Existence of electron and hole pockets and partial gap opening in the correlated semimetal ${\mathbf{Ca}}_{\mathbf{3}}{\mathbf{Ru}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}$

The electronic band structure of correlated ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ featuring an antiferromagnetic (AFM) as well as a structural transition has been determined theoretically at high temperatures, which has led to the understanding of the remarkable properties of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, such as the bulk spin-valve effects. However, its band structure and Fermi surface (FS) below the structural transition have not been resolved, even though a FS consisting of electron pockets was found experimentally. Here we report magnetoelectrical transport and thermoelectric measurements with the electric current and temperature gradient directed along the $a$ and $b$ axes, respectively, of an untwined single crystal of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. The thermopowers obtained along the two crystal axes were found to show opposite signs at low temperatures, demonstrating the presence of both electron and hole pockets on the FS. In addition, how the FS evolves across $T^{*}=30\mathrm{K}$ at which a distinct transition from coherent to incoherent behavior occurs was also inferred: the Hall and Nernst coefficient results suggest a temperature- and momentum-dependent partial gap opening in ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ below the structural transition with a possible Lifshitz transition occurring at $T^{*}$. The experimental demonstration of a correlated semimetal ground state in ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ calls for further theoretical studies of this remarkable material.

Figure 1

(a) Crystal structure of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. The red, green, and blue balls stand for Ca, Ru, and oxygen, respectively. (b) The top view of the unit cell with Ca cations neglected. (c) Zero-field resistivity of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ along the $b$ axis as a function of temperature. (d) Temperature dependence of normalized resistivity along the $a$ and $b$ axes. (e) Field dependence of the $b$-axis direction resistivity at 2 K for a magnetic field along the $c$ axis. (f) Shubnikov–de Haas oscillations (SdHOs) at 2 K along the $a$ and $b$ axes with the magnetic field along the $c$ axis obtained from $\rho \left(H\right)$ by subtracting the smooth background.

Figure 2

(a) Zero-field thermopower of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ along the $a$ and $b$ axes as a function of temperature. The inset's schematics show a low-temperature Fermi-surface schematic adopted from [22] and the direction of the thermal gradient in the $k$ space. (b) The temperature dependence of the thermopower anisotropy, defined as $\mathrm{\Delta }S=S_a-S_b$.

Figure 3

(a) Temperature dependence of the Hall coefficient in ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. The inset shows the field dependence of Hall resistivity at various temperatures. (b) Temperature dependence of the Nernst signal $e_y$ in ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. The inset shows the field dependence of the Nernst signal. The thermal gradient is along the $b$ axis.

Figure 4

The temperature dependence of thermal Hall $\tan {\theta }_{\alpha }$ and Hall angle $\tan {\theta }_H$ at 5 T. The inset: a schematic showing a possible Lifshitz transition driven by the shift of chemical potential. Below the structural transition, the band structure of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ consists of an electron and hole band at $M$ and $M^{\prime }$ points and another electronlike band. The chemical potential decreases with lowering temperature and misses the large electronlike band when cooling below $T^{*}$.