This is an introductory review of the physics of topological quantum matter with cold atoms.
Topological quantum phases, originally discovered and investigated in condensed matter …

Robust edge transport can occur when charged particles in crystalline lattices interact with
an applied external magnetic field. Such systems have a spectrum composed of bands of …

In this work, we use Floquet theory to theoretically study the influence of monochromatic
circularly and linearly polarized light on the Hofstadter butterfly—induced by a uniform …

The Kitaev model is an exactly solvable quantum spin model within the language of
constrained real fermions. In spite of numerous studies for magnetic fields along special …

In this study, we have constructed an extended version of Ginzburg-Landau theory of
superconductivity starting from the exponential non-standard Lagrangian. An extended …

The moiré potential of graphene on hexagonal boron nitride (hBN) generates a supercell
sufficiently large as to thread a full magnetic flux quantum Φ 0 for experimentally accessible …

The Hofstadter butterfly is one of the first and most fascinating examples of the fractal and
self-similar quantum nature of free electrons in a lattice pierced by a perpendicular magnetic …

We study the enumeration of closed walks of given length and algebraic area on the
honeycomb lattice. Using an irreducible operator realization of honeycomb lattice moves, we …

We study a variety of Hofstadter ladders in order to probe the interplay between interactions,
an applied magnetic field, and crystalline or quasiperiodic geometries. Motion will be …

The properties of the Hofstadter butterfly, a fractal, self-similar spectrum of a two-dimensional
electron gas, are studied in the case where the system is additionally illuminated with …