Session M70: Theory of Topological Materials I: New Methods and Classifications

A new spin on topological material modeling from topological quantum chemistry

The past several years have seen a flurry of activity in the prediction, modeling, and discovery of new topological materials. Much of this activity has been enabled by symmetry-based approaches to band theory such as the theory of topological quantum chemistry and symmetry-based indicators of band topology, allowing for the discovery of multifold nodal semimetals, higher-order topological insulators, and fragile topology. More than just a classification tool, however, symmetry-based approaches can also be used to model observables in topological materials. In this talk, I will show how topological quantum chemistry allows us to predict new phenomena in topological insulators and semimetals. Focusing first on magnetic materials, I will show how magnetic space group theory leads us to predict a novel non-dissipative viscosity coefficient in magnetic topological semimetals and allows us to compute its value in simple tight-binding models. Next, I will show how we can gain new insights into dynamical axion electrodynamics in Weyl charge-density wave systems using simple models built from magnetic band representations. Turning to time-reversal invariant systems, I will apply position space tools to the study of bulk signatures of higher order topological insulators and topological semimetals. For centrosymmetric systems I will show how higher order topology manifests in the bulk spin texture. Finally, for non-centrosymmetric semimetals I will show how topological quantum chemistry sheds light on the interplay between spin, chirality, and band topology.   

Applications of a novel interband topological index in condensed matter: optical selection rules and valley physics

We introduce a novel gauge-invariant, quantized interband index for condensed matter systems. We show how this index may be used to potentially: A) strengthen exciton optical selection rule theory into gauge invariant forms; and B) improve the topological description of so-called valleys in 2D materials. We provide numerical calculations of the interband index in model Hamiltonian systems as evidence for both applications A) and B).   

Comprehensive Catalogue of Nearest Neighbor Uniform Hopping Flat Band Models

Flat band systems have emerged recently as a topic of intense interest due to their ability to manifest topological correlated phenomena. Through frustration of hopping due to the topological connectedness of a tight binding lattice, flat bands can emerge in a variety of systems, allowing the study of exotic physics in a wide range of regimes. In this talk, I will discuss recent progress on high throughput computational searches for realistic novel flat band lattice models generated from materials databases. A wide variety of physically realizable models are obtained with exciting opportunities for further experimental and theoretical study.   

Periodic Table of Flat Bands and the Origin of Band Flatness

Flat bands provide a natural platform for emergent electronic states beyond Landau paradigm. However, it is still considered a great "luck" to find a new flat band. Sometimes we can do it through careful engineering (fine-tuning") of material properties, sometimes we can do it by twisting multilayer heterostructures, sometimes we involve magnetic fields to produce flat Landau levels. Is there something similar between these different cases of flat bands? It appears that in each of these cases we can point out on the common origin of the perfectly flat bands, which is the (self)-trapping in the real space. To find the essence of the phenomena, we investigate only the perfectly flat bands, which surprisingly form a "periodic table" depending on their topological and tight binding properties. The claim is that all the realistic flat band are derivatives of (7+1) classes of perfectly flat bands on the lattice, including radically different examples such as atomic insulator, Landau levels, and perfectly flat bands in twisted bilayer graphene. Through using the quantum geometric tensor we justify the remarkable connection between band flatness obstruction and the (higher) Chern numbers, an argument which is independent from the lattice symmetries.   

Assessing Chiral Induced Spin Selectivity (CISS) Effect for Quantum Computing Applications

Transport via quantum tunneling through organic molecules has an unexpectedly high efficiency in biological systems due to a lack of backscattering, making it an area of interest for developing new information technology applications. Biological chiral molecules have been experimentally demonstrated to produce spin-filtering in transmitted electrons. The spin-filtering properties of chiral molecules can be used to prepare electronic spins at room temperature, while the coherent transport properties can be used to facilitate room temperature qubit preparation and transport. Chiral molecular junctions have the potential to act as interconnects between nuclear spin nodes at the nanoscale, but the coherence of the electron transmission has not been verified. In this work, computational approaches to simulate electron transport in a simple chiral carbon wire are described. Electron transport is characterized by assessing the phase shift of the spin density matrix, obtaining the transmission function of the tunneling, and by obtaining the band structure of the topological material. The suitability of chiral interconnects for quantum computing applications is determined.   

Constant Berry curvature, GMP algebra and Chern insulators

Band geometry, especially the Berry curvature, has played an important role in topological systems. A non-vanishing Berry curvature leads to coordinates that do not commute and resembles the effects of a magnetic field. Motivated by the analog between Chern insulators and Landau levels, constant Berry curvature and the GMP algebra have been suggested as good conditions to realise fractional Chern insulators. We show that while in two-band models, there is a topological obstruction to make the Berry curvature exactly flat, it is possible to do so with three or more degrees of freedom per unit cell. However, through numerical calculations, we find that constant Berry curvature does not always improve realising bosonic fractional Chern insulator states. Moreover, we show that the GMP algebra, the Landau-level commutation relation for density operators, cannot be realised in lattice models with finite bands.   

Inverse scattering measurements map the topology of tilings

We show that diffraction features of 1D quasicrystals can be retrieved from a single topological quantity, the Čech cohomology group, H* = Z^2 , which encodes all relevant combinatorial information of tilings. We present a constructive way to calculate H* for a large variety of aperiodic tilings. By means of two winding numbers, we compare the diffraction features contained in H* to the gap labeling theorem, another topological tool used to label spectral gaps in the integrated density of states. In the light of this topological description, we discuss similarities and differences between families of aperiodic tilings, and the resilience of topological features against perturbations.   

Hyperbolic Matter in topolectric circuits: a novel experimental platform for topological states of matter

We introduce the theoretical foundation and first-ever experimental realization of hyperbolic matter, a novel state of matter in curved space that multifariously contradicts Euclidean geometric intuition. It is made of particles moving in the infinite two-dimensional hyperbolic plane. Curvature of space is emulated through a hyperbolic lattice using topolectric circuit networks relying on a newly developed complex-phase circuit element. The experiment is enabled by the theoretical insights from hyperbolic band theory that momentum space of two-dimensional hyperbolic matter is four-, six- or higher-dimensional. We experimentally realize hyperbolic graphene as an example of topologically nontrivial hyperbolic matter and compare measurements of Dirac particles and Berry curvature to hyperbolic band theory. Our work sets the stage to realize interacting and quantum hyperbolic matter to challenge our established theories of Physics in curved space.   

Currents of topological marker in dynamically controlled Chern Insulators

Motivated by the recent development of the local Chern marker theory we propose a new perspective on the dynamics of the topological markers. This approach allows us to introduce the currents of the marker explicitly. Our definition satisfies the lattice continuity equation and has a clear physical interpretation in terms of density currents. Using this method, we demonstrated numerically the position control of a topologically nontrivial subsystem inside a finite sample. We believe that our framework will help to understand the dynamics of inhomogeneous topological insulators.   

Non-linear topolectric circuits: A new frontier in synthetic metamaterial design

Topolectric circuits have proven themselves as a versatile, easily accessible and flexible platform to study topological states in metamaterials. As of yet, the majority of explored models are linear circuits, consisting only of resistors, capacitors, and inductors, despite the family of electric circuit elements being far larger. Circuit networks incorporating non-linear components, such as diodes, transistors or more complex analog multipliers, promise new intriguing phenomena, such as the interplay of non-linear chaos with topology. In this presentation, we will summarize the field's state of the art, which reaches from Floquet states in periodically driven networks to Soliton solutions of non-linear transmission lines. We will elaborate on the chances and challenges non-linearities pose, and argue that they will be paramount for the next step in metamaterial design.   

Computational design of graphene nanoribbons with tunable topological properties

During the last decade, on-surface synthesis techniques have paved the way to obtain atomically-precise bottom-up graphene nanoribbons (GNRs). In this context, the unprecedented level of control of the chemical substitution and overall morphology of the GNRs has given rise to the exploration of novel features in these systems, such as topological phases and magnetic properties.

In this work, Density Functional Theory simulations are performed to achieve atomic-level insights into the electronic structure and topological properties of a set of width-modulated pristine GNRs. The consequences of altering the ribbon morphology are studied by considering ribbons with sections of unequal widths that have different lengths. We found that GNRs from the same structural family can exhibit different Zak phases and that the proper combination of diverse segments allows tuning the band gap and topology of the composite system. Our results might prove relevant for the design of new experiments to further describe these materials, as well as for the development of novel devices in a vast assortment of applications in nanoelectronics.