Erratum: Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices

Yu, G. L.; Tu, J. S.; Kretinin, A. V.; Cao, Yang; Jalil, R.; Withers, Freddie; Пономаренко, Л. А.; Piot, B. A.; Potemski, M.; Elias, D. C.; Chen, X.; Watanabe, Kenji; Taniguchi, T.; Grigorieva, I. V.; Novoselov, Konstantin; Fal’ko, Vladimir I.; Geǐm, A. K.; Mishchenko, Artem

doi:10.1038/nphys3112

Cited by 3 publications

(6 citation statements)

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“…The regime where these two length scales are comparable exhibits very interesting phenomena like the Hofstadter butterfly 1 . Recently this regime has been accessed experimentally with observations of a stable Hofstadter spectrum in graphene superlattices [2][3][4][5][6] and realization of the Hofstadter Hamiltonian in cold atoms systems 7,8 . This has motivated us to investigate the effects of repulsive interactions in this regime.…”

Section: Introductionmentioning

confidence: 99%

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Effects of interaction in the Hofstadter regime of the honeycomb lattice

2016

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We investigate phases of spinless fermions on the honeycomb lattice with nearest neighbor interaction in the Hofstadter regime. The interaction induces incompressible nematic and ferri-electric phases with broken translation symmetry. Some of the transitions are accompanied by changes in the Hall conductivity. We study pair correlations and show that the quantum metric, averaged over the Brillouin zone, characterizes the shape of the pair correlation function.

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Section: Introductionmentioning

confidence: 99%

“…Appendix A: Chern numbers at half filling The single particle mean field Hamiltonian for the half filled case describing the CDW state is given in equation (6). The eigenvalue equation can be written as,…”

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confidence: 99%

Effects of interaction in the Hofstadter regime of the honeycomb lattice

2016

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“…Along with the discovery of two dimensional materials, the strong magnetic field effect also has been investigated in the lattice system. In particular, the realization of Moiré pattern by a single layer graphene on top of a boron-nitride crystal allowed a periodicity much larger than the lattice constant, thus, enabling the experimental realization of the fractal quantum Hall effect of the Hofstadter spectrum which had long been a theoretical concept [17][18][19][20][21] . When both strong magnetic field and spin orbit coupling (SOC) coexist, their combination could give rise to interesting topological phases.…”

Section: Introductionmentioning

confidence: 99%

Topological multiferroic phases in the extended Kane-Mele-Hubbard model in the Hofstadter regime

Mishra

Lee

2018

Phys. Rev. B

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We investigate the new quantum phases on the extended Kane-Mele-Hubbard model of honeycomb lattice in the Hofstadter regime. In this regime, orbital motion of the electrons can induce various topological phases with spontaneously broken symmetries when the spin orbit coupling and electron correlations coexist. Here, we consider the interaction effects in the Kane-Mele model and discuss possible phases in the presence of magnetic field at integer fillings of electrons. In particular, focusing on 2π/3 magnetic flux per plaquette, the realization of numerous quantum phases are discussed within the mean field framework; insulator with coplanar magnetic ordering, ferrimagnetic Chern insulator with nematic charge order, ferrimagnetic-ferrielectric Chern insulators etc. Many of these phase transitions are also accompanied with the change in the topological invariants of the system. Based on our theoretical study, we propose topological multiferroic phases with a scope of realization in 2D van-der Waals materials and optical lattice system where the significant interplay of magnetic field, spin orbit coupling and interactions can be engineered.

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“…The 2DEG in a periodic potential and magnetic field has been the cradle of several interesting and important theoretical concepts like the identification of a topological invariant with the Hall conductivity 3,4 and the existence of a fractal structure in the energy gaps, the Hofstadter butterfly 5,6 . Interest in this phenomenon has been recently revived with the experimental observation of the Hofstadter butterfly in graphene superlattices [7][8][9][10][11] and the realization of the Hofstadter Hamiltonian in the optical lattice systems 12,13 . This has motivated us to study the effect of interactions on the Hofstadter butterfly.…”

Section: Introductionmentioning

confidence: 99%

“…The Hall conductivity of each contour and the intercept are solutions of a Diophantine equation. This plot, the Landau fan diagram, is the experimental evidence of the Hofstadter butterfly in graphene superlattices [7][8][9][10][11] . Interaction can induce charge ordering that can break the translational symmetry of the system.…”

Section: Introductionmentioning

confidence: 99%

Translational symmetry breaking and the disintegration of the Hofstadter butterfly

2017

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We study the effect of interactions on the Hofstadter butterfly of the honeycomb lattice. We show that the interactions induce charge ordering that breaks the translational and rotational symmetries of the system. These phase transitions are prolific and occur at many values of the flux and particle density. The breaking of the translational symmetry introduces a new length scale in the problem and this affects the energy band diagram resulting in the disintegration of the fractal structure in the energy flux plot, the Hofstadter butterfly. This disintegration increases with increase in the interaction strength. Many of these phase transitions are accompanied with change in the Hall conductivity. Consequently, the disintegration of the Hofstadter butterfly is manifested in the Landau fan diagram also.

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Erratum: Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices

Cited by 3 publications

References 1 publication

Effects of interaction in the Hofstadter regime of the honeycomb lattice

Effects of interaction in the Hofstadter regime of the honeycomb lattice

Topological multiferroic phases in the extended Kane-Mele-Hubbard model in the Hofstadter regime

Translational symmetry breaking and the disintegration of the Hofstadter butterfly

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