550 citations · 1.8k across the 26 of their papers we have counts for
26 papers
Topological characterization of multifold band degeneracies in Altland-Zirnbauer symmetry classes
Askar Iliasov, Zoltán Guba, Tsuneya Yoshida +2
Topological degeneracies of energy bands in crystalline matter are conventionally characterized by invariants computed on an enclosing sphere over which the spectrum remains gapped…
Universal aspects of bulk density of states in non-Hermitian lattices
Mykhailo Pavliuk, Askar Iliasov, Emil J. Bergholtz +1
Non-Hermitian lattice Hamiltonians generally exhibit strong boundary sensitivity, with periodic and open boundary conditions producing distinct density of states (DOS) in the compl…
Topological states and flat bands in exactly solvable decorated Cayley trees
Wanda P. Duss, Askar Iliasov, Tomáš Bzdušek
We derive the full spectrum of decorated Cayley trees that constitute tree analogs of selected two-dimensional Euclidean lattices; namely of the Lieb, the double Lieb, the kagome,…
Topological non-Abelian gauge structures in Cayley-Schreier lattices
Zoltán Guba, Robert-Jan Slager, Lavi K. Upreti +1
Crystalline constructions known as Cayley-Schreier lattices have been suggested as a platform for realizing arbitrary gauge fields in synthetic crystals with real hopping amplitude…
Hopf Exceptional Points
Tsuneya Yoshida, Emil J. Bergholtz, Tomáš Bzdušek
Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanic…
Multifractal statistics of non-Hermitian skin effect on the Cayley tree
Shu Hamanaka, Askar A. Iliasov, Titus Neupert +2
Multifractal analysis is a powerful tool for characterizing the localization properties of wave functions. Despite its utility, this tool has been predominantly applied to disorder…
Topological linear response of hyperbolic Chern insulators
Canon Sun, Anffany Chen, Tomáš Bzdušek +1
We establish a connection between the electromagnetic Hall response and band topological invariants in hyperbolic Chern insulators by deriving a hyperbolic analog of the Thouless-K…
Hyperbolic non-Abelian semimetal
Tarun Tummuru, Anffany Chen, Patrick M. Lenggenhager +3
We extend the notion of topologically protected semi-metallic band crossings to hyperbolic lattices in a negatively curved plane. Because of their distinct translation group struct…
Non-Abelian hyperbolic band theory from supercells
Patrick M. Lenggenhager, Joseph Maciejko, Tomáš Bzdušek
Wave functions on periodic lattices are commonly described by Bloch band theory. Besides Abelian Bloch states labeled by a momentum vector, hyperbolic lattices support non-Abelian…
Symmetry and topology of hyperbolic Haldane models
Anffany Chen, Yifei Guan, Patrick M. Lenggenhager +3
Particles hopping on a two-dimensional hyperbolic lattice feature unconventional energy spectra and wave functions that provide a largely uncharted platform for topological phases…
Flat bands and band touching from real-space topology in hyperbolic lattices
Tomáš Bzdušek, Joseph Maciejko
Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and in classical electric-circuit networks, we study flat bands and band…
Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases
Anffany Chen, Hauke Brand, Tobias Helbig +11
Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. I…
Hyperbolic Topological Band Insulators
David M. Urwyler, Patrick M. Lenggenhager, Igor Boettcher +3
Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band s…
Triple nodal points characterized by their nodal-line structure in all magnetic space groups
Patrick M. Lenggenhager, Xiaoxiong Liu, Titus Neupert +1
We analyze triply degenerate nodal points [or triple points (TPs) for short] in energy bands of crystalline solids. Specifically, we focus on spinless band structures, i.e., when s…
Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
Aleksandra Nelson, Titus Neupert, A. Alexandradinata +1
Pontrjagin's seminal topological classification of two-band Hamiltonians in three momentum dimensions is hereby enriched with the inclusion of a crystallographic rotational symmetr…
Simulating hyperbolic space on a circuit board
Patrick M. Lenggenhager, Alexander Stegmaier, Lavi K. Upreti +12
The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A ke…
Universal higher-order bulk-boundary correspondence of triple nodal points
Patrick M. Lenggenhager, Xiaoxiong Liu, Titus Neupert +1
Triple nodal points are degeneracies of energy bands in momentum space at which three Hamiltonian eigenstates coalesce at a single eigenenergy. For spinless particles, the stabilit…
Multicellularity of delicate topological insulators
Aleksandra Nelson, Titus Neupert, Tomáš Bzdušek +1
Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by…
From triple-point materials to multiband nodal links
Patrick M. Lenggenhager, Xiaoxiong Liu, Stepan S. Tsirkin +2
We study a class of topological materials which in their momentum-space band structure exhibit three-fold degeneracies known as triple points. Focusing specifically on $\mathcal{P}…
Exceptional Topological Insulators
M. Michael Denner, Anastasiia Skurativska, Frank Schindler +4
We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within…
Geometric approach to fragile topology beyond symmetry indicators
Adrien Bouhon, Tomáš Bzdušek, Robert-Jan Slager
We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned…
Non-abelian topology of nodal-line rings in -symmetric systems
Apoorv Tiwari, Tomáš Bzdušek
Nodal lines inside the momentum space of three-dimensional crystalline solids are topologically stabilized by a -flux of Berry phase. Nodal-line rings in -symmetri…
Non-Abelian band topology in noninteracting metals
QuanSheng Wu, Alexey A. Soluyanov, Tomáš Bzdušek
Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line…
Three-dimensional Chiral Lattice Fermion in Floquet Systems
Xiao-Qi Sun, Meng Xiao, Tomáš Bzdušek +2
We show that the Nielsen-Ninomiya no-go theorem still holds on Floquet lattice: there is an equal number of right-handed and left-handed Weyl points in 3D Floquet lattice. However,…