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Abstract
We present evidence of topological surface states in βAg_{2}Te through firstprinciples calculations, periodic quantum interference effect and ambipolar electric field effect in single crystalline nanoribbon. Our firstprinciples calculations show that βAg_{2}Te is a topological insulator with a gapless Dirac cone with strong anisotropy. To experimentally probe the topological surface state, we synthesized high quality βAg_{2}Te nanoribbons and performed electron transport measurements. The coexistence of pronounced AharonovBohm oscillations and weak AltshulerAronovSpivak oscillations clearly demonstrates coherent electron transport around the perimeter of βAg_{2}Te nanoribbon and therefore the existence of topological surface states, which is further supported by the ambipolar electric field effect for devices fabricated by βAg_{2}Te nanoribbons. The experimental evidences of topological surface states and the theoretically predicted anisotropic Dirac cone of βAg_{2}Te suggest that the material may be a promising candidate of topological insulator for fundamental study and future spintronic devices.
L. W. acknowledges the support from Singapore National Research Foundation (RCA08/018) and MOE Tier 2 (MOE2010T22059). S. Q. S. thanks the Research Grant Council of Hong Kong under Grant No. HKU705110P. W. G. Z. acknowledges the Singapore A*STAR SERC 102 101 0019. T. Y. acknowledges NTUSUG M4080513. The authors thank Hongming Weng and Sergey V. Eremeev for their helpful discussion.
I. INTRODUCTION
II. BAND STRUCTURE CALCULATION
III. EXPERIMENT
IV. RESULTS AND DISCUSSION
A. AharonovBohm (AB) oscillation
B. Ambipolar electric gate effect
C. The shape of R(T) curves vs. cross section areas
V. CONCLUSION
Key Topics
 Surface states
 58.0
 Nanomaterials
 44.0
 Insulators
 23.0
 Dirac equation
 18.0
 Electrical resistivity
 12.0
Figures
The calculated surface band structure of the βAg_{2}Te film with the projected bulk band structure in the background (blue) to the 2D Brillouin zone whose shape is shown in the upper inset. The surface topological states are highlighted by the red lines. The bottom inset shows the expectation values of spin operator (S _{z}) of the surface band in βAg_{2}Te along k _{x} and k _{y} directions in momentum space. Three constantenergies, which cut through the surface state below the Dirac point, are plotted. The red (blue) color means the outofplane components pointing out(in) ward of the plane. The color scale, with blue and red, indicates the intensity of negative and positive values representing the projection S _{z}.
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The calculated surface band structure of the βAg_{2}Te film with the projected bulk band structure in the background (blue) to the 2D Brillouin zone whose shape is shown in the upper inset. The surface topological states are highlighted by the red lines. The bottom inset shows the expectation values of spin operator (S _{z}) of the surface band in βAg_{2}Te along k _{x} and k _{y} directions in momentum space. Three constantenergies, which cut through the surface state below the Dirac point, are plotted. The red (blue) color means the outofplane components pointing out(in) ward of the plane. The color scale, with blue and red, indicates the intensity of negative and positive values representing the projection S _{z}.
(a) TEM image of an as prepared nanoribbon with the inset showing the corresponding SAED pattern. (b) Transmission electron diffraction pattern simulated based on monoclinic Ag_{2}Te single crystal with cell parameters a = 8.164 Ǻ, b = 4.468 Ǻ, c = 8.977 Ǻ, space group P2_{1}/c (ICSD file number: 073402). The electrons are directed to the sample at zone axis [4 5] with energy at 300 KeV. (c) High resolution TEM image of a focused ion beam milled Ag_{2}Te nanoribbon with the inset showing the corresponding fast Fourier transform pattern. (d) EDS mapping for Ag_{2}Te nanoribbon.
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(a) TEM image of an as prepared nanoribbon with the inset showing the corresponding SAED pattern. (b) Transmission electron diffraction pattern simulated based on monoclinic Ag_{2}Te single crystal with cell parameters a = 8.164 Ǻ, b = 4.468 Ǻ, c = 8.977 Ǻ, space group P2_{1}/c (ICSD file number: 073402). The electrons are directed to the sample at zone axis [4 5] with energy at 300 KeV. (c) High resolution TEM image of a focused ion beam milled Ag_{2}Te nanoribbon with the inset showing the corresponding fast Fourier transform pattern. (d) EDS mapping for Ag_{2}Te nanoribbon.
(a) EDS spectrum of a Ag_{2}Te nanoribbon. Nanoribbons were grown on the Al_{2}O_{3} substrates. A small piece from the substrate was cut out for the EDS study. The spectrum was obtained by taking the data at several different points of the nanoribbon for 60 minutes. Al and O peaks in the spectrum are from the Al_{2}O_{3} substrate. There are no other prominent peaks observed in the EDs study. From the quantitative analysis, we obtain the atomic ratio Ag:Te = 2.02:1 for the nanowire. The inset of (a): Ag/Te molar ratio of nanoribbons obtained in different batch of growth. The molar ratio is about 2.02 for the 5 samples of different batch of growth. There were no samples found with significant deviation from this ratio. (b) AFM image of a Ag_{2}Te nanoribbon. To use freestanding nanoribbons for the AFM, we sonicated nanoribbons grown on the Al_{2}O_{3} substrates into the IPA solution, subsequently dripping the IPA solution to the SiO_{2} substrate. Samples used for the AFM scanning vary in the thickness up to 200 nm. No samples were found to have larger thicknesses. The nanoribbons exhibit uniform surfaces. Some large nanoribbons have steps as shown in Fig. 3(b) .
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(a) EDS spectrum of a Ag_{2}Te nanoribbon. Nanoribbons were grown on the Al_{2}O_{3} substrates. A small piece from the substrate was cut out for the EDS study. The spectrum was obtained by taking the data at several different points of the nanoribbon for 60 minutes. Al and O peaks in the spectrum are from the Al_{2}O_{3} substrate. There are no other prominent peaks observed in the EDs study. From the quantitative analysis, we obtain the atomic ratio Ag:Te = 2.02:1 for the nanowire. The inset of (a): Ag/Te molar ratio of nanoribbons obtained in different batch of growth. The molar ratio is about 2.02 for the 5 samples of different batch of growth. There were no samples found with significant deviation from this ratio. (b) AFM image of a Ag_{2}Te nanoribbon. To use freestanding nanoribbons for the AFM, we sonicated nanoribbons grown on the Al_{2}O_{3} substrates into the IPA solution, subsequently dripping the IPA solution to the SiO_{2} substrate. Samples used for the AFM scanning vary in the thickness up to 200 nm. No samples were found to have larger thicknesses. The nanoribbons exhibit uniform surfaces. Some large nanoribbons have steps as shown in Fig. 3(b) .
(a) Schematic diagram of four contact devices used in our transport experiments. (b) A scanning electron microscopy image of device in our experiments. The image shows one nanoribbon and six gold contacts on the nanoribbon.
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(a) Schematic diagram of four contact devices used in our transport experiments. (b) A scanning electron microscopy image of device in our experiments. The image shows one nanoribbon and six gold contacts on the nanoribbon.
(a) Magnetoresistance of a βAg_{2}Te nanoribbon (cross section area: 0.191 width (W) × 0.098 thickness (T) μm^{2}) with an applied magnetic field parallel to the current flowing direction at temperature 2 K, 4 K, 6 K, 8 K, and 10 K, respectively. The curves are vertically displaced for clarity. A clear resistance oscillation with a period of 0.227 Tesla (h/e) is observed, as shown by the dotted lines. The arrows indicate an oscillation with a period of 0.113 Tesla (h/2e). (b) The plot of the 2 K magnetoresistance in (a) in a wider field range from 0 Tesla to 9 Tesla. The arrow indicates the minimums of the oscillations with a period of h/2e. Inset shows the schematic diagram of the measurements. (c) The temperature dependence of the FFT spectra of the quantum oscillations. Locations of h/e and h/2e flux quantization are labeled. (d) The temperature dependence of the FFT amplitude of the h/e flux quantization (the AB effect). The solid line is the curve of the T^{−0.5} power law. (e) The ratio of the amplitude of two FFT peaks (A(h/e)/A(h/2e) at different temperatures. The power law fitting gives ∼T^{−0.38}.
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(a) Magnetoresistance of a βAg_{2}Te nanoribbon (cross section area: 0.191 width (W) × 0.098 thickness (T) μm^{2}) with an applied magnetic field parallel to the current flowing direction at temperature 2 K, 4 K, 6 K, 8 K, and 10 K, respectively. The curves are vertically displaced for clarity. A clear resistance oscillation with a period of 0.227 Tesla (h/e) is observed, as shown by the dotted lines. The arrows indicate an oscillation with a period of 0.113 Tesla (h/2e). (b) The plot of the 2 K magnetoresistance in (a) in a wider field range from 0 Tesla to 9 Tesla. The arrow indicates the minimums of the oscillations with a period of h/2e. Inset shows the schematic diagram of the measurements. (c) The temperature dependence of the FFT spectra of the quantum oscillations. Locations of h/e and h/2e flux quantization are labeled. (d) The temperature dependence of the FFT amplitude of the h/e flux quantization (the AB effect). The solid line is the curve of the T^{−0.5} power law. (e) The ratio of the amplitude of two FFT peaks (A(h/e)/A(h/2e) at different temperatures. The power law fitting gives ∼T^{−0.38}.
(a) V_{G} dependence of resistance at 2 K, 10 K and 50 K, respectively. (b) V_{G} dependence of Conductance at 2 K. It shows quasilinear behavior near the minimum conductance.
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(a) V_{G} dependence of resistance at 2 K, 10 K and 50 K, respectively. (b) V_{G} dependence of Conductance at 2 K. It shows quasilinear behavior near the minimum conductance.
The temperature dependence of normalized resistance (Δρ = ρ (T) − ρ (300 K)) at zero magnetic field of (a) sample A, (b) sample B and (c) sample C, respectively.
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The temperature dependence of normalized resistance (Δρ = ρ (T) − ρ (300 K)) at zero magnetic field of (a) sample A, (b) sample B and (c) sample C, respectively.
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Abstract
We present evidence of topological surface states in βAg_{2}Te through firstprinciples calculations, periodic quantum interference effect and ambipolar electric field effect in single crystalline nanoribbon. Our firstprinciples calculations show that βAg_{2}Te is a topological insulator with a gapless Dirac cone with strong anisotropy. To experimentally probe the topological surface state, we synthesized high quality βAg_{2}Te nanoribbons and performed electron transport measurements. The coexistence of pronounced AharonovBohm oscillations and weak AltshulerAronovSpivak oscillations clearly demonstrates coherent electron transport around the perimeter of βAg_{2}Te nanoribbon and therefore the existence of topological surface states, which is further supported by the ambipolar electric field effect for devices fabricated by βAg_{2}Te nanoribbons. The experimental evidences of topological surface states and the theoretically predicted anisotropic Dirac cone of βAg_{2}Te suggest that the material may be a promising candidate of topological insulator for fundamental study and future spintronic devices.
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