Alexander Lau

Alexander Lau
Polish Academy of Sciences | PAN · International Research Centre MagTop

PhD
Marie Skłodowska-Curie Research Fellow

About

27
Publications
5,622
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
359
Citations
Additional affiliations
November 2019 - present
Polish Academy of Sciences
Position
  • PostDoc Position
November 2017 - October 2019
Delft University of Technology
Position
  • PostDoc Position
October 2015 - February 2016
Technische Universität Dresden
Position
  • Teaching Assistent
Description
  • Course: Theoretical Electrodynamics
Education
April 2014 - March 2018
Technische Universität Dresden
Field of study
  • Physics
October 2011 - June 2012
University of Bristol
Field of study
  • Mathematics
October 2008 - December 2013
Technische Universität Dresden
Field of study
  • Physics

Publications

Publications (27)
Article
Full-text available
We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the partial polarizations which we show to be quantized in presence of a 1D mirror point. The topological invariant determines the g...
Article
Full-text available
We construct a two-dimensional higher-order topological phase protected by a quasicrystalline eightfold rotation symmetry. Our tight-binding model describes a superconductor on the Ammann-Beenker tiling hosting localized Majorana zero modes at the corners of an octagonal sample. In order to analyze this model, we introduce Hamiltonians generated by...
Preprint
Full-text available
Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat band systems are an ideal platform to study the competition of superconductivity and magnetism an...
Preprint
Full-text available
Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy...
Preprint
Full-text available
Magic-angle twisted bilayer graphene exhibits quasi-flat low-energy bands with van Hove singularities close to the Fermi level. These singularities play an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. In this work, we study the correspondence...
Article
Full-text available
In search of materials with three-dimensional flat band dispersions, using ab initio computations we investigate how topological phases evolve as a function of hydrostatic pressure and uniaxial strain in two types of superlattices: HgTe/CdTe and HgTe/HgSe. In short-period HgTe/CdTe superlattices, our analysis unveils the presence of isoenergetic no...
Preprint
Full-text available
In search of materials with three-dimensional flat band dispersions, using {\em ab-initio} computations, we investigate how topological phases evolve as a function of hydrostatic pressure and uniaxial strain in two types of superlattices: HgTe/CdTe and HgTe/HgSe. In short-period HgTe/CdTe superlattices, our analysis unveils the presence of isoenerg...
Article
Full-text available
Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat-band systems are an ideal platform to study the competition of superconductivity and magnetism an...
Article
Full-text available
We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order...
Preprint
Full-text available
Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat band systems are an ideal platform to study the competition of superconductivity and magnetism an...
Preprint
Full-text available
We establish a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-or...
Article
Full-text available
We study the influence of sample termination on the electronic properties of the novel quantum spin Hall insulator monolayer 1T′−WTe2. For this purpose, we construct an accurate, minimal four-orbital tight-binding model with spin-orbit coupling by employing a combination of density-functional theory calculations, symmetry considerations, and fittin...
Article
Full-text available
We theoretically show that IV–VI semiconducting compounds with low-temperature rhombohedral crystal structure represent a new potential platform for topological semimetals. By means of minimal k·p models, we find that the two-step structural symmetry reduction of the high-temperature rocksalt crystal structure, comprising a rhombohedral distortion...
Preprint
Full-text available
We construct a higher-order topological phase protected by a point group symmetry that is impossible in any crystalline system. The tight-binding model describes a superconductor on a quasicrystalline Ammann–Beenker tiling which hosts localized Majorana zero modes at the corners of an octagonal sample. The Majorana modes are protected by particle-h...
Preprint
Full-text available
We construct a higher-order topological phase protected by a point group symmetry that is impossible in any crystalline system. The tight-binding model describes a superconductor on a quasicrystalline Ammann-Beenker tiling which hosts localized Majorana zero modes at the corners of an octagonal sample. The Majorana modes are protected by particle-h...
Preprint
Full-text available
We study the influence of sample termination on the electronic properties of the novel quantum spin Hall insulator monolayer 1T'-WTe2. For this purpose, we construct an accurate, minimal 4-orbital tight-binding model with spin-orbit coupling by employing a combination of density-functional theory calculations, symmetry considerations, and fitting t...
Preprint
Full-text available
We study the influence of sample termination on the electronic properties of the novel quantum spin Hall insulator monolayer $1T'$-WTe$_2$. For this purpose, we construct an accurate, minimal 4-orbital tight-binding model with spin-orbit coupling by employing a combination of density-functional theory calculations, symmetry considerations, and fitt...
Article
Full-text available
We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions (3D), these states of matter are generally characterized by the presence of gapless boundary states at surfaces that respect the protecting spatial symmetry. We discuss the ap...
Preprint
Full-text available
We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions, these states of matter are generally characterized by the presence of gapless boundary states at surfaces that respect the protecting spatial symmetry. We discuss the appeara...
Preprint
Full-text available
We theoretically show that IV-VI semiconducting compounds with low-temperature rhombohedral crystal structure represent a new potential platform for topological semimetals. By means of minimal $\mathbf{k}\cdot\mathbf{p}$ models we find that the two-step structural symmetry reduction of the high-temperature rocksalt crystal structure, comprising a r...
Article
Full-text available
We propose a novel design for time-reversal invariant Weyl semimetals employing multilayer heterostructures comprising ordinary "trivial" insulators and nontrivial insulators with \textit{pairs} of protected Dirac cones on the surface. We consider both the case of weak topological insualtors, where surface Dirac cones are pinned to time-reversal in...
Article
Full-text available
The hallmark of Weyl semimetals is the existence of open constant-energy contours on their surface—the so-called Fermi arcs—connecting Weyl points. Here, we show that, for time-reversal symmetric realizations of Weyl semimetals, these Fermi arcs, in many cases, coexist with closed Fermi pockets originating from surface Dirac cones pinned to time-re...
Article
Full-text available
The Hofstadter model is a simple yet powerful Hamiltonian to study quantum Hall physics in a lattice system, manifesting its essential topological states. Lattice dimerization in the Hofstadter model opens an energy gap at half-filling. Here we show that even if the ensuing insulator has a Chern number equal to zero, concomitantly a doublet of edge...
Article
Full-text available
We show that a class of weak three-dimensional topological insulators feature one-dimensional Dirac electrons on their surfaces. Their hallmark is a line-like energy dispersion along certain directions of the surface Brillouin zone. These one-dimensional Dirac line degeneracies are topologically protected by a symmetry that we refer to as in-plane...
Article
Full-text available
The nontrivial topology of the electronic structure of iron pnictides can lead to the appearance of surface states. We study such states in various strip geometries with a focus on the superconducting phase. In the presence of unconventional superconducting pairing with $s_\pm$-wave gap structure, the topological states are quite robust and partly...
Article
Full-text available
The electronic structure of iron pnictides is topologically nontrivial, leading to the appearance of Dirac cones in the band structure for the antiferromagnetic phase. Motivated by the analogy with Dirac cones in graphene, we explore the possible existence of topologically protected surface states. Surprisingly, bands of surface states exist even i...

Network

Cited By