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Volumn 64, Issue 22, 2001, Pages

Electron dynamics in (formula presented) Evidence for the pseudogap state and unconventional c-axis response

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[No Author keywords available]

Indexed keywords


EID: 85038280468     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.224503     Document Type: Article
Times cited : (72)

References (102)
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    • The assignment of electrons as the charge carriers is based on the negative value of the Hall coefficient. However, a two band model with both electrons and holes acting as charge carriers has been proposed to account for the less than trivial behavior of the Hall coefficient. Wu Jiang, S.N. Mao, X.X. Xi, X. Jiang, J.L. Peng, T. Venkatesan, C.J. Lobb, and R.L. Greene, Phys. Rev. Lett. 73, 1291 (1994)
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    • A gaplike feature in (Formula presented) has been observed in NCCO by Onose and co-workers at 0.3 eV (Ref. 17). Similar structure has not been detected in other cuprates. The typical energy scale of the pseudogap in the hole doped cuprates is ∼90 meV. Recently, a “high-energy ‘pseudogap’-like suppression” of the angle resolved photoemission spectrum has been observed in NCCO; see N. P. Armitage, D. H. Lu, C. Kim, A. Damascelli, K. M. Shen, F. Ronning, D. L. Feng, P. Bogdanov, Z.-X. Shen, Y. Onose, Y. Taguchi, Y. Tokura, P. K. Mang, N. Kaneko, and M. Greven, Phys. Rev. Lett. 87, 147003 (2001). Additionally, tunneling spectroscopy results show that when a magnetic field is used to drive NCCO and (Formula presented) into the normal state below (Formula presented), a gaplike feature persists in the energy range where the superconducting gap is found
    • A gaplike feature in (Formula presented) has been observed in NCCO by Onose and co-workers at 0.3 eV (Ref. 17). Similar structure has not been detected in other cuprates. The typical energy scale of the pseudogap in the hole doped cuprates is ∼90 meV. Recently, a “high-energy ‘pseudogap’-like suppression” of the angle resolved photoemission spectrum has been observed in NCCO; see N. P. Armitage, D. H. Lu, C. Kim, A. Damascelli, K. M. Shen, F. Ronning, D. L. Feng, P. Bogdanov, Z.-X. Shen, Y. Onose, Y. Taguchi, Y. Tokura, P. K. Mang, N. Kaneko, and M. Greven, Phys. Rev. Lett. 87, 147003 (2001). Additionally, tunneling spectroscopy results show that when a magnetic field is used to drive NCCO and (Formula presented) into the normal state below (Formula presented), a gaplike feature persists in the energy range where the superconducting gap is found; see
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    • The different carrier densities for the two samples produced by the oxygen reducing procedure would dictate that (Formula presented) is crossing at (Formula presented) rather than saturating to a constant value
    • The different carrier densities for the two samples produced by the oxygen reducing procedure would dictate that (Formula presented) is crossing at (Formula presented) rather than saturating to a constant value.
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    • 85038333386 scopus 로고    scopus 로고
    • The plasma frequency, (Formula presented) is determined by integrating (Formula presented) up to the onset of interband transitions. For both samples we integrate (Formula presented) up to (Formula presented) and obtain (Formula presented) for the SC sample and (Formula presented) for the AF sample, independent of temperature. In the AF sample an interband transition becomes visible near (Formula presented) at low temperatures. In principle this should not be included in the integration of (Formula presented) when determining (Formula presented) However, we were unable to unambiguously separate this interband component from the intraband conductivity because of the complicated line shape. Therefore (Formula presented) is likely to be overestimated in the AF sample. From a rough comparison of the spectral weight in the intraband and this interband channel of (Formula presented), we estimate the error in (Formula presented) to be about 10%. We emphasize that this simply shifts the data down at all frequencies, and does not affect our analysis
    • The plasma frequency, (Formula presented) is determined by integrating (Formula presented) up to the onset of interband transitions. For both samples we integrate (Formula presented) up to (Formula presented) and obtain (Formula presented) for the SC sample and (Formula presented) for the AF sample, independent of temperature. In the AF sample an interband transition becomes visible near (Formula presented) at low temperatures. In principle this should not be included in the integration of (Formula presented) when determining (Formula presented) However, we were unable to unambiguously separate this interband component from the intraband conductivity because of the complicated line shape. Therefore (Formula presented) is likely to be overestimated in the AF sample. From a rough comparison of the spectral weight in the intraband and this interband channel of (Formula presented), we estimate the error in (Formula presented) to be about 10%. We emphasize that this simply shifts the data down at all frequencies, and does not affect our analysis.
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    • For (Formula presented) is not shown for the AF sample at 25 and 80 K, as another channel of absorption opens and the single component description of the electromagnetic response is not appropriate at these energies
    • For (Formula presented) is not shown for the AF sample at 25 and 80 K, as another channel of absorption opens and the single component description of the electromagnetic response is not appropriate at these energies.
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    • (private communication)
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    • The electron-phonon interaction (EPI) is an obvious candidate as the source of the structure in (Formula presented). However, while the EPI can qualitatively reproduce the shoulder in (Formula presented), it cannot alone account for all of the features observed in the temperature and frequency dependence. For example, models based on the EPI predict that at energies above the shoulder (Formula presented) will saturate at a constant value rather than continue to strongly increase as observed in Fig. 77. Another prediction is that at temperatures corresponding to roughly half of the energy of the phonon mode the low energy depression of (Formula presented) will be completely washed out. Again the experimental data contradicts these conclusions. If the carriers are coupling to a phonon mode even as high in energy as (Formula presented), the low energy depression should be nearly gone by 250 K. As Fig. 77 shows, the anomalous frequency dependence of (Formula presented) is a robust feature even at 292 K. For a more thorough comparison of models based on the EPI and experimental results for the cuprates, see Ref. c30
    • The electron-phonon interaction (EPI) is an obvious candidate as the source of the structure in (Formula presented). However, while the EPI can qualitatively reproduce the shoulder in (Formula presented), it cannot alone account for all of the features observed in the temperature and frequency dependence. For example, models based on the EPI predict that at energies above the shoulder (Formula presented) will saturate at a constant value rather than continue to strongly increase as observed in Fig. 77. Another prediction is that at temperatures corresponding to roughly half of the energy of the phonon mode the low energy depression of (Formula presented) will be completely washed out. Again the experimental data contradicts these conclusions. If the carriers are coupling to a phonon mode even as high in energy as (Formula presented), the low energy depression should be nearly gone by 250 K. As Fig. 77 shows, the anomalous frequency dependence of (Formula presented) is a robust feature even at 292 K. For a more thorough comparison of models based on the EPI and experimental results for the cuprates, see Ref. 30.
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    • Reported an observation of this feature in several different families of cuprates [cond-mat/0102244 (unpublished)]
    • The threshold structure in the spectra of (Formula presented) corresponds to a “kink” in the dispersion dependence probed through ARPES measurements. Recently, Z.X. Shen et al., reported an observation of this feature in several different families of cuprates [cond-mat/0102244 (unpublished)].
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    • An alternative explanation for these results is that the systems are macroscopically inhomogeneous, consisting of metallic and insulating regions. The mixed phase system can give rise to a peak in (Formula presented) (Ref. c52
    • An alternative explanation for these results is that the systems are macroscopically inhomogeneous, consisting of metallic and insulating regions. The mixed phase system can give rise to a peak in (Formula presented) (Ref. 52).
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    • Other cuprates that have shown low frequency peaks in (Formula presented) include (Formula presented) (Ref. underdoped (Formula presented) (Ref. 44) the three layered compound (Formula presented) (Ref. 45), the single layer (Formula presented) (Ref. 59) and the nonsuperconducting quasi-1D compound (Formula presented)
    • Other cuprates that have shown low frequency peaks in (Formula presented) include (Formula presented) (Ref. 43) underdoped (Formula presented) (Ref. 44) the three layered compound (Formula presented) (Ref. 45), the single layer (Formula presented) (Ref. 59) and the nonsuperconducting quasi-1D compound (Formula presented) (Ref. 60).
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    • It should be noted that there are substantial errors in the absolute value of (Formula presented) near the peak. The absorption is proportional to (Formula presented), which from examination of Fig. 11 is very small at low temperatures. Therefore our error in the absolute values of (Formula presented) of (Formula presented) causes a large uncertainty in (Formula presented). For example, a reduction of the 25 K reflectance by 1% cuts the magnitude of the peak in (Formula presented) by 50%. However, the relative error which is an order of magnitude smaller is the relevant error when applying Eq. (4). Taking this error into consideration Eq. (4) still accounts for less than 5% of the spectral weight corresponding to published values of the penetration depth
    • It should be noted that there are substantial errors in the absolute value of (Formula presented) near the peak. The absorption is proportional to (Formula presented), which from examination of Fig. 11 is very small at low temperatures. Therefore our error in the absolute values of (Formula presented) of (Formula presented) causes a large uncertainty in (Formula presented). For example, a reduction of the 25 K reflectance by 1% cuts the magnitude of the peak in (Formula presented) by 50%. However, the relative error which is an order of magnitude smaller is the relevant error when applying Eq. (4). Taking this error into consideration Eq. (4) still accounts for less than 5% of the spectral weight corresponding to published values of the penetration depth.
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    • The Theory of Superconductivity in the High-(Formula presented) Cuprates (Princeton University Press, Princeton, NJ, 1998)
    • P.W. Anderson, The Theory of Superconductivity in the High-(Formula presented) Cuprates (Princeton University Press, Princeton, NJ, 1998)
    • Anderson, P.W.1
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    • cond-mat/0008050 (unpublished)
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    • The observation of a pseudogap requires the analysis of the frequency dependence of (Formula presented) throughout the FIR. Over most of this range the electronic contribution to (Formula presented) is overwhelmed by the phonon response, therefore completely masking any changes in (Formula presented) from the electronic channel
    • The observation of a pseudogap requires the analysis of the frequency dependence of (Formula presented) throughout the FIR. Over most of this range the electronic contribution to (Formula presented) is overwhelmed by the phonon response, therefore completely masking any changes in (Formula presented) from the electronic channel.


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