Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session N19: Theoretical Developments in Topological States: Multipole Moments, Flat Bands, Local Markers, and Beyond |
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Sponsoring Units: DCMP Chair: Yu-Hang Li, University of California, Riverside Room: Room 211 |
Wednesday, March 8, 2023 11:30AM - 11:42AM |
N19.00001: Phononic real Chern insulator with protected corner modes in graphynes Jiaojiao Zhu, Shengyuan A Yang Higher-order topological insulators have attracted great research interest recently. Different from conventional topological insulators, higher-order topological insulators do not necessarily require spin-orbit coupling, which makes it possible to realize them in spinless systems. Here, we study phonons in 2D graphyne family materials. By using first-principle calculations and topology/symmetry analysis, we find that phonons in both graphdiyne and γ -graphyne exhibit a second-order topology, which belongs to the specific case known as real Chern insulator. We identify the nontrivial phononic band gaps, which are characterized by nontrivial real Chern numbers enabled by the spacetime inversion symmetry. The protected phonon corner modes are verified by the calculation on a finite-size nanodisk. In addition, we show that a 3D real Chern insulator state can be realized for phonons in 3D graphdiyne. Our study extends the scope of higher-order topology to phonons in real materials. The spatially localized phonon modes could be useful for novel phononic applications. |
Wednesday, March 8, 2023 11:42AM - 11:54AM |
N19.00002: Time-Reversal Soliton Pair in Two-Dimensional Topological Insulating Systems Yi-Chun Hung, Baokai Wang, Hsin Lin, Arun Bansil Solitons on the edges of two-dimensional systems with non-trivial topology, formed through the one-dimensional mass-kink mechanism, play an important role in driving the emergence of higher-order topological phases. In this connection, the existing work has focused on gaping a single edge Dirac cone by time-reversal symmetry breaking perturbations, which are not suitable for the edge solitons in time-reversal symmetric systems with multiple edge Dirac cones. Here, we discuss the mass-kink mechanism in systems where time-reversal symmetric perturbations open the gaps of time-reversal related Dirac cones. We thus explain the appearance of pairwise corner modes and predict the value of the corner charges. Furthermore, we have developed an efficient-numerical method based on real-space renormalization group using Green's functions to calculate the phase difference of the mass terms between the adjacent edges without using nano-disks and k·p modeling. Using this technique, we demonstrate that the in-gap corner modes and the corner charges in monolayer α-Sb are generated by the mass-kink mechanism that originates from gapping two pairs of edge Dirac cones with Sz-mixing spin-orbit coupling. |
Wednesday, March 8, 2023 11:54AM - 12:06PM |
N19.00003: Polarization and corner charge in Chern insulators Sachin Vaidya, Mikael C Rechtsman, Wladimir A Benalcazar The concept of multipole moments in crystals and their quantization under symmetries has led to the discovery of higher-order topological insulators. These multipole moments are understood from a localized description of electrons in terms of exponentially localized Wannier functions (ELWFs). For instance, the dipole moment can be calculated from the displacement of the ELWF centers from the ionic center; this has allowed for a topological classification of conventional insulators or “atomic limits” under crystalline symmetries. However, such a construction of ELWFs is impossible for Chern insulators (CIs) due to the non-zero Chern number that prevents a smooth gauge choice for the states. This presents a fundamental difficulty in defining multipole moments of the electronic states in CIs. |
Wednesday, March 8, 2023 12:06PM - 12:18PM |
N19.00004: Fractional disclination charge and discrete shift in the Hofstadter butterfly Yuxuan Zhang, Naren Manjunath, Gautam Nambiar, Maissam Barkeshli In the presence of crystalline symmetries, topological phases of matter acquire a host of invariants leading to non-trivial quantized responses. Here we study a particular invariant, the discrete shift S, for the square lattice Hofstadter model of free fermions. S is associated with a Z_{M} classification in the presence of M-fold rotational symmetry and charge conservation. S gives quantized contributions to (i) the fractional charge bound to a lattice disclination, and (ii) the angular momentum of the ground state with an additional, symmetrically inserted magnetic flux. S forms its own `Hofstadter butterfly', which we numerically compute, refining the usual phase diagram of the Hofstadter model. We propose an empirical formula for S in terms of density and flux per plaquette for the Hofstadter bands, and we derive a number of general constraints. We show that bands with the same Chern number may have different values of S, although odd and even Chern number bands always have half-integer and integer values of S respectively. |
Wednesday, March 8, 2023 12:18PM - 12:30PM |
N19.00005: Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies Naren Manjunath, Maissam Barkeshli, Gautam Nambiar, Yuxuan Zhang We show how topological phases of matter in (2+1)D can possess a non-trivial intrinsic quantized charge polarization P, even in the presence of non-zero Chern number and magnetic field. For invertible topological states, P is a Z_{2} × Z_{2}, Z_{3}, Z_{2}, or Z_{1} topological invariant in the presence of M = 2, 3, 4, or 6-fold rotational symmetry, lattice (magnetic) translational symmetry, and charge conservation. P manifests in the bulk of the system as (i) a fractional quantized contribution of P · b mod 1 to the charge bound to lattice disclinations and dislocations with Burgers vector b, (ii) a notion of linear momentum for additionally inserted magnetic flux, and (iii) an oscillatory system size dependent contribution to the effective 1d polarization on a cylinder. We study P in a variety of tight-binding models of spinless free fermions in a magnetic field. We derive predictions from topological field theory, which we match to numerical calculations for the effects (i)-(iii), demonstrating that these can be used to extract P from microscopic models in an intrinsically many-body way. We show how, given a high symmetry point O, there is a corresponding discrete shift S_{O}, such that P specifies the dependence of S_{O} on O. We derive colored Hofstadter butterflies, corresponding to the quantized value of P, which further refine the colored butterflies from the Chern number and discrete shift. |
Wednesday, March 8, 2023 12:30PM - 12:42PM Author not Attending |
N19.00006: Witten effect and integer classification of three-dimensional topological insulators Pallab Goswami, Alexander C Tyner The non-trivial third homotopy class of three-dimensional topological insulators leads to quantized, magneto-electric coefficient or axion angle θ=n π, with n being an integer valued three-dimensional, winding number. We probe integer classification of θ for non-magnetic and magnetic topological insulators by computing induced electric charge on test, magnetic monopoles or Witten effect. We show that both first-order and higher-order topological insulators can exhibit quantized, magneto-electric response, irrespective of the presence of gapless surface-states, and corner-localized-states. The important roles of fermion zero-modes, CP, and flavor symmetries are critically addressed. Our work outlines a unified theoretical framework for addressing topological response and topological quantum phase transitions of three-dimensional materials. |
Wednesday, March 8, 2023 12:42PM - 12:54PM |
N19.00007: Identification of novel spin Hall platforms using magnetic flux tubes Alexander C Tyner, Pallab Goswami Field theory arguments suggest the possibility of Z classification of quantum spin Hall effect with magnetic flux tubes, that cause separation of spin and charge degrees of freedom, and pumping of spin or Kramers pair. However, the proof of principle demonstration of spin-charge separation is yet to be accomplished for realistic, ab initio band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes to unambiguously identify, for the first time, two-dimensional materials supporting unit and double strength spin Chern numbers from first-principles data. Our work sets a new standard for prediction of two-dimensional, quantum spin-Hall materials, based on precise bulk invariant and universal topological response. |
Wednesday, March 8, 2023 12:54PM - 1:06PM |
N19.00008: Topological Triviality of Strictly Local Flat Hamiltonians Pratik Sathe, Rahul Roy The topological properties of an electronic band are closely related to the localization properties of wavefunctions spanning it. It has been shown that if a set of compactly supported Wannier-type functions spans a band or a set of bands, then the band(s) are necessarily topologically trivial. An interesting implication is that a flat band in a strictly local Hamiltonian is topologically trivial. We investigate this connection between flatness and topological triviality in the absence of lattice translational invariance. We argue that a 2d strictly local Hamiltonian without symmetries is trivial if all its bands are flat (or equivalently, if it has a finite number of distinct energies). |
Wednesday, March 8, 2023 1:06PM - 1:18PM |
N19.00009: Quantum phase transitions in strongly disordered topological insulators Caio H Lewenkopf, Bryan D Assunção, Gerson J Ferreira Topological phases of matter are usually characterized by the so-called topological invariants, e.g. the Chern number or the Z_{2} invariant, that assume translational invariance. Recent studies have shown that topological invariants can be used not only to characterize pristine and/or weakly disordered materials, but also noncrystalline systems such as topological Anderson insulators, amorphous systems, and quasicrystals. For such systems, due to the lack of Bloch periodicity, the topological characterization is done using local makers, like the local Chern number or the Bott index. However, why topological systems are immune to strong disorder and when a disorder-induced topological phase transition occurs are fundamental questions that remain open. This study provides insight on these issues by studying quantum phase transitions in topological Anderson insulators, more specifically, by investigating the criticality and the universality of local markers and the Bott index in a disorder-driven topological quantum phase transition. |
Wednesday, March 8, 2023 1:18PM - 1:30PM |
N19.00010: (Co)irrep invisible topology of perfectly flat bands Dumitru Calugaru, Aaron Chew, Luis Elcoro, Yuanfeng Xu, Andrei B Bernevig In previous work [1], the authors developed a powerful method for constructing flat band models, explaining the flat bands in a myriad of crystalline materials [2]. Using Topological Quantum Chemistry, we derived sufficient criteria (in terms of momentum-space irreps) for diagnosing topologically nontrivial (i.e. topologically fragile or symmetry-protected semimetalic) flat bands. In this work, we show that some flat bands can still harbor nontrivial topology manifesting itself through gapless points or fragile topology, but otherwise not diagnosable through momentum-space irreps. We build a comprehensive, systematic, orbital-based understanding of this new “irrep-invisible” topology in all 1651 Shubnikov Space Groups, using the machinery of real space invariants. Supplementing our analysis with homotopy arguments we derive gapless criteria for irrep-invisible flat band semimetals. Finally, in some recently identified semimetallic flat band materials, we show that irrep-invisible fragile topology can arise upon gapping the flat bands with spin-orbit coupling. |
Wednesday, March 8, 2023 1:30PM - 1:42PM |
N19.00011: Many-body index for quadrupole insulators Yasuhiro Tada, Masaki Oshikawa A quadrupole insulator hosts bound states at corners of the system under the open boundary condition and is expected to possess a “bulk quadrupole moment” under the periodic boundary condition. However, there have been conflicting discussions on the latter and characterization of a quadrupole insulator in terms of the bulk quadrupole moment is still an open problem especially for interacting systems. In this study, we propose a new index for characterization of an interacting quadrupole insulator which is closely related to the bulk quadrupole moment. It can naturally lead to a bulk-boundary correspondence and also are well compatible with the periodicity of the system. We demonstrate these properties for representative models. |
Wednesday, March 8, 2023 1:42PM - 1:54PM |
N19.00012: Local topological markers in odd spatial dimensions and their application to amorphous topological matter Julia D Hannukainen, Miguel F Martínez, Jens H Bardarson, Thomas Klein Kvorning Local topological markers, topological invariants evaluated by local expectation-values, are valuable for characterizing topological phases in materials lacking translation-invariance. The Chern marker, the Chern number expressed in terms of the Fourier transformed Chern character, is an easily applicable local marker in even dimensions, but there are no analogous expression for odd dimensions. We provide general analytic expressions for local markers for free-fermion topological states in odd dimensions protected by local symmetries: a Chiral marker, a local Z_{2} marker which in case of translation invariance is equivalent to the chiral winding number, and a Chern-Simons marker, a local Z_{2} marker characterizing all non-chiral phases in odd dimensions. We achieve this by introducing a one-parameter family P_{θ} of single-particle density matrices interpolating between a trivial state and the state of interest. By interpreting the parameter θ as an additional dimension, we calculate the Chern marker for the family P_{θ}. We demonstrate the practical use of these markers by characterizing the topological phases of two amorphous Hamiltonians in three dimensions: a topological superconductor (Z classification) and a topological insulator ( Z_{2} classification). |
Wednesday, March 8, 2023 1:54PM - 2:06PM Author not Attending |
N19.00013: Quantized bulk conductivity as a local Chern marker Peru d'Ornellas, Derek K Lee, Ryan Barnett A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, the Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has been done to propose several local analogs of the Chern number, called local markers, that can be used to characterize disordered systems. However, it was unclear whether the proposed markers represented a physically measurable property of the system. We propose a local marker starting from a physical argument, as a local cross conductivity measured in the bulk of the system. We find the explicit form of the marker for a noninteracting system of electrons on the lattice and show that it corresponds to existing expressions for the Chern number. Examples are discussed for a variety of disordered and amorphous systems, showing that it is precisely quantized to the Chern number and robust against disorder. |
Wednesday, March 8, 2023 2:06PM - 2:18PM |
N19.00014: Local markers identify topology in metals and gapless systems Alexander W Cerjan, Terry A Loring Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless systems which lack a bulk band gap. Here, we develop a theory of topological metals based on the system's spectral localizer and associated Clifford pseudospectrum, which can both determine whether a system exhibits boundary-localized states despite the presence of degenerate bulk bands and provide a measure of these states' topological protection even in the absence of a bulk band gap. We demonstrate the generality of this method across symmetry classes in two lattice systems, a Chern metal and a higher-order topological metal, and prove the topology of these systems is robust to relatively strong perturbations. The ability to define invariants for metallic and gapless systems allows for the possibility of finding topological phenomena in a broad range of natural, photonic, and other artificial materials that could not be previously explored. |
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