# Alexander LauPolish Academy of Sciences | PAN · International Research Centre MagTop

Alexander Lau

PhD

Marie Skłodowska-Curie Research Fellow

## About

27

Publications

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359

Citations

Introduction

Additional affiliations

Education

April 2014 - March 2018

October 2011 - June 2012

October 2008 - December 2013

## Publications

Publications (27)

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...