Strontium ruthenate (${\mathrm{Sr}}_2{\mathrm{RuO}}_4$) has long been thought to host a spin-triplet chiral $p$-wave superconducting state. However, the singletlike response observed in recent spin-susceptibility measurements casts serious doubts on this pairing state. Together with the evidence for broken time-reversal symmetry and a jump in the shear modulus $c_{66}$ at the superconducting transition temperature, the available experiments point towards an even-parity chiral superconductor with $k_z(k_x\pm i{k}_y)$-like $E_g$ symmetry, which has consistently been dismissed based on the quasi-two-dimensional electronic structure of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. Here, we show how the orbital degree of freedom can encode the two-component nature of the $E_g$ order parameter, allowing for a local orbital-antisymmetric spin-triplet state that can be stabilized by on-site Hund's coupling. We find that this exotic $E_g$ state can be energetically stable once a complete, realistic three-dimensional model is considered, within which momentum-dependent spin-orbit coupling terms are key. This state naturally gives rise to Bogoliubov Fermi surfaces.

Twisted bilayer graphene has recently attracted a lot of attention for its rich electronic properties and tunability. Here we show that for very small twist angles, $\alpha \ll 1°$, the application of a perpendicular electric field is mathematically equivalent to a new kind of artificial gauge field. This identification opens the door for the generation and detection of pseudo-Landau levels in graphene platforms within robust setups, which do not depend on strain engineering and therefore can be realistically harvested for technological applications. Furthermore, this new artificial gauge field leads to the development of highly localized modes associated with flat bands close to charge neutrality, which form an emergent kagome lattice in real space. Our findings indicate that for tiny angles biased twisted bilayer graphene is a promising platform that can realize frustrated lattices of highly localized states, opening a new direction for the investigation of strongly correlated phases of matter.

Twisted van der Waals materials have been shown to host a variety of tunable electronic structures. Here we put forward twisted trilayer graphene (TTG) as a platform to emulate heavy fermion physics. We demonstrate that TTG hosts extended and localized modes with an electronic structure that can be controlled by interlayer bias. In the presence of interactions, the existence of localized modes leads to the development of local moments, which are Kondo coupled to coexisting extended states. By electrically controlling the effective exchange between local moments, the system can be driven from a magnetic into a heavy fermion regime, passing through a quantum critical point, allowing one to electrically explore a generalized Doniach phase diagram. Our results put forward twisted graphene multilayers as a platform for the realization of strongly correlated heavy fermion physics in a purely carbon-based platform.

We propose a general scheme to probe the compatibility of arbitrary pairing states with a given normal state Hamiltonian by the introduction of a concept called superconducting fitness. This quantity gives a direct measure of the suppression of the superconducting critical temperature in the presence of key symmetry-breaking fields. A merit of the superconducting fitness is that it can be used as a tool to identify nontrivial mechanisms to suppress superconductivity under various external influences, in particular, magnetic fields or distortions, even in complex multiorbital systems. In the light of this concept we analyze the multiband superconductor ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ and propose a new mechanism for the suppression of superconductivity in multiorbital systems, which we call interorbital effect, as a possible explanation for the unusual limiting feature observed in the upper critical field of this material.

The character of the superconducting phase of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ is the topic of a longstanding discussion. The classification of the symmetry allowed order parameters has relied on the tetragonal symmetry of the lattice and on cylindrical Fermi surfaces, usually taken to be featureless, not including the nontrivial symmetry aspects related to their orbital content. Here we show how the careful account of the orbital degree of freedom and a three-dimensional description lead to a much richer classification of order parameters. We analyze the stability and degeneracy of these new order parameters from the perspective of the concept of superconducting fitness and propose new order parameter candidates which can systematically account for the observed phenomenology in this material.

Triple point fermions are elusive electronic excitations that generalize Dirac and Weyl modes beyond the conventional high-energy paradigm. Yet, finding real materials naturally hosting these excitations at the Fermi energy has remained challenging. Here we show that twisted bilayer graphene is a versatile platform to realize robust triple point fermions in two dimensions. In particular, we establish that the introduction of localized impurities lifts one of the two degenerate Dirac cones, yielding triple point fermions at charge neutrality. Furthermore, we show that the valley polarization is preserved for certain impurity locations in the Moiré supercell for both weak and strong impurity potentials. We finally show that in the presence of interactions, a symmetry-broken state with local magnetization can develop out of the triple point bands, which can be selectively controlled by electrostatic gating. Our results put forward twisted bilayer graphene as a simple solid-state platform to realize triple point fermions at charge neutrality and demonstrate the nontrivial role of impurities in Moiré systems.