Extended van Hove Singularity and Superconducting Instability in Doped Graphene

We have investigated the effects of doping on a single layer of graphene using angle-resolved photoemission spectroscopy. We show that many-body interactions severely warp the Fermi surface, leading to an extended van Hove singularity (EVHS) at the graphene $M$ point. The ground state properties of graphene with such an EVHS are calculated, analyzing the competition between a magnetic instability and the tendency towards superconductivity. We find that the latter plays the dominant role as it is enhanced by the strong modulation of the interaction along the Fermi line, leading to an energy scale for the onset of the pairing instability as large as 1 meV when the Fermi energy is sufficiently close to the EVHS.

Figure 1

Doping dependence of (upper) Fermi surface and (lower) band structure of $\pi$ bands along the $MK\Gamma$ directions, for various combinations of doping from (a) as-grown graphene, (b)–(h) graphene with Ca and/or K deposition as labeled. The scale bars in (f) apply to parts (a)–(f) only.

Figure 2

The spectral function for the sample in Fig. 1h (a) along and (b) across the $K\mathrm{\text{−}}{K}^{\prime }$ line through the $M$ point. The dotted black lines and the dashed black lines are model energy bands from the literature [4, 11, 12]. The full line is an empirical tight-binding model from this work. The red solid line is a guide to the measured energy band. The red arrows indicate the incoherent mode arising from phonon coupling as described in the text. The insets to (b) are, above, momentum distribution curves across the $M$ point as a function of binding energy, and, right, angle-integrated energy distribution at $M$.

Figure 3

(a)–(d) Tight-binding fits to various published graphene model band structures [4, 11, 12] and our empirical band structure [14]. The gray regions highlight the waist of the VHS, defined as the range where the width varies by $<5\%$. (e) The experimental Fermi surfaces for the samples in Figs. 1a, 1b, 1c, 1d, 1e, 1f, 1g, 1h, overlaid on an image of the constant-energy surface at the VHS from the sample in Fig. 1h (55 meV below $E_F$) [34].

Figure 4

Phase diagram showing the contours of constant coupling $|\lambda |$ (black lines) and constant transition temperature for the ferromagnetic instability (blue lines) as a function of the local Coulomb interaction $U$ and the Fermi energy $\mu$ relative to the VHS. The two colored regions correspond to different order parameters of the pairing instability with the symmetry of the $\cos (3\theta )$ representation (blue) and that of the $\{\cos (2\theta ),\sin (2\theta )\}$ representation (orange) of the point group.