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Volumn 81, Issue 10, 2010, Pages

De Haas-van alphen oscillations in high-temperature superconductors

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EID: 77954893928     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.100514     Document Type: Article
Times cited : (7)

References (33)
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    • we ignore "spin factors" in this Rapid Communication
    • we ignore "spin factors" in this Rapid Communication.
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    • J. M. Luttinger, Phys. Rev. 121, 1251 (1961) 10.1103/PhysRev.121.1251
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    • See, e.g., 10.1088/0305-4608/10/12/010;
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    • See, e.g., edited by R. E. Prange and S. M. Girvin (Springer-Verlag, New York
    • See, e.g., The Quantum Hall Effect, edited by, R. E. Prange, and, S. M. Girvin, (Springer-Verlag, New York, 1990).
    • (1990) The Quantum Hall Effect
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    • For exact 2d results for large Landau levels, see, 10.1103/PhysRevB.54. 5006
    • For exact 2d results for large Landau levels, see R. Moessner and J. T. Chalker, Phys. Rev. B 54, 5006 (1996). 10.1103/PhysRevB.54.5006
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    • Moessner, R.1    Chalker, J.T.2
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    • Such "nearly antiferromagnetic spin-fluctuation" models for conducting systems go back to, 10.1103/PhysRevLett.24.1433;
    • Such "nearly antiferromagnetic spin-fluctuation" models for conducting systems go back to T. Moriya, Phys. Rev. Lett. 24, 1433 (1970). They have been applied by many authors to high- T c systems 10.1103/PhysRevLett.24. 1433
    • (1970) Phys. Rev. Lett. , vol.24 , pp. 1433
    • Moriya, T.1
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    • Vertex corrections to Eq. for the spin-fluctuation model change the numerical results, but not the basic form, of ImΣ. For the NFL theory, perturbation expansions can be controlled by introducing N species of fermion, and doing either a 1/N expansion (see, 10.1016/0550-3213(94)90449-9;
    • Vertex corrections to Eq. for the spin-fluctuation model change the numerical results, but not the basic form, of I m Σ. For the NFL theory, perturbation expansions can be controlled by introducing N species of fermion, and doing either a 1 / N expansion (see J. Polchinski, Nucl. Phys B 422, 617 (1994) 10.1016/0550-3213(94)90449-9
    • (1994) Nucl. Phys B , vol.422 , pp. 617
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    • S.-S. Lee, Phys. Rev. B 80, 165102 (2009), or an eikonal expansion 10.1103/PhysRevB.80.165102
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    • (see, 10.1103/PhysRevLett.71.2118
    • (see D. V. Khveshchenko and P. C. E. Stamp, Phys. Rev. Lett. 71, 2118 (1993). Calculation of dHvA oscillations then involves simultaneous expansion in ω c / μ1, and either 1 / N or N. Here we take the ω c / μ expansion as primary (typically N = 2 anyway), and ignore vertex corrections-elsewhere we will give results in a 1 / N expansion. 10.1103/PhysRevLett.71.2118
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    • Khveshchenko, D.V.1    Stamp, P.C.E.2
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    • The self-energy Σ (z), and the coefficients Σr (z), can be found analytically for the spin-fluctuation model as a rather cumbersome function of elliptic integrals and exponential integrals
    • The self-energy Σ (z), and the coefficients Σ r (z), can be found analytically for the spin-fluctuation model as a rather cumbersome function of elliptic integrals and exponential integrals.
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    • Models in which fermions couple to fluctuation propagators of form have been studied extensively in high- Tc systems and for the FQHL; see, e.g., 10.1103/PhysRevB.46.5621;
    • Models in which fermions couple to fluctuation propagators of form have been studied extensively in high- T c systems and for the FQHL; see, e.g., P. A. Lee and N. Nagaosa, Phys. Rev. B 46, 5621 (1992) 10.1103/PhysRevB.46.5621
    • (1992) Phys. Rev. B , vol.46 , pp. 5621
    • Lee, P.A.1    Nagaosa, N.2
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    • For Lommel functions, see, Cambridge University Press, New York
    • For Lommel functions, see G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, New York, 1952), Sec. 10.7. The function S 2 (μ, ν; z) is also written as S μ, ν (z) in the literature.
    • (1952) A Treatise on the Theory of Bessel Functions
    • Watson, G.N.1
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    • It is convenient to do field-theoretical calculations at constant μ. To find, e.g., M at constant N, we calculate F=Ω+μN, with N=-TrImG/π; then MN =-F/B. For this case μ will oscillate. Experiments are done under both conditions-however experiments in high- Tc systems have shown no sign yet of oscillations of μ
    • It is convenient to do field-theoretical calculations at constant μ. To find, e.g., M at constant N, we calculate F=Ω+μN, with N=-TrImG/π; then MN =-F/B. For this case μ will oscillate. Experiments are done under both conditions-however experiments in high- Tc systems have shown no sign yet of oscillations of μ.
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    • We neglect a much smaller contribution to the magnetization going as Ωr /Bcos (rAF /eB )
    • We neglect a much smaller contribution to the magnetization going as Ωr /Bcos (rAF /eB ).


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