(Invited) High-Density, Flip-Chip Alkali Doping of Graphene and Observation of the Lifshitz Transition
Authors: Szkopek Thomas , Aygar Ayse Melis , Durnan Oliver , Bovey Sam , Grueneis Alexander 
Published: August 2024

The physical properties of 2D materials can be tuned by doping to extreme charge carrier density, enabling the investigation of phenomena such as superconductivity, charge density waves, band inversion and Lifshitz transitions. For example, it is variably estimated that an electron density of 3.7 − 5.1 × 1014 cm−2 is required in order to induce a Lifshitz transition in monolayer graphene [1,2]. At this charge density, the Fermi surface passes through the hyperbolic saddle point of graphene at the M-pointin the Brillouin zone, where the Fermi surface geometry changes and the density of states diverges at a van Hove singularity. Achieving charge density sufficient to reach the Lifshitz transition has been limited to chemical doping in ultra-high vacuum (UHV) conditions and observation by angle resolved photoemission spectroscopy (ARPES). Integrating experimental methods for charge transport measurements with UHV chemical doping conditions is typically difficult. Field-effect methods including dielectric gating and ionic liquid gating are readily integrated with charge transport measurements, but achieve lower charge carrier density than UHV chemical doping methods.

We report here an integrated flip-chip method to dope graphene by alkali vapour in the diffusive regime, suitable for charge transport measurements at ultra-high charge carrier density. We introduce a liquid cesium droplet source into a sealed cavity filled with inert gas (argon) to dope a monolayer graphene Hall bar on a quartz substrate by the process of cesium atom diffusion, adsorption and ionization at the graphene surface (Fig. a). Doping can be monitored by operando ac Hall measurement of longitudinal Rxx
and transverse Rxy
resistance of graphene (Fig. b). An optical image of a representative graphene Hall bar is shown in Fig. c (scale bar = 100 μm). The measured time dependent Rxx
and Rxy
during Cs exposure can be used to determine the time dependent electron density n and electron mobility μ.

Upon sealing, the flip-chip assembly containing doped graphene is stable in ambient conditions, enabling sample characterization by various means, including non-resonant Raman scattering measurement through the transparent quartz window. Charge transport versus temperature and magnetic field in a variable temperature insert was performed, including Hall measurements to B = 7 T (Fig. d). By these methods, we confirm that flip-chip doping with Cs can be used to achieve charge density exceeding 4 × 1014 cm−2 . The Lifshitz transition is observed via the inversion of cyclotron effective mass, corresponding to sign inversion of the Hall coefficient RH
(Fig. d). Employing a third-nearest-neighbour tight binding (3NNTB) calculation, we estimate the Fermi energies and Fermi surfaces corresponding to the charge densities observed by high field magnetotransport (Fig. e). At the Lifshitz transition, the Fermi surface transforms abruptly from that of electron pockets around the K and K' points, to a hole pocket around Γ. Further experimental observations will be discussed.

In summary, our findings show that chemical doping, hitherto restricted to ultra-high vacuum conditions, can be applied in a diffusive regime at ambient pressure in an inert gas environment. We anticipate that our flip-chip doping method can be applied to a variety of 2D materials and dopant speciies beyond monolayer graphene and Cs.

[1] P. Rosenzweig et al., "Overdoping graphene beyond the van Hove singularity", Physical Review Letters 125, 176403 (2020).

[2] A. Zaarour et al., "Flat band and Lifshitz transition in long-range-ordered supergraphene obtained by Erbium intercalation. Physical Review Research 5, 013099 (2023).

Figure 1