Direct visualization of gate-tunable flat bands in twisted double bilayer graphene

TL;DR

The paper addresses the lack of direct, momentum-resolved characterization of how twist, displacement field, and carrier density reshape flat bands in twisted double bilayer graphene (TDBG). Using micro-focused angle-resolved photoemission spectroscopy (microARPES) at a twist angle of 1.6°, the authors map the dispersion under electrostatic gating while varying back-gate voltage to tune the displacement field and carrier density. They observe multiple flat moiré minibands near charge neutrality, including a flat remote valence band, with conduction-band c1 and valence-band v1 becoming nearly flat around V_G=8–10 V, and report bandwidths on the order of tens of meV. The data indicate U/W ≳ 1 (with U ~ 50 meV and W in the tens of meV), signaling dominant Coulomb interactions and suggesting a favorable regime for interaction-driven correlated states; the formation and evolution of flat bands arise from the interplay between filling and displacement field, with no evidence of strong electron-phonon coupling signatures such as replica flat bands.

Abstract

The symmetry-broken correlated states in twisted double bilayer graphene (TDBG) can be tuned via several external knobs, including twist angle, displacement field, and carrier density. However, a direct, momentum-resolved characterization of how these parameters reshape the flat-band structure remains limited. In this study, we employ micro focused angle-resolved photoemission spectroscopy to investigate the flat-band dispersion of TDBG at a twist angle of 1.6, systematically varying the displacement field and carrier density via electrostatic gating. We directly observe multiple flat moir'e minibands near charge neutrality, including a flat remote valence band residing below the low-energy flat-band manifold. Furthermore, the dominant Coulomb repulsive energy over the flat- band bandwidth suggests favorable conditions for the emergence of interaction-driven correlated phenomena in TDBG. These findings establish that the formation and evolution of flat bands in TDBG arises from the interplay between the electron filling and the displacement field.

Figures (8)

• Figure 1: (a) Schematic diagram of TDBG/hBN/graphite on SiO$_2$ substrate. It illustrates a photoemission setup with a microfocus beam and gate voltage is applied on graphite. (b) The purple hexagon geometry of the mini Brillouin zone (mBZ) originated from top BG (blue hexagon) and bottom BG (red hexagon). The blue and red dots mark the locations of originals ${\rm{K_2}}$-point from top BG and ${\rm{K_1}}$ point from bottom BG. mBZ high symmetry points $\Gamma_{\rm{m}}$, $\rm{K}_{\rm{m}}$, and $\rm{M}_{\rm{m}}$ are indicated in purple hexagon.(c) Optical microscope image of the device. Top BG (blue), bottom BG (red), hBN (green), and graphite (purple) regions are indicated by different color lines. (d) Spatially dependent ARPES intensity integrated over energy and momentum within the dashed box in the left panel of (g). This image is generated from real space mapping the valence band spectra and integrating the signal. (e) The theoretical band structure of TDBG in the absence of interlayer interaction. (f) The perturbative interband hybridization through the interlayer tunneling. Here, the intrinsic bilayer gaps (2$\Delta_1$ and 2$\Delta_2$), and band offset (2$\Delta'$) due to a perpendicular electric field.(g) Energy-momentum dispersion of top BG, bottom BG, and TDBG at $\rm{V_G} = 0$ V. Scale bars = 0.1 Å$^{-1}$
• Figure 2: Snapshot of energy-momentum dispersion of (a) top BG (top panel), (b) bottom BG (middle panel), and (c) TDBG (bottom panel) at different $V_G=$ 2 V, 6 V, 8 V, and 10 V (from left to right). The scale bar indicates 0.1 Å$^{-1}$. Scale bars = 0.1 Å$^{-1}$ (d) Carrier densities, for both top and bottom BGs, are determined as $k_{\rm{F}}^2/\pi$. $k_{\rm{F}}$ is the Fermi momentum vector. The calculated displacement field (${D}_T$), determined from the carrier densities, is shown on the right axis. (e) The average EDCs extracted over the flat band region for different $V_G$. The solid black line indicates Lorentzian peaks fit at the $V_G = 6, 8, \rm{and}~10~\rm{V}$. Blue, green, red, and yellow arrows and lines demarcate peak positions and fittings corresponding to c1, v1, v2, and v3, respectively. (f) The fitted peak positions of c1, v1, and v2 from the EDC analysis at different $V_G$.
• Figure 3: (a) The top panel presents the energy-momentum dispersion of TDBG under an applied gate voltage of 10 V along different high-symmetry directions in the moiré Brillouin zone (mBZ). The cut directions are indicated by arrows in the purple hexagon (mBZ schematic) at the top-left corner. Scale bar = 0.1 Å$^{-1}$. The bottom panel shows the corresponding second-order derivative plots. The calculated band positions—c1, v1, v2, and v3—are represented by blue, green, red, and yellow dashed lines, respectively. (b) EDCs $\#1 – \#4$, extracted along the $\rm{K_1}$ – $\rm{K_2}$ cut direction from the top-left figure, illustrate the band positions. The corresponding color-coded arrows indicate the alignment of the extracted bands.
• Figure S1: A detailed step-by-step (1 to 8) sample fabrication method is shown schematically. A PC based PDMS stamp is used to pick up flakes. In a sequence of top BG, bottom BG, hBN, and graphite are picked up. After putting the stack on Si/SiO$_2$ chip, electrodes are designed. The prepared sample is annealed at $T$= 200 $^0\rm{C}$ and pressure $\sim10^{-9}~\rm{mbar}$ for 4 hr.
• Figure S2: (a) AFM scan of the heterostructure. (b) High profile scan along two lines. The scan results show the thickness of used hBN is about 15 nm