Quantum Transport Evidence for the Three-Dimensional Dirac Semimetal Phase in ${\mathrm{Cd}}_3{\mathrm{As}}_2$

We report the quantum transport properties of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystals in a magnetic field. A large linear quantum magnetoresistance is observed near room temperature. With decreasing temperature, the Shubnikov—de Haas oscillations appear in both the longitudinal resistance $R_{xx}$ and the transverse Hall resistance $R_{xy}$. From the strong oscillatory component $\mathrm{\Delta }{R}_{xx}$, a linear dependence of the Landau index $n$ on $1/B$ is obtained, and it gives an $n$-axis intercept between $1/2$ and $5/8$. This clearly reveals a nontrivial $\pi$ Berry’s phase, which is a distinguished feature of Dirac fermions. Our quantum transport results provide bulk evidence for the existence of a three-dimensional Dirac semimetal phase in ${\mathrm{Cd}}_3{\mathrm{As}}_2$.

Figure 1

(a) The longitudinal resistivity of a ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystal in zero magnetic field, with current in the (112) plane. A typical x-ray rocking curve of the (224) Bragg peak is shown in the inset. (b) The Hall resistance $R_{xy}$ at 200, 100, 50, and 1.5 K. There are clear oscillations of $R_{xy}$ at 1.5 K, as seen in the inset. (c) The Shubinikov—de Haas oscillations of longitudinal magnetoresistance (MR) at various temperatures, with the field perpendicular to the (112) plane. At 280 K, the MR is roughly linear without saturation, as high as 200% at $B=14.5\mathrm{T}$. At 1.5 K, the oscillations appear at a field as low as 2 T, reflecting the high mobility of charge carriers in ${\mathrm{Cd}}_3{\mathrm{As}}_2$.

Figure 2

(a) The oscillatory component $\mathrm{\Delta }{R}_{xx}$, extracted from $R_{xx}$ by subtracting a smooth background, as a function of $1/B$ at various temperatures. A single oscillation frequency $F=58.3\mathrm{T}$ is identified from fast Fourier transform spectra. (b) The temperature dependence of the relative amplitude of $\mathrm{\Delta }{R}_{xx}$ for the sixth Landau level. The solid line is a fit to the Lifshitz-Kosevich formula, from which we get the cyclotron effective mass $m^{*}\approx 0.044m_0$ and Fermi velocity $v_F\approx 1.1\times {10}^6\mathrm{m}/\mathrm{s}$.

Figure 3

(a) The high-field oscillatory components $\mathrm{\Delta }{R}_{xx}$ and $\mathrm{\Delta }{R}_{xy}$ at 1.5 K. The $\mathrm{\Delta }{R}_{xy}$ oscillations are phase shifted approximately by 90° with respect to the $\mathrm{\Delta }{R}_{xx}$ oscillations for the low Landau levels. No Landau level splitting is observed in our field range. (b) Landau index $n$ plotted against $1/B$. The closed circles denote the integer index ($\mathrm{\Delta }{R}_{xx}$ valley), and the open circles indicate the half integer index ($\mathrm{\Delta }{R}_{xx}$ peak). The index plot can be linearly fitted, giving the intercept $0.58\pm 0.01$. The measurements of another single crystal labeled as sample $B$ (see the Supplemental Material [39]) give a similar intercept $0.56\pm 0.03$. From the inset, both intercepts of $\mathrm{\Delta }{R}_{xx}$ lie between $\beta$ and $\beta +1/8(\beta =1/2)$, which is strong evidence for a nontrivial $\pi$ Berry’s phase of 3D Dirac fermions in ${\mathrm{Cd}}_3{\mathrm{As}}_2$.