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Flat bands and band touching from real-space topology in hyperbolic lattices

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-touching phenomena in such lattices. We analyze noninteracting …

Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases

We introduce and experimentally realize hyperbolic matter as a novel paradigm for topological states, made of particles moving in the hyperbolic plane with negative curvature. Curvature of space is emulated through a hyperbolic lattice using …

Hyperbolic topological band insulators

The Bloch band theory describes energy levels of crystalline media by a collection of bands in momentum space. These bands can be characterized by non-trivial topological invariants, which via bulk-boundary correspondence imply protected boundary …

Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

We study the Hatano-Nelson model, i.e., a one-dimensional non-Hermitian chain of spinless fermions with nearest-neighbor nonreciprocal hopping, in the presence of repulsive nearest-neighbor interactions. At half-filling, we find two $\mathcal{PT}$ …

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

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 spin-orbit coupling is negligible, and consider TPs formed along …

Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond

Pontrjagin's seminal topological classification of two-band Hamiltonians in three momentum dimensions is hereby enriched with the inclusion of a crystallographic rotational symmetry. The enrichment is attributed to a new topological invariant which …

Electric-circuit realization of a hyperbolic drum

The Laplace operator encodes the behaviour of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we …

Universal higher-order bulk-boundary correspondence of triple nodal points

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 stability of a triple nodal point requires two ingredients: rotation symmetry …