Letter pubs.acs.org/NanoLett
Electronic Properties of High-Quality Epitaxial Topological Dirac Semimetal Thin Films Jack Hellerstedt,† Mark T. Edmonds,*,† Navneeth Ramakrishnan,‡ Chang Liu,† Bent Weber,† Anton Tadich,§ Kane M. O’Donnell,∥ Shaffique Adam,⊥,‡ and Michael S. Fuhrer† †
School of Physics and Astronomy and Monash Centre for Atomically Thin Materials, Monash University, Victoria 3800, Australia Department of Physics and Centre for Advanced 2D Materials, National University of Singapore, 117551, Singapore § Australian Synchrotron, Clayton, Victoria 3168, Australia ∥ Curtin University, Perth, Western Australia 6102, Australia ⊥ Yale-NUS College, 6 College Avenue East, 138614, Singapore ‡
S Supporting Information *
ABSTRACT: Topological Dirac semimetals (TDS) are three-dimensional analogues of graphene, with linear electronic dispersions in three dimensions. Nanoscale confinement of TDSs in thin films is a necessary step toward observing the conventional-to-topological quantum phase transition (QPT) with increasing film thickness, gated devices for electric-field control of topological states, and devices with surface-state-dominated transport phenomena. Thin films can also be interfaced with superconductors (realizing a host for Majorana Fermions) or ferromagnets (realizing Weyl Fermions or T-broken topological states). Here we report structural and electrical characterization of large-area epitaxial thin films of TDS Na3Bi on single crystal Al2O3[0001] substrates. Charge carrier mobilities exceeding 6,000 cm2/(V s) and carrier densities below 1 × 1018 cm−3 are comparable to the best single crystal values. Perpendicular magnetoresistance at low field shows the perfect weak antilocalization behavior expected for Dirac Fermions in the absence of intervalley scattering. At higher fields up to 0.5 T anomalously large quadratic magnetoresistance is observed, indicating that some aspects of the low field magnetotransport (μB < 1) in this TDS are yet to be explained. KEYWORDS: Topological Dirac semimetal, thin film growth, scanning tunneling microscopy, magnetotransport result.9 Interfacing TDS thin films with superconductors could realize topological superconductivity and a host for Majorana Fermions,10 and interfacing with ferromagnets can break timereversal symmetry to produce Weyl Fermions and a variety of topologically nontrivial states.1 However, to date the only reports of thin film Na3Bi have used the conducting substrates graphene and Si[111], making electronic transport studies impossible.11,12 An additional challenge in electrical characterization of Na3Bi is the reactivity of sodium to ambient, which makes conventional ex situ measurement methods impossible without suitable passivation. Here we demonstrate high quality, c-axis oriented thin film Na3Bi on insulating Al2O3 [0001] substrates. We have characterized the films using low temperature magnetotransport and scanning tunnelling microscopy and spectroscopy (STM and STS) in situ in ultrahigh vacuum (UHV). Films are grown using a “two-step” method inspired by previous work on the topological insulator Bi2Se3.13,14 A thin (2 nm) nucleation layer is deposited under simultaneous Bi and Na flux at low
T
he topological Dirac semimetal is characterized by Dirac points, consisting of two degenerate Weyl points with opposite topological charge occurring at the same momentum. It was shown that the Weyl points can be protected from opening a gap by crystal symmetry, with the first such TDS compound predicted being Na3Bi,1 whose Dirac electronic structure was experimentally confirmed by angle-resolved photoemission spectroscopy (ARPES) on bulk single crystal samples.2 Further transport and scanning tunneling microscopy (STM) studies of bulk crystals have begun to address the implications of the chirality of these Weyl points, namely, the in-plane quadratic magnetoconductance due to the chiral anomaly,3−5 though these signatures remain controversial.6 Nanoscale confinement of the TDS state in thin films opens new possibilities to tune the topological state with thickness,7 electric field,8 and proximity coupling to superconductors and ferromagnets.1 In particular, detailed calculations on Na3Bi have predicted a conventional-to-topological quantum phase transition (QPT) occurs with increasing film thickness7 and that the QPT can also be tuned by electric field (by e.g. gate electrodes) to enable a topological transistor.8 In addition, TDS possess unusual Fermi arc surface states, and nanostructured TDS are proposed to exhibit unusual transport phenomena as a © XXXX American Chemical Society
Received: February 12, 2016 Revised: April 18, 2016
A
DOI: 10.1021/acs.nanolett.6b00638 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. Structure of Na3Bi thin films. All data correspond to 20 nm thick Na3Bi grown at 345 °C on α-Al2O3[0001]. (a) Schematic representation of device geometry showing location of Ti/Au pads used to make electrical contact to the Na3Bi film grown on sapphire. The inset shows the crystal structure of Na3Bi with the in-plane and c-axis lattice constants labeled, where Na and Bi atoms are colored green and purple, respectively. (b) Largescale STM image showing the morphology of Na3Bi with step height 4.7 Å (Vbias = 1 V, I = 100 pA, T = 5 K). Inset: Atomic-resolution STM image of surface with lattice constant 5.45 Å (Vbias = 500 mV, I = 200 pA, T = 5 K). (c) LEED image taken at 17.5 eV showing the 1 × 1 symmetry of the Na3Bi surface. (d) Scanning tunneling spectrum dI/dV vs V averaged over 20 nm × 20 nm area. (Bias modulation rms amplitude is 5 mV). The bias voltage position of minimum dI/dV is labeled ED = −35 mV and identified as the Dirac point energy.
(120 °C) temperature, followed by additional growth at a higher final temperature between 250 and 390 °C. Further details regarding sample preparation, growth, and characterization can be found in the Supporting Information. Figure 1 shows the crystalline quality of our Na3Bi thin films. Figure 1a shows a schematic of our device. Single crystal Al2O3[0001] is prepatterned with electrical contacts in van der Pauw geometry, and the Na3Bi is deposited on top, making electrical contact. Figure 1a inset shows the crystal structure of Na3Bi. Figure 1b shows STM topography at a temperature of 5 K, showing a large area (∼80 × 80 nm) atomically flat terrace, with a step height of 4.7 Å, consistent with the half-unit cell distance of 4.83 Å between NaBi planes.1 Atomic resolution of the surface (inset) shows a (1 × 1) termination with the expected in-plane lattice constant of 5.45 Å. The 1 × 1 triangular lattice rather than hexagonal lattice is strongly suggestive that the surface is Na-terminated. Figure 1c shows low energy electron diffraction (LEED) taken at 17.5 eV. The low background and sharp hexagonal diffraction pattern confirm that the (1 × 1) structure is coherent across the LEED spot size of ∼200 μm. Faintly visible is the same pattern rotated 30°, indicating the presence of a small fraction of the sample with that alignment. We note that similar quality LEED patterns were observed on samples grown across the range of final temperatures studied. Figure 1d) shows STS (differential conductance vs bias voltage) averaged over an area of 400 nm2. STS reflect the energy dependent local density of states of the
sample. The sharp dip near zero energy reflects the dip in LDOS at the Dirac point,4,15 with Dirac point energy ED = −35 meV, consistent with the n-type doping we measured via transport. We can use this value in conjunction with carrier density measured via transport (see below, ∼ 3.8 × 1018 cm−3) to estimate the average Fermi velocity in our samples, νF = 1.4 × 105 m/s, in reasonable agreement with the value 2.4 × 105 m/s obtained from ARPES.2 The ex situ prepared corner contacts (Figure 1a) allowed us to make van der Pauw measurements of the longitudinal and transverse resistivity ρxx and ρxy in magnetic field B up to 0.5 T at a temperature of 5 K, from which we extract the Hall carrier dρxy
−1
( )
density n = ed dB
and the Hall mobility μ = (neρxx)−1,
where d = 20 nm is the thickness, and e is the elementary charge. We note that ρxy(B) showed no deviation from linear field dependence in the entire range of field measured: the slope is reported as the Hall carrier density, and we omit plotting these data. Figure 2 shows μ (Figure 2a) and n (Figure 2b) plotted against the final growth temperature for each sample. Samples with a final temperature above 380 °C had a substantial reduction in measured mobility and intermittent electrical contact problems, probably indicating dewetting of the film on the substrate at these growth temperatures. Therefore, we discount these samples from further analysis. We observe a trend of decreasing n and increasing μ with increasing growth temperature, up to 360 °C. The highest B
DOI: 10.1021/acs.nanolett.6b00638 Nano Lett. XXXX, XXX, XXX−XXX
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The only materials parameters are the fine structure constant α = e2/κℏνF and the spin/valley degeneracy product g = 4.5 We estimate the effective fine structure constant for Na3Bi to be 17 between α = 0.06−0.17, based on κ ∼ 120+10 and a Fermi −30, 5 velocity between νF = 1.4 × 10 m/s from STS (Figure 1d), and νF = 2.43 × 105 m/s from single crystal ARPES experiments.2 Our data lie close to, but somewhat below (∼ an order of magnitude) the theoretical prediction of the mobility. There are several possible reasons for this. First, we may have assumed an incorrect value for alpha. If we take alpha as a fit parameter in the theory, the best fit to the data (green line in Figure 2c) yields α = 0.44, 2.5−7 times higher than expected. Second, the theory disregards other contributions to disorder in our samples, notably point defects, structural incoherence due to grain boundaries or strain effects, all of which should be expected to some degree for a large area, van der Waals epitaxial film. Third, the theory assumes nimp = n; however, the presence of both positively and negatively charged will cause nimp > n. For the latter two reasons, the theoretical prediction is an upper bound. Electrostatic control of the chemical potential through, e.g., gates, is one possible route to deconvolving the contributions of nimp and n to the conductivity and better understand what factors are currently limiting the mobility of our films. Figure 3a shows the transverse MR ρxx(B)/ρxx(B = 0) plotted as a function of perpendicular applied field, labeled according to the final growth temperature. An overall positive magnetoresistance (MR) is observed, with a cusp below ∼0.1 T. We first discuss the high field MR. For field values above 0.1 T the data are well-described by a quadratic dependence:18,19
Figure 2. Hall mobility and Hall carrier density of Na3Bi thin films measured at a temperature of 5 K for samples grown with different thermal profiles. (a) Mobility and (b) Hall carrier density (n-type) are plotted against the final growth temperature for the various samples. The 120−345 °C growth profile achieves the highest measured mobility (6310 cm2/vs) and lowest carrier density (4.6 × 1017 cm−3). The gray shaded region represents the range of final growth temperatures for which the sample quality significantly degrades. c) Log−log plot of experimental mobility vs carrier density (black squares). The red hashed region was calculated using eq 18 in ref 16 for best estimates of the effective fine structure constant α = 0.06− 0.17. The green dashed line is a fit to the experimental data yielding an effective fine structure constant α = 0.44.
ρxx (B) = ρxx (B = 0)[1 + A(μB)2 ]
Figure 3b shows the prefactor A determined from fits to eq 1 plotted as a function of carrier density n. In the simplest instance, a single band, two-dimensional system evinces zero transverse MR.20 There are several possible origins for the quadratic MR we observe. Multiple conduction bands of differing mobility and/or carrier density can produce quadratic low-field MR,21 however we exclude this possibility due to the close proximity of the Dirac point as measured by both Hall effect and STS. Another possible explanation is spatial inhomogeneity, for example in carrier density, known to give a quadratic MR at low field. However, to our knowledge all theories of spatial inhomogeneity give A < 1.18,22−26 This strict limit contrasts with the values we have obtained in the present work, ranging from ∼0.1−4.5 (Figure 3b). Notably, measurements on single crystal samples show similar unusually large quadratic MR coefficients A > 1 in the low field regime (μB ≪ 1).5 Recent theoretical efforts have been made to understand charge inhomogeneity in a Dirac semimetal system27,28 and propose that in the spatially inhomogeneous regime the Hall carrier density overestimates the average carrier density, and hence the mobility is underestimated and A overestimated. While the inhomogeneous theory can be made to be consistent with both the observed mobility and the large apparent A,28 we find this explanation very unlikely for our samples. The inhomogeneous regime is very small in Na3Bi (with α ∼ 0.1); the characteristic carrier density inhomogeneity is only a few percent of the impurity density, requiring donor and acceptor concentrations to also be balanced within a few percent. We find this scenario unlikely to occur generically in all our samples
measured mobility (6310 cm2/(V s)) and lowest carrier density (4.6 × 1017 cm−3) were measured on a sample grown at 345 °C. This lowest carrier density is still about an order of magnitude larger than the lowest reported bulk crystal value,3 however our observed range of doping (4.6 × 1017 to 1.7 × 1019 cm−3) falls within the range observed in bulk crystal values.5 Given the Fermi wavevector kF =
6π 2n g
1/3
( )
(1)
we can calculate the mean
free path l, which ranged between 75 and 135 nm for our samples. Increasing mobility with decreasing carrier density is consistent with expectations assuming that the impurities that give rise to doping are also responsible for the disorder limiting the mobility. To better understand the relationship between the mobility and carrier density, we plotted them against one another (Figure 2c). The red hashed region is the theoretical prediction for a TDS using the random phase approximation (RPA)16 assuming that all the impurities are dopants of a single sign; i.e., the impurity density nimp equals the carrier density n. C
DOI: 10.1021/acs.nanolett.6b00638 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 3. Transverse magnetoresistance (±0.5 T) of Na3Bi thin films at a temperature of 5 K. (a) Normalized magnetoresistance ρxx(B)/ρxx(B = 0) as a function of B for samples prepared at final growth temperatures indicated in the legend. “345* no flux” indicates growth without the postgrowth anneal in Na flux. Lines are fits to eq 1. (b) Quadratic coefficient of MR A from fits to eq 1 in (a) as a function of carrier density for the various films measured. (c) Residual magnetoconductance Δσ = σ(B) − σ(B = 0) vs B after subtraction of fit to eq 1 from data in (a). Fits are to the strong spin− orbit limit of the HLN theory (eq 2).29 The single fitting parameter, the coherence length Lϕ, is plotted against carrier density in (d). The colors of the points in (b) and (d) correspond to the sample growth temperatures indicated by the legend in (a).
the samples (20 nm), consistent with the assumption of twodimensionality. (Efforts to fit our data using a threedimensional theory for weak localization30,31 yielded poor fits regardless of the limiting cases in temperature and magnetic field used.) The coherence length Lϕ at densities above 6 × 1018 cm−3 exceeds 1 μm but is suppressed in lower carrier density samples, a phenomena that has been previously observed in other Dirac materials such as graphene32 and the Dirac surface state of bismuth selenide.33 The fact that our weak field MR is well-described by the HLN formula indicates that our Na3Bi films are well-described by noninteracting Dirac cones; i.e., intervalley scattering is weak.31 However, more careful study of the MR, including temperature and (electrostatically controlled) carrier density dependence, is necessary to make a quantitative assessment of the intervalley scattering rate, as well as any role of spin−orbit disorder.34 In summary, we have demonstrated the growth of electrically isolated, highly oriented, large area thin film Na3Bi on αAl2O3[0001] substrates. The high sample quality is reflected in a record high mobility and near-ideal weak antilocalization behavior. High-quality TDS thin films on insulators open a route toward novel topological phenomena and devices, including electric field control via gate electrodes, and interfacing with magnetic or superconducting materials.
across a range of growth conditions, where the observed Hall carrier density varies by almost 2 orders of magnitude. As mentioned above, spatial inhomogeneity has also been proposed as the origin of large MR, and in particular linear nonsaturating MR, in a number of systems.22,25 However, spatially inhomogeneous conductors still exhibit a quadratic MR [eq 1] at low enough fields μB ≪ 1, and in this regime experiment and modeling find that A is always less than 1.22,25,26 Again, the possibility remains that the mobility is underestimated, and A overestimated, due to inhomogeneity; this possibility requires further investigation. Lastly we discuss the low-field MR. Figure 3c shows the MR after subtracting the quadratic MR from fits to eq 1). We replot the low field data as the change in 2D conductivity (Δσ = σ(B) − σ(B = 0)), in units of e2/h, where h is the Planck’s constant. We find that the low-field MR data are well-described by the strong spin−orbit coupling limit of the Hikami-Larkin-Nagaoka (HLN) formula:29 σ(B) − σ(0) =
⎛1 Bϕ ⎞⎞ e 2 ⎛ ⎛ Bϕ ⎞ ⎜ln⎜ ⎟ − Ψ⎜ + ⎟⎟ ⎝2 2πh ⎝ ⎝ B ⎠ B ⎠⎠
(2)
where the only fit parameter is the phase coherence field Bϕ. Figure 3d shows the phase coherence length Lϕ =
h 8πeBϕ
as a
function of carrier density for the various films. In each instance the coherence length is substantially larger than the thickness of D
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(20) Hall, E. H. Am. J. Math. 1879, 2, 287−292. (21) Ziman, J. M. Principles of the Theory of Solids; Cambridge University Press, 1980 (22) Parish, M. M.; Littlewood, P. B. Nature 2003, 426, 162−165. (23) Adam, S.; Hwang, E. H.; Galitski, V. M.; Das Sarma, S. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 18392−18397. (24) Cho, S.; Fuhrer, M. S. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 081402. (25) Kozlova, N. V.; et al. Nat. Commun. 2012, 3, 1097. (26) Parish, M. Private Correspondence, 2015. (27) Skinner, B. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 1−5. (28) Ramakrishnan, N.; Milletari, M.; Adam, S. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 245120. (29) Hikami, S.; Larkin, A. I.; Nagaoka, Y. Prog. Theor. Phys. 1980, 63, 707−710. (30) Kawabata, K. Solid State Commun. 1980, 34, 431−432. (31) Lu, H. Z.; Shen, S. Q. Phys. Rev. B 2015, 34, 431−432. (32) Ki, D. K.; Jeong, D.; Choi, J. H.; Lee, H. J.; Park, K. S. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 125409. (33) Chen, J.; et al. Phys. Rev. Lett. 2010, 105, 1−4. (34) Adroguer, P.; Liu, W. E.; Culcer, D.; Hankiewicz, E. M. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 241402.
ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b00638. Detailed sample preparation methods, film growth parameters, and characterization technique specifics (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
J.H. and M.T.E. contributed equally to this work. J.H., M.T.E., and M.S.F. devised the experiments. J.H. and M.T.E. performed the growth, STM and transport. B.W. and C.L. aided the UHV experiments. J.H., M.T.E., C.L., A.T., and K.M.O. performed the LEED and growth of samples at the Australian Synchrotron. N.R. and S.A. assisted with the theoretical understanding and interpretation of the transport data. J.H., M.T.E., and M.S.F. analyzed the data and composed the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). LEED measurements were performed at the Soft X-ray Beamline of the Australian Synchrotron. J.H., M.T.E., B.W., and M.S.F. are supported by M.S.F.’s ARC Laureate fellowship (FL120100038). M.T.E. and B.W. garner additional support from their respective ARC DECRA fellowships (DE160101157 and DE160101334). S.A. and N.R. are supported under the National Research Foundation of Singapore’s fellowship program (NRF-NRFF2012-01).
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DOI: 10.1021/acs.nanolett.6b00638 Nano Lett. XXXX, XXX, XXX−XXX
