-2 Z_2 gauge theories are equivalent to several copies of Toric Codes while fracton topological order appears when certain degrees of freedom of the gauge fields are frozen. We demonstrate this result by identifying the conservation law under Higgsing and also by explicitly analyzing the model after Higgsing. |
Wednesday, March 7, 2018 4:06PM - 4:18PM |
P44.00009: Beyond Topological Order: Quantum Field Theory of X-Cube Fracton Order and Robust Degeneracy from Geometry Kevin Slagle, Yong-Baek Kim Topologically ordered quantum phases of matter are often characterized by their topological excitations and degeneracy. Recently however, exactly solvable 3D lattice models have been discovered for a new kind of phase beyond topological order in which the topological excitations exhibit remarkable mobility restrictions [1,2]. These phases can have so-called fracton topological excitations, which are immobile when isolated from other fractons. Additionally, in type I fracton orders, a pair of fractons can move along a 2D surface and so-called lineons can only move along straight lines. Unlike liquid topologically ordered phases which are only sensitive to topology (e.g. ground state degeneracy only depends on topology of spatial manifold), fracton orders are also sensitive to the geometry of the lattice and are thus beyond topological order. |
Wednesday, March 7, 2018 4:18PM - 4:30PM |
P44.00010: Spectral Functions and Exact Solutions of a Quantum Dimer Model for Topological Metals Matthias Punk, Sebastian Huber, Johannes Feldmeier I will present numerical results for the single electron spectral function of a quantum dimer model introduced in Ref. [1], which captures several properties of the pseudogap state in underdoped cuprates. This model features a metallic ground state with topological order, a so-called fractionalized Fermi liquid. Our results show a well developed pseudogap in the antinodal region of the Brillouin zone, with an angular dependence in accordance with photoemission experiments. Besides these numerical results I will also discuss an interesting exact solution of this model, which indicates that the ground state is indeed a fractionalized Fermi liquid. |
Wednesday, March 7, 2018 4:30PM - 4:42PM |
P44.00011: Excitonic instability in optically-pumped three-dimensional Dirac materials Anna Pertsova, Alexander Balatsky We discuss the possibility of achieving a transient excitonic condensate in optically-pumped three-dimensional (3D) DMs, such as Dirac and Weyl semimetals, described by non-equilibrium chemical potentials for photoexcited electrons and hole. We find that for pumped 3D DMs with screened Coulomb potential two possible excitonic phases exist, an excitonic insulator phase and the charge density wave phase originating from intranodal and internodal interactions, respectively. In the pumped case, the critical coupling for excitonic instability vanishes; therefore, the two phases coexist for arbitrarily weak coupling strengths. The excitonic gap in the charge density wave phase is always the largest one. We present the signatures of the transient excitonic condensate that could be probed by scanning tunneling spectroscopy, photoemission and optical conductivity measurements. Finally, we provide estimates of critical temperatures and excitonic gaps for existing and hypothetical 3D DMs. |
Wednesday, March 7, 2018 4:42PM - 4:54PM |
P44.00012: Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators SangEun Han, Eun-Gook Moon Topological Dirac / Weyl semi-metals is generically protected by a chiral symmetry, which refers to a lattice symmetry that protects energy gapless-ness of the semi-metals. A mirror symmetry in the Dirac semi-metal of the distorted spinel, BiZnSiO_{4}, is one prime example, and thus a chiral symmetry breaking transition is intrinsically tied to topological phase transitions. We find that a chiral symmetry order-parameter and the instantaneous long range Coulomb interaction in topological semi-metals reveal characteristic quantum critical behaviors. We show that a topological transition associated with a chiral symmetry is stable under the presence of the Coulomb interaction. Furthermore, the electron velocity always becomes faster than the order parameter velocity in three spatial dimensions. Thus, the transition is not relativistic. This implies a supersymmetry is forbidden by the long range Coulomb interaction in some chiral symmetry breaking transitions. Exact universal ratios of physical quantities such as energy gap are obtained, and further implications of our calculations with experimental consequences are also discussed. |
Wednesday, March 7, 2018 4:54PM - 5:06PM |
P44.00013: Non-zero Berry phase and anomaly in Hall resistivity on GdB_{4} : a new type of a magnetic semimetal with nontrivial topology WonHyuk Shon, Dong-Choon Rhyu, Kyoo Kim, Heon-Jung Kim, Jong-Soo Rhyee, Byung Min, Boyoun Kang, Beongki Cho, Sung-Jin Kim Electrical transport measurements were performed on high-quality GdB_{4} single crystal with high residual resistivity ratio (RRR) > 300 under applying magnetic fields up to 14 T. In the absence of magnetic field, the temperaturedependent electrical resistivity ρ(T) shows a metallic behavior with antiferromagnetic and hidden transitions at TN = 43 K and Tt = 6 K, respectively. With increasing magnetic fields, this metallic behavior turns into a seemingly “insulating” one with saturation at Tt < 6 K, which indicates partial gapping of the Fermi surface. At Tt < 6 K, evidences for a topologically non-trivial metallic state are found, such as extremely large magneto-resistance (73,000 % at 2 K, 9 T), non-zero Berry phase, anomalous contribution in Hall resistivity, and negative longitudinal magnetoresistance (LMR). Here we argue that the anomalous contribution in Hall resistivity and non-zero Berry phase are manifestations of a topological metallic state realizable when either spin chirality in the real space or topological node in the k space exists. The observation of negative LMR with weak antilocalization whose origin is Adler-Bell-Jackiw anomaly further supports the former scenario. |
Wednesday, March 7, 2018 5:06PM - 5:18PM |
P44.00014: Electronic correlations and chiral, nonlocal transport in surface states of HfNiSn single crystals Lucia Steinke, Hua He, Mason Klemm, Timothy Lovorn, Allan MacDonald, Meigan Aronson Topological insulators (TI), with metallic surface or edge states that are protected against backscattering, could see applications in low-power electronics and spintronics. In most TI identified to date, the valence and conduction band appear in reverse order compared to an equivalent monoatomic insulator. Here, we explore a different route towards topologically nontrivial states that may arise from metallic surface states in topologically trivial bulk insulators without such band inversion. We present first experimental work on high-quality single crystals of HfNiSn, where magnetotransport measurements show surface transport with weak anti-localization, consistent with a metallic surface state showing strong spin-orbit coupling, and nonlinear I(V) characteristics that indicate electronic correlations. A nonlocal transport component that violates Onsager reciprocity could imply chiral edge state conduction, qualitatively similar to quantum Hall edge states, yet in the absence of external magnetic fields. Common energy scales for electronic correlations and other transport anomalies suggest that the correlations themselves may play a decisive role in creating a topologically nontrivial state on the HfNiSn surface. |
Wednesday, March 7, 2018 5:18PM - 5:30PM |
P44.00015: Vectorial field STM study on a topological and correlated magnet Jiaxin Yin, Songtian Sonia Zhang, Ilya Belopolski, Guoqing Chang, Biao Lian, Hao Zheng, Shuang Jia, Zhongyi Lu, Hsin Lin, Ziqiang Wang, Wenhong Wang, Zahid Hasan We utilize a combination of vector magnetic field and high resolution scanning tunneling microscopy to visualize the electronic response to vector magnetization in an iron-tin topological magnet. Atomically resolved images of the cleaving surface show both an iron-tin kagome lattice and a tin honeycomb lattice. We find that a quantum electronic state from the kagome lattice couples strongly and 3D-anisotropically with the magnetization. Moreover, the orbital symmetry of this quantum state can be controlled by the vector magnetic field. These large and anisotropic electronic responses cannot be explained by conventional Zeeman physics, but strongly point to a topological origin. These results will help us understand the interplay between magnetism and topological order in a correlated magnet. |
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