Technical Comments

Intrinsic Versus Extrinsic Pseudogaps in Photoemission Spectra of Poorly Conducting Solids

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Science  04 Feb 2000:
Vol. 287, Issue 5454, pp. 767
DOI: 10.1126/science.287.5454.767a

In his report Robert Joynt (1) argued that the pseudogap observed in photoemission experiments in the manganites, and possibly in many other compounds, may be due to extrinsic loss effects. Joynt considered that the electric field created by the outgoing photoelectron would produce ohmic losses, lowering the kinetic energy of the ejected photoelectron. This would show up in the spectra as a pseudogap depression of weight near E F, even if there was not one in the true density of states, and should be most important for highly resistive samples. Although Joynt's general arguments are plausible, he was not able to determine the magnitude of many of the important parameters of his model, including at what resistivity these effects should become realizable in a high energy resolution experiment.

Joynt stated that the extrinsic loss effects are not expected to be momentum- or angle-dependent, so that we can test such extrinsic effects in an angle-resolved photoemission (ARPES) experiment. Figure 1 shows data obtained from a cleaved single crystal of the colossal magnetoresistive (CMR) manganite La1.2Sr1.8Mn2O7. The temperatures studied were well below T c (blue) and well above T c (red), between which there is about a two order of magnitude change in resistivity (see inset). The curves at k⃗ = (π, 0.28π) show a significant temperature-dependent shift away from EF with temperature, while the curves at k⃗ = (π, 0.09π) and k⃗ = (0.46π, 0) show an intermediate effect and a minimal effect, respectively. The minimal temperature-dependent changes observed at (0.46π, 0) put an upper limit on the magnitude of the effects that could be due to Joynt's extrinsic losses; hence, the dramatic changes observed at k⃗ = (π, 0.28π) should be of intrinsic origin. Because there is at some angles no effect from a two order of magnitude change of resistivity, it should also be clear that the weaker pseudogap observed at (π, 0.28π) at 50 K in the spectra is not due to ohmic losses [the pseudogap should be measured at the k⃗ where the peak is closest toEF , which occurs at (π, 0.28π)].

Figure 1

ARPES spectra from hv = 22.4 eV of La1.2Sr1.8- Mn2O7 at specifick⃗-space points, (π,0.28π) (a), (π,0.09 π) (b), and (0.46π, π) (c) at 200 K (red) and 50 K (blue). The square inset shows the location of the points (red ×) in the two-dimensional Brillouin zone with the predicted Fermi surface (green) (2). The resistivity versus temperature curve (3) is also shown in the right inset.

Because these samples have high resistivities of about 0.1 ohm-cm (three orders of magnitude larger than the value of 10−4ohm-cm at which Joynt expected these effects to become relevant), this should also alleviate concerns about these extrinsic effects for other samples with a conductivity of this order or better.

  • * Present address: Photon Factory, KEK, Tsukuba, Ibaraki 305-0821, Japan, E-mail: tomohiko.saitoh{at}kek.jp

REFERENCES AND NOTES

Response: Dessau and Saitoh present angle-resolved photoemission spectroscopy (ARPES) data on the layered manganite La1.2Sr1.8- Mn2O7 that show a temperature-dependent anisotropy. They correctly state that this anisotropic pseudogap in momentum space is unlikely to arise from the extrinsic effects that I pointed out in (1). However, it can be misleading to make conclusions about all poorly conducting solids based on observations in this system.

The losses calculated in (1) require a low dc conductivity as a necessary, but not sufficient, condition. This is evident from the examination of the loss function:Embedded Image(1-1)where σ(ω) is the frequency-dependent complex conductivity and v is the outgoing velocity (C ≈ 2.6 is a constant). If the absorptive part of the conductivity is zero at the relevant frequency, so is the loss function. The reason for presenting the calculations in the context of poorly conducting solids is that if |σ| >> ω (the usual case in a good metal), then this function is also small for typical experimental conditions.

A one-parameter picture of the loss function is not adequate, nor can one ignore the magnitude of the gap or pseudogap in question. This may be illustrated with La1.2- Sr1.8Mn2O7, where we have an in-plane dc resistivity ρ0 ≈ 0.1 ohm-cm at 200 K, an extremely high resistivity. This corresponds to an energy ℏ︀σ(0) = ℏ︀/ρ0 of about 6 meV. Since ℜσ(ω) is a decreasing function, this energy represents an upper bound to a crossover energy above which the extrinsic losses are expected to be negligible as the denominator in the second factor of Eq. 1 approaches 4. The observed shifts are of order 200 meV. The theory is not likely to be applicable to any pseudogap of this size in the very poor conductor La1.2Sr1.8Mn2O7, independent of anisotropy of this pseudogap. A full analysis would take account of the tetragonal crystal structure and the resulting tensorial nature of σ, but this would not change the qualitative conclusion.

The calculations in (1) are not a model but an application of standard electrodynamics. There are no unknown parameters once the frequency-dependent conductivity has been measured. Applications to specific materials may necessitate modeling of ℜσ(ω) if this quantity has not been accurately measured. Accurate determinations of pseudogaps or gaps in poorly conducting solids require both optical and photoemission measurements, followed by careful consideration of the characteristic frequencies revealed in such experiments.

REFERENCES AND NOTES

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