Growth of the optical conductivity in the Cu-O planes.

We have studied the development of the optical conductivity as electrons are added to the Cu- 0 planes in Pr2- Ce Cu04 — s by varying x (0«x «0. 2). In the metallic phases, contributions to the optical conductivity below 3 eV arise from three sources: mobile carriers, mid-infrared ex-citations, and charge-transfer excitations. The mobile carrier spectral weight grows roughly linearly with x, while the mid-infrared band appears to evolve at low doping via a transfer of spectral weight from the charge-transfer band. Comparing these results with hole doping in La2-, Sr Cu04-& indicates an electron-hole symmetry that is not anticipated by standard charge-transfer insulator models.

In spite of much study, little is understood about either the normal-state excitation spectrum of the high-T, compounds, ' or the manner in which this spectrum develops from the insulating phase as a function of doping. We address these issues here in an optical-reflectivity study of n type Pr2--, Ce"Cu04s for 0&x &0.2 and b-0. At x 0, Pr2 "Ce,Cu04 s is an insulator with negligible absorption below the charge-transfer gap (to-1.5 eV).
Our study indicates that light doping (x-0.04) gives rise to an unexpectedly large growth of spectral weight in the mid-infrared frequency range (i.e, 0.1 « to «0.5 eV), and an accompanying decrease in the charge-transfer band.
Further doping (0.04 & x «0.2) leads to an x-dependent increase in absorption at low frequencies (ra &0.1 eV), but causes little change in the mid-infrared or chargetransfer contributions. Notably, similar behavior has also been observed recently in p-type La2 -"Sr"Cu04 s, indicating a qualitative particle-hole symmetry associated with the doping process in high-T, cuprates. These optical results appear to be inconsistent with standard charge-transfer insulator models.
The optical measurements reported in this paper were performed on single crystals of T'-phase Pr2 -"Ce"- Large crystals (as large as 3x 3x0.1 cm3) with flat and shiny surfaces were grown on the surface of the flux. After they were mechanically removed from the flux, the crystals were annealed at 875 'C with Ar-gas flow for 5 h and then furnace cooled to room temperature. Magnetic measurements of crystals in the concentration range x «0.12 indicated that these samples were antiferromagnetic with sharp transition widths & 10 K. The x 0.2 crystal was nonmagnetic and nonsuperconducting (the superconducting phase occurs between 0.14«x «0.18). 5 The Ce concentrations in these crystals were determined from lattice-parameter measurements by x-ray diffraction, and are accurate to + 5%.
Furthermore, the nominal Q concentration was determined from neutron-scattering studies to be 4 oxygen atoms/unit cell, s and consequently no carriers are expected to arise from oxygen vacancies (i.e. , b-0). Pt doping from the crucible is believed to be negligible because impurity contributions are not apparent in the insulating (x 0) crystals. In-plane thermoelectric power in all crystals were measured to be negative at room temperature, indicating electronic carriers. Reflectivity spectra from 100 to 20000 cm ' (12.5 meV to 2.5 eV) were performed close to a normal-incidence configuration using a rapid scanning interferometer. Mirror optics were used to focus the modulated, collimated light beam from the spectrometer onto the sample, and then onto a variety of detectors covering the above frequency range. Note that the frequency is plotted on a logarithmic scale.
between 100 and 20000 cm ' for a series of Ce concentrations x. The most notable feature of these reflectivity spectra is the transition between insulating and metallic behavior that occurs with increased Ce substitution. The frequency-dependent R of undoped Pr2Cu04 s (x 0) is characteristic of an insulator, exhibiting a response dominated at low frequencies by phonon peaks, and at high frequencies by a peak in reflectivity near 12000 cm (1.5 eV). The latter peak, observed in the insulating phases of all high-T, cuprates, has been attributed to the onset of Cu-0 charge-transfer excitations. Upon substituting Ce + for Pr3+ (x ) 0), the appearance of metallic behavior is betrayed by two changes: a rapid increase in the low-frequency reflectivity due to absorption by electronic process, and the development of a plasma edge near 1 eV (8000 cm '). Notably, the changes in R shown in Light doping (x 0.04 electrons/unit cell) produces a large increase in low-frequency spectral weight, as well as a substantial decrease in spectral weight above the charge-transfer gap (ro )1. 5 eV). The change in the optical conductivity is more clearly illustrated in Fig. 3, which shows the incremental changes in conduc- cr; -cr~, is defined so that cr;crj =cr(x;)o(xj). The transfer of spectral weight as x changes across the metalinsulator transition is evident in Fig. 3(a), which plots the optical conductivity difference, cr;ej, between crystals with x 0.04 and x 0. Notably, increases in o below 1.5 eV consist of two parts: a contribution centered at ai 0, presumably arising from mobile carriers, and a broad mid-infrared absorption band centered near 0.4 eV (-3000 cm '). Further doping (x~0.04), as shown in Figs. 2 and 3(b), leads to a continued increase in the lowfrequency mobile carrier contribution, but to little additional change in the mid-infrared and charge-transfer bands. These differences in growth rate distinguish between the mobile carriers and the mid-infrared absorption even when the two bands are not spectroscopically resolved. The presence of this two-component a, and its behavior with doping, is similar to that observed in p-type high-T, compounds YBa2Cu30s+"(Ref. 8) and La2 -, Sr, Cu04-s. ' The doping dependence of the total integrated spectral weight below the charge-transfer band edge at 1.5 eV is shown for both Pry -, Ce"Cu04-s (triangles) and La2-, Sr, Cu04 s (solid circles) in Fig. 4. The integrated spectral weight, or normalized effective carrier density N, g(oi), is defined by 2m V~~Ñ efr(ai) 2 0'(ai )dro, xe where V"s is the unit-cell volume divided by 2 (for the two Cu atoms per unit cell), m is the free electron mass, and e is the electron charge. The dashed lines are the weight calculated by assuming that each acceptor or donor contributes one carrier with an effective mass m equal to the free electron mass m, . It is clear from Fig. 4 that the spectral weight below 1.5 eV is larger than that expected from the carrier concentration alone, suggesting that some charge-transfer spectral weight has shifted to low frequencies as a function of doping. Significantly, the integrated spectral weight below 4 eV in La2, Sr, -Cu04s was found to be approximately independent of doping, also indicating that spectral weight is redistributed to low frequencies from the charge-transfer band with doping. As illustrated in both Figs. 3(a) and 4, the redistribution of weight in Pr2 -, Ce, Cu04-s occurs at very low doping (x 0.04), while additional increases in spectral weight for x )0. 04 are consistent with increases in the donor concentration alone [ Fig. 3(b)]. Therefore, these data suggest two consequences of doping: first, the addition of x mobile carriers into a Drude-like band centered at ai 0, and second, an abrupt shifting of spectral weight from the charge-transfer gap to a mid-infrared band near the metal-insulator transition. Furthermore, a comparison of the two sides of Fig. 4 illustrates the qualitative symmetry between electron and hole doping.
The above experimental results are difficult to reconcile with simple models of doping in a charge-transfer insulator, in which one expects a weak dependence of spectral weight in the charge-transfer gap on doping, a spectral weight below the fundamental gap that scales with x, and a prominent particle-hole asymmetry that leads to more low-frequency spectral weight in the hole-doped than in the electron-doped materials. These simple expectations may be understood by first recalling that the Cu02 planes in Pr2Cu04 and La2Cu04 are believed to contain one hole per Cu02 unit, with the holes residing primarily on the Cu site. These materials are insulating because an energy difference eeq inhibits promotion of a hole from Cu to 0 orbitals (i.e. , charge transfer), and a larger correlation energy U inhibits double occupancy of a Cu site by holes.
When the Cu02 planes are doped by electrons, as is indicated by room-temperature Hall effect data in Pr2-, Ce"Cu04-s, the electrons eliminate holes by principally residing on Cu sites. Doping with x electrons/unit cell is expected to result in two optical processes: (1) The itinerant motion of holes, having relative spectral weight x (allowed because some Cu sites are now unoccupied); (2) charge-transfer absorption processes, having spectral weight (1x) (reduced from that in the insulator because x Cu sites no longer contain holes). In contrast, if the Cu02 planes are doped by holes, as is indicated in Lag -, Sr"Cu04-s by Hall effect data, 9 these carriers must reside on 0 sites. In this case, it is believed'o that each hole binds to a Cu spin, forming a local singlet. This binding should give rise to three allowed optical processes: (1) itinerant motion of singlets, having a spectral distribution centered at ai 0 with spectral weight x; (2) unbinding of the 0 hole from the Cu spin, giving a contribution centered at finite frequency aio-r~/e, -e& ( e, -e& and also having relative weight x; (3) Cu-0 charge-transfer processes, having spectral weight that is only weakly doping dependent (since the number of occupied Cu sites is not changed by hole doping). Quantitative calculations of these effects for a 2d Cu02 lattice with realistic parameters have not yet been performed. However, a particlehole asymmetry in the optical properties is expected within the above picture, as may be illustrated by compu- Prz, Ce, Cu04-s, and the concomitant decrease of weight above the -1.5 eV gap, is unexpected. This behavior also differs from that observed in BaPB~"Bi,Oi (Ref. 12) and in doped semiconductors" (e.g. , Si:P), where the low-frequency spectral weight N, ff scales linearly with the number of donors. Notably, a recent photoemission study on N12 -, Ce"Cu04-& has also concluded that electronic states near the Fermi level in the metallic phases evolve from higher-frequency states found in the insulating phase. ' Our results illustrate not only that low-frequency weight in the metallic phases derive specifically from the charge-transfer band in the insulating phase, but also that this transferred weight goes principally into a mid-infrared band as the system is lightly doped.
Nore added in proof U.sing a first-principles density functional description of the Cu-0 plane electronic structure, Hybertsen er a/. ' find that the low-frequency carrier dynamics of the high-T, cuprates exhibit a remarkable symmetry between electron and holes, in qualitative agreement with the data presented here.