Emergent Massless Dirac Fermions in Moiré Bands of Bilayer Graphene/hBN Superlattice

TL;DR

This work demonstrates that a hBN moiré potential applied to bilayer graphene selectively reconstructs the electronic spectrum, preserving a massive parabolic primary band ($t=4m$, $s=0$) while generating moiré secondary bands ($t=4m+2$, $s=4$) that host massless Dirac fermions with Berry phase $\pi$. Through dual-gated magnetotransport, the authors observe distinct Landau fans for the two bands, extract effective masses, and reveal a reduced Fermi velocity $v_M$ (~$3.6\times10^5$ m/s) in the secondary Dirac-like band, consistent with band flattening from the moiré potential. Berry phase analyses yield $\Phi_B=2\pi$ for the primary band and $\Phi_B=\pi$ for the secondary, confirming their respective topologies. The study combines precise twist-angle control, FFT-based band separation, and empirical effective-mass modeling to establish a platform for tunable topological quantum transport and potential correlated phases in BLG/hBN moiré systems.

Abstract

A superlattice of multilayer graphene and hBN has proven to be a promising pathway for engineering electronic band structures and topologies. In this work, we experimentally demonstrate the role of hBN alignment in inducing topological band reconstruction in bilayer graphene (BLG) superlattices. Our study establishes that while the primary band retains its massive chiral naure, the secondary bands host massless, chiral fermions. Magnetotransport measurements, including Quantum Hall, temperature-dependent Shubnikov-de Haas oscillations, and Berry phase analysis, confirm the distinct topological nature of these bands. A significantly reduced Fermi velocity in the moiré secondary band indicates band flattening induced by the moiré potential. Our study provides a pathway for controlling topological quantum transport in BLG/hBN superlattices.

Figures (7)

• Figure 1: Characteristics of the moiré device (a) Schematic of the device layers indicating moiré pattern formation between BLG and top hBN (b) Plot of ${R_{xx}}$ as a function of $n$ measured at $T = 2$$\mathrm{K}$ . The moiré satellite peaks at $n_{M} = \pm 3.20\times 10^{16}~\mathrm= 4n_0$ are marked with dashed blue line. (c) Plot of BZ magnetoconductance oscillations versus $1/B$ for different carrier densities measured at $T = 100$$\mathrm{K}$. The numbers next to each plot refers to $n$ (in units of $10^{16}~\mathrm{m^{-2}}$). (d) The Fourier spectrum of the BZ oscillations measured at $n=4.1\times10^{16}$$\mathrm{m^{-2}}$ exhibiting a single prominent peak at $f_{BZ} =33.2$ T. (e) Three-dimensional schematic of the first and second electron and hole bands at the $K$-valley.
• Figure 2: Quantum oscillations revealing signatures of Dirac band (a) 2-D map of $R_{xx}$ as a function of moiré band filling $n/n_{0}$ and magnetic field $B$, showing Landau fan patterns emerging from the primary band ($n/n_{0} = 0$) and secondary bands ($n/n_{0} = \pm 4$). (b) 2-D map of $R_{xx}$ as a function of $B$ and filling fraction $\nu_\mathrm{P} = nh/eB$ of the primary band. White dashed lines mark prominent minima at $\nu_\mathrm{P} = 4m$ ($m \in \mathbb{Z}$), characteristic of bilayer graphene. (c) Line cut of panel (b) at $B = 1$ T, showing clear $R_{xx}$ minima at $\nu_\mathrm{P} = 4m$. (d) 2-D map of $R_{xx}$ as a function of $B$ and the effective filling fraction of secondary band $\nu_\mathrm{M} = (n - 4n_{0})h/eB$. White dashed lines highlight minima at $\nu_\mathrm{M} = 4m + 2$, indicative of Dirac-like Landau level structure. (e) Line cut of panel (d) at $B = 4.5$ T, showing clear $R_{xx}$ minima at $\nu_\mathrm{M} = 4m + 2$. The color scales in panels (a), (b), and (d) are identical.
• Figure 3: Effective mass from SdH oscillations (a) SdH oscillations in $R_{xx}$ plotted as a function of inverse magnetic field ($1/B$) at $n = 4.05 \times 10^{16}~\mathrm{m}^{-2}$ ($n/n_0 = 5.06$). (b) FFT of the oscillations at $T = 20~\mathrm{mK}$, showing two dominant frequencies attributed to contributions from the primary and secondary bands, indicated by arrows. (c) Plot of the extracted frequencies with normalized carrier density ($n/n_0$). The blue open circles (red filled circles) are the data for the primary (secondary) band. The blue (red) line represents the fit given by $n= g_sg_veB^P_F/h$ ($|n-4n_0|= g_sg_veB^M_F/h$) for the primary band (secondary band), with $g_sg_v=4$ being the spin and valley degeneracy. (d) Amplitude of SdH oscillations versus $T$ for the primary (blue open circles) and secondary bands (red filled circles). Dashed lines fit the LK formula. (e) Normalized effective mass of the primary band $m^*_{\mathrm{P}}/m_e$ as a function of $n/n_0$. The dashed line marks the average value $m^*_{\mathrm{P}}/m_e = 0.035$. (f) Normalized effective mass of the secondary band $m^*_{\mathrm{M}}/m_e$ plotted versus $n/n_0$. The red dashed line is a fit to $m^*_{\mathrm{M}}/m_e = A\left| (n-4n_0)/n_0 \right|^{\alpha}$. The error bars in panels (e) and (f) are calculated from the standard deviation of $m^*$ values obtained from LK fits over different magnetic field windows.
• Figure 4: Berry phase analysis (a) Plots of Landau index $\mathrm{N_{P}}$ vs $1/B$, for primary band showing intercept $\beta=1$ ($\phi_B = 2\pi$) over a range of carrier density $n/n_0$. (b) Zoomed in plots of (a), highlighting the intercept of $\beta=1$. (c) Plots of Landau index $\mathrm{N_{M}}$ vs $1/B$ for secondary band, showing intercept $\beta=0.5$ ($\phi_B = \pi$) over a range of carrier density $n/n_0$. (d) Zoomed in plots of (c), highlighting the intercept of $\beta=0.5$.
• Figure S1: Raman spectra of BLG flakes. Plots of the $\mathrm{2D}$ Raman peak of the bilayer graphene used to fabricate the device. The black-filled circles are the experimentally measured Raman spectra. The red solid line is the cumulative of the four Lorentzians fitted to it; the four Lorentzians are also individually shown. Inset: Optical images of the BLG flake -- the area marked by the black line marks the portion used for device fabrication. Scale bar: 20 $\mu$m.