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The ground state of large Hubbard $U$ limit of a honeycomb lattice near half-filling is known to be a singlet $d+id$-wave superconductor. It is also known that this $d+id$ superconductor exhibits a chiral $p+ip$ pairing locally at the Dirac…
For layered materials, the interlayer stacking is a critical degree of freedom tuning electronic properties, while its microscopic characterization faces great challenges. The transition-metal dichalcogenide 1T-TaS$_2$ represents a novel…
Higher-order topological phases are gapped phases of matter that host gapless corner or hinge modes. For the case of superconductors, corner or hinge modes are gapless Majorana modes or Majorana zero modes. To construct 3d higher-order…
Topological insulators in the Bi$_2$Se$_3$ family manifest helical Dirac surface states that span the topologically ordered bulk band gap. Recent scanning tunneling microscopy measurements have discovered additional states in the bulk band…
Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…
One of the holy grails of materials science, unlocking structure-property relationships, has largely been pursued via bottom-up investigations of how the arrangement of atoms and interatomic bonding in a material determine its macroscopic…
Topological flat bands have gained extensive interest as a platform for exploring the interplay between nontrivial band topology and correlation effects. In recent studies, strongly correlated phenomena originating from a topological flat…
The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly…
We propose the creation of a two-dimensional topological semimetal in a semiconductor artificial lattice with triangular symmetry. An in-plane magnetic field drives a quantum phase transition between the topological insulating and…
The existence and topological classification of lower-dimensional Fermi surfaces is often tied to the crystal symmetries of the underlying lattice systems. Artificially engineered lattices, such as heterostructures and other superlattices,…
Topological nodal-line semimetals (NLSs) are unique materials, which harbor one-dimensional line nodes along with the so-called drumhead surface states arising from nearly dispersionless two dimensional surface bands. However, a direct…
We introduce a two-band model of three-dimensional nodal line semimetals, the Fermi surface of which at half-filling may form various one-dimensional configurations of different topology. We study the symmetries and "drumhead" surface…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
We present a comprehensive study of the band alignments of two-dimensional (2D) semiconducting materials and highlight the possibilities of forming momentum-matched type I, II and III heterojunctions; an enticing possibility being atomic…
Topological band theory provides a conceptual framework to predict or even engineer robust metallic states at the boundaries of topologically distinct phases. The bulk-boundary correspondence requires that a topological electronic phase…
Topological semimetals with nodal line are a novel class of topological matter extending the concept of topological matter beyond topological insulators and Weyl/Dirac semimetals. Here, we show that a Floquet topological semimetal with…
Although two-dimensional periodic structures have functioned as the primary platform for exploring topological phenomena, recent advances have substantially expanded this research boundary to include more intricate, aperiodic structures:…
The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a…
The carbon monolayer band structure calculated in the approximation of weakly interacting {\pi} electrons corresponds to massless electron excitations known as Dirac fermions not previously observed in any other material. However, if strong…
Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions…