Probing the Fermi surface of three-dimensional Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ through the de Haas–van Alphen technique

We have observed Shubnikov–de Haas and de Haas–van Alphen effects in the single crystals of the three-dimensional Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ up to 50 K, traceable at fields as low as 2 and 1 T, respectively. The values of the Fermi wave vector, the Fermi velocity, and the effective cyclotron mass of the charge carrier, calculated from both techniques, are close to each other and match well with earlier reports. However, the de Haas–van Alphen effect clearly reflects the existence of two different Fermi surface cross sections along certain directions and a nontrivial Berry's phase, which is the signature of a three-dimensional Dirac fermion in ${\mathrm{Cd}}_3{\mathrm{As}}_2$.

Figure 1

X-ray diffraction pattern of powdered single crystals of ${\mathrm{Cd}}_3{\mathrm{As}}_2$. Black, experimental data; red, the calculated pattern; blue, the difference between experimental and calculated intensities; green, the Bragg positions.

Figure 2

(a) Temperature dependence of the resistivity of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ crystal. (b) Magnetic field dependence of magnetoresistance (MR) at various temperatures when the field was applied along the [100] direction. The inset shows the temperature dependence of MR at a field of 9 T.

Figure 3

(a) The oscillatory component $\Delta R_{xx}$ of MR (after subtracting a smooth background) as a function of 1/$B$ at various temperatures with magnetic field along the [100] direction; the inset shows the oscillation frequency after fast Fourier transform. (b) $\Delta R_{xx}$ for magnetic field along the [$02\overline{1}]$ direction; the inset shows the corresponding frequency.

Figure 4

(a) Magnetic field (along the [$02\overline{1}]$ direction) dependence of the diamagnetic moment at temperatures of 2 and 20 K. (b) Oscillating part of the susceptibility $\Delta \chi =d\left(M\right)/dB$ vs 1/$B$; de Haas–van Alphen (dHvA) effect. The inset shows the oscillation frequency after the fast Fourier transform of the dHvA oscillations.

Figure 5

Oscillating part of the susceptibility $\Delta \chi =d\left(M\right)/dB$ vs 1/$B$ (dHvA effect) for magnetic field along the [100] direction; the inset shows oscillation frequency at 55.20 T after the fast Fourier transform is found from the dHvA effect.

Figure 6

(a) Landau index $n$ plotted against 1/$B$ (solid circles denote the peak position) from the SdH oscillation (from the linear extrapolation of the fitted line, the intercept for $B\parallel$ [100] is 0.32 and for $B\parallel$ [$02\overline{1}]$ is 0.20). (b) Landau index $n+1/4$ plotted against 1/$B$ (solid circles denote the peak position) from the dHvA oscillation (intercept at 0.23 and 0.35 for two parallel lines). (c) The quantum oscillations of susceptibility $\Delta \chi (1/B)$ and of resistance $\Delta R(1/B)$ at 10 K. (d) Temperature dependence of the relative amplitude of quantum oscillation for the ninth Landau level, where $Ra$ and $Rb$ are the oscillation amplitudes in the SdH oscillation for $B\parallel$ [100] and $B\parallel \left[02\overline{1}\right]$, respectively, and $m$ corresponds to the oscillation in susceptibility. The solid line is a fit to the Lifshitz-Kosevich formula [Eq. (1)].

Figure 7

Magnetoresistance of a ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystal with current along the [012] direction and the magnetic field applied along the [100] direction.

Figure 8

Temperature dependence of the thermoelectric power of a ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystal.

Figure 9

Oscillating part of magnetization $▵m$ [after subtracting a smooth background] vs 1/$B$ (dHvA effect) for magnetic field along the [012] direction; the inset shows the frequency of oscillation after the fast Fourier transform is found from the dHvA effect.

Figure 10

The Landau index $n+1/4$ plotted against 1/$B$ (solid circles denote the peak position) from the dHvA oscillation for magnetic field along the [100] direction (intercept at 0.18).