Electron Spectroscopy Group: Research

The outstanding questions in the field of high-T_c superconductivity include the identification of the pairing mechanism producing the Cooper pair and the nature of the low-energy elementary excitations that are coupled.  Can the latter be thought of as quasiparticles of the Landau type or do they represent spin-charge separated modes in the normal state?  If the latter, do they condense into electrons in the superconducting state? Does the pairing involve magnetic excitations or the more traditional lattice excitations?  With these questions in mind, a considerable amount of effort in the Electron Spectroscopy group has been expended to examining the nature of the elementary excitations and their interactions.  Photoemission and infra-red optical conductivity are techniques that are ideally suited for such studies.  Optical conductivity measurements are bulk sensitive whereas photoemission tends to be more surface sensitive and ideally requires samples that are cleavable.  However both techniques provide direct access to scattering rates which are related to the imaginary part of the self energy.  In the case of photoemission, the scattering rates may be determined from measurements of the photoemitted intensity as a function of either binding energy or of momentum.  The latter type of measurement was pioneered by the Electron Spectroscopy group at BNL and is now universally used.

Scattering rates provide information on the nature of the excitation.  In a Fermi liquid the elementary excitations show a quadratic dependence on binding energy and temperature.  In non-Fermi liquids it is highly likely that the scattering rates will show some other dependence that could in fact be linear.  3D systems support single particle electron like excitations or quasiparticles.  1-D systems on the other hand have no single particle like excitations.  Here the elementary excitations are collective excitations that carry away the spin and charge independently.  What is the situation in the cuprates, systems where we know that the superconductivity is associated with the 2-D copper oxide planes.  At optimal doping, these materials are considered to be non-Fermi liquids in the normal state.  As one moves towards the underdoped regime one anticipates more insulating like behavior.  In the overdoped regime on the other hand, the consensus is that the behavior is more Fermi liquid like.

Angle Resolved Photoemission Spectroscopy (ARPES)

Angle Resolved Photoemission spectroscopy (ARPES) has focused on both the high-temperature superconductors as well as other low-dimensional systems.  In a study of optimally doped Bi₂Sr₂CaCu₂O_8+d, (BSCCO), carried out in the late 90’s, the BNL photoemission group reported the observation of a mass-enhancement in the electronic dispersion in the vicinity of the Fermi level.  Since that first observation, the mass enhancement has continued to be the subject of intense research activity and controversy.  In a second study, the BNL group reported the observation that the “kink” is stronger in the underdoped region of the phase diagram and that there is an observable change in the mass-enhancement ongoing through the transition temperature T_c.  These changes are reduced and eventually disappear as one moves further into the overdoped region.  The observed temperature dependence of the mass-enhancement appears identical to that reported in neutron scattering studies of a magnetic resonant mode observed in the superconducting state.  As such, the BNL group has suggested that most of the mass-renormalization reflects coupling to spin excitations in the  system.  In an alternative approach, the Stanford and Berkeley groups have suggested that the energy of the kink is very close to the energy observed for optical phonons in the system.  Thus, in their picture, the mass-enhancement reflects coupling of the electrons to these phonon modes.  In such a model one does not expect any particular change in the mass-enhancement at the superconducting transition and indeed they do not report any.  However, in a recent optical conductivity study, Timusk and co-workers reported temperature dependent changes in the low energy excitation spectrum that were nearly identical to those observed by the BNL ARPES group.

Fig. 1.  Energy versus momentum intensity maps in BISCO as a function of doping.  The spectra correspond to emission in the nodal direction.  The mass renormalization or kink in the vicinity of the Fermi level is clearly visible.

Fourier Transform Infrared (FTIR) Spectroscopy

The infrared program is geared primarily towards using infrared and visible radiation to probe the electronic and vibrational properties of solids. The reflectance of a material is a complex quantity, with an amplitude and a phase. During a typical experiment, we only measure the reflected amplitude of the radiation. However, if the reflectance is measured over a wide enough range, then it is possible using the Kramers-Kronig relations to calculate the phase: once the amplitude and phase are known, then other optical response functions may be calculated, specifically the real part of the complex conductivity. The experiments on the infrared optical properties of solids are conducted on a Bruker IFS113v Fourier transform infrared (FTIR) interferometer in the Department of Physics and on a Bruker IFS66v/S FTIR instrument at the U10A beamline at the , where various probes have been built to measure the transmission or the absolute reflectance of solids or thin films.  In addition, a Bruker IFS113v is used as an "off-line" instrument to bench-test optics and to perform routine spectroscopy.

Infrared studies have been carried out on a variety of correlated electron systems, in particular:

• High-temperature superconductors and parent materials

• Spin and charge-density wave systems ("stripes")

• High dielectric constant materials

• Collosal magnetoresistance materials

• Organic conductors (1D & 2D)

• Conducting polymers

The materials that I am presently looking at are the so-called "bad metals", which would characterize most of the transition metal oxides which are not insulators.

The unconventional conductivity and superconductivity of many of the bad metals is thought to involve collective excitations which typically occur at very low energies, either in the microwave region or in the very far infrared. The low-energy part of the infrared spectrum, or the far infrared, is a region where conventional infrared sources (i.e., globar and Hg arc lamps) are very weak. One of the programs here at Brookhaven National Laboratory is to use the National Synchrotron Light Source as a source of infrared radiation. At long wavelengths, it may be possible to realize an advantage in brightness of several orders of magnitude over a conventional blackbody infrared source; this is especially useful when examining small samples.

In detailed optical conductivity studies we have explored the nature of scaling relations in the cuprates.  The best known attempt to establish a scaling law in the hole-doped materials is the Uemura relation, which states that the superfluid density (r_sµ 1/l²), a measure of the number of carriers in the superconducting state, is proportional to T_c.  However, the Uemura relation works only in the underdoped regime, and is not applicable at all along the c axis.  An initial attempt to determine a scaling relation along the c axis (r_sµs_dc) was only partially successful.  Shown in the figure below, we have recently determined a universal scaling relation, r_sµs_dcT_c, that is valid in the a-b planes, as well as along the c axis; it also holds regardless of doping level, nature of dopant (electrons vs holes) or crystal structure.  This scaling relation is a surprising result that should provide new insights into the origins of the superconductivity in these materials [Nature 430, 539 (2004)].

Current projects involve examining the polarized optical properties detwinned single crystals of the copper-oxygen high-temperature superconductor YBa₂Cu₃O_6+x (YBCO) at a variety of doping levels in the normal and superconducting states, with particular emphasis placed on the underdoped region.  The La_2-xBa_xCuO₄ (LBCO) material is also being studied near the x~1/8 concentration, where the critical temperature is observed to be suppressed due to the formation of charge stripes; the notion of competing order parameters is also being examined in the nickelate La₂NiO_4+d and the Sr_14-xCa_xCu₂₄O₄₁ two-leg ladder systems, as well as in the simpler Sr₂CuO₃ quasi-one dimensional material.  The electron-doped systems (Nd,Pr)_2-xCe_xCuO₄ are also being studied to determine of electron-hole symmetry exists within the cuprates, as well as if the underdoped region of the phase diagram, which is rather difficult to achieve in the electron-doped materials, is similar to that of the hole-doped materials.  In all of the infrared studies, we are also trying to develop methods of determining the spectral function and to compare it with information about the spectral function that may be determined from ARPES studies of these materials.

Last modified: Tuesday, June 10, 2008 11:44 AM.

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