Fermi surface gapping in the Dirac material ${\mathrm{Ca}}_{1-x}{\mathrm{Na}}_x{\mathrm{MnBi}}_2$

The newly designed $A{\mathrm{MnBi}}_2$ ($A=\text{alkaline}$ as well as rare-earth atom) materials based on quasi-two-dimensional bismuth layers provide a suitable playground to address the physics of Dirac fermions, in connection with magnetism and structural changes. Here, we perform an optical investigation as a function of temperature of ${\mathrm{Ca}}_{1-x}{\mathrm{Na}}_x{\mathrm{MnBi}}_2$, which reveals a vestigial linear frequency-dependent behavior of the optical conductivity in the midinfrared, ascribed to electronic interband transitions involving Dirac bands. Furthermore, we uncover optical signatures for a partial gapping of the Fermi surface, for energy scales up to 0.2 eV, at the onset of the spin reorientation transition which also manifests as an anomaly in the dc transport data. This may reveal the inclination towards a Fermi surface instability in topological materials, possibly related to a density-wave order.

Figure 1

Optical reflectivity $R\left(\omega \right)$ of selected ${\mathrm{Ca}}_{1-x}{\mathrm{Na}}_x{\mathrm{MnBi}}_2$ compositions at 300 K, $T_s$, and 10 K, emphasizing its $T$ dependence in the MIR range and highlighting the $R\left(\omega \right)$ plasma edge (vertical arrows at the plasma edge onset). The $R\left(\omega \right)$ curves for each doping are shifted vertically for clarity, and their axis covers the same interval everywhere. The inset shows $\rho \left(T\right)$ normalized at 300 K for the measured compositions. The thin dotted lines mark $T_s$ (see text).

Figure 2

Temperature dependence of the real part ${\sigma }_1\left(\omega \right)$ of the optical conductivity of ${\mathrm{Ca}}_{1-x}{\mathrm{Na}}_x{\mathrm{MnBi}}_2$, highlighting the excitation spectrum at FIR and MIR frequencies. The inset in (a) displays $\mathrm{\Delta }{\sigma }_1\left(\omega \right)$ at $T_s$, which underscores the ${\sigma }_1\left(\omega \right)\sim \omega$ behavior after removing its metallic intraband contribution (thin dashed line in the main panel for $x=0$), obtained by adding two Drude terms. The ${\sigma }_1\left(\omega \right)\sim \omega$ trend is emphasized in (b) and (c) for data at $T_s$ (dotted lines), as well. The inset in (c) displays ${\sigma }_1\left(\omega \right)$ at 300 K for all investigated Na doping above 3000 and up to $2.5\times {10}^4{\mathrm{cm}}^{-1}$. The blue dashed lines across (b) and (c) emphasize the split into two peaks of the MIR absorption at 10 K (i.e., $<T_s$) upon increasing $x$.

Figure 3

The integrated spectral weight (SW) after Eq. (1), normalized by the same quantity at $T_s$, is shown at $T<T_s$ and as a function of the cutoff frequency ${\omega }_c$. The insets show $\text{SW}({\omega }_c;T)$ at 300 K, $T_s$, and 10 K. The horizontal thick gray dashed line in each panel represents the estimated FS gapping from the $\rho \left(T\right)$ data (see text) [27].