Superconducting transitions in flat-band systems
Abstract
The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive Hubbard model on a bipartite lattice with unequal number of sites in each sublattice must have nonzero spin S at half-filling. Recently, there has been interest in Lieb geometries due to the possibility of novel topological insulator, nematic, and Bose-Einstein condensed (BEC) phases. In this paper, we extend the understanding of the attractive Hubbard model on the Lieb lattice by using Determinant Quantum Monte Carlo to study real space charge and pair correlation functions not addressed by the Lieb theorems. Specifically, our results show unusual charge and charge transfer signatures within the flat band, and a reduction in pairing order at ρ = 2/3 and ρ = 4/3, the points at which the flat band is first occupied and then completely filled. Lastly, we compare our results to the case of flat bands in the Kagome lattice and demonstrate that the behavior observed in the two cases is rather different.
- Authors:
-
- Univ. of California, Davis, CA (United States). Physics Dept.
- Univ. of Nice Sophia Antipolis (France)
- CNRS-UNS-NUS-NTU International Joint Research Unit (Singapore); Ecole Normale Superieure, Paris (France). Kastler Brossel Lab.; National Univ. of Singapore (Singapore). Centre for Quantum Technologies and Dept. of Physics
- Univ. of Nice Sophia Antipolis (France); National Univ. of Singapore (Singapore). Centre for Quantum Technologies; Inst. Univ. of France, Paris (France)
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1344110
- Alternate Identifier(s):
- OSTI ID: 1180268
- Grant/Contract Number:
- NA0001842; NNSA-DE-NA0001842-0
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics
- Additional Journal Information:
- Journal Volume: 90; Journal Issue: 9; Journal ID: ISSN 1098-0121
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Iglovikov, V. I., Hébert, F., Grémaud, B., Batrouni, G. G., and Scalettar, R. T. Superconducting transitions in flat-band systems. United States: N. p., 2014.
Web. doi:10.1103/PhysRevB.90.094506.
Iglovikov, V. I., Hébert, F., Grémaud, B., Batrouni, G. G., & Scalettar, R. T. Superconducting transitions in flat-band systems. United States. https://doi.org/10.1103/PhysRevB.90.094506
Iglovikov, V. I., Hébert, F., Grémaud, B., Batrouni, G. G., and Scalettar, R. T. Thu .
"Superconducting transitions in flat-band systems". United States. https://doi.org/10.1103/PhysRevB.90.094506. https://www.osti.gov/servlets/purl/1344110.
@article{osti_1344110,
title = {Superconducting transitions in flat-band systems},
author = {Iglovikov, V. I. and Hébert, F. and Grémaud, B. and Batrouni, G. G. and Scalettar, R. T.},
abstractNote = {The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive Hubbard model on a bipartite lattice with unequal number of sites in each sublattice must have nonzero spin S at half-filling. Recently, there has been interest in Lieb geometries due to the possibility of novel topological insulator, nematic, and Bose-Einstein condensed (BEC) phases. In this paper, we extend the understanding of the attractive Hubbard model on the Lieb lattice by using Determinant Quantum Monte Carlo to study real space charge and pair correlation functions not addressed by the Lieb theorems. Specifically, our results show unusual charge and charge transfer signatures within the flat band, and a reduction in pairing order at ρ = 2/3 and ρ = 4/3, the points at which the flat band is first occupied and then completely filled. Lastly, we compare our results to the case of flat bands in the Kagome lattice and demonstrate that the behavior observed in the two cases is rather different.},
doi = {10.1103/PhysRevB.90.094506},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 9,
volume = 90,
place = {United States},
year = {Thu Sep 11 00:00:00 EDT 2014},
month = {Thu Sep 11 00:00:00 EDT 2014}
}
Web of Science
Works referenced in this record:
From antiferromagnetic ordering to magnetic textures in the two-dimensional Fermi-Hubbard model with synthetic spin-orbit interactions
journal, December 2013
- Minář, Jiří; Grémaud, Benoît
- Physical Review B, Vol. 88, Issue 23
Flat bands, Dirac cones, and atom dynamics in an optical lattice
journal, October 2010
- Apaja, V.; Hyrkäs, M.; Manninen, M.
- Physical Review A, Vol. 82, Issue 4
Mean-field theories of the two-band model and the magnetism in high- oxides
journal, May 1989
- Olés, Andrzej M.; Zaanen, Jan
- Physical Review B, Vol. 39, Issue 13
Pseudospin and nonlinear conical diffraction in Lieb lattices
journal, September 2012
- Leykam, Daniel; Bahat-Treidel, Omri; Desyatnikov, Anton S.
- Physical Review A, Vol. 86, Issue 3
Crossover from Bardeen-Cooper-Schrieffer to Bose-Einstein Condensation and the Unitary Fermi Gas
journal, March 2014
- Randeria, Mohit; Taylor, Edward
- Annual Review of Condensed Matter Physics, Vol. 5, Issue 1
Mott transition and ferrimagnetism in the Hubbard model on the anisotropic kagome lattice
journal, May 2011
- Yamada, A.; Seki, K.; Eder, R.
- Physical Review B, Vol. 83, Issue 19
Topological phases for fermionic cold atoms on the Lieb lattice
journal, June 2011
- Goldman, N.; Urban, D. F.; Bercioux, D.
- Physical Review A, Vol. 83, Issue 6
Charge transfer excitations and superconductivity in “ionic” metals
journal, June 1987
- Varma, C. M.; Schmitt-Rink, S.; Abrahams, Elihu
- Solid State Communications, Vol. 62, Issue 10
Enhanced Superconductivity in Quasi Two-Dimensional Systems
journal, June 1986
- Hirsch, J. E.; Scalapino, D. J.
- Physical Review Letters, Vol. 56, Issue 25
Fermi-surface instabilities and superconducting d -wave pairing
journal, May 1987
- Scalapino, D. J.; Loh, E.; Hirsch, J. E.
- Physical Review B, Vol. 35, Issue 13
Theory of high- superconductivity in oxides
journal, June 1987
- Emery, V. J.
- Physical Review Letters, Vol. 58, Issue 26
Band gaps and electronic structure of transition-metal compounds
journal, July 1985
- Zaanen, J.; Sawatzky, G. A.; Allen, J. W.
- Physical Review Letters, Vol. 55, Issue 4
Antiferromagnetic, charge-transfer, and pairing correlations in the three-band Hubbard model
journal, July 1991
- Scalettar, R. T.; Scalapino, D. J.; Sugar, R. L.
- Physical Review B, Vol. 44, Issue 2
Mean-field analysis of intra-unit-cell order in the Emery model of the CuO plane
journal, October 2011
- Fischer, Mark H.; Kim, Eun-Ah
- Physical Review B, Vol. 84, Issue 14
Two theorems on the Hubbard model
journal, March 1989
- Lieb, Elliott H.
- Physical Review Letters, Vol. 62, Issue 10
Localization of electronic wave functions due to local topology
journal, October 1986
- Sutherland, Bill
- Physical Review B, Vol. 34, Issue 8
Theory of the pseudogap state of the cuprates
journal, April 2006
- Varma, C. M.
- Physical Review B, Vol. 73, Issue 15
Spectral and transport properties of the two-dimensional Lieb lattice
journal, March 2013
- Niţă, M.; Ostahie, B.; Aldea, A.
- Physical Review B, Vol. 87, Issue 12
Topological insulators on the Lieb and perovskite lattices
journal, August 2010
- Weeks, C.; Franz, M.
- Physical Review B, Vol. 82, Issue 8
Nearly Flatbands with Nontrivial Topology
journal, June 2011
- Sun, Kai; Gu, Zhengcheng; Katsura, Hosho
- Physical Review Letters, Vol. 106, Issue 23
Topological flat band models with arbitrary Chern numbers
journal, December 2012
- Yang, Shuo; Gu, Zheng-Cheng; Sun, Kai
- Physical Review B, Vol. 86, Issue 24
-orbital counterpart of graphene: Cold atoms in the honeycomb optical lattice
journal, June 2008
- Wu, Congjun; Das Sarma, S.
- Physical Review B, Vol. 77, Issue 23
Flat Bands and Wigner Crystallization in the Honeycomb Optical Lattice
journal, August 2007
- Wu, Congjun; Bergman, Doron; Balents, Leon
- Physical Review Letters, Vol. 99, Issue 7
Structural Prediction and Phase Transformation Mechanisms in Calcium at High Pressure
journal, July 2009
- Yao, Yansun; Klug, Dennis D.; Sun, Jian
- Physical Review Letters, Vol. 103, Issue 5
Bose condensation in flat bands
journal, November 2010
- Huber, Sebastian D.; Altman, Ehud
- Physical Review B, Vol. 82, Issue 18
High-temperature surface superconductivity in topological flat-band systems
journal, June 2011
- Kopnin, N. B.; Heikkilä, T. T.; Volovik, G. E.
- Physical Review B, Vol. 83, Issue 22
High-temperature surface superconductivity in rhombohedral graphite
journal, April 2013
- Kopnin, N. B.; Ijäs, M.; Harju, A.
- Physical Review B, Vol. 87, Issue 14
Proposed realization of itinerant ferromagnetism in optical lattices
journal, November 2010
- Zhang, Shizhong; Hung, Hsiang-hsuan; Wu, Congjun
- Physical Review A, Vol. 82, Issue 5
Single Dirac cone with a flat band touching on line-centered-square optical lattices
journal, January 2010
- Shen, R.; Shao, L. B.; Wang, Baigeng
- Physical Review B, Vol. 81, Issue 4
Sign problem in the numerical simulation of many-electron systems
journal, May 1990
- Loh, E. Y.; Gubernatis, J. E.; Scalettar, R. T.
- Physical Review B, Vol. 41, Issue 13
Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981
- Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L.
- Physical Review D, Vol. 24, Issue 8
Numerical study of the two-dimensional Hubbard model
journal, July 1989
- White, S. R.; Scalapino, D. J.; Sugar, R. L.
- Physical Review B, Vol. 40, Issue 1
Ground-state staggered magnetization of two-dimensional quantum Heisenberg antiferromagnets
journal, February 1988
- Huse, David A.
- Physical Review B, Vol. 37, Issue 4
Cdw and sdw Mediated Pairing Interactions
journal, August 1987
- Bickers, N. E.; Scalapino, D. J.; Scalettar, R. T.
- International Journal of Modern Physics B, Vol. 01, Issue 03n04
Charge transfer excitations and superconductivity in “ionic” metals
journal, December 1993
- Varma, C. M.; Schmitt-Rink, S.; Abrahams, Elihu
- Solid State Communications, Vol. 88, Issue 11-12
Proposed realization of itinerant ferromagnetism in optical lattices
text, January 2008
- Zhang, Shizhong; Hung, Hsiang-hsuan; Wu, Congjun
- arXiv
Topological Insulators on the Lieb and Perovskite Lattices
text, January 2010
- Weeks, C.; Franz, M.
- arXiv
Flat bands, Dirac cones and atom dynamics in an optical lattice
text, January 2010
- Apaja, V.; Hyrkäs, M.; Manninen, M.
- arXiv
Nearly-flat bands with nontrivial topology
text, January 2010
- Sun, Kai; Gu, Zheng-Cheng; Katsura, Hosho
- arXiv
Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
text, January 2011
- Goldman, N.; Urban, D. F.; Bercioux, D.
- arXiv
Mean-Field Analysis of Intra-Unit-Cell Order in the Emery Model of the CuO$_2$ Plane
text, January 2011
- Fischer, Mark Hannes; Kim, Eun-Ah
- arXiv
Topological flat band models with arbitrary Chern numbers
text, January 2012
- Yang, Shuo; Gu, Zheng-Cheng; Sun, Kai
- arXiv
Spectral and transport properties of the two-dimensional Lieb lattice
text, January 2013
- Niţă, M.; Ostahie, B.; Aldea, A.
- arXiv
Works referencing / citing this record:
Topological states in engineered atomic lattices
journal, March 2017
- Drost, Robert; Ojanen, Teemu; Harju, Ari
- Nature Physics, Vol. 13, Issue 7
Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice
journal, November 2015
- Taie, Shintaro; Ozawa, Hideki; Ichinose, Tomohiro
- Science Advances, Vol. 1, Issue 10
Artificial flat band systems: from lattice models to experiments
journal, January 2018
- Leykam, Daniel; Andreanov, Alexei; Flach, Sergej
- Advances in Physics: X, Vol. 3, Issue 1
Magnon-impurity interaction effect on the magnonic heat capacity of the Lieb lattice
journal, December 2018
- Le, P. T. T.; Hoi, B. D.; Yarmohammadi, Mohsen
- AIP Advances, Vol. 8, Issue 12
Magnetic Shell Structure of 2D-Trapped Fermi Gases in the Flat-Band Lieb Lattices
journal, January 2019
- Jeong, Joo-Hyeok; Park, Hyunjoon; Kim, Dongkyu
- Applied Sciences, Vol. 9, Issue 3
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
journal, March 2018
- Cao, Yuan; Fatemi, Valla; Demir, Ahmet
- Nature, Vol. 556, Issue 7699
Dual Dirac cones in elastic Lieb-like lattice metamaterials
journal, February 2019
- Li, Bing; Li, Zheng; Christensen, Johan
- Applied Physics Letters, Vol. 114, Issue 8
Magnetization, -wave superconductivity, and non-Fermi-liquid behavior in a crossover from dispersive to flat bands
journal, September 2019
- Kumar, Pramod; Vanhala, Tuomas I.; Törmä, Päivi
- Physical Review B, Vol. 100, Issue 12
Enhanced correlations and superconductivity in weakly interacting partially flat-band systems: A determinantal quantum Monte Carlo study
journal, June 2019
- Huang, Edwin W.; Vaezi, Mohammad-Sadegh; Nussinov, Zohar
- Physical Review B, Vol. 99, Issue 23
Emergence of asymmetric fermionic order in interacting birefringent fermions
journal, June 2019
- Wang, Yi-Xiang; Li, Fuxiang
- Physical Review B, Vol. 99, Issue 24
Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice
text, January 2015
- Taie, Shintaro; Ozawa, Hideki; Ichinose, Tomohiro
- arXiv
Unconventional superconductivity in nearly flat bands in twisted bilayer graphene
text, January 2018
- Roy, Bitan; Juricic, Vladimir
- arXiv
Pairing and superconductivity in the flat band: Creutz lattice
text, January 2018
- Mondaini, Rubem; Batrouni, G. George; Grémaud, Benoît
- arXiv
Enhanced correlations and superconductivity in weakly interacting partially flat band systems: a determinantal quantum Monte Carlo study
text, January 2018
- Huang, Edwin W.; Vaezi, Mohammad-Sadegh; Nussinov, Zohar
- arXiv
Magnetization, d-wave superconductivity and non-Fermi liquid behavior in a crossover from dispersive to flat bands
text, January 2019
- Kumar, Pramod; Vanhala, Tuomas I.; Törmä, Päivi
- arXiv