Inhomogeneous electronic states of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">La</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">Sr</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mi mathvariant="normal">Cu</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>probed by scanning tunneling spectrosc

Kato, Takuya; Okitsu, S.; Sakata, Hideaki

doi:10.1103/physrevb.72.144518

Cited by 53 publications

(44 citation statements)

References 28 publications

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“…For example, spatial variations of the superconducting energy gap and of the local density of states spectrum have been observed in scanning tunneling microscopy ͑STM͒ experiments. [1][2][3][4][5]7,6,8 There have also been a number of reports of magnetic and charge orderings in these materials, which also indicate inhomogeneities. [9][10][11][12][13][14][15][16][17] Other studies of cuprates have shown that electronic states within certain energy ranges show checkerboardlike spatial modulations.…”

Section: Introductionmentioning

confidence: 99%

Effects of inhomogeneities and thermal fluctuations on the spectral function of a modeld-wave superconductor

Valdez-Balderas

Stroud

2008

Phys. Rev. B

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We compute the spectral function A͑k , ͒ of a model two-dimensional high-temperature superconductor at both zero and finite temperatures T. The model consists of a two-dimensional BCS Hamiltonian with d-wave symmetry, which has a spatially varying, thermally fluctuating, complex gap ⌬. Thermal fluctuations are governed by a Ginzburg-Landau free energy functional. We assume that an areal fraction c ␤ of the superconductor has a large ⌬ ͑␤ regions͒, while the rest has a smaller ⌬ ͑␣ regions͒, both of which are randomly distributed in space. We find that A͑k , ͒ is most strongly affected by inhomogeneity near the point k = ͑ ,0͒ ͑and the symmetry-related points͒. For c ␤ Ӎ 0.5, A͑k , ͒ exhibits two double peaks ͑at positive and negative energies͒ near this k point if the difference between ⌬ ␣ and ⌬ ␤ is sufficiently large in comparison to the hopping integral; otherwise, it has only two broadened single peaks. The strength of the inhomogeneity required to produce a split spectral function peak suggests that inhomogeneity is unlikely to be the cause of a second branch in the dispersion relation, such as has been reported in underdoped LSCO. Thermal fluctuations also affect A͑k , ͒ most strongly near k = ͑ ,0͒. Typically, peaks that are sharp at T = 0 become reduced in height, broadened, and shifted toward lower energies with increasing T; the spectral weight near k = ͑ ,0͒ becomes substantial at zero energy for T greater than the phase-ordering temperature.

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Section: Introductionmentioning

confidence: 99%

Effects of inhomogeneities and thermal fluctuations on the spectral function of a modeld-wave superconductor

Valdez-Balderas

Stroud

2008

Phys. Rev. B

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“…[44][45][46][47] The wavelength of zone boundary phonons is two unit cells, which is about 4 times shorter than the length scale of the inhomogeneity measured by STM and NQR. 14,15 Thus the distribution of the zone boundary phonon frequencies in a medium with inhomogeneous force constants directly reflects the distribution of the force constants.…”

Section: Effectmentioning

confidence: 99%

Effects of charge inhomogeneities on elementary excitations inLa2−xSrxCuO4

et al. 2011

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Purely local experimental probes of many copper oxide superconductors show that their electronic states are inhomogeneous in real space. For example, scanning tunneling spectroscopic (STS) imaging shows strong variations in real space, and according to nuclear quadrupole resonance (NQR) studies the charge distribution in the bulk varies on the nanoscale. However, the analysis of the experimental results utilizing spatially-averaged probes often ignores this fact. We have performed a detailed investigation of the doping-dependence of the energy and line width and position of the zone-boundary Cu-O bond-stretching vibration in La2−xSrxCuO4 by inelastic neutron scattering. Both our new results as well as previously reported angle-dependent momentum widths of the electronic spectral function detected by angle-resolved photoemission can be reproduced by including the same distribution of local environments extracted from the NQR analysis.

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“…[1][2][3][4][5][6][7][8] Typically, in some spatial regions, which we call ␣ regions, the LDOS has a small gap and large coherence peaks, while in other regions, the ␤ regions, the LDOS has a larger gap and reduced coherence peaks. The percentage of the area occupied by ␣ and ␤ regions, respectively, depends on the doping concentration.…”

Section: E Inhomogeneitiesmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8] Among the cuprates, Bi 2 Sr 2 CaCu 2 O 8+x ͑Bi2212͒ is one of the most extensively studied in STM experiments. The LDOS spectrum shows that some regions of that material, which we will call ␣ regions, have a small energy gap with large and narrow coherence peaks ͑reminiscent of the spectra observed in bulk superconducting materials͒, while other regions, which we will call ␤ regions, have a larger gap, but smaller and broadened peaks ͑which are reminiscent of the spectra seen in bulk pseudogap phase of some materials.…”

Section: Introductionmentioning

confidence: 99%

Single-particle density of states of a superconductor with a spatially varying gap and phase fluctuations

Valdez-Balderas

Stroud

2006

Phys. Rev. B

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Recent experiments have shown that the superconducting energy gap in some cuprates is spatially inhomogeneous. Motivated by these experiments, and using exact diagonalization of a model d-wave Hamiltonian, combined with Monte Carlo simulations of a Ginzburg-Landau free energy functional, we have calculated the single-particle local density of states LDOS ͑ , r͒ of a model high-T c superconductor as a function of temperature. Our calculations include both quenched disorder in the pairing potential and thermal fluctuations in both phase and amplitude of the superconducting gap. Most of our calculations assume two types of superconducting regions: ␣ with a small gap and large superfluid density, and ␤ with the opposite. If the ␤ regions are randomly embedded in an ␣ host, the LDOS on the ␣ sites still has a sharp coherence peak at T = 0, but the ␤ component does not, in agreement with experiment. An ordered arrangement of ␤ regions leads to oscillations in the LDOS as a function of energy. The model leads to a superconducting transition temperature T c well below the pseudogap temperature T c0 and has a spatially varying gap at very low T, both consistent with experiments in underdoped Bi2212. Our calculated LDOS ͑ , r͒ shows coherence peaks for T Ͻ T c , which disappear for T Ͼ T c , in agreement with previous work considering phase but not amplitude fluctuations in a homogeneous superconductor. Well above T c , the gap in the LDOS disappears.

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Inhomogeneous electronic states ofLa2−xSrxCuO4probed by scanning tunneling spectrosc

Cited by 53 publications

References 28 publications

Effects of inhomogeneities and thermal fluctuations on the spectral function of a modeld-wave superconductor

Effects of inhomogeneities and thermal fluctuations on the spectral function of a modeld-wave superconductor

Effects of charge inhomogeneities on elementary excitations inLa2−xSrxCuO4

Single-particle density of states of a superconductor with a spatially varying gap and phase fluctuations

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