Molecular beam epitaxy of three-dimensionally thick Dirac semimetal Cd3As2 films

TL;DR

This paper reports the successful growth of high-mobility, three-dimensional thick Cd3As2 films via molecular beam epitaxy, revealing unique quantum transport phenomena including Hall plateau-like structures and unconventional magnetic orbits.

Contribution

It introduces a method to produce high-quality 3D Cd3As2 films with low carrier density and high mobility, enabling new insights into their quantum transport properties.

Findings

Achieved highest electron mobility of 3×10^4 cm^2/Vs in 3D Cd3As2 films.

Observed Hall plateau-like structures in thick films despite their 3D nature.

Detected unconventional magnetic orbits distinct from semiclassical Weyl-orbit predictions.

Abstract

Rapid progress of quantum transport study in topological Dirac semimetal, including observations of quantum Hall effect in two-dimensional (2D) Cd$_{\mathrm{3}}$As$_{\mathrm{2}}$ samples, has uncovered even more interesting quantum transport properties in high-quality and three-dimensional (3D) samples. However, such 3D Cd$_{\mathrm{3}}$As$_{\mathrm{2}}$ films with low carrier density and high electron mobility have been hardly obtained. Here we report the growth and characterization of 3D thick Cd$_{\mathrm{3}}$As$_{\mathrm{2}}$ films adopting molecular beam epitaxy. The highest electron mobility ($\mu$ = 3 $\times$ 10$^{4}$ cm$^{2}$/Vs) among the reported film samples has been achieved at a low carrier density ($\textit{n} = 5$ $\times$ 10$^{16}$ cm$^{-3}$). In the magnetotransport measurement, Hall plateau-like structures are commonly observed in spite of the 3D thick films ($\textit{t} = 120$ nm). On the other hand, field angle dependence of the plateau-like structures and corresponding Shubunikov-de Haas oscillations rather shows a 3D feature, suggesting the appearance of unconventional magnetic orbit, also distinct from the one described by the semiclassical Weyl-orbit equation.

Equations

$$\frac{1}{B_n}=\frac{e}{S_k}\left[2\pi (n+\gamma )\cos \theta -t(k_{\mathrm{W}\parallel }(\theta )+2k_{\mathrm{F}\parallel }(\theta ))\right]$$

Full text

Topological Dirac semimetal (DSM) is characterized by surface Fermi arcs and bulk Dirac dispersions along any directions in three-dimensional (3D) momentum space YoungPRL2012 ; WangPRB2012 ; WangPRB2013 ; YangNatCommun2014 ; ArmitageRevModPhys2018 . As DSM is driven into other exotic topological phases including Weyl semimetal, topological insulator, and trivial insulator such as by symmetry breaking or dimensionality control WangPRB2012 ; WangPRB2013 ; LiuNatMater2014 ; UchidaNatComm2017 ; CollinsNature2018 , it has attracted both theoretical and experimental research efforts as an ideal parent material. DSM has also gathered significant interest because of its characteristic quantum transport originating from the non-trivial electronic structure; for examples, surface conduction based on Fermi-arcs WanPRB2011 and negative magnetoresistance induced by chiral anomaly SonPRB2013 ; BurkovPRL2014 . In paticular, the existence of novel orbital trajectories under a magnetic field, so called Weyl-orbit, which consists of both the surface Fermi-arcs and bulk chiral modes, has been predicted PotterNatComm2014 ; ZhangSciRep2016 .

Among the candidates of DSM, Cd3As2 is one of the most studied materials hosting simple band structure aroud the Dirac points NeupaneNatComm2014 ; LiuNatMater2014 ; JeonNatMater2014 ; BorisenkoPRL2014 ; NishihayaPRB2018 . So far, a number of studies have been reported on the quantum transport in Cd3As2 HePRL2014 ; LiangNatMater2015 ; WangNatComm2016 ; MollNature2016 , including observations of quantum Hall effect (QHE) UchidaNatComm2017 ; NishihayaSciAdv2018 ; ZhangNatComm2017_2 ; ZhangNature2018 ; StemmerPRL2018 ; LinPRL2019 . Particularly, QHE observed even in three-dimensional Cd3As2 nano-plates (t = 70 $\sim$ 80 nm) ZhangNatComm2017_2 ; ZhangNature2018 ; LinPRL2019 has indicated the quantization of two-dimensional (2D) surface states to demand subsequent studies for investigating its origin. However, most of bulk Cd3As2 samples, synthesized by such as melt growth NeupaneNatComm2014 ; LiuNatMater2014 ; JeonNatMater2014 ; ZhaoPRX2015 ; NarayananPRL2015 and chemical vapor deposition ZhangNatComm2017_2 ; ZhangNature2018 ; LinPRL2019 , has relatively high carrier density ($\geq$ 1018 cm*-3*). Therefore, fabrication of Cd3As2 films with lower carrier density and higher electron mobility has been required. In order to realize it, molecular beam epitaxy (MBE) is an useful technique, since the films can be grown by individually controlling the flux of each element. While there have been some reports on the MBE growth of Cd3As2 films StemmerAPLMat2016 ; StemmerPRB2017 ; StemmerPRB2018 ; XiuNPG2015 ; XiuSciRep2016 ; ChengNJP2016 ; XiuPRB2018 , the films showing quantum transport have not been thick enough to reflect the 3D nature of topological Dirac semimetal. In spite of its necessity, high-quality 3D Cd3As2 films have been hardly obtained mainly because of the high volatility of elements that require a low growth temperature.

Here we report MBE growth and characterization of 3D thick Cd3As2 films. The highest electron mobility has been achieved among the reported film samples. Even in the thickness regime of t $>$ 100 nm, Hall plateau-like structures are observed together with Shubnikov-de Haas oscillations. Though the details of mechanisms are still unclear, the unconventional behaviors suggest the importance of coexistence of surface and bulk quantum states.

Cd3As2 films were grown in an EpiQuest RC1100 MBE system on single crystalline (111) CdTe substrates (see also supplemental material for details). CdTe has a zincblende structure, and the lattice mismatch between Cd3As2 and CdTe is 2.3 %. The molecular beams were provided from a conventional Knudsen cell containing Cd (6N, Osaka Asahi Co.) and an MBE-Komponenten valved cracker source containing As (7N5, Furukawa Co.), respectively. The reservoir temperature of the cracker source was set to 600 ∘C to sublimate arsenic as tetramers (As4). The CdTe substrate was etched using 0.01 % Br2-methanol to remove native oxides just before loading it into the MBE chamber StemmerAPLMat2018 . Prior to the growth, the substrate was heated up to 500 ∘C with supplying As flux. After confirming the change of the in situ reflection high-energy electron diffraction (RHEED) pattern, from a three-dimensional transmission pattern to a streak pattern, the substrate was cooled down to the growth temperature of 200 ∘C. The beam equivalent pressures were measured by an ionization gauge, and were set to 1.4 $\times$ 10-4 Pa for Cd and 1.2 $\times$ 10-4 Pa for As4 during the co-deposition growth. This As-rich growth condition serves to reduce the carrier density of the Cd3As2 films, because As deficiency is a major origin of the electron carriers in Cd3As2. The film thickness was set at 120 nm, and the growth rate was about 0.7 $\mathrm{\AA}$/s.

Figure 1 summarizes fundamental characterization results of a Cd3As2 thick film (sample A). As shown in the x-ray diffraction (XRD) $\theta$-2$\theta$ scan (Fig. 1(a)), the reflections from the {1 1 2} lattice planes of Cd3As2 are observed without any impurity phases. The rocking curve of the (2 2 4) Cd3As2 film peak is shown in Fig. 1(b). The full width at half maximum (FWHM) of the film peak is 0.59*∘, which is still broader than the bulk values HePRL2014 . An XRD reciprocal space map around the (10 2 12) Cd3As2* film and the (5 1 3) CdTe substrate peaks is shown in Fig. 1(c). The in-plane lattice constant along [1 $\overline{1}$ 0] and the out-of-plane lattice spacing along [1 1 2] of the Cd3As2 film are calculated to be 17.81 $\mathrm{\AA}$ and 7.321 $\mathrm{\AA}$, respectively, indicating that the Cd3As2 film is free from strain by the CdTe substrate.

A RHEED pattern taken along [1 1 $\overline{1}$] azimuth of the Cd3As2 film is shown in Fig. 1(d). It shows a typical streak pattern, indicative of two-dimensionally flat film surface. The corresponding atomic force microscopy (AFM) image and the thickness profile are shown in Fig. 1(e) and (f). The Cd3As2 film has step and terrace structure, and the step height corresponds to the lattice spacing of the Cd3As2 (112) planes ($\sim$ 7 $\mathrm{\AA}$). Figure 1(g) shows temperature dependence of the resistance $R_{\mathrm{xx}}$. The semiconducting temperature dependence down to 2 K also indicates the suppression of the As deficiency or electron carriers.

Figures 2(a)–(c) show out-of-plane transverse magnetoresistance $R_{\mathrm{xx}}$ and Hall resistance $R_{\mathrm{yx}}$ of typical Cd3As2 thick films (samples A, B, and C) measured at 2 K. The Cd3As2 samples were cut into 5 mm $\times$ 1 mm for transport measurement using the conventional four-terminal method. For the side electrodes flowing electric current, silver paste was attached to cover both of the entire sides and to avoid the current-jetting effect induced by inhomogeneous current flow ReisNJP2016 . Reflecting the low carrier densities as deduced from the Hall slope, Shubunikov-de Haas oscillations are few but clearly observed for all the three samples. If an isotropic 3D Fermi surface is assumed for given carrier densities, the magnetic field where the system reaches the quantum limit is estimated at about 4, 5, and 7 T for samples A, B, and C, respectively. On the other hand, the quantum oscillations corresponding to higher filling factors of $\nu$ = 4 or 8 are observed around these fields. They are not the lowest filling factors, since the double ($\nu$ = 4, 6, $\ldots$) or four-fold ($\nu$ = 8, 12, $\ldots$) degeneracy is observed within the measurement field range.

The low-temperature electron mobility $\mu$ and carrier density n of our thick films (red closed circles) are summarized in Fig. 2(d) together with other reported data. The mobility reaches a maximum of $\mu$ = 3 $\times$ 104 cm2/Vs for sample A, while the carrier density is reduced down to n = 5 $\times$ 1016 cm*-3*, which is one-and-a-half order of magnitude lower than the previously reported PLD-grown films (blue diamonds) UchidaNatComm2017 ; NakazawaSciRep2018 . The reduction of the carrier density is owing to the suppression of As deficiency by the As-rich growth condition.

To investigate the origins of the quantum oscillations in $R_{\mathrm{xx}}$ and the plateau-like structure in $R_{\mathrm{yx}}$, the field angle dependence of $R_{\mathrm{xx}}$ and $R_{\mathrm{yx}}$ was measured. Figures 3 (a) and (b) show their dependence taken for sample A, where the magnetic field is tilted from the out-of-plane direction ($\theta$ = 0*∘) to the current direction ($\theta$ = 90∘). The quantum oscillations in $R_{\mathrm{xx}}$ and the plateau-like structures in $R_{\mathrm{yx}}$ remain to be resolved up to $\theta$ = 75∘. For clarity, $R_{\mathrm{xx}}$, $\frac{-d^{2}R_{\mathrm{xx}}}{dB^{2}}$, and $\frac{-dR_{\mathrm{yx}}}{dB}$ are compared for each field angle in Figs. 3(c)–(f). Even under rotation of $\theta$, the peak and valley positions confirmed in the derivatives do not largely shift. This field-angle-independent behavior of $R_{\mathrm{xx}}$ indicates that the 3D Fermi surface is realized in the thick Cd3As2* film, also consistent with thickness dependence previously studied using Cd3As2 films UchidaNatComm2017 . On the other hand, plateau-like structures in $R_{\mathrm{yx}}$ are indicative of a 2D electronic state (Figs. 2(a)–(c) and Fig. 3(b)). Namely, the correspondence of the oscillation phases between the derivative of the Hall resistance ($\frac{-dR_{\mathrm{yx}}}{dB}$) and the oscillation component of the magnetoresistance ($\frac{-d^{2}R_{\mathrm{xx}}}{dB^{2}}$) is a sign of the quantum Hall state. This coexistence of the 2D feature and its 3D angle dependence can not be explained either by a simple 2D nor 3D model.

Novel orbital trajectory, so called Weyl-orbit, has been theoretically predicted for topological semimetals under a magnetic field PotterNatComm2014 ; ZhangSciRep2016 , where the two Fermi arcs on opposite surfaces of the sample are connected by the bulk chiral mode ($N=0$ Landau level). Quantum oscillations from the Weyl-orbit occur at the following magnetic fields,

[TABLE]

where $n$ is the index of the Landau level, $\gamma$ is the constant phase offset, $S_{k}$ is the $k$-space area enclosed by the two Fermi arcs combined, $\theta$ is the tilting angle of the magnetic field from the surface normal. $k_{\mathrm{W}\parallel}(\theta)$ and $k_{\mathrm{F}\parallel}(\theta)$ are the field parallel components of the wave vector from +1 to -1 chirality Weyl nodes and that of the Fermi wave vector, respectively. However, the observed 3D angle dependence can not be explained even by the semiclassical Weyl-orbit picture. If the observed quantum oscillations can be described by Eq.(1), the angle-independent behavior is understood in a way that the total change in the right side of Eq.(1) is nearly independent of $\theta$. But, the second term $-t(k_{\mathrm{W}\parallel}(\theta)+2k_{\mathrm{F}\parallel}(\theta))$ does not change such that it compensates the change in the first term $2\pi(n+\gamma)\mathrm{cos}\theta$. Moreover, the right side of the Eq. (1) can even take negative values for a part of the measured range of $\theta$, for such low-carrier-density samples. To understand the characteristic quantum transport emerging in the 3D thick films, systematic control of the Fermi level such as by chemical substitution or electrostatic gating will be necessary as a future work.

In summary, 3D thick Cd3As2 films with low carrier density and high electron mobility have been obtained by using molecular beam epitaxy. The electron mobility of $\mu$ = 3 $\times$ 104 cm2/Vs, the highest value among the reported film samples, has been achieved. The coexistence of Hall plateau-like structure and 3D field angle dependence can not be interpreted by either simple 2D or 3D model. The MBE-grown Cd3As2 films will be an ideal platform for further investigation of the quantum Hall state based on unconventional magnetic orbits which are also distinct from the one described by the semiclassical Weyl-orbit equation.

We acknowledge H. Ishizuka, H. Sakai, Y. Araki, K. Muraki, N. Nagaosa, and Y. Tokura for fruitful discussions. We also thank M. Tanaka and S. Ohya for technical advice about the handling of arsenides. This work was supported by JST PRESTO Grant No. JPMJPR18L2 and CREST Grant No. JPMJCR16F1, Japan, and by Grant-in-Aids for Scientific Research (B) No. JP18H01866 from MEXT, Japan.