Abstract
Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat band systems are an ideal platform to study the competition of superconductivity and magnetism and their possible coexistence. Recent advances in the field of twisted bilayer graphene highlight this in the context of two-dimensional materials. Two dimensions, however, put severe restrictions on the stability of the low-temperature phases due to enhanced fluctuations. Only three-dimensional flat bands can solve the conundrum of combining the exotic flat-band phases with stable order existing at high temperatures. Here, we present a way to generate such flat bands through strain engineering in topological nodal-line semimetals. We present analytical and numerical evidence for this scenario and study the competition of the arising superconducting and magnetic orders as a function of externally controlled parameters. We show that the order parameter is rigid because the quantum geometry of the Bloch wave functions leads to a large superfluid stiffness. Using density-functional theory and numerical tight-binding calculations we further apply our theory to strained rhombohedral graphite and CaAgP materials.
Highlights
The study of correlated many-particle states in flat-band systems goes back to the consideration of few-particle nuclear-physics systems in the 1960s when Belyaev demonstrated that, in the presence of degenerate single-particle states, interactions can lead to a pairing gap increasing linearly with the interaction strength [1]
We show that the zeroth pseudo-Landau level (PLL) forms a 3D flat band, which evolves from the drumhead surface states of the nodal-line semimetals (NLSMs), and we obtain wave functions thereof
We have proposed a feasible way to create 3D flat bands by applying strain to a nodal-line semimetal
Summary
The study of correlated many-particle states in flat-band systems goes back to the consideration of few-particle nuclear-physics systems in the 1960s when Belyaev demonstrated that, in the presence of degenerate single-particle states, interactions can lead to a pairing gap increasing linearly with the interaction strength [1]. One would expect that the zeroth PLL forms a 3D flat band, while the higher PLLs are flat only in two dimensions and have a dispersion along the nodal line. We show that the zeroth PLL forms a 3D flat band, which evolves from the drumhead surface states of the NLSM, and we obtain wave functions thereof. Using these wave functions and assuming competition between magnetism and superconductivity, we obtain the phase diagram of the system as a function of the filling factor and the interaction strengths. We study the properties of 3D flat bands for the material examples of NLSMs belonging to the CaAgP material class and of rhombohedral graphite
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