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Charge-Density-Wave induced modifications to the quasiparticle self-energy in 2H TaSe2

The self-energy of the photo-hole in 2H-TaSe2 is measured by angle-resolved photoemission spectroscopy (ARPES) as a function of binding energy and temperature. In the charge-density wave (CDW) state, a structure in the self- energy is detected at ~ 65 meV that can not be explained by electron-phonon scattering. A reduction in the scattering rates below this energy indicates the collapse of a major scattering channel with the formation of the CDW state, accompanying the appearance of a bosonic"mode"in the excitation spectrum of the system.

In general the quasi 2-D electronic systems have a weaker tendency towards the formation of Charge-Density-Wave (CDW) and Spin-Density-Wave (SDW) instabilities than their 1-D counterparts. This is because the Fermi surfaces in 2-D (generalized cylinders) can only be partially nested. However, under favorable nesting conditions, or driven by saddle-point singularities, the electronic susceptibility may be enhanced enough for a CDW to develop. Since the Fermi surface is only partially gapped, the system may retain metallic character even in the CDW state. The 2-D character and the existence of an anisotropic gap make these systems similar to the high T C superconductors (HTSCs). In particular, the low-energy one-electron-like excitations ("quasiparticles") may show certain similarities. Angle resolved photoelectron spectroscopy (ARPES) represents a powerful technique for studying the one-electron properties in lowdimensional materials. It measures the occupied component of the single-particle spectral function A(k, ω), thus providing direct insight into the fundamental many-body interactions of the system. The technique has the important advantage that it momentum resolves. Studies of momentum-resolved gaps and self-energies, as well as their temperature dependencies, can help in understanding the fundamental mechanisms responsible for producing a variety of phases in strongly correlated lowdimensional systems. As such, not only are the more exotic systems currently under investigation, but many "simple" systems are also being reinvestigated. Indeed, in recent studies, the effects of the electron-phonon coupling on single-particle states have been directly observed [1,2]. The change in a state's width and dispersion near the Fermi level provide a signature of the electron-phonon coupling. However, similar effects have been detected in some systems where such a correspondence cannot be established. For example, in the cuprate superconductor, Bi 2 Sr 2 CaCu 2 O 8+δ , a "kink" in the dispersion and a narrowing of the state, has been also detected [3]. However, in that system, the doping and temperature dependencies rule out the electron-phonon coupling as the mechanism and point towards a different type of coupling resulting in modifications of the single-particle spectrum [4].
In the present paper, we report a detailed ARPES study of low-energy electronic excitations in 2H-TaSe 2 . 2H-TaSe 2 undergoes a second-order transition to an incommensurate CDW at 122 K, followed by a first-order lock-in transition to a 3 × 3 commensurate CDW phase at 90 K [5]. The driving mechanism for the CDW transition is still under debate. The two most recent ARPES studies have provided alternative explanations: Liu et al [6] found the opening of a large gap in the extended saddle band region when the system entered the CDW state; Straub et al [7], in a study of 2H-NbSe 2 , concentrated on the nesting properties of the Fermi surface, and found large portions that, although not gapped, could be nested. In both studies, the corresponding "nesting vectors" cannot be easily related to the CDW wave vector.
In the present study we concentrate on the properties of the one-particle excitation spectrum and provide evidence of a possible collective mode that exists in the CDW state. This mode causes significant renormalization of the one-particle spectrum at low energies. Simultaneously, the one-particle scattering rates at low energies are greatly reduced in the CDW state, indicating a collapse of the phase space available for scattering. The mode may be attributed to the electron-hole pair creation in those regions that are gapped, or more precisely, to the scattering from fluctuations associated with the CDW order parameter. The observation of a mass or velocity renormalization in the ungapped region of the Fermi surface accompanying the formation of a gap elsewhere in the zone is very reminiscent of the behavior observed for the high Tc superconducting materials, as discussed above [3,4].
The experiment reported here was carried out on a high resolution photoemission facility based on undulator beamline U13UB at the National Synchrotron Light Source. This facility employs a Scienta SES-200 electron spectrometer which simultaneously collects a large energy (0.5 to 1 eV) and angular window (∼ 12 • ) of the -0.10 -0.05 0.00 0.05 photoelectrons. This reduces the time needed for data acquisition and ensures that the whole region of interest in k-space, is recorded under identical conditions of temperature and surface cleanliness. The combined instrumental energy resolution was set to ∼ 6 meV, small enough to make no significant contribution to the photoemission peak widths measured here. The angular resolution was better than ∼ 0.2 • , translating into a momentum resolution of ∼ 0.005Å −1 at the 15.2 eV photon energy used in the study. Samples, grown by a chemical reaction with iodine as a transport agent [8], were mounted on a liquid He cryostat and cleaved in situ in the UHV chamber with base pressure 3 × 10 −9 Pa. The temperature was measured using a silicon sensor mounted near the sample and was rechecked by fitting the Fermi edge, taking account of the full experimental energy resolution. Figure 1 shows the photoemission intensity, recorded in the CDW state at T = 34 K, as a function of binding energy and momentum along the line through the two-dimensional Brillouin zone indicated in the inset of the figure. The figure shows a band crossing the Fermi level at a point on the hole-like Fermi surface S C , centered at Γ [9]. This particular Fermi surface is preserved in the CDW transition with no gap forming, independent of k F [6,7]. The most remarkable feature in figure 1 is the "kink" in the band's dispersion, accompanied by a sharpening in the vicinity of the Fermi level. Also shown in the figure are cuts through the intensity at constant momenta or energy distribution curves (EDCs). In this energy range, the EDCs show a two-peaked structure, behavior that is characteristic of the interaction of the photo-hole with some excitation of the system with energy range limited approximately to the energy scale of the "kink" (see [1,2] and references therein). Such an interaction renormalizes the mass and lifetime of the photo-hole but conserves the total charge. The self-energy, Σ(k, ω), describes this interaction, the real part corresponding to the shift in energy and the imaginary part the scattering rate or inverse lifetime. Both components of the self energy may be extracted directly from an ARPES spectrum since the spectral intensity I(k, ω) is given by I 0 (k)A(k, ω)f (ω) where A(k, ω) represents the spectral function, I 0 (k) incorporates the dipole matrix elements, and f (ω) is the Fermi distribution function. As recently noted by LaShell et al [2], in the limit of a momentum independent self energy and matrix elements, the spectral intensity takes the simple form: where ǫ k is the non-interacting dispersion. The real and imaginary components of the self-energy, ReΣ(ω) and ImΣ(ω), may then be extracted directly from a momentum-distribution curve (MDC), the intensity as a function of momentum at constant binding energy. With this method, the fitting is possible without imposing any particular model for the interaction. We approximate the non-interacting dispersion with a second-order polynomial [10] that coincides with the measured dispersion at k = k F and at higher binding energies, close to the bottom of the band: ReΣ = 0 for ω = 0 and ω < −200 meV. Figure 2 shows several MDCs with corresponding fits. In contrast to the lineshapes in fig. 1(b) for EDCs, the lineshapes in figure 2 are approximately Lorentzian at low binding energies developing an asymmetry at higher binding energies. The latter asymmetry mostly reflects the quadratic term in the non-interacting dispersion. The advantage of using MDCs in the analysis is obvious in that the self-energies are more dependent on energy than on momentum.
The results of the fitting procedure, which produces pairs of ReΣ and ImΣ for every MDC are shown in Fig. 3 for several temperatures. We have also included ImΣ obtained by fitting EDCs when the latter have a Lorentzian lineshape. The real part of the self-energy is concentrated in the region of binding energies less than 150 meV. At the lowest temperature, it has a maximum at a binding energy of ∼ 65 meV, approximately coincident with the value corresponding to the sharp drop in ImΣ. Such behavior is indicative of the scattering of the photo-hole from some collective excitation or "mode" of the system. The striking similarity with the behavior recently observed in an ARPES study of the photo-hole interacting with phonons [1,2] would point to the electronphonon coupling as the source of this behavior. This would imply the presence of ∼ 70 meV phonons in the CDW state. However the highest calculated and measured phonon frequency is ∼ 40 meV [11]. The measured temperature dependence of the self-energy also argues against phonons. With increasing temperature, the peak in ReΣ loses its magnitude and the structure shifts to lower energies. At a temperature of 111 K, only a small peak is left at a binding energy of ∼30 meV and this survives in the normal state to at least 160 K. This peak may be of the same CDW origin, but may also be caused by conventional electron-phonon coupling, since it is within the range of the phonon spectrum.
At low temperatures the imaginary part of the selfenergy or scattering rate shows a sharp reduction for binding energies lower than 70 meV. As the temperature increases, this reduction becomes less pronounced. A more detailed temperature dependence for ImΣ(0) is shown in Fig. 4. The in-plane resistivity and the Drude scattering rate measured by Vescoli et al [12] are also shown. In a simple Drude-type model, the conductivity (the inverse of resistivity) in a 2-D system is proportional to the integral of k F l(k F ) over the Fermi surface, weighted by geometrical factors defined by the field direction. Here k F is the Fermi wave vector and l(k F ) = 1/∆k(k F ) = v 0 F (k F )/ImΣ(ω = 0, k F ) is the mean free path, v 0 F (k F ) being the bare Fermi velocity. The striking similarity between the scattering rates measured here and the resistivity indicates that this component of the Fermi surface plays an essential role in the transport. Indeed, similar behavior is found over the whole central Fermi surface, S C , while the sections centered at K points and flat saddle regions show much higher scattering rates and/or are gapped in the CDW state [6]. In addition to a significant zero-temperature offset [13], the single-particle scattering rate measured here has an approximately six times larger change over the same temperature interval than the Drude one. This is because transport currents are insensitive to small-angle scattering, whereas ARPES is sensitive to all scattering events.
The unusually large zero-temperature offset in the normal state resistivity measurements may be caused by conventional impurity/defect scattering, which usually adds a constant temperature-independent term to the normal state resistivity. However, for 2H-TaSe 2 all published resistivity curves [12,14] appear to scale in a similar fashion over the whole temperature range, indicating some form of intrinsic disorder in the normal state. As suggested by Vecsoli et al [12], this may reflect the presence of fluctuating incoherent CDW segments. To resolve this, it would be instructive to study in more detail the effect of intentionally introduced defects on the resistivity.
We have discussed the experimental observations in terms of scattering from some form of collective mode. It is also possible that the opening of the gap in the "saddle regions" with an associated reduction in the phase space available for scattering would be sufficient to explain the binding energy and temperature dependence of the selfenergy. However, the opening of the gap in the singleparticle spectrum implies a modification to the response function with the possible simultaneous appearance of a new collective "mode". The self-energy behaves then as if the hole was scattered from this mode. The two pictures are equivalent if electronic correlations dominate.
As pointed out by Vescoli et al [12], the in-plane optical response in 2H-TaSe 2 is very similar to that measured in high T C superconductors. In both systems one can resolve a Drude component and a mid-IR component in the gapped low temperature phases. As the Fermi surfaces in both systems are only partially gapped, it is tempting to connect the Drude component in the optical response to portions that are not gapped, while the mid-IR component seems to reflect the gapped regions. Whether the mid-IR structure itself points to the presence of the new mode is not clear. The presence of the well-known resonance in the spin response function of HTSCs shows that a mode with well-defined quantum numbers may indeed be formed. Recently, the strong connection between the commensurate resonance magnetic peak in neutron scattering [15] and the mid-IR optical structure in HTSCs has been noted [16]. Similarities in the optical response would then imply the possibility of a similar mode in the 2H-TaSe 2 . More detailed studies of the charge and spin response of the system may help to resolve the nature of this mode.
In summary we have shown that the single-particle self-energy in 2H-TaSe 2 shows significant changes with the opening of the CDW gap implying the existence of a new type of collective excitation, associated with the CDW. Indeed, the observations suggest that the photohole is scattering from fluctuations in the CDW state. We believe that the observed behavior warrants further theoretical investigation in view of the strong similarities with the behavior observed in HTSCs. The authors would like to acknowledge useful discussions with L. Forró, N. V. Muthukumar and A. Tsvelik. The BNL research was supported in part by the U.S. DOE under DE-AC02-98CH10886. The Boston University research was supported in part by the U.S. Department of Energy under DE-FG02-98ER45680. Experiments were undertaken at the NSLS, which is supported by the U.S. DOE, Divisions of Materials and Chemical Sciences.