Angle-resolved photoemission spectroscopy study of a system with a double charge density wave transition: ErTe3

The electronic structures of ${\mathrm{ErTe}}₃$, having double charge density wave (CDW) transitions, have been investigated by performing polarization- and temperature ($T$)-dependent angle-resolved photoemission spectroscopy (ARPES) and Er $4d\ensuremath{\rightarrow}4f$ resonant PES measurements for high-quality single crystals. It is found that Er $4f$ electrons do not contribute directly to CDW formation. The shadow Fermi surfaces (FSs) are clearly observed, arising from band folding due to the interlayer interaction. Twofold symmetric FS, but with weak FS reconstruction, is observed in the CDW phase of ${\mathrm{ErTe}}₃$, which is similar to that of ${\mathrm{PrTe}}₃$ having the CDW modulation vector $Q\ensuremath{\approx}5/7\phantom{\rule{4pt}{0ex}}{c}^*\ensuremath{\approx}5/7\phantom{\rule{4pt}{0ex}}{a}^*$. Very good agreement is found between the constant energy maps and ARPES measured in the CDW phase and the density functional theory band calculation for the non-CDW phase, implying very weak and only partial CDW-induced FS reconstruction in ${\mathrm{ErTe}}₃$. Very weak and similar circular dichroism is observed along different symmetry lines in both FS and ARPES, suggesting weak chiral orbital and spin polarizations in the Te $5p$ orbitals. $T$-dependent FS and ARPES measurements reveal closing of the CDW gap on heating but no clear changes across ${T}_{\mathrm{CDW}2}$ and ${T}_{\mathrm{CDW}1}$, supporting the very weak CDW distortion in ${\mathrm{ErTe}}₃$. The origin of the very weak CDW reconstruction in ${\mathrm{ErTe}}₃$ is likely to be the small ionic sizes of Er ions and the concomitant small volume that give rise to the imperfect FS nesting and the reduced density of states at the Fermi level. The very weak FS reconstruction at the first CDW transition along ${c}^*$ is considered to be a reason why there exists a second CDW transition further along ${a}^*$, which elucidates the observed double CDW transitions in ${\mathrm{ErTe}}₃$.