Dispersion-Selective Band Engineering in an Artificial Kagome Superlattice (2024)

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  Figure 1

  High-order kagome potential and sample layout of the artificial kagome device. (a)Three harmonic components of a kagome superlattice potential. Points at the corner of each hexagon are the corresponding first (red), second (blue), and third (green) harmonics in the reciprocal space that defines $U_1$, $U_2$, and $U_3$ terms in Eq.(1). (b)–(d)Real-space distributions of the modeled potential with $U_1+U_2+U_3$ (b), $U_1$ (c), and $U_2+U_3$ (d)terms, respectively. Black hexagon and black arrows in (b) are the primitive unit cell and the lattice vectors, respectively. The long-wavelength triangular component and shared-corner triangular component of the kagome potential are illustrated by black lines in (c) and (d), respectively. (e)Side-view schematic of the artificial-lattice device. $V_{\text{g}}$ is applied on the prepatterned few-layer graphite (PFG). (f)Scanning electron microscopy image of the PFG with an artificial kagome-lattice pattern.

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  Figure 2

  Spectral weight redistribution of the multiple Dirac resistance peaks. (a),(b) Longitudinal resistance $R_{xx}$ map as a function of $n$ and $V_{\mathrm{Si}}$, and corresponding line cuts, measured at $T=1.5\mathrm{K}$. The curves in (b) are shifted for clarity. The red and green arrows point to the IDP and the SDPs, respectively. (c),(d) Hall resistance $R_{xy}$ at $B=0.1\mathrm{T}$ as a function of $n$ and $V_{\mathrm{Si}}$, and corresponding line cuts.

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  Figure 3

  Calculated DOS and band structures of the artificial kagome lattice. (a)DOS map as a function of $n$ and $V_{\mathrm{on}\text{−}\mathrm{site}}$. (b)–(d)Band structures and DOS at different $V_{\mathrm{on}\text{−}\mathrm{site}}$, with the intrinsic Dirac bands and satellite Dirac bands highlighted by red and green, respectively. The red and green arrows in (a)–(d)point to the IDPs and SDPs, respectively. The zero-energy points are fixed at the IDPs for a better comparison with experiments (see Supplemental Fig.S10 [23]). (e)Distributions of electronic states in real space corresponding to the different sites marked in (c). The unit cell of the kagome superlattice and the artificial-lattice sites are outlined by the red dashed rhomboid and white dashed circles, respectively.

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  Figure 4

  Spectral weight redistribution of the Dirac bands induced by magnetic field. (a),(b) Longitudinal resistance $R_{xx}$ map as a function of $n$ and $B$, and corresponding line cuts, at $V_{\mathrm{Si}}=-60\mathrm{V}$. (c),(d) Hall resistance $R_{xy}$ map as a function of $n$ and $B$, and corresponding line cuts. The red and green arrows in (a)–(d)indicate the positions of IDP and SDP, respectively.

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