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Title: Dynamic properties of superconductors: Anderson-Bogoliubov mode and Berry phase in the BCS and BEC regimes

Abstract

We analyze the evolution of the dynamics of a neutral s-wave superconductor between BCS and BEC regimes. We consider 2d case, when BCS-BEC crossover occurs already at weak coupling as a function of the ratio of the two scales – the Fermi energy E F and the bound state energy for two fermions in a vacuum, E 0. BCS and BEC limits correspond to E F » E 0 and E F « E 0, respectively. The chemical potential μ = E F - E 0 changes the sign between the two regimes. We use the effective action approach, derive the leading terms in the expansion of the effective action in the spatial and time derivative of the slowly varying superconducting order parameter Δ(r, τ), and express the action in terms of derivative of the phase Φ(r, τ) of Δ(r, τ) = Δe iΦ(r,τ). The action contains (∇Φ) 2 and $$\dot{Φ}$$ 2 terms, which determine the dispersion of collective phase fluctuations, and iπA$$\dot{Φ}$$ term. For continuous Φ(r, τ), the latter reduces to the contribution from the boundary and does not affect the dynamics. We show that this longwavelength action does not change through BCS-BEC crossover. We apply our approach to a moving vortex, for which Φ is singular at the center of the vortex core, and iπA vort$$\dot{Φ}$$ term affects vortex dynamics. We find that this term has two contributions. One comes from the states away from the vortex core and has Avort,1 = n/2, where n is the fermion density. The other comes from electronic states inside the vortex core and has A vort,2 = -n 0/2, where n 0 is the fermion density at the vortex core. This last term comes from the continuous part of the electronic spectrum and has no contribution from discrete levels inside the core; it also does not change if we add impurities. We interpret this term as the contribution to vortex dynamics in the continuum limit, when the spacing between energy levels ω is set to zero, while fermionic lifetime τ can be arbitrary. The total Avort = (n-n 0)/2 determines the transversal force acting on the vortex core, πA vort$$\dot{R}$$ × $$\hat{z}$$, where $$\dot{R}$$ is the velocity of the vortex core and $$\hat{z}$$ a unit vector perpendicular to the 2d sample. The difference (n - n 0)/2 changes through the BEC-BCS crossover as n 0 nearly compensates n in the BCS regime, but vanishes in the BEC regime.

Authors:
ORCiD logo [1];  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of Minnesota, Minneapolis, MN (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1558221
Alternate Identifier(s):
OSTI ID: 1513326
Report Number(s):
LA-UR-19-21884
Journal ID: ISSN 2469-9950; PRBMDO
Grant/Contract Number:  
89233218CNA000001; 89233218NCA000001; SC0014402
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 17; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Mozyrsky, Dima V., and Chubukov, Andrey. Dynamic properties of superconductors: Anderson-Bogoliubov mode and Berry phase in the BCS and BEC regimes. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.99.174510.
Mozyrsky, Dima V., & Chubukov, Andrey. Dynamic properties of superconductors: Anderson-Bogoliubov mode and Berry phase in the BCS and BEC regimes. United States. doi:10.1103/PhysRevB.99.174510.
Mozyrsky, Dima V., and Chubukov, Andrey. Fri . "Dynamic properties of superconductors: Anderson-Bogoliubov mode and Berry phase in the BCS and BEC regimes". United States. doi:10.1103/PhysRevB.99.174510.
@article{osti_1558221,
title = {Dynamic properties of superconductors: Anderson-Bogoliubov mode and Berry phase in the BCS and BEC regimes},
author = {Mozyrsky, Dima V. and Chubukov, Andrey},
abstractNote = {We analyze the evolution of the dynamics of a neutral s-wave superconductor between BCS and BEC regimes. We consider 2d case, when BCS-BEC crossover occurs already at weak coupling as a function of the ratio of the two scales – the Fermi energy EF and the bound state energy for two fermions in a vacuum, E0. BCS and BEC limits correspond to EF » E0 and EF « E0, respectively. The chemical potential μ = EF - E0 changes the sign between the two regimes. We use the effective action approach, derive the leading terms in the expansion of the effective action in the spatial and time derivative of the slowly varying superconducting order parameter Δ(r, τ), and express the action in terms of derivative of the phase Φ(r, τ) of Δ(r, τ) = ΔeiΦ(r,τ). The action contains (∇Φ)2 and $\dot{Φ}$2 terms, which determine the dispersion of collective phase fluctuations, and iπA$\dot{Φ}$ term. For continuous Φ(r, τ), the latter reduces to the contribution from the boundary and does not affect the dynamics. We show that this longwavelength action does not change through BCS-BEC crossover. We apply our approach to a moving vortex, for which Φ is singular at the center of the vortex core, and iπAvort$\dot{Φ}$ term affects vortex dynamics. We find that this term has two contributions. One comes from the states away from the vortex core and has Avort,1 = n/2, where n is the fermion density. The other comes from electronic states inside the vortex core and has Avort,2 = -n0/2, where n0 is the fermion density at the vortex core. This last term comes from the continuous part of the electronic spectrum and has no contribution from discrete levels inside the core; it also does not change if we add impurities. We interpret this term as the contribution to vortex dynamics in the continuum limit, when the spacing between energy levels ω is set to zero, while fermionic lifetime τ can be arbitrary. The total Avort = (n-n0)/2 determines the transversal force acting on the vortex core, πAvort$\dot{R}$ × $\hat{z}$, where $\dot{R}$ is the velocity of the vortex core and $\hat{z}$ a unit vector perpendicular to the 2d sample. The difference (n - n0)/2 changes through the BEC-BCS crossover as n0 nearly compensates n in the BCS regime, but vanishes in the BEC regime.},
doi = {10.1103/PhysRevB.99.174510},
journal = {Physical Review B},
number = 17,
volume = 99,
place = {United States},
year = {2019},
month = {5}
}

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Works referenced in this record:

Twisting in superfluid A 3 and consequences for hydrodynamics at T=0
journal, January 1986


BCS–BEC crossover: From high temperature superconductors to ultracold superfluids
journal, June 2005


The motion of flux lines in type II superconductors
journal, September 1966

  • Nozières, P.; Vinen, W. F.
  • The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, Vol. 14, Issue 130
  • DOI: 10.1080/14786436608211964

BCS to Bose crossover: Broken-symmetry state
journal, June 1997

  • Engelbrecht, Jan R.; Randeria, Mohit; Sáde Melo, C. A. R.
  • Physical Review B, Vol. 55, Issue 22
  • DOI: 10.1103/PhysRevB.55.15153

Reentrant BCS-BEC Crossover and a Superfluid-Insulator Transition in Optical Lattices
journal, December 2012


Effective action approach to the Leggett's mode in two-band superconductors
journal, November 2002


Phase fluctuations, dissipation, and superfluid stiffness in d -wave superconductors
journal, April 2001


Superconductor-Insulator Transition and Fermi-Bose Crossovers
journal, May 2016


Low-energy phase-only action in a superconductor: A comparison with the XY model
journal, May 2004


Crossover from BCS-superconductivity to Bose-condensation
journal, January 1992


Two-band superfluidity from the BCS to the BEC limit
journal, October 2006


Shape Resonances in superconducting gaps in a 2DEG at oxide- oxide interface
journal, August 2014


Bose condensation in an attractive fermion gas: From weak to strong coupling superconductivity
journal, May 1985

  • Nozi�res, P.; Schmitt-Rink, S.
  • Journal of Low Temperature Physics, Vol. 59, Issue 3-4
  • DOI: 10.1007/BF00683774

Topological charge and chiral anomalies in fermi superfluids
journal, August 1987


Bound states, Cooper pairing, and Bose condensation in two dimensions
journal, February 1989


Resonant and crossover phenomena in a multiband superconductor: Tuning the chemical potential near a band edge
journal, November 2010


Phase fluctuations in superconductors: From Galilean invariant to quantum XY models
journal, September 2001


Ultra-cold polarized Fermi gases
journal, October 2010


Superconductivity in an electron band just above the Fermi level: possible route to BCS-BEC superconductivity
journal, February 2014

  • Okazaki, K.; Ito, Y.; Ota, Y.
  • Scientific Reports, Vol. 4, Issue 1
  • DOI: 10.1038/srep04109

Bound Fermion states on a vortex line in a type II superconductor
journal, May 1964


Insulator, metal, or superconductor: The criteria
journal, April 1993

  • Scalapino, Douglas J.; White, Steven R.; Zhang, Shoucheng
  • Physical Review B, Vol. 47, Issue 13
  • DOI: 10.1103/PhysRevB.47.7995

Microscopic theory of vortex dynamics in homogeneous superconductors
journal, September 1999


Vortex Dynamics and the Hall Anomaly: A Microscopic Analysis
journal, November 1995

  • van Otterlo, Anne; Feigel'man, Mikhail; Geshkenbein, Vadim
  • Physical Review Letters, Vol. 75, Issue 20
  • DOI: 10.1103/PhysRevLett.75.3736

Evolution of the dynamics of neutral superconductors between BCS and BEC regimes: The variational approach
journal, June 2018

  • Chubukov, Andrey V.; Mozyrsky, Dmitry
  • Low Temperature Physics, Vol. 44, Issue 6
  • DOI: 10.1063/1.5037555

Quantum Phase Slips and Transport in Ultrathin Superconducting Wires
journal, February 1997


Theory of fluctuation conductivity from interband pairing in pnictide superconductors
journal, May 2009


Phase Fluctuations and BCS-LP Crossover in 2D Short Coherence Length Superconductors
journal, March 2000


Band-edge BCS–BEC crossover in a two-band superconductor: physical properties and detection parameters
journal, October 2014


Superconductivity in a two-dimensional Fermi gas: Evolution from Cooper pairing to Bose condensation
journal, January 1990


Field-induced superconducting phase of FeSe in the BCS-BEC cross-over
journal, November 2014

  • Kasahara, Shigeru; Watashige, Tatsuya; Hanaguri, Tetsuo
  • Proceedings of the National Academy of Sciences, Vol. 111, Issue 46
  • DOI: 10.1073/pnas.1413477111

Spectral Flow in Vortex Dynamics of 3 He-B and Superconductors
journal, December 1995


Spectral flow, Magnus force, and mutual friction via the geometric optics limit of Andreev reflection
journal, November 1996


Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases
journal, August 2015


Theory of ultracold atomic Fermi gases
journal, October 2008

  • Giorgini, Stefano; Pitaevskii, Lev P.; Stringari, Sandro
  • Reviews of Modern Physics, Vol. 80, Issue 4
  • DOI: 10.1103/RevModPhys.80.1215

Observation of pseudogap behaviour in a strongly interacting Fermi gas
journal, July 2010

  • Gaebler, J. P.; Stewart, J. T.; Drake, T. E.
  • Nature Physics, Vol. 6, Issue 8
  • DOI: 10.1038/nphys1709

Structure of Vortex Lines in Pure Superconductors
journal, November 1969


Superfluid current in He 3 - A at T = 0
journal, November 1983


Mutual friction in superfluid He 3 : Effects of bound states in the vortex core
journal, November 1991


Dynamics and effective actions of BCS superconductors
journal, July 1999

  • van Otterlo, A.; Golubev, D. S.; Zaikin, A. D.
  • The European Physical Journal B, Vol. 10, Issue 1
  • DOI: 10.1007/s100510050836

Calculation of Partition Functions
journal, July 1959


Crossover from BCS to Bose superconductivity: Transition temperature and time-dependent Ginzburg-Landau theory
journal, November 1993

  • Sá de Melo, C. A. R.; Randeria, Mohit; Engelbrecht, Jan R.
  • Physical Review Letters, Vol. 71, Issue 19
  • DOI: 10.1103/PhysRevLett.71.3202

Tuning across the BCS-BEC crossover in the multiband superconductor Fe 1+ y Se x Te 1− x : An angle-resolved photoemission study
journal, April 2017


Quasiparticle Scattering by Quantum Phase Slips in One-Dimensional Superfluids
journal, August 2004


From effective BCS action to vortex dynamics
journal, April 1997

  • Volovik, G. E.
  • Journal of Experimental and Theoretical Physics Letters, Vol. 65, Issue 8
  • DOI: 10.1134/1.567405

Superfluid transition temperature in a trapped gas of Fermi atoms with a Feshbach resonance
journal, March 2003


Fermi Liquid Theory of Dilute Submonolayer 3He on Thin 4He II Film: Dimer Bound State and Cooper Pairs
journal, June 1983


Effective Lagrangians for BCS superconductors at T =0
journal, March 1995


Origin of the Magnus force on a vortex in fermion superfluids and superconductors
journal, October 1995


Crossover from Bardeen-Cooper-Schrieffer to Bose-Einstein Condensation and the Unitary Fermi Gas
journal, March 2014


Current-current Fermi-liquid corrections to the superconducting fluctuations on conductivity and diamagnetism
journal, January 2012


Nernst effect from fluctuating pairs in the pseudogap phase of the cuprates
journal, January 2011


Superfluid Precursor Effects in a Model of Hybridized Bosons and Fermions
journal, May 1995


Non-analytic vortex core and non-linear vortex flow in bosonic superfluids
journal, November 2015


Superconductivity in a system with preformed pairs
journal, February 1997


Theory of the Motion of Vortices in Superconductors
journal, November 1965


Excitation spectrum and superfluid density of He 3 - A at T = 0
journal, October 1984


Reply to “Comment on ‘Diamagnetism and Cooper pairing above T c in cuprates' ”
journal, February 2013


Phase diagram of a two-component Fermi gas with resonant interactions
journal, February 2008

  • Shin, Yong-il; Schunck, Christian H.; Schirotzek, André
  • Nature, Vol. 451, Issue 7179
  • DOI: 10.1038/nature06473

Reactive effects of core fermion excitations on the inertial mass of a vortex
journal, July 1995

  • Šimánek, E.
  • Journal of Low Temperature Physics, Vol. 100, Issue 1-2
  • DOI: 10.1007/BF00753834

Berry’s phase and the Magnus force for a vortex line in a superconductor
journal, April 1993


Vortices in superconducting films: Statistics and fractional quantum Hall effect
journal, March 1996