Anisotropic Fermi Surface and Quantum Limit Transport in High Mobility Three-Dimensional Dirac Semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$

Three-dimensional topological Dirac semimetals have a linear dispersion in 3D momentum space and are viewed as the 3D analogues of graphene. Here, we report angle-dependent magnetotransport on the newly revealed ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystals and clearly show how the Fermi surface evolves with crystallographic orientations. Remarkably, when the magnetic field lies in the [112] or $[44\overline{1}]$ axis, magnetoresistance oscillations with only single period are present. However, the oscillation shows double periods when the field is applied along the $[1\overline{\mathbf{1}}0]$ direction. Moreover, aligning the magnetic field at certain directions also gives rise to double period oscillations. We attribute the observed anomalous oscillation behavior to the sophisticated geometry of Fermi surface and illustrate a complete 3D Fermi surface with two nested anisotropic ellipsoids around the Dirac points. Additionally, a submillimeter mean-free path at 6 K is found in ${\mathrm{Cd}}_3{\mathrm{As}}_2$ crystals, indicating ballistic transport in this material. By measuring the magnetoresistance up to 60 T, we reach the quantum limit ($n=1$ Landau level) at about 43 T. These results improve the knowledge of the Dirac semimetal material ${\mathrm{Cd}}_3{\mathrm{As}}_2$ and also pave the way for proposing new electronic applications based on 3D Dirac materials.

Popular Summary

Dirac semimetals are a new class of topological materials that resemble three-dimensional analogs of graphene with a linear energy dispersion in three-dimensional momentum space. Owing to recent in-depth investigations of topological materials, the Dirac semimetal phase has been realized in solids such as single-crystal ${\mathrm{Cd}}_3{\mathrm{As}}_2$. Aside from the vigorous characterization method of photoemission spectroscopy, transport measurements are indispensable for revealing many exotic emergent physical phenomena around the Fermi surface where electrons can have ultrahigh mobility. Here, we systematically study the angular-dependent magnetotransport in single-crystal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ at low temperatures and high magnetic fields of up to 60 T.

We employ a needlelike high-quality ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystal in our experiments. We analyze Shubnikov–de Haas oscillations—changes in conductivity—in three magnetic field directions, and we surprisingly find anomalous two-period Shubnikov–de Haas oscillations when the magnetic field is oriented in particular directions. We attribute our observations to the sophisticated geometry of the Fermi surface, which possesses two nested anisotropic ellipsoids around the Dirac points. Moreover, when we track the magnetoresistance up to 60 T, the ${\mathrm{Cd}}_3{\mathrm{As}}_2$ crystal reaches the quantum limit (corresponding to the lowest Landau level) at approximately 43 T and demonstrates quantum linear magnetoresistance above 43 T as well as Zeeman splitting at high magnetic fields. Additionally, a submillimeter mean-free path at 6 K is revealed, which indicates a macroscopic ballistic transport region in this material.

We expect that our results will pave the way for detecting new topological phases such as topological superconductivity or for proposing potential applications in electronics based on three-dimensional Dirac materials.

Figure 1

Sample structure of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystal. (a) HAADF STEM image of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystal. Scale bar represents 1 nm. Inset shows the crystal XRD image. (b) Schematic structure for the angular-dependent magnetotransport measurements in ${\mathrm{Cd}}_3{\mathrm{As}}_2$ system. Sample is rotated in $(1\overline{\mathbf{1}}0)$ plane and (112) plane, characterized by the angle $\theta$ and $\phi$, respectively. The sample size is not to scale. (c) Resistivity of sample 1 as a function of temperature. The inset shows the resistivity falling to quite low value about $11.6\mathrm{n}\mathrm{\Omega }\mathrm{cm}$ at 6 K and then reaching zero resistivity within instrumental resolution. (d) $\rho$ ($T$) behavior of sample 2. The inset shows an optical image of the measured ${\mathrm{Cd}}_3{\mathrm{As}}_2$ sample. Standard four-probe method is used to measure the transport property.

Figure 2

SdH oscillations for ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystal (sample 2) in different magnetic field directions, along the [112], $[44\overline{\mathbf{1}}]$, and $[1\overline{\mathbf{1}}0]$ axes ($B_{[112]}$, $B_{[44\overline{\mathbf{1}}]}$, and $B_{[1\overline{\mathbf{1}}0]}$). (a)–(c) Magnetoresistivity measured in the perpendicular field $B_{[112]}$, the parallel fields $B_{[44\overline{\mathbf{1}}]}$, and $B_{[1\overline{\mathbf{1}}0]}$ at different temperatures, respectively. (d),(e) The oscillatory component of $\mathrm{\Delta }\rho$ extracted from $\rho$ by subtracting a fourth-polynomial background, as a function of $1/B$ at various temperatures in $B_{[112]}$ and $B_{[44\overline{\mathbf{1}}]}$ directions. (f) The LK theory fitting to the $\mathrm{\Delta }\rho$ ($B$) curve measured at $T=2\mathrm{K}$ in the parallel field $B_{[1\overline{\mathbf{1}}0]}$ with two frequencies (red solid curve). Inset shows the FFT analysis with two frequencies in $B_{[1\overline{\mathbf{1}}0]}$ direction.

Figure 3

Landau level index plots for ${\mathrm{Cd}}_3{\mathrm{As}}_2$ single crystal (sample 2) in $B_{[112]}$ and $B_{[44\overline{\mathbf{1}}]}$ directions. (a) Landau level index plot of the Fermi surface in the perpendicular field $B_{[112]}$. The maxima of $\mathrm{\Delta }\rho$ are assigned to be the integer indices (solid circles) while the minima of $\mathrm{\Delta }\rho$ are plotted by open circles as half-integer indices. The intercept is close to 0.3. (b) Landau level plot for oscillations in $\mathrm{\Delta }\rho$ measured at 2 K in the parallel field $B_{[44\overline{\mathbf{1}}]}$. Solid line is a linear fitting to the data, giving the intercept about 0.2. (c) SdH oscillations measured in the pulsed high magnetic field in the perpendicular field $B_{[112]}$. (d) The index plot of $1/B$ versus $n$ measured in pulsed high magnetic field. The intercept is about 0.38.

Figure 4

Angular dependence of SdH oscillations at different magnetic field directions (sample 2). (a) SdH oscillations in $\mathrm{\Delta }\rho$ for various magnetic field angles from $B_{[112]}$ ($\theta =0\mathrm{deg}$, $B$ in the [112] direction) to $B_{[44\overline{\mathbf{1}}]}$ ($\theta =90\mathrm{deg}$,$B$ in the $[44\overline{\mathbf{1}}]$ direction). (b) SdH oscillations rotate from $B_{[44\overline{\mathbf{1}}]}$ ($\phi =0\mathrm{deg}$,$B$ in the $[44\overline{\mathbf{1}}]$ direction) to $B_{[1\overline{\mathbf{1}}0]}$ ($\phi =90\mathrm{deg}$,$B$ in the $[1\overline{\mathbf{1}}0]$ direction). Figure 1 depicts the definition of $\theta$ and $\phi$.

Figure 5

Theoretical analysis of 3D nested anisotropic Fermi surface in ${\mathrm{Cd}}_3{\mathrm{As}}_2$. Panels (a)–(c) show the largest cross section of Fermi surface versus the magnetic field orientation. The Fermi surface is two nested anisotropic ellipsoids. Panel (d) shows the schematic plot of the Fermi surface for $B_{[1\overline{\mathbf{1}}0]}$ direction with an overlapping region. The figures are not drawn to scale.

Figure 6

High magnetic field transport measurement of Sample 3 up to 60 T. (a) Magnetoresistivity measured in the perpendicular field $B_{[112]}$ at different temperatures at $T=4.2\mathrm{K}$ up to 60 T. Zeeman splitting features can be observed at higher magnetic field. Inset shows the SdH oscillations after subtracting the polynomial background. (b) Landau level index plot. The $n=1$ Landau Level is reached at $B=43\mathrm{T}$. Quantum linear magnetoresistance is observed at the field higher than 43 T.