Fermi Surface Evolution Across Multiple Charge Density Wave Transitions in ErTe3 Page: 4 of 4
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transitions. The large gaps observed at low temperatures
for this family allow us to observe the gap opening despite
thermal broadening effects. Fig. 3a-c show the FS data
taken at different temperatures for one side of the inner
FS and Fig. 3d-g show the temperature dependence of
p,/pz bands near the large and small gaps with a CDW
and without. At T 200 K only one gap is evident, while
at T 300 K the inner FS square is fully closed as ex-
pected from a structure unmodulated by any CDW [17].
To track the temperature evolution of the leading edge
gap, the spectra were first divided by the temperature
dependent Fermi-Dirac function convoluted with an en-
ergy resolution function [21]. Such a procedure allows the
determination of the center of the energy gap ensuring
accurate measurements of gap values. In addition, since
the center of the energy gap is observed below EF, CDW
q-vectors used in the TB model can be determined di-
rectly from the data resulting in c* - qcDW1 ~ 0.70(0)c*
and a* - qcDW2 ~ 0.68(5)a*. The CDW wave vectors
determined from ARPES are in excellent agreement with
the lattice modulation vectors observed in x-ray data [15].
The leading edge gap was then determined by fitting mo-
mentum distribution curve peaks with Lorentz functions
and tracking the point of inflection in the fitted band
dispersion after denoising via wavelet shrinkage. Instead
of tracking the gaps at k= 0 and kz 0, temperature
dependent data were taken at k-points where the gap
maxima with no FS intensity are observed. Fig. 3h sum-
marizes the temperature dependent data showing both
gaps closing. A mean-field order parameter curve scaled
to the maximum observed gap is also plotted for compar-
ison. The smaller A2 and larger A1 gaps are observed to
close at Tc2 ~ 160 K and Tci ~ 280 K, respectively, in
good agreement with the transport and x-ray data [15].
The development of the gaps appears to be second order
within the experimental uncertainty as no hysteresis has
been observed. While the closing of the gaps is suggestive
of a mean-field type behavior, A1(T) is somewhat sup-
pressed from the mean-field curve. In addition, it should
be noted that 2A1/kBTCl is ~ 2(2A2/kBTC2) while the
area of the FS gapped by A1 is ~ 3 times the area gapped
by N2.The observed q-vectors, the observation of CDW gaps
below the Fermi-level and the use of an electron-phonon
coupled model Hamiltonian may suggest the FS plays
little role in the formation of the CDWs [11]. However,
caution is advised as the model FS in Fig. 2a is not the
one electron eigenvalues resulting from the mixing of the
different bands. To accurately model the FS, the calcu-
lated spectral weight (p, and pz eigenvectors) had to be
used. The FS in Fig. 3c is also a poor match for the
model FS eigenvalues with no CDWs because the bare
bands folded back into the reduced 3D Brillouin zone are
too weak to be observed. Lowering of the ground state
energy is achieved by gapping the FS and the model spec-
tral weight suggest the shape of the FS could still play a
significant role in the CDW formation.
Both CDWs exist within the same Te plane [15], thus
both CDWs modulate the positions of the same Te atoms.
Hence, ErTe3 offers a unique opportunity to directly
study the crossover from quasi-1D to quasi-2D behav-
ior. Upon initial inspection, each CDW appears uni-
directional and completely decoupled. However, suppres-
sion of A1 (T) from the mean-field curve, the discrepancy
between 2A1/kBTC2 and 2A2/kBTC2 still need to be ex-
plained. Such discrepancies may arise due to the inter-
play between the two many body states. Subtle com-
plexities arising from the crystal structure could inter-
fere with the delicate balance between the lattice and
electronic energies, allowing for interactions between the
two CDWs to arise. More experimental and theoretical
work is required to explore such possibilities.
Acknowledgments
We thank S. Kivelson, H. Yao, E. -A. Kim, J. Laverock
and S. B. Dugdale for insightful discussions regarding our
data and model. SSRL is operated by the DOE Office of
Basic Energy Science, Division of Chemical Science and
Material Science. This work is supported by DOE Office
of Science, Division of Materials Sciences, with contract
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Moore, R. G. Fermi Surface Evolution Across Multiple Charge Density Wave Transitions in ErTe3, article, May 3, 2010; United States. (https://digital.library.unt.edu/ark:/67531/metadc928402/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.