Patterning antidots, which are regions of potential hills that repel electrons, into well-defined antidot lattices creates fascinating artificial periodic structures, leading to anomalous transport properties and exotic quantum phenomena in two-dimensional systems. Although nanolithography has brought conventional antidots from the semiclassical regime to the quantum regime, achieving precise control over the size of each antidot and its spatial period at the atomic scale has remained challenging. However, attaining such control opens the door to a new paradigm, enabling the creation of quantum antidots with discrete quantum hole states, which, in turn, offer a fertile platform to explore novel quantum phenomena and hot electron dynamics in previously inaccessible regimes. Here we report an atomically precise bottom-up fabrication of a series of atomic-scale quantum antidots through a thermal-induced assembly of a chalcogenide single vacancy in PtTe2. Such quantum antidots consist of highly ordered single-vacancy lattices, spaced by a single Te atom, reaching the ultimate downscaling limit of antidot lattices. Increasing the number of single vacancies in quantum antidots strengthens the cumulative repulsive potential and consequently enhances the collective interference of multiple-pocket scattered quasiparticles inside quantum antidots, creating multilevel quantum hole states with a tunable gap from the telecom to far-infrared regime. Moreover, precisely engineered quantum hole states of quantum antidots are geometry protected and thus survive on oxygen substitutional doping. Therefore, single-vacancy-assembled quantum antidots exhibit unprecedented robustness and property tunability, positioning them as highly promising candidates for advancing quantum information and photocatalysis technologies.
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J. Lu acknowledges support from MOE grants (MOE2019-T2-2-044, MOE-T2EP50121-0008, MOE-T2EP10221-0005) and MOE (Singapore) through the Research Centre of Excellence program (grant no. EDUN C-33-18-279-V12, I-FIM) and Agency for Science, Technology and Research (A*STAR) under its AME IRG Grant (project no. M21K2c0113). A.R. acknowledges the National Research Foundation, Prime Minister Office, Singapore, under its Medium Sized Centre Programme and the support by Yale-NUS College (through grant no. R-607-265-380-121).
The authors declare no competing interests.
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STM image at a, negative sample bias (VS = − 2.5V) and b, positive sample bias (VS = 2.5V) for a single Te vacancy (A) and an oxygen substitute (B). The atomic structure of the upper layer Te and middle layer Pt is overlapped to the atom-resolved STM image. c-f, simulated STM image for SV and O substitute in negative and positive sample bias. g, dI/dV spectra taken at pristine region, defect A and B. h, calculated LDOS for pristine PtTe2, SV and O substitute.
a, STM image before O2 dosing, showing several hexamers on the surface. b, STM image after O2 dosing, shows hexamers decorated with different number of protrusions on the corners. The setpoint is VS = − 2.5 V, It = 300 pA. c, Energy diagram for O2 adsorption and dissociation process at Te vacancy site. The inset shows the atomic structure of the initial state (IS), two transition states (TS) and two final states (FS) of the system. Atomic structure for d, O substitution e, O-O substitution at Te vacancy site (both top view and side view) and f, 3V3O2. Note: the supercell (4 × 4 × 3) consisting of three layers of PtTe2 is used in DFT calculations. Only the top layer is present to enhance clarity and better illustrate the adsorption configuration of O atoms at the SV site. Corresponding nc-AFM simulations for h, O substitution, i, O-O substitution and j, 3V3O2. g, STM image at VS = 1mV. k, nc-AFM image for 3V3O2.
a, b, Calculated band structure for bulk PtTe2 with false color scale to indicate the contributions from Pt and Te orbitals. Projected density of states for c, pristine PtTe2, d, single Te vacancy, e, O substitution and f, O-O substitution.
a, top view of atomic structure for a Te single vacancy at the surface of a three-layer PtTe2 model. b, side view of the supercell (4 × 4 × 3) used in DFT calculations. The black rectangle marks the zoom in region in a. c, three-dimensional isosurface of the charge density difference for a Te single vacancy. d, two-dimensional slice of charge density difference at upper Te atom layer for a Te single vacancy. e, constant height STM image for illustrating the line directions and positions. f, corresponding dI/dV mapping with marked lines. g-h, Color-coded dI/dV spectra for L1 and L2.
a, Schematic illustration of self-assembled vacancy-based QADs formed on PtTe2 surface. Typical STM images of PtTe2 surface after thermal annealing at b, 120 ∘C for 1 hour, c, 140 ∘C for 1 hour, d, 150 ∘C for 2 hours and e, 160 ∘C for 1 hour. The setpoint is VS = − 2.5 V, It = 300 pA. f, Histogram of the statistics results of the percentage of SV and different sized QADs under different conditions.
a-d, STM images with the dashed lines to mark the positions for taking the line KPFM at different-sized of QADs. e, Summary of the line KPFM results, the height is fixed at the setpoint of VS = − 2.5 V, It = 300 pA. A larger LCPD indicates more negative charge accumulation at the certain position. f, Frequency shift measured as a function of applied sample bias at the center of the edge for each QADs. The black cross marked the peak position for each parabolic curves from fitting.
a, c, e, STM image for hexamer, decamer and pentadecamer. V1 marks the vacancies at the corners, V2 marks the second vacancies at the edges of the QADs (counting from the corners), V3 marks the central vacancies at the edges of pentadecamer, V4 marks the inner vacancies and cross marks the center of pentadecamer. The setpoint is VS = − 2.5 V, It = 300 pA. b, d, f, Schematic illustration for the potential wells and calculation units for hexamer, decamer and pentadecamer. Dark blue marks the vacancy center and light blue marks the surrounding Pt atoms. Red marks the calculation units for taking spectral functions. g-i, Point dI/dV spectra taken at labelled vacancies, QAD center and bare surface. The dashed line indicates the extra edge state at V2 and V3. j, l, n,dI/dV map for the extra state at edges for each QAD. The setpoint is marked at bottom right. k, m, o, Simulation of the corresponding edge state at the energy marked at bottom right.
a-c, STM image for 3V3O2, hexamer and trimer. V1 marks the vacancy at the corners, V2 marks the vacancy at the edges and cross marks the center where the spectra were taken. The setpoint is VS = − 2.5 V, It = 300 pA. d, Comparison between the STS curves taken at the center of 3V3O2, hexamer and trimer. e, Comparison between the STS curves taken at the corners of 3V3O2, hexamer and trimer. f, Comparison between the STS curves taken at the edge of 3V3O2, hexamer and trimer. The spectra taken on the bare surface are shown in red as a reference curve.
Atomic model illustrates the corresponding diffusion pathways a, directly to the neighboring position. c, through the neighboring Te position in the bottom sublayer. e, through the neighboring position above the Te position in the bottom sublayer. g, through the neighboring Pt position. i, through the neighboring Te position in the top sublayer. The arrow in dashed line indicates the pathway of a Te atom migrate from the initial position to the final position, which is equal to a vacancy migration to the opposite direction. b,d,f,h,j, The energy barrier for the corresponding diffusion pathways.
a, Simulation at the energy E = 3.1 eV for scattering from the BB in hexamer. b, Simulation at the same energy with a but from the TB. c, Result of adding a and b with the ratio that marked in a and b. d, g, Simulation at the energy E = 3.07 eV and E = 3.22 eV for scattering from the BB in decamer. e, h, Simulation at the same energy with d, g, but from the TB. f, i, Results of adding d and e, g and h with the same ratio.
Raw data for Fig. 1d.
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Raw data for Extended Data Fig. 4g,h.
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Raw data for Extended Data Fig. 7g–i.
Raw data for Extended Data Fig. 8d–f.
Raw data for Extended Data Fig. 9b,d,f,h,j.
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Fang, H., Mahalingam, H., Li, X. et al. Atomically precise vacancy-assembled quantum antidots. Nat. Nanotechnol. (2023). https://doi.org/10.1038/s41565-023-01495-z