Superconducting transitions in flat-band systems

Iglovikov, V. I.; Hébert, F.; Grémaud, B.; Batrouni, G. G.; Scalettar, R. T.

doi:10.1103/PhysRevB.90.094506

Superconducting transitions in flat-band systems

Journal Article · Thu Sep 11 00:00:00 EDT 2014 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PhysRevB.90.094506· OSTI ID:1344110

Iglovikov, V. I. ^[1]; Hébert, F. ^[2]; Grémaud, B. ^[3]; Batrouni, G. G. ^[4]; Scalettar, R. T. ^[5]

Univ. of California, Davis, CA (United States). Physics Dept.; The Regents of the University of California, Davis
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)
Univ. of California, Davis, CA (United States). Physics Dept.

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, Davis, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0001842

OSTI ID:: 1344110

Alternate ID(s):: OSTI ID: 1180268

Journal Information:: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 9 Vol. 90; ISSN 1098-0121; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Flat Bands and Wigner Crystallization in the Honeycomb Optical Lattice Wu, Congjun; Bergman, Doron; Balents, Leon Physical Review Letters, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevLett.99.070401	journal	August 2007
Flat bands, Dirac cones, and atom dynamics in an optical lattice Apaja, V.; Hyrkäs, M.; Manninen, M. Physical Review A, Vol. 82, Issue 4 https://doi.org/10.1103/physreva.82.041402	journal	October 2010
Proposed realization of itinerant ferromagnetism in optical lattices Zhang, Shizhong; Hung, Hsiang-hsuan; Wu, Congjun Physical Review A, Vol. 82, Issue 5 https://doi.org/10.1103/physreva.82.053618	journal	November 2010
Topological phases for fermionic cold atoms on the Lieb lattice Goldman, N.; Urban, D. F.; Bercioux, D. Physical Review A, Vol. 83, Issue 6 https://doi.org/10.1103/physreva.83.063601	journal	June 2011
Pseudospin and nonlinear conical diffraction in Lieb lattices Leykam, Daniel; Bahat-Treidel, Omri; Desyatnikov, Anton S. Physical Review A, Vol. 86, Issue 3 https://doi.org/10.1103/physreva.86.031805	journal	September 2012
Localization of electronic wave functions due to local topology Sutherland, Bill Physical Review B, Vol. 34, Issue 8 https://doi.org/10.1103/physrevb.34.5208	journal	October 1986
Fermi-surface instabilities and superconducting d -wave pairing Scalapino, D. J.; Loh, E.; Hirsch, J. E. Physical Review B, Vol. 35, Issue 13 https://doi.org/10.1103/physrevb.35.6694	journal	May 1987
Ground-state staggered magnetization of two-dimensional quantum Heisenberg antiferromagnets Huse, David A. Physical Review B, Vol. 37, Issue 4 https://doi.org/10.1103/physrevb.37.2380	journal	February 1988
Mean-field theories of the two-band model and the magnetism in high- T c oxides Olés, Andrzej M.; Zaanen, Jan Physical Review B, Vol. 39, Issue 13 https://doi.org/10.1103/physrevb.39.9175	journal	May 1989
Numerical study of the two-dimensional Hubbard model White, S. R.; Scalapino, D. J.; Sugar, R. L. Physical Review B, Vol. 40, Issue 1 https://doi.org/10.1103/physrevb.40.506	journal	July 1989
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Antiferromagnetic, charge-transfer, and pairing correlations in the three-band Hubbard model Scalettar, R. T.; Scalapino, D. J.; Sugar, R. L. Physical Review B, Vol. 44, Issue 2 https://doi.org/10.1103/physrevb.44.770	journal	July 1991
Theory of the pseudogap state of the cuprates Varma, C. M. Physical Review B, Vol. 73, Issue 15 https://doi.org/10.1103/physrevb.73.155113	journal	April 2006
p x , y -orbital counterpart of graphene: Cold atoms in the honeycomb optical lattice Wu, Congjun; Das Sarma, S. Physical Review B, Vol. 77, Issue 23 https://doi.org/10.1103/physrevb.77.235107	journal	June 2008
Single Dirac cone with a flat band touching on line-centered-square optical lattices Shen, R.; Shao, L. B.; Wang, Baigeng Physical Review B, Vol. 81, Issue 4 https://doi.org/10.1103/physrevb.81.041410	journal	January 2010
Topological insulators on the Lieb and perovskite lattices Weeks, C.; Franz, M. Physical Review B, Vol. 82, Issue 8 https://doi.org/10.1103/physrevb.82.085310	journal	August 2010
Bose condensation in flat bands Huber, Sebastian D.; Altman, Ehud Physical Review B, Vol. 82, Issue 18 https://doi.org/10.1103/physrevb.82.184502	journal	November 2010
Mott transition and ferrimagnetism in the Hubbard model on the anisotropic kagome lattice Yamada, A.; Seki, K.; Eder, R. Physical Review B, Vol. 83, Issue 19 https://doi.org/10.1103/physrevb.83.195127	journal	May 2011
High-temperature surface superconductivity in topological flat-band systems Kopnin, N. B.; Heikkilä, T. T.; Volovik, G. E. Physical Review B, Vol. 83, Issue 22 https://doi.org/10.1103/physrevb.83.220503	journal	June 2011
Mean-field analysis of intra-unit-cell order in the Emery model of the CuO 2 plane Fischer, Mark H.; Kim, Eun-Ah Physical Review B, Vol. 84, Issue 14 https://doi.org/10.1103/physrevb.84.144502	journal	October 2011
Topological flat band models with arbitrary Chern numbers Yang, Shuo; Gu, Zheng-Cheng; Sun, Kai Physical Review B, Vol. 86, Issue 24 https://doi.org/10.1103/physrevb.86.241112	journal	December 2012
Spectral and transport properties of the two-dimensional Lieb lattice Niţă, M.; Ostahie, B.; Aldea, A. Physical Review B, Vol. 87, Issue 12 https://doi.org/10.1103/physrevb.87.125428	journal	March 2013
High-temperature surface superconductivity in rhombohedral graphite Kopnin, N. B.; Ijäs, M.; Harju, A. Physical Review B, Vol. 87, Issue 14 https://doi.org/10.1103/physrevb.87.140503	journal	April 2013
From antiferromagnetic ordering to magnetic textures in the two-dimensional Fermi-Hubbard model with synthetic spin-orbit interactions Minář, Jiří; Grémaud, Benoît Physical Review B, Vol. 88, Issue 23 https://doi.org/10.1103/physrevb.88.235130	journal	December 2013
Monte Carlo calculations of coupled boson-fermion systems. I Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L. Physical Review D, Vol. 24, Issue 8 https://doi.org/10.1103/physrevd.24.2278	journal	October 1981
Structural Prediction and Phase Transformation Mechanisms in Calcium at High Pressure Yao, Yansun; Klug, Dennis D.; Sun, Jian Physical Review Letters, Vol. 103, Issue 5 https://doi.org/10.1103/physrevlett.103.055503	journal	July 2009
Nearly Flatbands with Nontrivial Topology Sun, Kai; Gu, Zhengcheng; Katsura, Hosho Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/physrevlett.106.236803	journal	June 2011
Band gaps and electronic structure of transition-metal compounds Zaanen, J.; Sawatzky, G. A.; Allen, J. W. Physical Review Letters, Vol. 55, Issue 4 https://doi.org/10.1103/physrevlett.55.418	journal	July 1985
Enhanced Superconductivity in Quasi Two-Dimensional Systems Hirsch, J. E.; Scalapino, D. J. Physical Review Letters, Vol. 56, Issue 25 https://doi.org/10.1103/physrevlett.56.2732	journal	June 1986
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Topological Insulators on the Lieb and Perovskite Lattices Weeks, C.; Franz, M. arXiv https://doi.org/10.48550/arxiv.1004.5172	text	January 2010
Flat bands, Dirac cones and atom dynamics in an optical lattice Apaja, V.; Hyrkäs, M.; Manninen, M. arXiv https://doi.org/10.48550/arxiv.1008.4684	text	January 2010
Nearly-flat bands with nontrivial topology Sun, Kai; Gu, Zheng-Cheng; Katsura, Hosho arXiv https://doi.org/10.48550/arxiv.1012.5864	text	January 2010
Topological Phases for Fermionic Cold Atoms on the Lieb Lattice Goldman, N.; Urban, D. F.; Bercioux, D. arXiv https://doi.org/10.48550/arxiv.1101.4500	text	January 2011
Mean-Field Analysis of Intra-Unit-Cell Order in the Emery Model of the CuO$_2$ Plane Fischer, Mark Hannes; Kim, Eun-Ah arXiv https://doi.org/10.48550/arxiv.1106.6060	text	January 2011
Topological flat band models with arbitrary Chern numbers Yang, Shuo; Gu, Zheng-Cheng; Sun, Kai arXiv https://doi.org/10.48550/arxiv.1205.5792	text	January 2012
Spectral and transport properties of the two-dimensional Lieb lattice Niţă, M.; Ostahie, B.; Aldea, A. arXiv https://doi.org/10.48550/arxiv.1301.1807	text	January 2013

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