Related papers: Hyperbolic Band Theory under Magnetic Field and Di…
We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. We define the magnetic Fuchsian group associated with a higher genus Riemann surface. By imposing the magnetic boundary conditions for…
Hyperbolic lattices underlie a new form of quantum matter with potential applications to quantum computing and simulation and which, to date, have been engineered artificially. A corresponding hyperbolic band theory has emerged, extending…
The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit…
We study the dynamics of carriers in graphene subjected to an inhomogeneous magnetic field. For a magnetic field with an hyperbolic profile the corresponding Dirac equation can be analyzed within the formalism of supersymmetric quantum…
Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tessellation of 2D hyperbolic space, a non-Euclidean space of uniform negative curvature. To describe the single-particle…
Periodic lattices in hyperbolic space are characterized by symmetries beyond Euclidean crystallographic groups, offering a new platform for classical and quantum waves, demonstrating great potentials for a new class of topological…
This paper presents a theory of interaction-induced band-flattening in strongly correlated electron systems. We begin by illustrating an inherent connection between flat bands and index theorems, and presenting a generic prescription for…
The exciting discovery of bi-dimensional systems in condensed matter physics has triggered the search of their photonic analogues. In this letter, we describe a general scheme to reproduce some of the systems ruled by a tight-binding…
This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to…
In this paper the Dirac-Weyl equation on a hyperbolic surface of graphene under magnetic fields is considered. In order to solve this equation analytically for some cases, we will deal with vector potentials symmetric under rotations around…
Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum electrodynamics and electric-circuit networks, where particles coherently hop on a discrete tessellation of two-dimensional negatively curved space.…
The honeycomb lattice sets the basic arena for numerous ideas to implement electronic, photonic, or phononic topological bands in (meta-)materials. Novel opportunities to manipulate Dirac electrons in graphene through band engineering arise…
Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence…
We find a systematic reappearance of massive Dirac features at the edges of consecutive minibands formed at magnetic fields B_{p/q}= p\phi_0/(qS) providing rational magnetic flux through a unit cell of the moire superlattice created by a…
We show that four narrow zigzag dice lattice ribbons, which have the minimal widths among their separate categories, constitute a unique collection of systems to study physics related to one-dimensional Dirac cones and flat bands. In zero…
The notion of Dirac cones, wherein two or more bands become degenerate at a certain momentum, is the starting point for the study of topological phases. Dirac cones have been thoroughly explored in fermionic systems such as graphene, Weyl…
We demonstrate from a fundamental perspective the physical and mathematical origins of band warping and band non-parabolicity in electronic and vibrational structures. Remarkably, we find a robust presence and connection with pairs of…
A way to represent the band structure that distinguishes between energy-momentum and energy-crystal momentum relationships is proposed upon the band-unfolding concept. This momentum-resolved band structure offers better understanding of the…
We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic…
We study the band structures of hybrid graphene quantum dots subject to a magnetic flux and electrostatic potential. The system is consisting of a circular single layer graphene surrounded by an infinite bilayer graphene. By solving the…