Research ArticleMATERIALS SCIENCE

Spatial charge inhomogeneity and defect states in topological Dirac semimetal thin films of Na3Bi

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Science Advances  22 Dec 2017:
Vol. 3, no. 12, eaao6661
DOI: 10.1126/sciadv.aao6661
  • Fig. 1 Large-area morphology and spectroscopy of 20-nm Na3Bi on Si(111).

    (A) Large-area (400 nm × 380 nm) topographic STM image (bias voltage V = −3 V and tunnel current I = 50 pA). Inset: Atomic-resolution STM image with a lattice constant of 5.45 Å (taken on a separate 20-nm Na3Bi film) showing an individual Na vacancy at the surface. (B) STM topography (V = 300 mV and I = 250 pA) on a 45 nm × 45 nm region of Na3Bi. (C) STM topography (V = −550 mV and I = 200 pA) on a 30 nm × 30 nm region of Na3Bi. (D) STM topography (V = −50 mV and I = 100 pA) on a 30 nm × 30 nm region of Na3Bi on sapphire [α-Al2O3(0001)]. (E) Area-averaged scanning tunneling spectra (vertically offset for clarity) corresponding to four different regions of the sample. Black spectra corresponding to the region in (B) and red spectra (topography not shown) were taken immediately after growth, whereas the blue spectra corresponding to the region in (C) and green spectra (topography not shown) were taken 1 week after growth. Feature ED reflects the Dirac point, which corresponds to the minimum in the LDOS, and D represents the resonance feature (discussed in the main text).

  • Fig. 2 Charge puddling profiles of p-type and n-type Na3Bi.

    (A) Dirac point energy map of the 45 nm × 45 nm (90 pixels × 90 pixels) region of p-type Na3Bi on Si(111) (V = −250 mV and I = 250 pA), corresponding to region A represented in Fig. 1B. Scale bar, 15 nm. (B) Dirac point energy map of the 30 nm × 30 nm (60 pixels × 60 pixels) region of n-type Na3Bi Si(111) corresponding to region B of Fig. 1C (V = −150 mV and I = 200 pA). Scale bar, 10 nm. (C) Dirac point energy map of the 30 nm × 30 nm (60 pixels × 60 pixels) region of n-type Na3Bi Si(111) grown on α-Al2O3(0001) (labeled region C) (V = −150 mV and I = 200 pA). Scale bar, 10 nm. (D) Upper, middle, and lower panels representing histograms of the Dirac point energy maps in (A) to (C), respectively. The histograms are color-coded to reflect the intensity scale in the corresponding Dirac point energy map. (E) Plot of spatial coherence length as a function of Fermi energy, comparing the experimental data for region A (red triangle), region B (blue triangle), and region C (purple diamond) to theoretical predictions (shaded region) where the upper bound (solid line) is defined using vF = 2.4 × 105 ms−1 and α = 0.069, whereas the lower bound (dashed line) uses vF = 1.4 × 105 ms−1 and α = 0.174 (24).

  • Fig. 3 Determining the bound state defect resonance.

    (A) Map of the dI/dV magnitude at the defect resonance energy, where defects are shown as red circles. (B) dI/dV point spectra (taken on region B) on/off the defect site, at locations corresponding to the defect site (black), then 1 nm (red), 3 nm (purple), 5 nm (green), and 7 nm (brown) away from the defect. (C) Crystal structure of Na3Bi, with the surface-terminated Na labeled Na(2) (gold), with the remaining Na atoms in blue with the Na bonded to Bi in the hexagonal lattice labeled Na(1) and the Bi atoms in gray. (D) Comparison between DFT calculations of the DOS for Na3Bi with an Na(2) vacancy at the surface of a 2 × 2 × 3 cell (red curve), an Na(2) vacancy inside a 2 × 2 × 2 cell (blue curve), and a bulk Na(2) vacancy (black curve) and the experimental STS curve for a 20-nm Na3Bi film (green curve). Energy scales of all spectra have been corrected so that 0 eV reflects the Dirac point. A vertical offset has been applied for clarity. (E) Accompanying electronic band structures for bulk Na3Bi with an Na(2) vacancy (left), an Na(2) vacancy inside a 2 × 2 × 2 cell (middle), and an Na(2) vacancy at the surface of a 2 × 2 × 3 cell (right).

  • Fig. 4 Tip-induced ionization rings around large defects.

    (A) STM topography (V = −250 mV and I = 250pA) on a 60 nm × 60 nm region of Na3Bi. Fixed-bias dI/dV maps taken at (B) −196 mV, (C) −216 mV, and (D) −236 mV over the same region as (A) showing a ring-like feature centered around a large vacancy site highlighted by the dashed circle in (A).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/12/eaao6661/DC1

    section S1. Determining the Dirac point position from dI/dV spectra

    section S2. Demonstrating the spatial and energy correspondence between STS measurements of the Na3Bi Dirac point and defect quasi-bound state

    section S3. Demonstrating that charge puddling is correlated with Na(2) vacancies

    section S4. Correlation of resonance state in dI/dV spectra with lattice defects

    section S5. Calculation of puddle coherence length from autocorrelation analysis

    section S6. Theory discussion on correlation length, impurity density, and mobility

    section S7. DFT calculations of Na vacancies in the Na3Bi lattice

    fig. S1. Determining the Dirac point position from the dI/dV spectra.

    fig. S2. STM topography of region A (as in Fig. 1C) showing the 1 × 1 Na3Bi (001), Na(2)-terminated surface, with vacancy point defects and unidentified impurities visible.

    fig. S3. Frequency histogram of the measured Dirac point and Na(2) vacancy quasi-bound state (STS peak, ~30 mV below the Dirac point) features extracted from STS of region A.

    fig. S4. Radially averaged correlation profiles for spatial profiles of key STS features in region A.

    fig. S5. STM topography and charge puddling map of p-type Na3Bi on region A.

    fig. S6. Spatial dependence of defect resonance.

    fig. S7. Electronic structure of pristine and defective Na3Bi.

    fig. S8. Total DOS of pristine and defective Na3Bi.

    fig. S9. Comparison of calculated total DOS and projected DOS on surface for Na3Bi with Na(2) vacancy.

    fig. S10. Comparison of calculated total DOS and projected DOS on individual atomic layers for Na3Bi with Na(2) vacancy.

    table S1. Charged impurity density for EF » Erms calculated using Thomas– Fermi and RPA for both region A, B, and C.

    table S2. Mobility for EF » Erms calculated using Thomas– Fermi and RPA for both region A, B, and C.

    References (3539)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Determining the Dirac point position from dI/dV spectra
    • section S2. Demonstrating the spatial and energy correspondence between STS measurements of the Na3Bi Dirac point and defect quasi-bound state
    • section S3. Demonstrating that charge puddling is correlated with Na(2) vacancies
    • section S4. Correlation of resonance state in dI/dV spectra with lattice defects
    • section S5. Calculation of puddle coherence length from autocorrelation analysis
    • section S6. Theory discussion on correlation length, impurity density, and mobility
    • section S7. DFT calculations of Na vacancies in the Na3Bi lattice
    • fig. S1. Determining the Dirac point position from the dI/dV spectra.
    • fig. S2. STM topography of region A (as in Fig. 1C) showing the 1 × 1 Na3Bi (001), Na(2)-terminated surface, with vacancy point defects and unidentified impurities visible.
    • fig. S3. Frequency histogram of the measured Dirac point and Na(2) vacancy quasi-bound state (STS peak, ~30 mV below the Dirac point) features extracted from STS of region A.
    • fig. S4. Radially averaged correlation profiles for spatial profiles of key STS features in region A.
    • fig. S5. STM topography and charge puddling map of p-type Na3Bi on region A.
    • fig. S6. Spatial dependence of defect resonance.
    • fig. S7. Electronic structure of pristine and defective Na3Bi.
    • fig. S8. Total DOS of pristine and defective Na3Bi.
    • fig. S9. Comparison of calculated total DOS and projected DOS on surface for Na3Bi with Na(2) vacancy.
    • fig. S10. Comparison of calculated total DOS and projected DOS on individual atomic layers for Na3Bi with Na(2) vacancy.
    • table S1. Charged impurity density for EF »Erms calculated using Thomas– Fermi and RPA for both region A, B, and C.
    • table S2. Mobility for EF »Erms calculated using Thomas– Fermi and RPA for both region A, B, and C.
    • References (35–39)

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