Quantum Geometry and Flat Band Bose-Einstein Condensation

Julku, Aleksi; Bruun, Georg M.; Törmä, Païvi

doi:10.1103/physrevlett.127.170404

Cited by 46 publications

(30 citation statements)

References 43 publications

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“…Our work, alongside the accompanying study in Ref. [64], establishes important connections between the quantum geometry and physical quantities of a BEC, showing how the geometric properties of quantum states can be utilized to reach the strongly correlated regime. This can have important consequences, especially in systems where the interactions between particles are inherently small compared to kinetic tunneling energies and quantum correlations and depletion are weak, e.g., in photonic or polaritonic platforms.…”

Section: Discussionmentioning

confidence: 56%

“…Our present work accompanies the joint study of Ref. [64] and together these two works establish fundamental relations between the quantum geometry and BEC. We show that bosonic condensation and superfluidity can be stable in a flat band if there is a finite quantum metric and a quantum distance between the condensed state and noncondensed states of the band.…”

Section: Introductionmentioning

confidence: 71%

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Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

2021

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The quantum geometry of Bloch states fundamentally affects a wide range of physical phenomena. The quantum Hall effect, for example, is governed by the Chern number, and flat-band superconductivity by the distance between the Bloch states: the quantum metric. While understanding quantum geometry phenomena in the context of fermions is well established, less is known about the role of quantum geometry in bosonic systems where particles can undergo Bose-Einstein condensation (BEC). In conventional single-band or continuum systems, excitations of a weakly interacting BEC are determined by the condensate density and the interparticle interaction energy. In contrast to this, we discover here fundamental connections between the properties of a weakly interacting BEC and the underlying quantum geometry of a multiband lattice system. We show that, in the flat-band limit, the defining physical quantities of BEC, namely, the speed of sound and the quantum depletion, are dictated solely by the quantum geometry. We find that the speed of sound becomes proportional to the quantum metric of the condensed state. Furthermore, the quantum distance between the Bloch functions forces the quantum depletion and the quantum fluctuations of the density-density correlation to obtain finite values for infinitesimally small interactions. This is in striking contrast to dispersive bands where these quantities vanish with the interaction strength. Additionally, we show how in the flat-band limit the supercurrent is carried by the quantum fluctuations and is determined by the Berry connections of the Bloch states. Our results reveal how nontrivial quantum geometry allows reaching strong quantum correlation regime of condensed bosons even with weak interactions. This is highly relevant, for example, for polariton and photon BECs where interparticle interactions are inherently small. Our predictions can be experimentally tested with flat-band lattices already implemented in ultracold gases and various photonic platforms.

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Section: Discussionmentioning

confidence: 56%

Section: Introductionmentioning

confidence: 71%

Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

2021

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“…For instance, light-matter interactions in TBG reflect the underlying quantum geometry as well [148,149]. Recently, quantum geometry was predicted to stabilize Bose-Einstein condensates in flat bands [150], relevant for bosonic condensates in ultracold gas and polariton systems, or even for 2D moiré materials at the bosonic end of the BCS-BEC crossover [98].…”

Section: Discussionmentioning

confidence: 99%

Superfluidity and Quantum Geometry in Twisted Multilayer Systems

Törmä¹,

Peotta²,

Bernevig³

2021

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Designer 2D materials where the constituent layers are not aligned may result in band structures with dispersionless, "flat" bands. Twisted bilayer graphene has been found to show correlated phases as well as superconductivity related to such flat bands. In parallel, theory work has discovered that superconductivity and superfluidity is determined by the quantum geometry and topology of the band structure. These recent key developments are merging to a flourishing research topic: understanding the possible connection and ramifications of quantum geometry on the induced superconductivity and superfluidity in moiré multilayer and other flat band systems. This article presents an introduction to how quantum geometry governs superfluidity in platforms including, and beyond, graphene. We explain how a new type of topology discovered in TBG could affect superconductivity, pinpoint the geometric contribution in its Beretzinskii-Kosterlitz-Thouless (BKT) critical temperature, and mention moiré materials beyond TBG. Ultracold gases are introduced as a complementary platform for quantum geometric effects and a comparison is made to moiré materials. An outlook sketches the prospects of twisted multilayer systems in providing the route to room temperature superconductivity.

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“…The geometric concept of distance has been well recognized in quantum information theory [15][16][17], and it has also begun to attract interest also in condensed matter physics [18][19][20][21][22][23]. Examples include the collective excitations of quantum Hall states [24][25][26][27][28] and bosonic phenomena such as superfluidity and Bose-Einstein condensation [29][30][31] in flat bands.…”

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confidence: 99%

Quantum Metric Induced Phases in Moiré Materials

Abouelkomsan¹,

Yang²,

Bergholtz³

2022

Preprint

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We show that, quite generally, quantum geometry plays a major role in determining the low-energy physics in strongly correlated lattice models at fractional band fillings. We identify limits in which the Fubini Study metric dictates the ground states and show that this is highly relevant for Moiré materials leading to symmetry breaking and interaction driven Fermi liquids. This phenomenology stems from a novel interplay between the quantum geometry and interactions which is absent in continuum Landau levels but generically present in lattice models where these terms tend to destabilize e.g. fractional Chern insulators. We explain this as a consequence of the fundamental asymmetry between electrons and holes for band projected normal ordered interactions, as well as from the perspective of a self-consistent Hartree-Fock calculation. These basic insights about the role to the quantum metric turn, when dominant, an extremely strongly coupled problem into an effectively weakly coupled one, and may also serve as a guiding principle for designing material setups.

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Quantum Geometry and Flat Band Bose-Einstein Condensation

Cited by 46 publications

References 43 publications

Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

Superfluidity and Quantum Geometry in Twisted Multilayer Systems

Quantum Metric Induced Phases in Moiré Materials

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