Session A54: Defects, Disorder, and Quasiperiodicity in Topological Materials

Evidence for topological surface states in amorphous Bi2Se3

Crystalline symmetries and classification schemes have played a central role in the identification of topological materials [1-3]. We address whether amorphous topological materials, which lie beyond this classification, exist in the solid state [4]. Amorphous Bi₂Se₃ thin films show a metallic behavior and an increased bulk resistance. The low field magnetoresistance due to weak antilocalization reveals a significant number of two-dimensional surface conduction channels. Angle-resolved photoemission spectroscopy data is consistent with a dispersive two-dimensional surface state with a distinct node. Spin resolved photoemission spectroscopy shows this state has an anti-symmetric spin-texture resembling that of the surface state of crystalline Bi₂Se₃. Experimental results are consistent with an amorphous tight-binding model that utilizes a realistic amorphous structure. Evidence of amorphous materials with topological properties uncovers topological matter outside the current classification scheme, enabling materials discovery and scalable topological devices.
[1] T. Zhang, et al., Nature 566, 475 (2019)
[2] M. G. Vergniory, et al., Nature 566, 480 (2019)
[3] F. Tang, et al., Nature 566, 486 (2019)
[4] P. Corbae, et al., submitted (2019)   

Atypical Highly-Dispersive Band Structure in Putative Amorphous Topological Insulator

In typical amorphous and highly disordered materials, Anderson Localization guarantees flat valence bands. This effect is so dramatic and pervasive in the amorphous field of study that the density of states is assumed to be momentum-independent, serving as the full characterization of an amorphous system's electronic structure. In this work, we discover an exception to this rule in amorphous Bi₂Se₃ films. Angle-resolved photoemission spectroscopy uncovers an amorphous surface-state band structure with strong momentum-dependence and spin-momentum locking. We observe a Fermi surface with repeated annuli and reveal a spherically-parameterized momentum-space picture that warrants a re-evaluation of amorphous band structure on the most fundamental level.
  

Towards Realistic Amorphous Topological Insulators

The topological properties of materials are, until now, associated with the features of their crystalline structure, although translational symmetry is not an explicit requirement of the topological phases. Recent studies of hopping models on random lattices have demonstrated that amorphous materials can display a non-trivial topology. Using ab initio calculations we show that amorphous materials can also display topological insulator properties. More specifically, we present a realistic study of the electronic and transport properties of amorphous bismuthene systems, showing that they are topological insulators. These systems are characterized by the topological index Z₂=1 and bulk-edge duality, and their linear conductance is quantized, G=2e²/h, for Fermi energies within the topological gap. Our study opens the path to the investigation of amorphous topological insulator materials.   

Numerical signatures of disordered topological phases

We investigate a number of numerical signatures which distinguish the topological and trivial phases of clean and disordered insulators. In particular, we consider two dimensional systems and suggest a procedure for numerically constructing a sequence of maximally localized mutually orthogonal states which span the Hilbert space. The localization lengths of states constructed using our procedure is numerically shown to diverge as a power law for systems with non-zero Chern number, and conversely saturate for systems with zero Chern number. We construct and numerically verify a scaling argument which suggests this exponent is universal. Finally, we discuss extensions of this approach to other spatial dimensions and symmetry classes.   

Topological Phase Transition in a Disordered Inversion-Symmetric Chain

Topological crystalline phases are states which are protected by crystalline symmetries. When translational invariance is broken by bulk disorder, the topological nature of these states may change depending on the type of disorder that is applied. In this work, we characterize the phases of a one-dimensional (1D) chain with inversion and chiral symmetries where the disorder preserves the inversion symmetry on every configuration. By using a basis-independent formulation for the inversion invariant and chiral winding number, we are able to construct phase diagrams for both quantities when disorder is present. Unlike the chiral winding number, the inversion invariant is prone to fluctuations past the spectral gap closing at strong disorder. Using the real-space renormalization group, we are able to compare how differently the inversion invariant and chiral winding number behave at low energies when disorder is present.   

Dislocation defect as a bulk probe of monopole charge of multi-Weyl semimetals

We consider the electronic scattering in multi-Weyls semimetals due to dislocations defects which can be represented as an emergent effective magnetic field. We use partial wave analysis to analytically obtain the transmitted current and the conductance. From the conductance peaks as a function of the bias voltage, we can deduce monopole charge
$n$ of the corresponding multi-Weyl semimetal as well as the effective flux of the dislocation defect. We argue that this provides a simple and a robust way to measure the monopole charge of a multi-Weyl semimetal.
  

Bound-state spectrum of superconductors with magnetic-texture defects

Recent experiments [1] provided evidence for zero-energy Majorana bound states (MBSs) when magnetic adatoms are deposited onto a superconductor. Such observations are reconcilable by means of 0D-like defects which trap MBSs. Existing explanations rely on the presence of isolated magnetic skyrmions or vortices in the spin-orbit coupling field. These need to be contrasted to the standard mechanism, in which MBSs are trapped in vortices of the superconducting order parameter. Inspired from the above, we explore a novel promising path towards realizing MBSs, which relies on 0D defects in the order parameter describing a textured magnetic order that coexists with spin-singlet superconductivity. This scenario appears relevant for iron-pnictides, where a theoretical study [2] has revealed that textured magnetism is accessible in doped BaFe₂As₂ and LaFeAsO. Here, we perform a thorough numerical investigation of the bound-state energy spectrum arising when vortices are introduced in the order parameter of spin-spiral and -whirl magnetic orders. Our preliminary results indicate that the defect-induced MBSs are accessible in superconductors which yield a nodal spectrum in the absence of the magnetic order.

[1] Ménard et al, Nat. Com. 10, 2587 (2019)
[2] Christensen et al, PRX 8, 041022 (2018)   

In-gap excitations due to defects in topological superconductor with spin-orbit coupling

Recent microscopy experiments on superconducting monolayer of lead(Pb) grown over clusters of cobalt atoms have raised urgent questions about in-gap electronic states in presence of strong spin-orbit coupling and magnetism.
Using analytics and numerics we find that a topological defect in Rashba spin-orbit coupling (in contrast to a vortex in superconducting pairing) fully explains puzzling features of this experiment: 1) Two different zero-modes, one point-like at center of cluster and the other ring-shaped around it; 2) The zero mode pair is protected by a large energy gap; 3) The localization lengthscale inside the cluster is far smaller than superconducting coherence length , but comparable to it outside. The theory predicts that this is a Majorana pair, with remarkable isolation in energy thanks to the defect in strong spin-orbit coupling. We discuss the role of magnetic textures in our theoretical scenario.   

CT-symmetric Non-linear Topological Defect Modes

Topologically protected states have recently been a subject of increasing interest due to their unique robustness against disorder. Such property is beneficial for a variety of photonics applications ranging from lasers to optical isolators and receiver protectors. On the other hand, an essential piece of information associated with the interplay between optical nonlinearities and topological protection is still missing. Such a question cannot be ignored, since nonlinearity is prevalent in realistic circumstances. Using a non-linear SSH model we have theoretically analyzed the topological nature of an emerging nonlinear defect mode associated with a non-linear defect. To this end, we have devised a theoretical formalism which is based on Green’s functions and prove that for certain type of nonlinearities the nonlinear defect mode is spectrally protected by a charge-conjugation (CT) symmetry. We demonstrate the validity of our study via direct measurements using a CROW SSH array in the microwave domain.   

Aperiodic Topological Boundary Modes: Revisiting Quasi-Periodic Localization

Although physical systems are generically aperiodic, most work on non-interacting topological materials focuses on translation-invariant cases. These systems are well described by band theory and perturbatively resistant to the disorder of real world conditions, however, the regime of strong aperiodicity is not frequently discussed in the context of topological materials. Aiming to better understand such systems, this work generalizes key results in translation-invariant systems to their aperiodic counterparts. We then apply these techniques to the canonical Andre-Aubrey-Harper (AAH) Model and its 1D Metal-Insulator Transition (MIT). We uncover a deep connection between the known non-commutative topological properties of the model and the MIT. This not only highlights the power of this non-commutative technology, but also separates the AAH model from its disordered counterparts. The 1D MIT in the AAH model and its peculiar properties are indeed topological in nature. This suggests quasiperiodic systems form their own special class of topological materials distinct from their translation-invariant counterparts.   

The existence of robust edge currents in Sierpinsky Fractals

We investigate the Hall conductivity in a Sierpinski carpet, a fractal of Hausdor dimension d_f = ln(8)/ ln(3) ≈ 1.893, subject to a perpendicular magnetic field. We compute the Hall conductivity using linear response and the recursive Green function method. Our main finding is that edge modes, corresponding to a maximum Hall conductivity of at least σ_xy = ± e²/h, seems to be generically present for arbitrary finite field strength, no mater how one approaches the thermodynamic limit of
the fractal. We discuss a simple counting rule to determine the maximal number of edge modes in terms of paths through the system with a fixed width. This quantized edge conductance, as in the case of the conventional Hofstadter problem, is stable with respect to disorder and thus a robust feature of the system.   

Tracking the mechanism behind graphene ripple inversion with LAMMPs

Freestanding graphene spontaneously forms ripples. If a sheet is under sufficient compressive strain, the ripples form a bi-stable system (concave or convex). The rate at which a ripple inverts is lower than the small thermal oscillation frequency. This rate decreases with increased compressive strain, and increases with increased temperature. We ran ten simulations, using LAMMPs molecular dynamics simulation software, for a single ripple of graphene, with different compressive strains at 3000 K. The z-component (out of plane) average and center values were tracked to identify when inversion occurs. Atoms that make up a cross-section of the ripple were also tracked. Changes in the cross-section profile that occur during inversion show that the mechanism behind inversion is the formation of smaller sub-ripples.   

Anomalous Hall effect in chiral superconductors from impurity superlattices

Unlike anomalous quantum Hall insulators, clean single-band chiral superconductors do not exhibit intrinsic Hall effect at the one-loop approximation. Finite ac Hall conductance was found to emerge beyond one-loop, such as with vertex corrections associated with extrinsic random impurity scatterings. In this work, we consider the effect of impurities embedded in chiral superconductors in a superlattice pattern, instead of in random distributions. The impurity-induced Bogoliubov quasiparticle bound states hybridize to form subgap bands, constituting an emergent low-energy effective theory whose anomalous Hall effect can be studied with ease. We demonstrate that the occurrence of the Hall effect depends on the superlattice geometry and the parity of the chiral pairing. In particular, due to the composite particle-hole character of the subgap states, the Hall conductance arises at the one-loop level of the current-current correlator in our effective model. Generalized to random impurities, our theory sheds new light on the physics of impurity-induced anomalous Hall conductivity in chiral superconductors.   

Disorder perturbations of topological superconductor surface fluids: Semiclassical geodesic approach

We consider the interplay between topology and disorder on the surface fluids of topological
superconductors (TSCs). In the case of a single 2D Majorana cone, only “quenched gravitational disorder
(QGD)” is allowed, i.e. a static modulation of the effective speed of light. Although disorder effects near
zero energy have been understood for a long time, recent numerical results uncovered an unexpected
result: finite energy TSC surface states form “stacks” of quantum critical wave functions, with universal,
energy-independent statistics [1,2,3]. In classes CI and AIII, one finds stacks of quantum Hall plateau
transition states [1,2]. For the single Majorana cone with QGD in class DIII, the stacked critical states
appear to belong to a new class [3]. In order to shed light on the DIII results, we consider a semiclassical
approach. We find that kinetic theory predicts a divergent conductivity at all temperatures. We further
study the statistical properties of the null geodesics in the 2+1-D quenched random spacetime metric
that can be associated to QGD.
[1] S. A. A. Ghorashi, Y. Liao, M. S. Foster, Phys. Rev. Lett. 121, 016802 (2018)
[2] B. Sbierski, J. Karcher, M. S. Foster, unpublished
[2] S. A. A. Ghorashi and M. S. Foster, arXiv:1903.11086   

Antisite defect enhanced thermoelectric performance of topological crystalline insulators

As the first experimentally established topological crystalline insulator (TCI), SnTe also exhibits superior thermoelectricity upon proper doping; yet to date, whether such doping will preserve or destroy the salient topological properties in achieving outstanding thermoelectric performance remains elusive. Using first-principles calculations combined with Boltzmann transport theory, we uncover the elegant role of antisite defect in optimally enhancing the thermopower of SnTe while simultaneously preserving its topological nature. We first show that Sn_Te antisite defect effectively induces pronounced variations in the low-energy density of states rather than rigidly shifting the chemical potential, resulting in higher Seebeck coefficient and power factor. Next, we demonstrate that in a wide temperature range the Seebeck coefficient of antisite doped SnTe distinctly outperforms previously identified systems invoking extrinsic dopants. We further confirm that such intrinsic antisite doping preserves the nontrivial topology, which in turn favors high electrical conductivity and thermoelectricity. These findings render antisite doping as a natural and powerful avenue to optimize the overall thermoelectric performance of TCIs and related systems.