Related papers: High-order fractal states in graphene superlattice…
Cyclotron motion of charge carriers in metals and semiconductors leads to Landau quantization and magneto-oscillatory behavior in their properties. Cryogenic temperatures are usually required to observe these oscillations. We show that…
Electrons exposed to a two-dimensional (2D) periodic potential and a uniform, perpendicular magnetic field exhibit a fractal, self-similiar energy spectrum known as the Hofstadter butterfly. Recently, related high-temperature quantum…
The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to the trivial case of low Bloch band filling where…
Electrons on the lattice subject to a strong magnetic field exhibit the fractal spectrum of electrons, which is known as the Hofstadter butterfly. In this work, we investigate unconventional superconductivity in a three-dimensional…
Self-similarity and fractals have fascinated researchers across various disciplines. In graphene placed on boron nitride and subjected to a magnetic field, self-similarity appears in the form of numerous replicas of the original Dirac…
Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum,…
In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands…
Moir\'e superlattices with long-range periodicity exhibit Hofstadter energy spectra under accessible magnetic fields, enabling the exploration of emergent quantum phenomena through a hierarchy of fractal states. However, higher-order…
The presence of periodic modulation in graphene leads to a reconstruction of the band structure and formation of minibands. In an external uniform magnetic field, a fractal energy spectrum called Hofstadter butterfly is formed. Particularly…
We investigate the electronic properties in the Bloch electron on a square lattice with vacancies in the uniform magnetic field. We show that a single vacancy site introduced to the system creates a defect energy level in every single…
Two-dimensional electron systems in both magnetic fields and periodic potentials are described by Hofstadter butterfly, a fundamental problem of solid-state physics. While moir\'e systems provide a powerful method to realize this spectrum,…
This is a short review of the recent progresses on Hofstadter butterfly in graphene, organized in the following. We first briefly introduce the Hofstadter butterfly, including the theoretic toy model of Bloch electrons in the magnetic…
We calculate the energy bands for graphene monolayers when electrons move through a periodic electrostatic potential in the presence of a uniform perpendicular magnetic field. We clearly demonstrate the quantum fractal nature of the energy…
We study mean-field states resulting from the pairing of electrons in time-reversal broken fractal Hofstadter bands, which arise in two-dimensional lattices where the unit cell traps magnetic flux $\Phi = (p/q)\Phi_0$ comparable to the flux…
Localized electrons subject to applied magnetic fields can restart to propagate freely through the lattice in delocalized magnetic Bloch states (MBSs) when the lattice periodicity is commensurate with the magnetic length. Twisted graphene…
In the presence of a magnetic field and an external periodic potential, the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this…
We show that superlattices based on zero-gap semiconductors such as graphene and mercury telluride exhibit characteristic Bloch--Zener oscillations that emerge from the coherent superposition of Bloch oscillations and multiple Zener…
The Hofstadter butterfly spectral patterns of lattice electrons in an external magnetic field yield some of the most beguiling images in physics. Here we explore the magneto-electronic spectra of systems with moire spatial patterns,…
Fractal electronic spectra arising from the competition between lattice periodicity and magnetic flux are a fundamental hallmark of two-dimensional quantum systems. While the spectral properties of Hofstadter butterflies are well…
When subjected to a strong magnetic field, electrons on a two-dimensional lattice acquire a fractal energy spectrum called Hofstadter's butterfly. In addition to its unique recursive structure, the Hofstadter butterfly is intimately linked…