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Spin excitations in layered cuprates: a Fermi-liquid approach
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10.1063/1.2215367
/content/aip/journal/ltp/32/6/10.1063/1.2215367
http://aip.metastore.ingenta.com/content/aip/journal/ltp/32/6/10.1063/1.2215367
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic phase diagram of hole-doped cuprates. High- superconductivity occurs in the vicinity of an antiferromagnetic phase transition. The corresponding superconducting order parameter below the superconducting transition temperature is of -wave symmetry. In the overdoped region, i.e., , the cuprates behave like a conventional Fermi liquid, whereas in the underdoped regime below the pseudogap temperature one finds strong antiferromagnetic (AF) correlations. As we will discuss below, Cooper pairing can basically be described by the exchange of AF spin fluctuations (often called paramagnons). The doping region between and (shaded region) may be due to local phase-incoherent Cooper-pair formation. Only below do these pairs become phase coherent.

Image of FIG. 2.
FIG. 2.

Picture of the Fermi surface for the layered cuprates in the first BZ. The arrows show the electronic states connected by the antiferromagnetic wave vector . The dotted lines and signs refer to the -wave symmetry of the superconducting gap.

Image of FIG. 3.
FIG. 3.

INS results for optimally doped taken from Ref. 13 at the antiferromagnetic wave vector for the normal and superconducting states.

Image of FIG. 4.
FIG. 4.

Measured dispersion of the resonant excitations away from the antiferromagnetic wave vector along the diagonal of the first BZ as taken from Ref. 17. The vertical dashed region indicates the position of the silent bands.

Image of FIG. 5.
FIG. 5.

Cooper pairing in the cuprates due to coupling of carriers (holes or electrons) in planes to antiferromagnetic spin fluctuations characterized by the spin susceptibility ( refers to the matrix Green’s function of quasiparticles).

Image of FIG. 6.
FIG. 6.

ARPES results for the renormalized energy dispersion along the direction of the first Brillouin zone, taken from Ref. 22. The horizontal axis shows the distance in the normalized units .

Image of FIG. 7.
FIG. 7.

Calculated Fermi surface for the for the first few BZs using a tight-binding energy dispersion from Eq. (12) with and optimal doping. The arrows indicate three different scattering processes as described in the text.

Image of FIG. 8.
FIG. 8.

Frequency dependence of at the antiferromagnetic wave vector . It reveals a jump because of the -wave symmetry of the superconducting gap.

Image of FIG. 9.
FIG. 9.

Numerical results for the resonance peak in the weak-coupling limit from Ref. 34 for optimal doping. Imaginary part of the RPA spin susceptibility (in units of states/eV) at wave vector for , 2, 3, and 4 (from bottom to top). The resonance frequency was found at .

Image of FIG. 10.
FIG. 10.

Imaginary part of the RPA spin susceptibility at calculated within the FLEX approximation, taken from Ref. 34 for optimal doping. For the normal state one gets and in the superconducting state . Assuming , one finds that .

Image of FIG. 11.
FIG. 11.

Calculated results taken from Ref. 34 for the resonance frequency versus doping. In the overdoped regime one finds a constant ratio of .

Image of FIG. 12.
FIG. 12.

Schematic behavior of and within the RPA, , for various momenta .

Image of FIG. 13.
FIG. 13.

RPA results for magnetic excitations in a -wave superconductor. is obtained from Eq. (36) as a function of momentum (along the diagonal ) and frequency in the superconducting state, taken from Ref. 35. The arrows indicate the positions of the resonance modes.

Image of FIG. 14.
FIG. 14.

Intensity patterns of the resonance excitations for and taken from Ref. 35.

Image of FIG. 15.
FIG. 15.

Illustration of the possible drastic changes of the Fermi surface due to various parameters of the orthorhombicity, as adopted from Ref. 37. The arrows show the change of the phase space for the bond scattering.

Image of FIG. 16.
FIG. 16.

Calculated normalized two-dimensional intensity plot of for constant energy of taken from Ref. 37, without and with inclusion of orthorhombicity . Note that two of the four incommensurate peaks are suppressed.

Image of FIG. 17.
FIG. 17.

Calculated spectral density from Ref. 39 of the quasiparticles in hole-doped cuprates at along and (inset) directions of the first BZ. The dashed line denotes the unrenormalized chemical potential. In both directions at energies of approximately a kink occurs, since the velocity of quasiparticles changes.

Image of FIG. 18.
FIG. 18.

Positions of the peaks in the spectral density versus (energy dispersion) along the direction of the BZ, calculated in Ref. 39 for optimally hole-doped cuprates. Inset: change in the peak positions of in the superconducting state. Note that in underdoped cuprates the kink feature shifts to lower frequencies due to decreasing of . In the overdoped regime the kink feature should become less pronounced and isotropic in different directions of the BZ.

Image of FIG. 19.
FIG. 19.

Comparison of the quasiparticle damping in the normal state for optimal doping and the overdoped case taken from Ref. 40. The solid curves are calculated at and the dashed curves refer to . The upper curves correspond to the antinodal wave vector , whereas the lower curves correspond to the nodal one both on the Fermi line. For comparison, we also show in results for the superconducting state (, dashed-dotted curve). Note that for both doping concentrations a linear behavior for larger frequencies and a vanishing anisotropy for in the overdoped case.

Image of FIG. 20.
FIG. 20.

Calculated frequency dependence of the quasiparticle self-energy at the nodal point in the first BZ taken from Ref. 39 for optimally hole-doped cuprates. The solid curves correspond to the normal state at , whereas the dashed curves to the superconducting state at . In the normal state one clearly sees approximately at a crossover from Fermi liquid behavior to a non-Fermi-liquid behavior for low-energy frequencies as a function of temperature. We show in the inset the behavior of calculated at very low temperatures without superconductivity (, dashed curve). Note that the behavior of the self-energy will become more Fermi-liquid-like in the overdoped regime, and thus the kink feature will be less pronounced.

Image of FIG. 21.
FIG. 21.

Calculated frequency dependence of the quasiparticle self-energy at the anti-nodal point in the first BZ taken from Ref. 41 for optimally hole-doped cuprates. The solid curve correspond to the normal state at , whereas the dashed curves correspond to the superconducting state at . Inset: the corresponding superconducting gap function versus frequency.

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/content/aip/journal/ltp/32/6/10.1063/1.2215367
2006-06-01
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spin excitations in layered cuprates: a Fermi-liquid approach
http://aip.metastore.ingenta.com/content/aip/journal/ltp/32/6/10.1063/1.2215367
10.1063/1.2215367
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