Van-Hove tuning of Fermi surface instabilities through compensated metallicity

Abstract

Van-Hove (vH) singularities in the vicinity of the Fermi level facilitate the emergence of electronically mediated Fermi surface instabilities. This is because they provide a momentum-localized enhancement of density of states promoting selective electronic scattering channels. High-temperature topological superconductivity has been argued for in graphene at vH filling which, however, has so far proven inaccessible due to the demanded large doping from pristine half filling. We propose compensated metallicity as a path to unlock vH-driven pairing close to half filling in an electronic honeycomb lattice model. Enabled by an emergent multi-pocket fermiology, charge compensation is realized by strong breaking of chiral symmetry from intra-sublattice hybridization, while retaining vH dominated physics at the Fermi level. We conclude by proposing tangible realizations through quantum material design.

Figures (5)

• Figure 1: Absence of chiral symmetry and compensated metallicity (a) Real space lattice structure and hybridization elements of the honeycomb Hubbard model, as given in Eq. \ref{['eqn:model']}. (b) Single particle dispersion of the kinetic terms of Eq. \ref{['eqn:model']}. Finite next-nearest neighbor hybridization breaks particle-hole symmetry and shifts the lower van-Hove singularity towards the Fermi level at half filling (dashed line). (c) Fermi surfaces at half filling within the hexagonal BZ, corresponding to the $t_2/t_1$ hopping values shown in (b). Electron (hole) pockets are indicated by crossed (diagonal) hatching. The perfectly nested outer FS is indicated by dashed line. (d) Lower vH filling and associated DoS at the Fermi level as a function of $t_2/t_1$. The dashed lines indicate $t_2/t_1$ values of (b) and (c). The opening of the electron pocket (ep) around $\Gamma$ (gray) shifts the vH towards pristine half filling ($n=1$). The numeric density of states (DOS) at an interval around vH is indicated along the vH line.
• Figure 2: Many body analysis at lower van-Hove singularity. (a) Leading eigenvalue of the bare susceptibility $\chi_0$ (Eq. \ref{['eqn:bare_susc']}). Both the dependence on $t_2$ along lower van-Hove (lvH) filling and the doping dependence at fixed long range hopping is depicted. The inset shows the full band-resolved fluctuation spectrum including intra-pocket (ep and hp) and inter-pocket (ip) contributions at $t_2=0.85 \, t_1$ and $n=1.0$. (b) Resulting phases for Fermi level detuning $\Delta E$ from lvHs at intermediate interaction scale $U = 1.5\, t_1$. The intensity of the color indicates the SC pairing strength, which is proportional to the transition temperature $T_c$. (c) Superconducting gaps of the chiral $d$-wave ($E_2$) and $s_{\pm}$ ($A_1$) phase, respectively. Each of the two leading basis functions of the inversion odd $E_2$ irrep is shown in one half of the BZ. Almost identical to the leading $E_2$ gap function for Germanene structure tuned to vH filling via compressive strain (Ge-$E_2$, details in SM), the superconducting pairing is exclusively situated on the outer vH pocket. All calculations were performed with $( 800 \times 800 )$ integral points and an inverse temperature $\beta = 250 / t_1$ to obtain converged results.
• Figure S1: Critical cutoffs $\Lambda_C$ for the leading instabilities in the FRG as a function of onsite repulsion and doping around the lower vHs (dashed line). All values are given in units of $t_1$. The gray region indicates where the data becomes unreliable due to finite momentum resolution. The obtained results are consistent with the RPA results presented in Figure 2(b) of the main paper.
• Figure S2: Xene lattice parameter with applied biaxial strain. (a) Real space position of the honeycomb sublattice sites in a buckled structure with (next) nearest neighbour distance $\delta$ ($a$). (b) Dependence of relative bond lengths for the Xene structures silicene, germanene and stanene on strain. The strain is quantified as the enforced relative compression of the lattice constant of the fully relaxed structure. The black line indicates the $\delta / a$ ratio for the ideal honeycomb structure considered in the main text. (c) Energy offset of the upper van-Hove point from the Fermi level as a function of compressive strain for the different Xene compounds. (d) Density functional theory band structures of silicene (Si), germanene (Ge), and stanene (St) for different values of strain. The dashed line indicates pristine half filling for each strain value individually.
• Figure S3: Orbital character on the FS for germanene strained by $6\%$. Two exemplary $sp_2$ orbitals are shown on the left. The $p_z$ orbital is mainly contributing to the outer Fermi pocket that is facilitating the $E_2$ SC phase. These properties are recovered qualitatively by silicene and stanene.