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Amelio I, Goldman N. Lasing in Non-Hermitian Flat Bands: Quantum Geometry, Coherence, and the Fate of Kardar-Parisi-Zhang Physics. PHYSICAL REVIEW LETTERS 2024; 132:186902. [PMID: 38759172 DOI: 10.1103/physrevlett.132.186902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Revised: 04/03/2024] [Accepted: 04/08/2024] [Indexed: 05/19/2024]
Abstract
We show that lasing in flat-band lattices can be stabilized by means of the geometrical properties of the Bloch states, in settings where the single-particle dispersion is flat in both its real and imaginary parts. We illustrate a general projection method and compute the collective excitations, which display a diffusive behavior ruled by quantum geometry through a peculiar coefficient involving gain, losses and interactions, and entailing resilience against modulational instabilities. Then, we derive an equation of motion for the phase dynamics and identify a Kardar-Parisi-Zhang term of geometric origin. This term is shown to exactly cancel whenever the real and imaginary parts of the laser nonlinearity are proportional to each other, or when the uniform-pairing condition is satisfied. We confirm our results through numerical studies of the π-flux diamond chain. This Letter highlights the key role of Bloch geometric effects in nonlinear dissipative systems and KPZ physics, with direct implications for the design of laser arrays with enhanced coherence.
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Affiliation(s)
- Ivan Amelio
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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Kitamura T, Daido A, Yanase Y. Spin-Triplet Superconductivity from Quantum-Geometry-Induced Ferromagnetic Fluctuation. PHYSICAL REVIEW LETTERS 2024; 132:036001. [PMID: 38307086 DOI: 10.1103/physrevlett.132.036001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2023] [Revised: 11/19/2023] [Accepted: 11/29/2023] [Indexed: 02/04/2024]
Abstract
We show that quantum geometry induces ferromagnetic fluctuation resulting in spin-triplet superconductivity. The criterion for ferromagnetic fluctuation is clarified by analyzing contributions from the effective mass and quantum geometry. When the non-Kramers band degeneracy is present near the Fermi surface, the Fubini-Study quantum metric strongly favors ferromagnetic fluctuation. Solving the linearized gap equation with the effective interaction obtained by the random phase approximation, we show that the spin-triplet superconductivity is mediated by quantum-geometry-induced ferromagnetic fluctuation.
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Affiliation(s)
- Taisei Kitamura
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Akito Daido
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Youichi Yanase
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Chen SA, Law KT. Ginzburg-Landau Theory of Flat-Band Superconductors with Quantum Metric. PHYSICAL REVIEW LETTERS 2024; 132:026002. [PMID: 38277583 DOI: 10.1103/physrevlett.132.026002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 12/07/2023] [Indexed: 01/28/2024]
Abstract
Recent experimental studies unveiled highly unconventional phenomena in the superconducting twisted bilayer graphene (TBG) with ultraflat bands, which cannot be described by the conventional BCS theory. For example, given the small Fermi velocity of the flat bands, the superconducting coherence length predicted by BCS theory is more than 20 times shorter than the measured values. A new theory is needed to understand many of the unconventional properties of flat-band superconductors. In this Letter, we establish a Ginzburg-Landau (GL) theory from a microscopic flat-band Hamiltonian. The GL theory shows how the properties of the physical quantities such as the critical temperature, superconducting coherence length, upper critical field, and superfluid density are governed by the quantum metric of the Bloch states. One key conclusion is that the superconducting coherence length is not determined by the Fermi velocity but by the size of the optimally localized Wannier functions which are limited by the quantum metric. Applying the theory to TBG, we calculated the superconducting coherence length and the upper critical fields. The results match the experimental ones well without fine-tuning of parameters. The established GL theory provides a new and general theoretical framework for understanding flat-band superconductors with the quantum metric.
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Affiliation(s)
- Shuai A Chen
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - K T Law
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
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Jalali-Mola Z, Grass T, Kasper V, Lewenstein M, Bhattacharya U. Topological Bogoliubov Quasiparticles from Bose-Einstein Condensate in a Flat Band System. PHYSICAL REVIEW LETTERS 2023; 131:226601. [PMID: 38101336 DOI: 10.1103/physrevlett.131.226601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Revised: 09/07/2023] [Accepted: 10/23/2023] [Indexed: 12/17/2023]
Abstract
For bosons with flat energy dispersion, condensation can occur in different symmetry sectors. Here, we consider bosons in a kagome lattice with π-flux hopping, which, in the presence of mean-field interactions, exhibit degenerate condensates in the Γ and the K point. We analyze the excitation above both condensates and find strikingly different properties: For the K-point condensate, the Bogoliubov-de Gennes (BdG) Hamiltonian has broken particle-hole symmetry and exhibits a topologically trivial quasiparticle band structure. However, band flatness plays a key role in breaking the time-reversal symmetry of the BdG Hamiltonian for a Γ-point condensate. Consequently, its quasiparticle band structure exhibits nontrivial topology, characterized by nonzero Chern numbers and by the presence of edge states. Although quantum fluctuations energetically favor the K-point condensate, the interesting properties of the Γ-point condensate become relevant for anisotropic hopping. The topological properties of the Γ-point condensate get even richer in the presence of extended Bose-Hubbard interactions. We find a topological phase transition into a topological condensate characterized by high Chern number and also comment on the realization and detection of such excitations.
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Affiliation(s)
- Zahra Jalali-Mola
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Tobias Grass
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- DIPC-Donostia International Physics Center, Paseo Manuel de Lardizábal 4, 20018 San Sebastián, Spain
- Ikerbasque-Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
| | - Valentin Kasper
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- Nord Quantique, 3000 boulevard de l'Université (P1-ACET), Sherbrooke J1K 0A5, Quebec, Canada
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA, Passeig de Lluís Companys 23, 08010 Barcelona, Spain
| | - Utso Bhattacharya
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
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Jin KH, Jiang W, Sethi G, Liu F. Topological quantum devices: a review. NANOSCALE 2023; 15:12787-12817. [PMID: 37490310 DOI: 10.1039/d3nr01288c] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/26/2023]
Abstract
The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.
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Affiliation(s)
- Kyung-Hwan Jin
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea
| | - Wei Jiang
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Gurjyot Sethi
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA.
| | - Feng Liu
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA.
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Jiang G, Barlas Y. Pair Density Waves from Local Band Geometry. PHYSICAL REVIEW LETTERS 2023; 131:016002. [PMID: 37478459 DOI: 10.1103/physrevlett.131.016002] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Revised: 03/27/2023] [Accepted: 05/18/2023] [Indexed: 07/23/2023]
Abstract
A band-projection formalism is developed for calculating the superfluid weight in two-dimensional multiorbital superconductors with an orbital-dependent pairing. It is discovered that, in this case, the band geometric superfluid stiffness tensor can be locally nonpositive definite in some regions of the Brillouin zone. When these regions are large enough or include nodal singularities, the total superfluid weight becomes nonpositive definite due to pairing fluctuations, resulting in the transition of a BCS state to a pair density wave (PDW). This geometric BCS-PDW transition is studied in the context of two-orbital superconductors, and proof of the existence of a geometric BCS-PDW transition in a generic topological flat band is established.
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Affiliation(s)
- Guodong Jiang
- Department of Physics, University of Nevada, Reno, Reno, Nevada 89502, USA
| | - Yafis Barlas
- Department of Physics, University of Nevada, Reno, Reno, Nevada 89502, USA
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Sethi G, Cuma M, Liu F. Excitonic Condensate in Flat Valence and Conduction Bands of Opposite Chirality. PHYSICAL REVIEW LETTERS 2023; 130:186401. [PMID: 37204894 DOI: 10.1103/physrevlett.130.186401] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2022] [Revised: 07/01/2022] [Accepted: 04/14/2023] [Indexed: 05/21/2023]
Abstract
Excitonic Bose-Einstein condensation (EBEC) has drawn increasing attention recently with the emergence of 2D materials. A general criterion for EBEC, as expected in an excitonic insulator (EI) state, is to have negative exciton formation energies in a semiconductor. Here, using exact diagonalization of a multiexciton Hamiltonian modeled in a diatomic kagome lattice, we demonstrate that the negative exciton formation energies are only a prerequisite but insufficient condition for realizing an EI. By a comparative study between the cases of both conduction and valence flat bands (FBs) versus that of a parabolic conduction band, we further show that the presence and increased FB contribution to exciton formation provide an attractive avenue to stabilize the excitonic condensate, as confirmed by calculations and analyses of multiexciton energies, wave functions, and reduced density matrices. Our results warrant a similar many-exciton analysis for other known and/or new candidates of EIs and demonstrate the FBs of opposite parity as a unique platform for studying exciton physics, paving the way to material realization of spinor BEC and spin superfluidity.
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Affiliation(s)
- Gurjyot Sethi
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA
| | - Martin Cuma
- Center for High Performance Computing, University of Utah, Salt Lake City, Utah 84112, USA
| | - Feng Liu
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA
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Herzog-Arbeitman J, Peri V, Schindler F, Huber SD, Bernevig BA. Superfluid Weight Bounds from Symmetry and Quantum Geometry in Flat Bands. PHYSICAL REVIEW LETTERS 2022; 128:087002. [PMID: 35275691 DOI: 10.1103/physrevlett.128.087002] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Revised: 01/10/2022] [Accepted: 02/04/2022] [Indexed: 06/14/2023]
Abstract
Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms-even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean field. Hence, obstructed bands are distinguished from trivial bands in the presence of interactions by the nonzero lower bound imposed on their superfluid weight.
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Affiliation(s)
| | - Valerio Peri
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Frank Schindler
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - Sebastian D Huber
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, 48009 Bilbao, Spain
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