Aharonov–Bohm oscillations in Dirac semimetal Cd₃As₂ nanowires

Abstract

Three-dimensional Dirac semimetals, three-dimensional analogues of graphene, are unusual quantum materials with massless Dirac fermions, which can be further converted to Weyl fermions by breaking time reversal or inversion symmetry. Topological surface states with Fermi arcs are predicted on the surface and have been observed by angle-resolved photoemission spectroscopy experiments. Although the exotic transport properties of the bulk Dirac cones have been demonstrated, it is still a challenge to reveal the surface states via transport measurements due to the highly conductive bulk states. Here, we show Aharonov–Bohm oscillations in individual single-crystal Cd₃As₂ nanowires with low carrier concentration and large surface-to-volume ratio, providing transport evidence of the surface state in three-dimensional Dirac semimetals. Moreover, the quantum transport can be modulated by tuning the Fermi level using a gate voltage, enabling a deeper understanding of the rich physics residing in Dirac semimetals.

Introduction

The Dirac fermions in graphene and topological insulators are confined in a two-dimensional plane, while in a three-dimensional (3D) Dirac semimetal the Dirac fermions are extended to the 3D space^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,24,25}, and the oscillating period is described by the Φ/Φ₀, where Φ is the magnetic flux enclosed by the path of the surface carriers and Φ₀=h/e. These quantum oscillations have been observed in topological insulator nanoribbons and nanowires, which are still called as A–B oscillations in the recent literatures^26,27,28. Particularly, the helical surface states in topological insulator accumulate an additional π Berry phase after travelling a closed trajectory, resulting in the conductance peaks are situated at the magnetic flux of (refs 26, 27, 28), which is very distinct from ordinary h/e oscillations in normal metal rings²⁹.

Here we report the A–B oscillations in individual Cd₃As₂ nanowires to demonstrate the transport properties of the surface states in Dirac semimetals. A π A–B effect that the conductance oscillations peak at odd integers of h/2e with a period of h/e is observed, providing transport evidence of the topological surface states of Cd₃As₂ nanowires. The A–B oscillations are tunable by altering the Fermi level of the nanowire via gate voltage, giving deeper insight of the 3D Dirac semimetal with Dirac fermion bulk states and Fermi arc surface states.

Results

Characterizations

The Cd₃As₂ nanowires were synthesized via chemical vapour deposition method, which are with high aspect ratio and right stoichiometry (Supplementary Fig. 1). The Cd₃As₂ nanowires are of single crystalline nature and grown along the [112] direction, as shown by the high-resolution transmission electron microscopy image in Fig. 1a. The surface of individual nanowires is usually covered by a thin amorphous layer ∼5 nm forming a core-cell structure (Supplementary Fig. 2), which may help to maintain the clean Cd₃As₂ surface immunized from the environment³⁰.

Figure 1: Magnetotransport of a nanowire with diameter ∼115 nm (Device 1).

(a) High-resolution transmission electron microscopy image of a typical nanowire indicates <112> growth direction with interplanar space ∼0.73 nm. Scale bar, 5 nm. (b) Schematic diagram of the four-terminal device with applied magnetic field aligned with the length. (c) Resistance as a function of magnetic field at different temperatures from 1.5 to 20 K. (d) The oscillations in conductance as a function of magnetic field after subtracting background. (e) FFT spectrums of the conductance oscillations. (f) Plot of the temperature dependence of the FFT peak amplitude. The dashed line indicates the fitting by the T⁻¹ dependence.

The schematic representation of the device and measurement configuration is shown in Fig. 1b. The temperature-dependent resistance manifests semiconducting-like behaviours (Supplementary Fig. 3), similar to other 3D Dirac semimetal materials, such as Na₃Bi, and is attributed to the low carrier density^{Device fabrication}

The Cd₃As₂ nanowire devices were fabricated on a Si substrate with 285 nm SiO₂ layer. To make the nanowire direction can be parallel with the direction of the magnetic field, microstrips were first prefabricated on a SiO₂/Si square substrate as marks, which are parallel to one side of the square substrate. Then, the nanowire was transferred from the as-grown substrate to the SiO₂/Si square substrate, and the nanowire direction was aligned parallel to the prefabricated marks by a micromanipulator. The individual nanowire devices were fabricated using standard electron beam lithography techniques. To form ohmic contacts between Cd₃As₂ nanowires and electrodes, the amorphous layer of the nanowire was removed in situ by Ar⁺ etching treatment in the metal deposition chamber. Then, ∼150-nm-thick Au electrodes were deposited. The linear current–voltage curve (Supplementary Fig. 9) indicates the Ohmic contacts between the nanowire and the electrodes.

Transport measurements

The SiO₂/Si square substrate with the Cd₃As₂ nanowire devices was mounted onto the sample holder in an Oxford commercial variable temperature insert to make the nanowire parallel to the direction of the magnetic field. The sample holder can be rotated continuously by an electric motor to change the angle between E and B. The electrical signals were measured using a four-terminal method by Stanford SR830 lock-in amplifiers at frequency of 17.7 Hz.