Orbital limit and Gaussian fluctuation effects in flat-band superconductors with pseudomagnetic fields

In this work we study a molecular graphene model on the top of a superconductor in the presence of pseudomagnetic fields induced by coplanar strain fields. With the pseudomagnetic fields and the attractive interaction induced from the substrate, a flat-band superconductor can be achieved according to mean field analysis on the effective Hamiltonian. Based on a semiclassical approximation, we first show that the orbital limit is hugely enhanced by the pseudomagnetic fields. The physical reason is that the orbital angular momenta locking at $K$ and $K^{\prime }$ valleys due to the pseudomagnetic fields suppress the orbital magnetization from external magnetic fields. Considering the vanishing bandwidth in this system, we then study the effects of Gaussian fluctuations in both Hartree and pairing channels. We show that in the dilute limit, the phase transition is dominated by collective modes with critical temperatures much lower than the mean field results. At half-filling, our method gives no corrections to the mean field critical temperatures.

Figure 1

(a) Simplified sketch of the model discussed in the main text. Molecules (bigger green spheres) are placed as triangular lattice on the top of a superconducting thin film, consequently the electrons (smaller yellow spheres) are squeezed into the middle region and form honeycomb lattice. The pseudomagnetic field can be induced by three coplanar ${120}^{\circ }$ strain fields. (b) The Brillouin zone of the formed honeycomb lattice with the high symmetric points $(K,\mathrm{\Gamma },M,K^{\prime })$ pointed out. The normal state low energy physics lies at $K$ and $K^{\prime }$ points, described by a Dirac Hamiltonian. With the strain fields, electrons at $K$ and $K^{\prime }$ valleys experience opposite pseudomagnetic fields $B_p$ and $-B_p$ along $z$ direction.

Figure 2

(a) The critical temperature $T_c$ as a function of the filling factor $\nu$. The inserted figure is the zoom-in view of the rectangular region. (b) The order parameter as a function of temperature for two different fillings as stated in the figure. In both figures, the dashed curves represent the results calculated with Gaussian fluctuations (GF) effect while the solid curves are calculated from merely mean field theory (MF).