Effects of interaction in the Hofstadter regime of the honeycomb lattice

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

doi:10.1103/physrevb.93.125134

Cited by 16 publications

(20 citation statements)

References 28 publications

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“…6a. As described in our previous work 24 , there is always a scaling solution for this interacting problem which satisfies the self consistency equations. The state corresponding to this solution is the same as the noninteracting case.…”

Section: Effect Of Interactionsmentioning

confidence: 75%

“…In this paper, we investigate whether this actually happens. In our recent paper 24 , we had studied the effect of interaction in one of the many systems required to realize the Hofstadter butterfly in honeycomb lattice, lattice with flux per plaquette φ = 1/3 (in units of h/e). We studied the interaction induced translational symmetry broken phases in the Hofstadter regime of the honeycomb lattice for this flux value.…”

Section: Introductionmentioning

confidence: 99%

“…To solve this interacting problem, we use mean field approximation discussed in our previous work 24 ,…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Effect Of Interactionsmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

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Translational symmetry breaking and the disintegration of the Hofstadter butterfly

2017

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“…Although we give more results in this regime when we discuss scattering-rate below, we do not enter into the many details for this case since numerous studies have already tackled the interacting Hofstadter butterfly. [8][9][10][11][12][13][14] In the Landau regime, i.e. when the k y dependence of the eigenvalues in the Harper matrix Eq.…”

Section: Resultsmentioning

confidence: 99%

“…The effect of interactions on Hofstadter's butterfly has already been studied by various methods such as meanfield theory [8][9][10] , DMFT for the Falicov-Kimball model 11 or real-space DMFT [12][13][14] . The latter approach generalizes DMFT 15,16 to the case where the electromagnetic vector potential breaks translational invariance, by using a set of quantum impurities, one for each inequivalent site of the lattice.…”

Section: Introductionmentioning

confidence: 99%

Orbital effect of the magnetic field in dynamical mean-field theory

2017

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The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms, calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical meanfield theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the singleparticle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime. II. THE DYNAMICAL MEAN-FIELD EQUATIONS WITH MAGNETIC FIELDHere we derive 17 the DMFT equations when the orbital effect of the magnetic field is taken into account in arXiv:1710.01396v1 [cond-mat.str-el]

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Unconventional self-similar Hofstadter superconductivity from repulsive interactions

2022

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Fractal Hofstadter bands have become widely accessible with the advent of moiré superlattices, opening the door to studies of the effect of interactions in these systems. In this work we employ a renormalization group (RG) analysis to demonstrate that the combination of repulsive interactions with the presence of a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Specifically, the number of Van Hove singularities at the Fermi energy can be controlled by varying the flux per unit cell and the electronic filling, leading to instabilities toward nodal superconductivity and chiral topological superconductivity with Chern number $${{{{{{{\mathcal{C}}}}}}}}=\pm 6$$ C = ± 6 . The latter is characterized by a self-similar fixed trajectory of the RG flow and an emerging self-similarity symmetry of the order parameter. Our results establish Hofstadter quantum materials such as moiré heterostructures as promising platforms for realizing novel reentrant Hofstadter superconductors.

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Effects of interaction in the Hofstadter regime of the honeycomb lattice

Cited by 16 publications

References 28 publications

Translational symmetry breaking and the disintegration of the Hofstadter butterfly

Translational symmetry breaking and the disintegration of the Hofstadter butterfly

Orbital effect of the magnetic field in dynamical mean-field theory

Unconventional self-similar Hofstadter superconductivity from repulsive interactions

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