Superfluidity and Quantum Geometry in Twisted Multilayer Systems

Törmä, Païvi; Peotta, Sebastiano; Bernevig, B. Andrei

doi:10.48550/arxiv.2111.00807

Cited by 10 publications

(16 citation statements)

References 149 publications

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“…A very intriguing experimental platform to test our results is twisted bilayer graphene [26][27][28][29][30][31][32][33].…”

Section: B Outlookmentioning

confidence: 90%

“…Its imaginary part is the well established Berry curvature characterizing the topological phase of the band, while its real part is the quantum metric. The study of the quantum metric, and thus also the quantum geometric tensor, has attracted attention on many fronts in the recent past including superconducting systems [6][7][8][9], quantum phase transitions [10,11], magnetic signatures [12][13][14][15], quantum topology and geometry [16][17][18][19][20], flat band systems [21], in nonadiabatic evolution [22], as marker distinguishing insulators from metals [23], non-hermitian systems [24,25], in twisted bilayer graphene [26][27][28][29][30][31][32][33] and in dimensions higher than two [34][35][36][37][38][39][40][41]. Theoretical measurements have been proposed and measurements of the quantum geometric tensor have been performed in [42][43][44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

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Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields

Northe,

Palumbo,

Sturm

et al. 2021

Preprint

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Ideal Chern insulating phases arise in two-dimensional systems with broken time-reversal symmetry. They are characterized by having nearly-flat bands, and a uniform quantum geometry -which combines the Berry curvature and quantum metric -and by being incompressible. In this work, we analyze the role of the quantum geometry in ideal Chern insulators aiming to describe transport in presence of external out-of-plane magnetic and electric fields. We firstly show that in the absence of external perturbations, novel Berry connections appear in ideal Chern insulating phases. Secondly, we provide a detailed analysis of the deformation of the quantum geometry once weak out-of-plane magnetic fields are switched on. The perturbed Berry curvature and quantum metric provide an effective quantum geometry, which is analyzed in the insulating regime and provides an application of our novel connections. The conditions under which the Girvin-MacDonald-Platzman algebra is realized in this situation are discussed. Furthermore, an investigation of electrical transport due to the new effective quantum geometry is presented once an electric field is added. Restricting to the case of two bands in the metallic regime the quantum metric appears as measurable quantum mechanical correction in the Hall response. Our findings can be applied, for instance, to rhombohedral trilayer graphene at low energies.

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“…A very intriguing experimental platform to test our results is twisted bilayer graphene [26][27][28][29][30][31][32][33].…”

Section: B Outlookmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields

Northe,

Palumbo,

Sturm

et al. 2021

Preprint

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show abstract

“…We now discuss lower bound of superfluid weight within the mean-field approximation. We adopt the exact-flat-band approximation [49,[60][61][62][63], where we choose the normal-state flat bands to be exactly-flat. By using the formalism of Euler obstructed Cooper pairing, we obtain a lower bound for the trace of the zerotemperature superfluid weight for the C 2z T -invariant pairing in Eq.…”

Section: Bounded Superfluid Weightmentioning

confidence: 99%

Euler Obstructed Cooper Pairing in Twisted Bilayer Graphene: Nematic Nodal Superconductivity and Bounded Superfluid Weight

Yu¹,

Xie²,

Wu³

et al. 2022

Preprint

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Magic-angle twisted bilayer graphene (MATBG) hosts normal-state nearly-flat bands with nonzero Euler numbers and shows superconductivity. In this work, we study the effects of the nontrivial normal-state band topology on the intervalley C2zT -invariant mean-field Cooper pairing order parameter in MATBG. We show that the pairing order parameter can always be split into a trivial channel and an Euler obstructed channel in all gauges for the normal-state basis, generalizing the previously-studied channel splitting in the Chern gauge. The nonzero normal-state Euler numbers require the pairing gap function of the Euler obstructed channel to have zeros, while the trivial channel can have a nonvanishing pairing gap function. When the pairing is spontaneously nematic, we find that a sufficiently-dominant Euler obstructed channel with two zeros typically leads to nodal superconductivity. Under the approximation of exactly-flat bands, we find that the mean-field zero-temperature superfluid weight is generally bounded from below, no matter whether the Euler obstructed channel is dominant or not, generalizing the previously-derived bound for the uniform s-wave pairing. We numerically verify these statements for pairings derived from a local attractive interaction. Our work suggests that Euler obstructed Cooper pairing may play an essential role in the superconducting MATBG.

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“…In a flat band the effective mass m * diverges and one would expect the superfluid weight to vanish. On the contrary, it has been found that, besides the band dispersion, also the quantum geometry of the Bloch wave functions contributes to the superfluid weight [24][25][26][27][28][29][30][31][32][33]. In particular, in the case of a well isolated flat band the superfluid weight originates purely from the quantum geometry and can be written as…”

mentioning

confidence: 99%

Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion

Lau¹,

Peotta²,

Pikulin³

et al. 2022

Preprint

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Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy is large, the contribution due to the quantum geometry is negligible, but in the opposite limit of flat-band superconductors the superfluid weight originates purely from the quantum geometry of Bloch wave functions. Here, we study how the energy band dispersion and the quantum geometry affect the disorder-induced suppression of the superfluid weight. Surprisingly, we find that the disorder-dependence of the superfluid weight is universal across a variety of models, and independent of the quantum geometry and the flatness of the dispersion. Our results suggest that a flat-band superconductor is as resilient to disorder as a conventional superconductor.

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Superfluidity and Quantum Geometry in Twisted Multilayer Systems

Cited by 10 publications

References 149 publications

Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields

Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields

Euler Obstructed Cooper Pairing in Twisted Bilayer Graphene: Nematic Nodal Superconductivity and Bounded Superfluid Weight

Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion

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