期刊
NEW JOURNAL OF PHYSICS
卷 24, 期 1, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1367-2630/ac4126
关键词
topological physics; Hofstadter model; quantum Hall effect; optics
资金
- EU [694683, 899794, 847648, LCF/BQ/PI19/11690013, LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012, LCF/BQ/PR21/11840013]
- Foundational Questions Institute Fund [FQXi-IAF19-05]
- ANR Research Collaborative Project 'Qu-DICE' [ANR-PRC-CES47]
- Royal Society [UF160112, RGF\EA\180121, RGF\R1\180071]
- ERC AdG NOQIA
- Agencia Estatal de Investigacion - MCIN/AEI [CEX2019-000910-S, PID2019-106901GB-I00, PCI2019-111828-2, RTC2019-007196-7]
- Fundacio Cellex
- Fundacio Mir-Puig
- Generalitat de Catalunya through the CERCA program, AGAUR [2017 SGR 134, CAT U16-011424]
- ERDF Operational Program of Catalonia
- National Science Centre, Poland [2016/20/W/ST4/00314]
- Marie Sklodowska-Curie grant STREDCH [101029393]
- 'La Caixa' Junior Leaders fellowships [ID100010434]
- EU FEDER Quantumcat
- National Science Foundation [NSF PHY-1748958]
This paper investigates the analogy between the topological properties of Hofstadter Hamiltonians and the diffraction figures resulting from optical gratings. By establishing a one-to-one relation between Diophantine equations and the Bragg condition, the influence of structural disorder on the robustness of diffraction figures in optical gratings is discussed, which can be analogous to the robustness of transverse conductance in the quantum Hall effect.
In two, three and even four spatial dimensions, the transverse responses experienced by a charged particle on a lattice in a uniform magnetic field are fully controlled by topological invariants called Chern numbers, which characterize the energy bands of the underlying Hofstadter Hamiltonian. These remarkable features, solely arising from the magnetic translational symmetry, are captured by Diophantine equations which relate the fraction of occupied states, the magnetic flux and the Chern numbers of the system bands. Here we investigate the close analogy between the topological properties of Hofstadter Hamiltonians and the diffraction figures resulting from optical gratings. In particular, we show that there is a one-to-one relation between the above mentioned Diophantine equation and the Bragg condition determining the far-field positions of the optical diffraction peaks. As an interesting consequence of this mapping, we discuss how the robustness of diffraction figures to structural disorder in the grating is a direct analogue of the robustness of transverse conductance in the quantum Hall effect.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据