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Related papers: Quantized heat flow in the Hofstadter butterfly

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In this work, we report original properties inherent to independent particles subjected to a magnetic field by emphasizing the existence of regular structures in the energy spectrum's outline. We show that this fractal curve, the well-known…

Mesoscale and Nanoscale Physics · Physics 2009-07-14 N. Goldman

A striking example of frustration in physics is Hofstadter's butterfly, a fractal structure that emerges from the competition between a crystal's lattice periodicity and the magnetic length of an applied field. Current methods for…

Mesoscale and Nanoscale Physics · Physics 2025-03-04 Catalin D. Spataru , Wei Pan , Alexander Cerjan

Motivated by recent experimental attempts to detect the Hofstadter butterfly, we numerically calculate the Hall conductivity in a modulated two-dimensional electron system with disorder in the quantum Hall regime. We identify the critical…

Mesoscale and Nanoscale Physics · Physics 2015-06-25 Mikito Koshino , Tsuneya Ando

The realization of artificial gauge fields in ultracold atomic gases has opened up a path towards experimental studies of topological insulators and, as an ultimate goal, topological quantum matter in many-body systems. As an alternative to…

Strongly Correlated Electrons · Physics 2020-10-29 Leo Stenzel , Andrew L. C. Hayward , Claudius Hubig , Ulrich Schollwöck , Fabian Heidrich-Meisner

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…

At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and…

Transport properties provide important access to a solid's quasiparticles, such as quasiparticle density, mobility, and scattering. The transport of heat can be particularly revealing because, in principle, all types of excitations in a…

Strongly Correlated Electrons · Physics 2019-09-19 Christian Hess

We show that all the bands of the Hofstadter model on the torus have an exactly flat dispersion and Berry curvature when a special system size is chosen. This result holds for any hopping and Chern number. Our analysis therefore provides a…

Strongly Correlated Electrons · Physics 2014-09-24 Thomas Scaffidi , Steven H. Simon

The Hofstadter model illustrates the notion of topological quantum numbers and how they account for the quantization of the Hall conductance. It gives rise to colorful fractal diagrams of butterflies where the colors represent the…

Mathematical Physics · Physics 2007-05-23 J. E. Avron , D. Osadchy

We give a perspective on the Hofstadter butterfly (fractal energy spectrum in magnetic fields), which we have shown to arise specifically in three-dimensional(3D) systems in our previous work. (i) We first obtain the `phase diagram' on a…

Mesoscale and Nanoscale Physics · Physics 2009-11-07 M. Koshino , H. Aoki , T. Osada , K. Kuroki , S. Kagoshima

We revisit the problem of self-similar properties of the Hofstadter butterfly spectrum, focusing on spectral as well as topological characteristics. In our studies involving any value of magnetic flux and arbitrary flux interval, we single…

Disordered Systems and Neural Networks · Physics 2014-12-16 Indubala Satija

The energy spectrum of massless Dirac fermions in graphene under two dimensional periodic magnetic modulation having square lattice symmetry is calculated. We show that the translation symmetry of the problem is similar to that of the…

Mesoscale and Nanoscale Physics · Physics 2018-10-24 Manisha Arora , Sankalpa Ghosh

Hofstadter's butterfly, the predicted energy spectrum for non-interacting electrons confined to a two-dimensional lattice in a magnetic field, is one of the most remarkable fractal structures in nature. At rational ratios of magnetic flux…

Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system…

Quantum Gases · Physics 2020-03-17 Gal Shavit , Moshe Goldstein

Topological quantum numbers are often used to characterise the topological order of phase having protected gapless edge modes when the system is kept in a space with the boundary. The famous examples in this category are the quantized…

Mesoscale and Nanoscale Physics · Physics 2024-07-09 Saurabh Kumar Srivastav , Anindya Das

Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…

Strongly Correlated Electrons · Physics 2013-09-10 Emil J. Bergholtz , Zhao Liu

Energy bands of electrons in a square lattice potential threaded by a uniform magnetic field exhibit a fractal structure known as the Hofstadter butterfly. Here we study a Fermi gas in a 2D optical lattice within a linear cavity with a tilt…

Quantum Gases · Physics 2020-02-06 Elvia Colella , Farokh Mivehvar , Francesco Piazza , Helmut Ritsch

Topological bandstructures interfering with moir\'e superstructures give rise to a plethora of emergent phenomena, which are pivotal for correlated insulating and superconducting states of twisttronics materials. While quasiperiodicity was…

Mesoscale and Nanoscale Physics · Physics 2024-03-28 Tobias Herrig , Christina Koliofoti , Jedediah H. Pixley , Elio J. König , Roman-Pascal Riwar

For a three-dimensional lattice in magnetic fields we have shown that the hopping along the third direction, which normally tends to smear out the Landau quantization gaps, can rather give rise to a fractal energy spectram akin to…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 M. Koshino , H. Aoki , K. Kuroki , S. Kagoshima , T. Osada

The Hofstadter energy spectrum of twisted bilayer graphene is found to have recursive higher-order topological properties. We demonstrate that higher-order topological insulator (HOTI) phases, characterized by localized corner states, occur…

Mesoscale and Nanoscale Physics · Physics 2023-11-16 Sun-Woo Kim , Sunam Jeon , Moon Jip Park , Youngkuk Kim