Flat electronic bands from cooperative moiré and charge order

Abstract

The formation of flat electronic bands from long-wavelength superperiodic moiré potentials in van der Waals heterostructures underpins the creation and control of a host of highly-tuneable correlated and topological phases. The underlying moiré periodicity is, however, typically considered a fixed property of the heterostructure. Here, we show how the development of a charge-density wave (CDW) in one of the constituent materials can create an emergent moiré periodicity, realising a superperiodic potential in TiSe$_2$/graphite epitaxial heterostructures with an order-of-magnitude longer wavelength than that expected from the normal-state lattice mismatch. We demonstrate how this drives the formation of a remarkably strong band flattening, which can be readily deactivated by carrier doping across the CDW phase transition, opening new prospects for engineering moiré matter by exploiting the rich many-body states of the parent compounds of 2D heterostructures.

Figures (11)

• Figure 1: Monolayer-TiSe$_2$/graphite van der Waals heterostructures. (a) Schematic side view of the crystal structure of a single TiSe$_2$ layer grown epitaxially on a graphite substrate. (b) Corresponding top view of the Ti atom layer, showing the $(2\times2)$ unit cell arising from the periodic lattice distortion associated with its CDW instability (arrows indicate the directions of the atomic displacements). (c) Moiré superlattice formed from the lattice mismatch between the top-most graphite layer and the $(1\times1)$ undistorted (normal-state) structure of the TiSe$_2$ layer. The corresponding moiré unit cell is shown in yellow. (d) Brillouin zones corresponding to the original graphite (black) and $(1\times1)$ TiSe$_2$ (blue) structures, and the reconstructed Brillouin zones associated with the CDW (dashed blue) and moiré (yellow) unit cells. A putative small secondary moiré zone is shown in red, arising due to the interplay of the original moiré periodicity and the charge order.
• Figure 2: Moiré periodicities in the normal and charge-ordered state of ML-TiSe$_2$. (a) Low-energy electron diffraction pattern measured from a ML-TiSe$_2$/Gr heterostructure using a low-energy electron microscope (see Methods SuppInfo) in the normal state of TiSe$_2$ ($T=300$ K). The inset shows a magnified view with enhanced contrast. (b) Corresponding simulation (see Section I of SuppInfo) showing the expected reciprocal space pattern for the moiré heterostructure formed between the graphite and TiSe$_2$ layers, in good agreement with our measured data. (c) STM topography measured at $T=1.8$ K (tunnelling setpoint $V_{s} = 220$ mV, $I_{s}=100$ pA), deep within the CDW state. The inset shows a high-resolution magnified view highlighting the CDW $2 \times 2$ periodicity (tunnelling setpoint $V_{s} = 60$ mV, $I_{s}=420$ pA). (d) Fourier transform of the STM topography showing the primary TiSe$_2$ and graphite Bragg peaks together with a rich array of charge-order ($\mathbf{q}_{\mathrm{CDW}}$) and substrate-induced moiré ($\mathbf{q}_\mathrm{m}^{\mathrm{lat}}$) peaks, as well as additional Bragg spots due to the co-operative effect of both ($\mathbf{q}_\mathrm{m}^{\mathrm{CDW}}$). The corresponding CDW and hybrid moiré unit cells are shown in blue and red in (c), respectively. (e) Bragg peaks expected from our moiré lattice calculations (see Section I of SuppInfo), in good agreement with those measured in (d).
• Figure 3: Flat band formation. (a) Overview of the electronic structure of ML-TiSe$_2$/Gr as measured by ARPES ($h\nu=150$ eV, LH-polarisation, $T=18$ K). The insets show magnified views of the Fermi surface in the vicinity of the K-point of the graphite Brillouin zone ($h\nu=80$ eV, LH-pol) and M-point of the TiSe$_2$ zone ($h\nu=37$ eV, LH-pol), respectively. (b) Dispersion measured along $\Gamma$-M ($h\nu=30$ eV, LH-pol.). (c) Magnified view ($h\nu=20$ eV, LH-pol., left) and corresponding second-derivative analysis (right) close to the top of the valence band backfolded by the CDW. (d) Selected EDCs extracted from close to M$_\mathrm{TiSe_2}$, and corresponding fitted peak positions (open circles), showing the formation of flat electronic bands. (e) Schematic illustration of backfolding of three elliptical conduction band pockets by the $3\mathbf{q}$ CDW instability in TiSe$_2$, and (f) corresponding effective model of the electronic structure in the CDW state, including symmetry-selective band hybridisations antonelli_orbital-selective_2022, projected onto the Ti 3$d$ and Se 4$p$ atomic orbitals. (g) Continuum model calculations incorporating a periodic potential defined by the hybrid CDW-moiré wavevector $\mathbf{q}_\mathrm{m}^{\mathrm{CDW}}$, projected onto the states of the original cell, and (h) corresponding simulated spectral function.
• Figure 4: Control via carrier doping. (a) Schematic doping-dependent phase diagram of ML-TiSe$_2$, showing the suppression of CDW order with increasing electron doping watson_strong-coupling_2020, and the expected emergence morosan_superconductivity_2006li_controlling_2015 of a superconducting (SC) dome at low temperature. (b-d) Electronic structure measurements in the CDW state: (b) measurements of the conduction band at $\Gamma$ ($h\nu=25$ eV, LH-pol.), with a magnified view inset; (c) measurements of the valence band at $\Gamma$ ($h\nu=17.5$ eV, LH-pol.); (d) overview measurements along $\Gamma$-M ($h\nu=39$ eV, LV-pol.). (e-g) Equivalent measurements following the deposition of dilute (sub-monolayer) coverage of Rb atoms on the surface, causing an electron doping and the suppression of the CDW. The approximate locations of our measured samples in the TiSe$_2$ phase diagram are indicated by the arrows in (a).
• Figure :