Nonequilibrium dynamics of superconductivity in the attractive Hubbard model

Chern, Gia-Wei; Barros, Kipton Marcos

doi:10.1103/PhysRevB.99.035162

Title: Nonequilibrium dynamics of superconductivity in the attractive Hubbard model

Journal Article · Tue Jan 15 00:00:00 EST 2019 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.99.035162· OSTI ID:1572325

Chern, Gia-Wei ^[1];

^[2]

Univ. of Virginia, Charlottesville, VA (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We present a framework of semiclassical superconductivity (SC) dynamics that properly includes effects of spatial fluctuations for the attractive Hubbard model. We consider both coherent and adiabatic limits. To model the coherent SC dynamics, we develop a real-space von Neumann equation based on the time-dependent Hartree-Fock-Bogoliubov theory. Applying our method to interaction quenches in the negative-U Hubbard model, we show that the relaxation of SC order at weak coupling is dominated by Landau-damping. At strong coupling, we find a two-stage relaxation of the pairing field: a collapse of the synchronized oscillation of Cooper pairs due to spatial inhomogeneity, followed by a slow relaxation to a quasistationary state. SC dynamics in the adiabatic limit is described by a quantum Landau-Lifshitz equation with Ginzburg-Landau relaxation. Numerical simulations of the pump-probe process show that long-time recovery of the pairing field is dominated by defect dynamics. Here, our results demonstrate the important role of spatial fluctuations in both limits.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1572325

Alternate ID(s):: OSTI ID: 1492910

Report Number(s):: LA-UR-18-31201; PRBMDO; TRN: US2100059

Journal Information:: Physical Review B, Vol. 99, Issue 3; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 3 works

Citation information provided by
Web of Science

References (59)

The theory of ferromagnetic resonance at high signal powers Suhl, H. Journal of Physics and Chemistry of Solids, Vol. 1, Issue 4 https://doi.org/10.1016/0022-3697(57)90010-0	journal	January 1957
The kernel polynomial method Weiße, Alexander; Wellein, Gerhard; Alvermann, Andreas Reviews of Modern Physics, Vol. 78, Issue 1 https://doi.org/10.1103/RevModPhys.78.275	journal	March 2006
Imaging the nanoscale phase separation in vanadium dioxide thin films at terahertz frequencies Stinson, H. T.; Sternbach, A.; Najera, O. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-05998-5	journal	September 2018
Twisting Anderson pseudospins with light: Quench dynamics in terahertz-pumped BCS superconductors Chou, Yang-Zhi; Liao, Yunxiang; Foster, Matthew S. Physical Review B, Vol. 95, Issue 10 https://doi.org/10.1103/PhysRevB.95.104507	journal	March 2017
Densities of States of Mega-Dimensional Hamiltonian Matrices Silver, R. N.; RÖDer, H. International Journal of Modern Physics C, Vol. 05, Issue 04 https://doi.org/10.1142/S0129183194000842	journal	August 1994
Theory of phase-ordering kinetics Bray, A. J. Advances in Physics, Vol. 43, Issue 3 https://doi.org/10.1080/00018739400101505	journal	June 1994
Relaxation and Prethermalization in an Isolated Quantum System Gring, M.; Kuhnert, M.; Langen, T. Science, Vol. 337, Issue 6100 https://doi.org/10.1126/science.1224953	journal	September 2012
Nonequilibrium Dynamics and Thermodynamics of a Degenerate Fermi Gas Across a Feshbach Resonance Andreev, A. V.; Gurarie, V.; Radzihovsky, L. Physical Review Letters, Vol. 93, Issue 13 https://doi.org/10.1103/PhysRevLett.93.130402	journal	September 2004
Cosmological experiments in condensed matter systems Zurek, W. H. Physics Reports, Vol. 276, Issue 4 https://doi.org/10.1016/S0370-1573(96)00009-9	journal	November 1996
Two-dimensional negative- U Hubbard model Moreo, A.; Scalapino, D. J. Physical Review Letters, Vol. 66, Issue 7 https://doi.org/10.1103/PhysRevLett.66.946	journal	February 1991
Anomalous density for Bose gases at finite temperature Boudjemâa, A.; Benarous, M. Physical Review A, Vol. 84, Issue 4 https://doi.org/10.1103/PhysRevA.84.043633	journal	October 2011
A real space auxiliary field approach to the BCS-BEC crossover Tarat, Sabyasachi; Majumdar, Pinaki The European Physical Journal B, Vol. 88, Issue 3 https://doi.org/10.1140/epjb/e2015-50284-6	journal	March 2015
Dynamical Vanishing of the Order Parameter in a Fermionic Condensate Yuzbashyan, Emil A.; Dzero, Maxim Physical Review Letters, Vol. 96, Issue 23 https://doi.org/10.1103/PhysRevLett.96.230404	journal	June 2006
Synchronization in the BCS Pairing Dynamics as a Critical Phenomenon Barankov, R. A.; Levitov, L. S. Physical Review Letters, Vol. 96, Issue 23 https://doi.org/10.1103/PhysRevLett.96.230403	journal	June 2006
Charge and pairing dynamics in the attractive Hubbard model: Mode coupling and the validity of linear-response theory Bünemann, Jörg; Seibold, Götz Physical Review B, Vol. 96, Issue 24 https://doi.org/10.1103/PhysRevB.96.245139	journal	December 2017
Stability of Superflow for Ultracold Fermions in Optical Lattices Burkov, A. A.; Paramekanti, Arun Physical Review Letters, Vol. 100, Issue 25 https://doi.org/10.1103/PhysRevLett.100.255301	journal	June 2008
Pairing Dynamics of Polar States in a Quenched $p$ -Wave Superfluid Fermi Gas Yoon, Sukjin; Watanabe, Gentaro Physical Review Letters, Vol. 119, Issue 10 https://doi.org/10.1103/PhysRevLett.119.100401	journal	September 2017
Pair annihilation of pointlike topological defects in the ordering process of quenched systems Toyoki, Hiroyasu Physical Review A, Vol. 42, Issue 2 https://doi.org/10.1103/PhysRevA.42.911	journal	July 1990
Theory of Nonequilibrium Superconductivity Kopnin, Nikolai Oxford University Press https://doi.org/10.1093/acprof:oso/9780198507888.001.0001	book	May 2001
Time-Dependent Ginzburg–Landau Analysis of Inhomogeneous Normal-Superfluid Transitions Kopnin, N. B.; Thuneberg, E. V. Physical Review Letters, Vol. 83, Issue 1 https://doi.org/10.1103/PhysRevLett.83.116	journal	July 1999
Phase Fluctuations in Strongly Coupled $d$ -Wave Superconductors Mayr, Matthias; Alvarez, Gonzalo; Şen, Cengiz Physical Review Letters, Vol. 94, Issue 21 https://doi.org/10.1103/PhysRevLett.94.217001	journal	June 2005
Collective Rabi Oscillations and Solitons in a Time-Dependent BCS Pairing Problem Barankov, R. A.; Levitov, L. S.; Spivak, B. Z. Physical Review Letters, Vol. 93, Issue 16 https://doi.org/10.1103/PhysRevLett.93.160401	journal	October 2004
All-optical nonequilibrium pathway to stabilising magnetic Weyl semimetals in pyrochlore iridates Topp, Gabriel E.; Tancogne-Dejean, Nicolas; Kemper, Alexander F. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-06991-8	journal	October 2018
Time-Dependent Ginzburg-Landau Theory of Nonequilibrium Relaxation Binder, K. Physical Review B, Vol. 8, Issue 7 https://doi.org/10.1103/PhysRevB.8.3423	journal	October 1973
First-principles calculation of electronic transport in low-dimensional disordered superconductors Conduit, G. J.; Meir, Y. Physical Review B, Vol. 84, Issue 6 https://doi.org/10.1103/PhysRevB.84.064513	journal	August 2011
Nonthermal Antiferromagnetic Order and Nonequilibrium Criticality in the Hubbard Model Tsuji, Naoto; Eckstein, Martin; Werner, Philipp Physical Review Letters, Vol. 110, Issue 13 https://doi.org/10.1103/PhysRevLett.110.136404	journal	March 2013
Light-induced collective pseudospin precession resonating with Higgs mode in a superconductor Matsunaga, R.; Tsuji, N.; Fujita, H. Science, Vol. 345, Issue 6201 https://doi.org/10.1126/science.1254697	journal	July 2014
Higgs Amplitude Mode in the BCS Superconductors ${Nb}_{1 − x} {Ti}_{x} N$ Induced by Terahertz Pulse Excitation Matsunaga, Ryusuke; Hamada, Yuki I.; Makise, Kazumasa Physical Review Letters, Vol. 111, Issue 5 https://doi.org/10.1103/PhysRevLett.111.057002	journal	July 2013
Cooper pair turbulence in atomic Fermi gases Dzero, M.; Yuzbashyan, E. A.; Altshuler, B. L. EPL (Europhysics Letters), Vol. 85, Issue 2 https://doi.org/10.1209/0295-5075/85/20004	journal	January 2009
Phase diagram of the two-dimensional negative- U Hubbard model Scalettar, R. T.; Loh, E. Y.; Gubernatis, J. E. Physical Review Letters, Vol. 62, Issue 12 https://doi.org/10.1103/PhysRevLett.62.1407	journal	March 1989
Superconductivity in narrow-band systems with local nonretarded attractive interactions Micnas, R.; Ranninger, J.; Robaszkiewicz, S. Reviews of Modern Physics, Vol. 62, Issue 1 https://doi.org/10.1103/RevModPhys.62.113	journal	January 1990
Real-time measurement of the emergence of superconducting order in a high-temperature superconductor Madan, I.; Kusar, P.; Baranov, V. V. Physical Review B, Vol. 93, Issue 22 https://doi.org/10.1103/PhysRevB.93.224520	journal	June 2016
Ultrafast Modification of Hubbard $U$ in a Strongly Correlated Material: Ab initio High-Harmonic Generation in NiO Tancogne-Dejean, Nicolas; Sentef, Michael A.; Rubio, Angel Physical Review Letters, Vol. 121, Issue 9 https://doi.org/10.1103/PhysRevLett.121.097402	journal	August 2018
Reexamination of Quenches in $^{4} He$ (and $^{3} He$ ) Karra, G.; Rivers, R. J. Physical Review Letters, Vol. 81, Issue 17 https://doi.org/10.1103/PhysRevLett.81.3707	journal	October 1998
Time-Dependent Density Functional Theory and the Real-Time Dynamics of Fermi Superfluids Bulgac, Aurel Annual Review of Nuclear and Particle Science, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-nucl-102212-170631	journal	October 2013
Theory of dynamic critical phenomena Hohenberg, P. C.; Halperin, B. I. Reviews of Modern Physics, Vol. 49, Issue 3 https://doi.org/10.1103/RevModPhys.49.435	journal	July 1977
Fermions in 2D Optical Lattices: Temperature and Entropy Scales for Observing Antiferromagnetism and Superfluidity Paiva, Thereza; Scalettar, Richard; Randeria, Mohit Physical Review Letters, Vol. 104, Issue 6 https://doi.org/10.1103/PhysRevLett.104.066406	journal	February 2010
Quantum Quench in One Dimension: Coherent Inhomogeneity Amplification and “Supersolitons” Foster, Matthew S.; Yuzbashyan, Emil A.; Altshuler, Boris L. Physical Review Letters, Vol. 105, Issue 13 https://doi.org/10.1103/PhysRevLett.105.135701	journal	September 2010
Random-Phase Approximation in the Theory of Superconductivity Anderson, P. W. Physical Review, Vol. 112, Issue 6 https://doi.org/10.1103/PhysRev.112.1900	journal	December 1958
Coupling of Higgs and Leggett modes in non-equilibrium superconductors Krull, H.; Bittner, N.; Uhrig, G. S. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms11921	journal	June 2016
Dynamics of the BCS-BEC Crossover in a Degenerate Fermi Gas Szymańska, M. H.; Simons, B. D.; Burnett, K. Physical Review Letters, Vol. 94, Issue 17 https://doi.org/10.1103/PhysRevLett.94.170402	journal	May 2005
Efficient Langevin simulation of coupled classical fields and fermions Barros, Kipton; Kato, Yasuyuki Physical Review B, Vol. 88, Issue 23 https://doi.org/10.1103/PhysRevB.88.235101	journal	December 2013
Transient Dynamics of $d$ -Wave Superconductors after a Sudden Excitation Peronaci, Francesco; Schiró, Marco; Capone, Massimo Physical Review Letters, Vol. 115, Issue 25 https://doi.org/10.1103/PhysRevLett.115.257001	journal	December 2015
From sudden quench to adiabatic dynamics in the attractive Hubbard model Mazza, Giacomo Physical Review B, Vol. 96, Issue 20 https://doi.org/10.1103/PhysRevB.96.205110	journal	November 2017
Theory of Laser-Controlled Competing Superconducting and Charge Orders Sentef, M. A.; Tokuno, A.; Georges, A. Physical Review Letters, Vol. 118, Issue 8 https://doi.org/10.1103/PhysRevLett.118.087002	journal	February 2017
Electromagnetic response during quench dynamics to the superconducting state: Time-dependent Ginzburg-Landau analysis Kennes, D. M.; Millis, A. J. Physical Review B, Vol. 96, Issue 6 https://doi.org/10.1103/PhysRevB.96.064507	journal	August 2017
Nanoscale electrodynamics of strongly correlated quantum materials Liu, Mengkun; Sternbach, Aaron J.; Basov, D. N. Reports on Progress in Physics, Vol. 80, Issue 1 https://doi.org/10.1088/0034-4885/80/1/014501	journal	November 2016
Topology of cosmic domains and strings Kibble, T. W. B. Journal of Physics A: Mathematical and General, Vol. 9, Issue 8 https://doi.org/10.1088/0305-4470/9/8/029	journal	August 1976
Relaxation and Persistent Oscillations of the Order Parameter in Fermionic Condensates Yuzbashyan, Emil A.; Tsyplyatyev, Oleksandr; Altshuler, Boris L. Physical Review Letters, Vol. 96, Issue 9 https://doi.org/10.1103/PhysRevLett.96.097005	journal	March 2006
Breakdown of Scaling in the Nonequilibrium Critical Dynamics of the Two-Dimensional $XY$ Model Bray, A. J.; Briant, A. J.; Jervis, D. K. Physical Review Letters, Vol. 84, Issue 7 https://doi.org/10.1103/PhysRevLett.84.1503	journal	February 2000
Radio-frequency spectroscopy of the attractive Hubbard model in a trap Datta, Sanjoy; Singh, Viveka Nand; Majumdar, Pinaki Physical Review A, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevA.89.053609	journal	May 2014
Solution of the problem of catastrophic relaxation of homogeneous spin precession in superfluid 3He-B Bunkov, Yu. M.; L’vov, V. S.; Volovik, G. E. JETP Letters, Vol. 83, Issue 12 https://doi.org/10.1134/S0021364006120022	journal	August 2006
Towards quantum turbulence in cold atomic fermionic superfluids Bulgac, Aurel; Forbes, Michael McNeil; Wlazłowski, Gabriel Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 50, Issue 1 https://doi.org/10.1088/1361-6455/50/1/014001	journal	December 2016
Spin-wave turbulence beyond the parametric excitation threshold Zakharov, V. E.; L'vov, V. S.; Starobinets, S. S. Soviet Physics Uspekhi, Vol. 17, Issue 6 https://doi.org/10.1070/PU1975v017n06ABEH004404	journal	June 1975
The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition Endres, Manuel; Fukuhara, Takeshi; Pekker, David Nature, Vol. 487, Issue 7408 https://doi.org/10.1038/nature11255	journal	July 2012
Inhomogeneity of the ultrafast insulator-to-metal transition dynamics of VO2 O’Callahan, Brian T.; Jones, Andrew C.; Hyung Park, Jae Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms7849	journal	April 2015
Coarsening dynamics of the XY model Yurke, B.; Pargellis, A. N.; Kovacs, T. Physical Review E, Vol. 47, Issue 3 https://doi.org/10.1103/PhysRevE.47.1525	journal	March 1993
Quench-Induced Floquet Topological $p$ -Wave Superfluids Foster, Matthew S.; Gurarie, Victor; Dzero, Maxim Physical Review Letters, Vol. 113, Issue 7 https://doi.org/10.1103/PhysRevLett.113.076403	journal	August 2014
Gradient-based stochastic estimation of the density matrix Wang, Zhentao; Chern, Gia-Wei; Batista, Cristian D. The Journal of Chemical Physics, Vol. 148, Issue 9 https://doi.org/10.1063/1.5017741	journal	March 2018

Similar Records

Ginzburg–Landau expansion in strongly disordered attractive Anderson–Hubbard model

Journal Article · Sat Jul 15 00:00:00 EDT 2017 · Journal of Experimental and Theoretical Physics · OSTI ID:1572325

Kuleeva, N. A.

Attractive Hubbard model: Homogeneous Ginzburg–Landau expansion and disorder

Journal Article · Mon Feb 15 00:00:00 EST 2016 · Journal of Experimental and Theoretical Physics · OSTI ID:1572325

Kuleeva, N. A.

Magnetic excitations, nonclassicality, and quantum wake spin dynamics in the Hubbard chain

Journal Article · Fri Aug 05 00:00:00 EDT 2022 · Physical Review. B · OSTI ID:1572325

Laurell, Pontus; Scheie, Allen; Tennant, D. Alan; +3 more

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Material Science

Title: Nonequilibrium dynamics of superconductivity in the attractive Hubbard model

Citation Formats

References (59)

Similar Records

Related Subjects