Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method

Abstract

We present an algorithm to determine topological invariants of inhomogeneous systems, such as alloys, disordered crystals, or amorphous systems. Based on the kernel polynomial method, our algorithm allows us to study samples with more than $10^7$ degrees of freedom. Our method enables the study of large complex compounds, where disorder is inherent to the system. We use it to analyse Pb${}_{1-x}$Sn${}_x$Te and tighten the critical concentration for the phase transition.

arXiv comment4 pages + supplemental material

References in corpus (57)

• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological quantum matter with symmetries
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Topological Crystalline Insulators in the SnTe Material Class
• Kwant: a software package for quantum transport
• The (High Quality) Topological Materials In The World
• The Kernel Polynomial Method
• Experimental realization of a topological crystalline insulator in SnTe
• Catalogue of Topological Electronic Materials
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• Topological classification of crystalline insulators through band structure combinatorics
• Topological Anderson Insulator
• Nearsightedness of Electronic Matter
• Theory of the topological Anderson insulator
• Photonic Topological Anderson Insulators
• Amorphous topological insulators constructed from random point sets
• Mapping topological order in coordinate space
• Observation of Dirac node formation and mass acquisition in a topological crystalline insulator
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Experimental realization of on-chip topological nanoelectromechanical metamaterials
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Scattering theory of topological insulators and superconductors
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Tunability of the k-space Location of the Dirac Cones in the Topological Crystalline Insulator Pb1-xSnxTe
• Topological phases without crystalline counterparts
• K-Theory and Pseudospectra for Topological Insulators
• Localization Bounds for an Electron Gas
• Robust spin-polarized midgap states at step edges of topological crystalline insulators
• Real-space calculation of the conductivity tensor for disordered topological matter
• Experimental observation of Dirac-like surface states and topological phase transition in Pb${}_{1-x}$Sn${}_x$Te(111) films
• Statistical Topological Insulators
• AIII and BDI Topological Systems at Strong Disorder
• Topological insulators beyond the Brillouin zone via Chern parity
• Orbital Magnetization as a Local Property
• Topological Marker Currents in Chern Insulators
• Topological edge floppy modes in disordered fiber networks
• Real space mapping of topological invariants using artificial neural networks
• Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker
• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• Coupled-layer description of topological crystalline insulators
• Quantum transport in disordered systems under magnetic fields: A study based on operator algebras
• Surface-state-dominated transport in crystals of the topological crystalline insulator In-doped Pb${}_{1-x}$Sn${}_x$Te
• A New Numerical Method for ${\mathbb{Z}}_2$ Topological Insulators with Strong Disorder
• Topological phase transitions in bulk

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• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Kibble-Zurek behavior in disordered Chern insulators
• Local Topological Markers in Odd Dimensions
• Amorphous topological phases protected by continuous rotation symmetry
• Invariants of disordered semimetals via the spectral localizer
• Criticality in amorphous topological matter -- beyond the universal scaling paradigm
• Anderson-Kitaev spin liquid
• Probing topology in nonlinear topological materials using numerical $K$-theory
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Phase transitions and scale invariance in topological Anderson insulators
• Structural disorder-driven topological phase transition in noncentrosymmetric BiTeI
• Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula
• Hinge Spin Polarization in Magnetic Topological Insulators Revealed by Resistance Switch
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Exceptional dynamics of interacting spin liquids
• Nonlinear Hall effect on a disordered lattice
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• Replica Higher-Order Topology of Hofstadter Butterflies in Twisted Bilayer Graphene
• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Electron-phonon coupling and superconductivity in the doped topological-crystalline insulator (Pb${}_{0.5}$Sn${}_{0.5}$)${}_{1-x}$In${}_x$Te
• Disorder-Induced Delocalization in Magic-Angle Twisted Bilayer Graphene
• 1D quasicrystals and topological markers
• Quantum Hall effect and Landau levels without spatial long-range correlations
• A spectrum adaptive kernel polynomial method
• Polarization textures in crystal supercells with topological bands
• Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker
• Evaluation of real-space second Chern number using the kernel polynomial method
• Emergent fractals in dirty topological crystals
• Regularized universal topological markers for Dirac systems
• Isotropic 3D topological phases with broken time reversal symmetry
• Quantum Hall Effect without Chern Bands
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
• Markov Inequality as a Tool for Linear-Scaling Estimation of Local Observables
• Physical Pictures for Quasisymmetry in Crystals