Yuval Oreg

We develop a theoretical framework for probing superconductivity with momentum resolution using the quantum twisting microscope (QTM), a planar tunneling device where a graphene tip is rotated relative to a two-dimensional sample. Because of in-plane momentum conservation, the QTM directly measures the superconducting spectral function along well-defined trajectories in momentum space. The relative intensities of electron and hole excitations encode the Bogoliubov coherence factors, revealing the momentum dependence of the pairing magnitude. Three C_{3z}-related tunneling channels enable direct detection of rotational symmetry breaking, as well as nodal points in the superconducting order parameter. We apply our framework to superconductivity within the Bistritzer-MacDonald model of noninteracting electrons and the topological heavy-fermion model, which accounts for electron-electron interactions. Together, these capabilities establish the QTM as a direct probe of the pairing symmetry and microscopic origin of superconductivity in two-dimensional materials.

The tunable band structure and non-trivial topology of multilayer rhombohedral graphene lead to a variety of correlated electronic states with isospin orders—meaning ordered states in the combined spin and valley degrees of freedom—dictated by the interplay of spin–orbit coupling and Hund’s exchange interactions. However, methods for mapping local isospin textures and determining the exchange energies are currently lacking. Here we image the magnetization textures in tetralayer rhombohedral graphene using a nanoscale superconducting quantum interference device. We observe sharp magnetic phase transitions that indicate spontaneous time-reversal symmetry breaking. In the quarter-metal phase, the spin and orbital moments align closely, providing a bound on the spin–orbit-coupling energy. We also show that the half-metal phase has a very small magnetic anisotropy, which provides an experimental lower bound on the intervalley Hund’s exchange interaction energy. This is found to be close to its theoretical upper bound. The ability to resolve the local isospin texture and the different interaction energies will allow a better understanding of the phase transition hierarchy and the numerous correlated electronic states arising from spontaneous and induced isospin symmetry breaking in graphene heterostructures.

Recently, exotic superconductivity emerging from a spin-and-valley-polarized metallic phase has been discovered in rhombohedral tetralayer graphene. To explain this observation, we study the role of electron-electron interactions in driving flavor symmetry breaking, using the Hartree-Fock (HF) approximation, and in stabilizing superconductivity mediated by repulsive interactions. Though mean-field HF correctly predicts the isospin flavors and reproduces the experimental phase diagram, it overestimates the band renormalization near the Fermi energy and suppresses superconducting instabilities. To address this, we introduce a physically motivated scheme that includes internal screening in the HF calculation. Using this formalism, we find superconductivity arising from the spin-valley polarized phase, on the electron-doped side, for a range of electric fields and electron dopings. Our findings reproduce the experimental observations and reveal a p-wave, finite-momentum, time-reversal-symmetry-broken superconducting state, encouraging further investigation into exotic phases in graphene multilayers.

The relative twist angle between layers of near-lattice-matched van der Waals materials is critical for the emergent phenomena associated with moiré flat bands^1,2,3. However, the concept of angle rotation control is not exclusive to moiré superlattices in which electrons directly experience a twist-angle-dependent periodic potential. Instead, it can also be used to induce programmable symmetry-breaking perturbations with the goal of stabilizing desired correlated states. Here we experimentally demonstrate ‘moiréless’ twist-tuning of superconductivity together with other correlated orders in Bernal bilayer graphene proximitized by tungsten diselenide. The precise alignment between the two materials systematically controls the strength of induced Ising spin–orbit coupling (SOC), profoundly altering the phase diagram. As Ising SOC is increased, superconductivity onsets at a higher displacement field and features a higher critical temperature, reaching up to 0.5 K. Within the main superconducting dome and in the strong Ising SOC limit, we find an unusual phase transition characterized by a nematic redistribution of holes among trigonally warped Fermi pockets and enhanced resilience to in-plane magnetic fields. The superconducting behaviour is theoretically compatible with the prominent role of interband interactions between symmetry-breaking Fermi pockets. Moreover, we identify two additional superconducting regions, one of which descends from an inter-valley coherent normal state and shows a Pauli-limit violation ratio exceeding 40, among the highest for all known superconductors^4,5,6,7. Our results provide insights into ultraclean graphene superconductors and underscore the potential of utilizing moiréless-twist engineering across a wide range of van der Waals heterostructures.

Flat-band moiré graphene systems are a quintessential platform for investigating correlated phases of matter. Various interaction-driven ground states have been proposed, but despite extensive experimental effort, there has been little direct evidence that distinguishes between various phases, in particular near the charge neutrality point. Here we probe the fine details of the density of states and the effects of Coulomb interactions in alternating-twist trilayer graphene by imaging the local thermodynamic quantum oscillations with a nanoscale scanning superconducting quantum interference device. We find that the charging self-energy due to occupied electronic states is most important in explaining the high-carrier-density physics. At half-filling of the conduction flat band, we observe ferromagnetic-driven symmetry breaking, suggesting that it is the most robust mechanism in the hierarchy of phase transitions. Near charge neutrality, where exchange energy dominates over charging self-energy, we find a nematic semimetal ground state, which is theoretically favoured over gapped states in the presence of heterostrain. In this semimetallic phase, the flat-band Dirac cones migrate towards the mini-Brillouin zone centre, spontaneously breaking the threefold rotational symmetry. Our low-field local quantum oscillation technique can be used to explore the ground states of many strongly interacting van der Waals systems.

The coexistence of superconductivity and magnetism within a single material system represents a long-standing goal in condensed matter physics. Van der Waals-based moiré superlattices provide an exceptional platform for exploring competing and coexisting broken symmetry states. Alternating twisted trilayer graphene (TTG) exhibits robust superconductivity at the magic angle of 1.57° and 1.3°, with suppression at intermediate twist angles. In this study, we investigate the intermediate regime and uncover evidence of orbital magnetism. As previously reported, superconductivity is suppressed near the charge neutrality point (CNP) and emerges at larger moiré fillings. Conversely, we find orbital magnetism most substantial near the CNP, diminishing as superconductivity develops. This complementary behavior is similarly observed in the displacement field phase space, highlighting a competitive interplay between the two phases. Utilizing gate-defined Josephson junctions, we probe orbital magnetism by electrostatically tuning the weak links into the magnetic phase, revealing an asymmetric Fraunhofer interference pattern. The estimated orbital ferromagnetic ordering temperature is approximately half the superconducting critical temperature, coinciding with the onset of Fraunhofer asymmetry. Our findings suggest that the observed orbital magnetism is driven by valley polarization and is distinct from the anomalous Hall effect reported at integer fillings in twisted graphene systems. These results offer insights into the interplay between superconductivity and magnetism in moiré superlattices.