Interplay between band crossing and charge density wave instabilities

Our measurements of the Hall coefficient in rare-earth tritelluride compounds reveal a strong hysteresis between cooling and warming in the low-temperature range where a second unidirectional charge density wave (CDW) occurs. We show that this effect results from the interplay between two instabilities: band crossing of the Te $p_x$ and $p_y$ orbitals at the Fermi level and CDW, which have a close energy gain and compete. Calculation of the electron susceptibility at the CDW wave vector with and without band anticrossing reconstruction of the electron spectrum yields a satisfactory estimation of the temperature range of the hysteresis in Hall effect measurements.

Figure 1

Hall constant of (a) ${\mathrm{ErTe}}_3$, (b) ${\mathrm{HoTe}}_3$, and (c) ${\mathrm{TbTe}}_3$ as a function of temperature. Red circles correspond to cooling, and blue squares correspond to warming.

Figure 2

Schematic representation of the Fermi surface (FS) in ${\mathrm{RTe}}_3$. Main figure: The full FS with the ${\mathrm{CDW}}_1$-gapped region shaded by gray. In the crossing region, highlighted by a solid yellow circle, two FS reconstructions are possible: with band anticrossing shown in the upper right inset, and with an energy gap due to ${\mathrm{CDW}}_2$ shaded by gray in the lower right inset.

Figure 3

Calculated electron susceptibility. (a) The electron susceptibility contributions without (solid blue and green lines) and with the band crossing reconstruction (dashed red and black lines). The upper two curves (blue and red) show the calculated “diagonal” intraband contributions $\chi$, while the two lower curves (green and black) show “off-diagonal” interband contributions $\mathrm{\Delta }\chi$ to susceptibility. (b) Total susceptibility ${\chi }_{\text{total}}=\chi +\mathrm{\Delta }\chi$ as a function of wave vector $Q_x$ near its maximum without (solid blue line) and with the band crossing reconstruction (dashed red line). (c) The temperature dependence of maximal total susceptibility without (solid blue line) and with the band crossing reconstruction (dashed red line).