Translational symmetry breaking and the disintegration of the Hofstadter butterfly

Mishra, Archana; Hassan, S. R.; Shankar, R.

doi:10.1103/physrevb.95.035140

Cited by 6 publications

(3 citation statements)

References 34 publications

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“…Introducing electron-electron interactions is known to produce a rich set of symmetry-broken phases in graphene for weak fields. [34][35][36][37] There have been a few investigations into interaction effects in the Hofstadter regime, [38][39][40][41][42] but a full picture remains to be developed. GM thanks David Mross for a vauable discussion.…”

Section: Discussionmentioning

confidence: 99%

Stability of zero-energy Dirac touchings in the honeycomb Hofstadter problem

2020

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We study the band structure of electrons hopping on a honeycomb lattice with 1/q (q integer) flux quanta through each elementary hexagon. In the nearest neighbor hopping model the two bands that eventually form the n = 0 Landau level have 2q zero energy Dirac touchings. In this work we study the conditions needed for these Dirac points and their stability to various perturbations. We prove that these touchings and their locations are guaranteed by a combination of an anti-unitary particle-hole symmetry and the lattice symmetries of the honeycomb structure. We also study the stability of the Dirac touchings to one-body perturbations that explicitly lower the symmetry.

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Section: Discussionmentioning

confidence: 99%

Stability of zero-energy Dirac touchings in the honeycomb Hofstadter problem

2020

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“…On the other hand the on-site Hubbard interaction drives the system towards an anti-ferromagnetic configuration which is also an insulating state [15]. Recently it is shown that interaction also induces charged ordering in the Hofstadter butterfly [16,17], however for Bose-Hubbard model in the presence of magnetic field such charge density order is absent [18,19]. On varying the on-site Hubbard interaction in presence of disorder, the system therefore undergoes a transition from disorder driven insulator to correlation driven insulator.…”

Section: Introductionmentioning

confidence: 99%

Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field

Mandal¹,

Gupta²

2022

J. Phys.: Condens. Matter

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We study the revival of Hofstadter butterfly due to the competition between disorder and elec- tronic interaction using mean field approximation of unrestricted Hartree Fock method at zero tem- perature for two dimensional square and honeycomb lattices. Interplay of disorder and electronic correlation to nullify each other is corroborated by the fact that honeycomb lattice needs more strength of electronic correlation owing to its less co-ordination number which enhances the effect of disorder. The extent of revival of the butterfly is better in square lattice than honeycomb lattice due to higher coordination number. The effect of disorder and interaction is also investigated to study entanglement entropy and entanglement spectrum. We find that for honeycomb lattice area law of entanglement entropy is obeyed in all cases but for square lattice there is some departure from area law for larger subsystems. The entanglement spectrum have the reflection symmetry of the original butterfly of the Hofstadter spectrum. The interaction induces a gap in the entanglement spectrum as well conforming the correspondence between physical spectrum and entanglement spectrum. The effect of disorder closes the interaction induced gap in the entanglement spectrum establishing the nullification of interaction due to disorder and vice versa

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“…There are many studies related to the interaction driven quantum Hall and quantum spin Hall phases [24][25][26][27][28][29] . In addition, the effect of interactions in the Hofstadter regime has also been studied extensively, showing spontaneous breaking of translational and rotational symmetries of the system prompting topological transitions [30][31][32][33][34][35][36] . Similarly, interplay of interactions and SOC on the lattice system has also been widely explored and several exotic phases such as Mott topological insulators and magnetic Chern insulators have been investigated as an outcome 16,24,28,[37][38][39][40][41][42][43] .…”

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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Translational symmetry breaking and the disintegration of the Hofstadter butterfly

Cited by 6 publications

References 34 publications

Stability of zero-energy Dirac touchings in the honeycomb Hofstadter problem

Stability of zero-energy Dirac touchings in the honeycomb Hofstadter problem

Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field

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

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