Cloning of Dirac fermions in graphene superlattices

Cloning of Dirac fermions in graphene superlattices

| L. A. Ponomarenko, R. V. Gorbachev, G. L. Yu, D. C. Elias, R. Jalil, A. A. Patel, A. Mishchenko, A. S. Mayorov, C. R. Woods, J. R. Wallbank, M. Mucha-Kruczynski, B. A. Piot, M. Potemski, I. V. Grigorieva, K. S. Novoselov, F. Guinea, V. I. Fal'ko, A. K. Geim
Graphene superlattices, formed by aligning graphene with hexagonal boron nitride (hBN), exhibit unique electronic properties. When placed on a boron nitride substrate, the moiré potential induced by the lattice mismatch leads to profound changes in graphene's electronic spectrum. Second-generation Dirac points appear as pronounced peaks in resistivity, accompanied by a reversal of the Hall effect, indicating a change in the sign of the effective mass within graphene's conduction and valence bands. Quantizing magnetic fields lead to Zak-type cloning of the third generation of Dirac points, observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices enable the study of rich physics expected for incommensurate quantum systems and demonstrate the possibility to controllably modify electronic spectra of 2D atomic crystals by using their crystallographic alignment within van der Waals heterostructures. The moiré potential leads to the formation of superlattice minibands, which are observed as new low-field oscillations and internal structures within Landau levels. The spectral reconstruction occurs near the edges of the superlattice's Brillouin zone, characterized by wavevector G = 4π/√3D and energy E_S = ħv_F G/2 (D is the superlattice period and v_F is graphene's Fermi velocity). The alignment of graphene and hBN with accuracy ≈1° is crucial for observing moiré minibands in transport properties, as it determines the superlattice period D and the energy scale E_S. The transport properties of aligned graphene devices show standard peaks in resistivity at zero n, graphene's main neutrality point (NP). Additional peaks appear symmetrically at high doping n = ±n_s. The sign reversal of Hall resistivity indicates the presence of hole(electron)-like carriers in the conduction(valence) band of graphene. The extra NPs are attributed to the superlattice potential induced by hBN, resulting in minibands with isolated secondary Dirac points. This interpretation aligns with theory and tunneling features reported in previous studies. The transport characteristics of aligned devices are typical for graphene on hBN, with conductivity σ(n) varying linearly with n and described by constant mobility μ. Around the secondary NPs, σ depends linearly on (n - n_s). The hole-side secondary NP exhibits low-T μ similar to the main NP, while the electron-side secondary NP shows higher μ. However, the main and secondary NPs exhibit different temperature dependences of both μ and minimum conductivities. The observed σ(T) do not support the idea of significant energy gaps induced by the superlattice. Quantization in graphene superlattices is observed as plateaus in ρ_xy and zeros in ρ_xx at filling factors v ≡ nφ₀/B = ±2, 6,Graphene superlattices, formed by aligning graphene with hexagonal boron nitride (hBN), exhibit unique electronic properties. When placed on a boron nitride substrate, the moiré potential induced by the lattice mismatch leads to profound changes in graphene's electronic spectrum. Second-generation Dirac points appear as pronounced peaks in resistivity, accompanied by a reversal of the Hall effect, indicating a change in the sign of the effective mass within graphene's conduction and valence bands. Quantizing magnetic fields lead to Zak-type cloning of the third generation of Dirac points, observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices enable the study of rich physics expected for incommensurate quantum systems and demonstrate the possibility to controllably modify electronic spectra of 2D atomic crystals by using their crystallographic alignment within van der Waals heterostructures. The moiré potential leads to the formation of superlattice minibands, which are observed as new low-field oscillations and internal structures within Landau levels. The spectral reconstruction occurs near the edges of the superlattice's Brillouin zone, characterized by wavevector G = 4π/√3D and energy E_S = ħv_F G/2 (D is the superlattice period and v_F is graphene's Fermi velocity). The alignment of graphene and hBN with accuracy ≈1° is crucial for observing moiré minibands in transport properties, as it determines the superlattice period D and the energy scale E_S. The transport properties of aligned graphene devices show standard peaks in resistivity at zero n, graphene's main neutrality point (NP). Additional peaks appear symmetrically at high doping n = ±n_s. The sign reversal of Hall resistivity indicates the presence of hole(electron)-like carriers in the conduction(valence) band of graphene. The extra NPs are attributed to the superlattice potential induced by hBN, resulting in minibands with isolated secondary Dirac points. This interpretation aligns with theory and tunneling features reported in previous studies. The transport characteristics of aligned devices are typical for graphene on hBN, with conductivity σ(n) varying linearly with n and described by constant mobility μ. Around the secondary NPs, σ depends linearly on (n - n_s). The hole-side secondary NP exhibits low-T μ similar to the main NP, while the electron-side secondary NP shows higher μ. However, the main and secondary NPs exhibit different temperature dependences of both μ and minimum conductivities. The observed σ(T) do not support the idea of significant energy gaps induced by the superlattice. Quantization in graphene superlattices is observed as plateaus in ρ_xy and zeros in ρ_xx at filling factors v ≡ nφ₀/B = ±2, 6,
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