Unconventional self-similar Hofstadter superconductivity from repulsive interactions

Shaffer, Daniel; Wang, Jian; Santos, Luiz

doi:10.1038/s41467-022-35316-z

Cited by 16 publications

(3 citation statements)

References 113 publications

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“…In this study, since we are interested on vortex physics, we only focus on integer fluxes that are far from the Harper-Hofstadter limit even for no disorder. Likewise, recent reports [68,69] on Hofstadter superconductivity are for clean systems and for a strength of the magnetic field much larger than the one considered in the paper. Therefore, there is no overlap with our results.…”

Section: Model and Methodsmentioning

confidence: 57%

Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

Fan,

Garcia Garcia

2023

SciPost Phys.

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We study the interplay of vortices and disorder in a two-dimensional disordered superconductor at zero temperature described by the Bogoliubov-de Gennes (BdG) self-consistent formalism for lattices of sizes up to 100×100 where the magnetic flux is introduced by the Peierls substitution. We model substantially larger lattice size than in previous approaches (≤36×36) which has allowed us to identify a rich phase diagram as a function of the magnetic flux and the disorder strength. For sufficiently weak disorder, and not too strong magnetic flux, we observe a slightly distorted Abrikosov triangular vortex lattice. An increase in the magnetic flux leads to an unexpected rectangular vortex lattice. A further increase in disorder, or flux, gradually destroys the lattice symmetry though strong vortex repulsion persists. An even stronger disorder leads to deformed single vortices with an inhomogeneous core. As the number of vortices increases, vortex overlap becomes more frequent. Finally, we show that global phase coherence is a feature of all these phases and that disorder enhances substantially the critical magnetic flux with respect to the clean limit with a maximum on the metallic side of the insulating transition.

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Section: Model and Methodsmentioning

confidence: 57%

Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

Fan,

Garcia Garcia

2023

SciPost Phys.

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“…This is a noteworthy advancement in the field [16,33,34]. The atomic and electronic structure of vdW heterostructures is subject to periodic modulation by Moiré superlattices (MSLs), leading to the appearance of several phenomena such as the formation of shear solitons and topological point defects [35][36][37][38], secondary Dirac cones [39][40][41], and Hofstadter butterfly states [33,[42][43][44]. In addition, flat bands were discussed back in 2011; such flat energy bands are of interest and may localize the presence of electronic states.…”

Section: Introductionmentioning

confidence: 99%

Emerging Characteristics and Properties of Moiré Materials

Wang,

Song,

Sun

et al. 2023

Nanomaterials

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In recent years, scientists have conducted extensive research on Moiré materials and have discovered some compelling properties. The Moiré superlattice allows superconductivity through flat-band and strong correlation effects. The presence of flat bands causes the Moiré material to exhibit topological properties as well. Modulating electronic interactions with magnetic fields in Moiré materials enables the fractional quantum Hall effect. In addition, Moiré materials have ferromagnetic and antiferromagnetic properties. By tuning the interlayer coupling and spin interactions of the Moiré superlattice, different magnetic properties can be achieved. Finally, this review also discusses the applications of Moiré materials in the fields of photocurrent, superconductivity, and thermoelectricity. Overall, Moiré superlattices provide a new dimension in the development of two-dimensional materials.

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“…On the other hand, defying expectations that the weak coupling regime (U W ) in Chern bands leads to a stable Fermi liquid (FL) fixed point, recent analysis [29,30] has uncovered new FL instabilities in partially filled Hofstadter bands [31] (generally supporting non-zero Chern number [32]) due to the interplay of repulsive interactions and logarithmic Van Hove singularities (VHS). In such fractal bands, the magnet flux per unit cell acts a control knob changing the landscape of VHSs and opening new interaction channels.…”

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confidence: 99%

Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model

Castro¹,

Shaffer²,

Wu³

et al. 2023

Preprint

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While advances in electronic band theory have brought to light new topological systems, understanding the interplay of band topology and electronic interactions remains a frontier question. In this work, we predict new interacting electronic orders emerging near higher-order Van Hove singularities present in the Chern bands of the Haldane model. We classify the nature of such singularities and employ unbiased renormalization group methods that unveil a complex landscape of electronic orders, which include ferromagnetism, density-waves and superconductivity. Importantly, we show that repulsive interactions can stabilize long-sought pair-density-wave state and an exotic Chern supermetal, which is a new class of non-Fermi liquid with anomalous quantum Hall response. This framework opens a new path to explore unconventional electronic phases in two-dimensional chiral bands through the interplay of band topology and higher-order Van Hove singularities.

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Unconventional self-similar Hofstadter superconductivity from repulsive interactions

Cited by 16 publications

References 113 publications

Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

Emerging Characteristics and Properties of Moiré Materials

Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model

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