Theory of Hofstadter superconductors

Shaffer, Daniel; Wang, Jian; Santos, Luiz

doi:10.1103/physrevb.104.184501

Cited by 32 publications

(44 citation statements)

References 172 publications

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“…x ) flowing independently, consistent with the fact that there are four q/2-dimensional irreps in this case [31].…”

Section: B Vertices and Susceptibilitiessupporting

confidence: 78%

“…For q = 3, we find that, at 1/6 and 5/6 lattice filling, SC and SDW are nearly degenerate when both are at perfect nesting, while CDW is favored at half-filling. A small symmetry-allowed detuning from perfect nesting in the SDW therefore favors the pairing instability, which necessarily breaks a subset of the MTG symmetries [31]. We find that the resulting SC state is a fully gapped chiral topological phase with Chern number C = ±6 that preserves a Z q subgroup of the MTG.…”

Section: Introductionmentioning

confidence: 83%

“…As shown in [31], unlike the charge-0 orders, the charge-2 SC orders transform according to q or q/2 irreps of the MTG for odd and even q respectively. This means that in general there are are q or q/2 degenerate flows in the SC channels corresponding to each choice of in Eq.…”

Section: B Vertices and Susceptibilitiesmentioning

confidence: 96%

“…This is especially relevant for moiré systems since their nanometer scale unit cells enable the realization of Hofstadter bands in experimentally accessible magnetic fields at which the magnetic flux per super unit cell Φ = BA uc is comparable to the flux quantum Φ 0 = 2π /e = 2π in natural units [9][10][11][12][13][14][15]. Beyond the rich phenomena in Hofstadter-Chern insulators [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], a recent classification [31] has shown that Hofstadter bands may support novel Hofstadter super- * luiz.santos@emory.edu conductors (HSC) characterized by spontaneous breaking of the magnetic translation group (MTG) symmetries [32][33][34], leading to multi-component finite momentum Cooper pairing similar to pair-density wave states [35]. HSCs embody a new form of reentrant superconductivity in Hofstadter bands, in which the large flux per unit cell makes the magnetic length comparable to the lattice scale, thus generalizing the Landau level reentrant SC state.…”

Section: Introductionmentioning

confidence: 99%

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Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions

Shaffer¹,

Wang²,

Santos³

2022

Preprint

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The interplay of lattice potential and magnetic field gives rise to fractal Hofstadter bands that have long been associated with quantum Hall phenomena. In this work, we show that Hofstadter bands are also a rich platform to realize unconventional superconductivity driven entirely by repulsive interactions. Unlike Landau levels, Hofstadter bands have finite bandwidth and display a rich manifold of Van Hove singularities, whose number can be tuned as a function of the magnetic flux Φ = 2π(p/q)( /e) per unit cell. Exploring this control knob, we perform a weak coupling renormalization group (RG) analysis for the fermionic Hofstadter-Hubbard model on a square lattice, which establishes a rich competition of electronic orders, from which electronic pairing emerges as a low energy instability. Remarkably, some of these fixed points are characterized by an emergent self-similarity, which reflects the non-trivial renormalization of the bare Hubbard interaction in fractal Hofstadter bands. Our main predictions are (i) nodal d-wave superconductivity near 1/4 and 3/4 fillings in the π-flux lattice (Φ = h/2e); (ii) chiral topological superconductivity with Chern number C = ±6 near 1/6 and 5/6 fillings in the ±2π/3-flux lattice (Φ = ±h/3e). The latter arises when the interactions flow to a self-similar fixed trajectory of the RG flow and are characterized by a self-similarity symmetry that enforces a polynomially decaying real space order parameter. Our work opens a new route in the pursuit of reentrant superconductivity in a wide class of Hofstadter quantum materials including synthetic lattices and moiré heterostructures.

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“…x ) flowing independently, consistent with the fact that there are four q/2-dimensional irreps in this case [31].…”

Section: B Vertices and Susceptibilitiessupporting

confidence: 78%

Section: Introductionmentioning

confidence: 83%

Section: B Vertices and Susceptibilitiesmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions

Shaffer¹,

Wang²,

Santos³

2022

Preprint

Self Cite

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“…However, multicomponent systems may exhibit a different kind of ordering associated with the long-range order of electron quadruplets [3][4][5][6][7][8][9][10][11][12][13][14]. Related phases have also been discussed in strongly correlated ultracold atoms [15][16][17] and other models [18,19].…”

Section: Introductionmentioning

confidence: 99%

Effects of intercomponent couplings on the appearance of time-reversal symmetry breaking fermion quadrupling state in two-component London models

Maccari,

Babaev

2022

Preprint

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A detection of bosonic metallic state that breaks the Z2 time-reversal symmetry has been recently reported in Ba1−xKxFe2As2 with a doping level x ≈ 0.8. This is a metallic state of fermionic quadruplets that breaks time-reversal symmetry. As such, it has no condensate of Cooper pairs but has a long-range order between fermionic quartets. In the present manuscript, we investigate the emergence of this phase in a two-component London model via Monte Carlo simulations as a function of various intercomponent couplings.

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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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Theory of Hofstadter superconductors

Cited by 32 publications

References 172 publications

Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions

Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions

Effects of intercomponent couplings on the appearance of time-reversal symmetry breaking fermion quadrupling state in two-component London models

Unconventional self-similar Hofstadter superconductivity from repulsive interactions

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