Half- and quarter-metals in rhombohedral trilayer graphene.

Ferromagnetism is most common in transition metal compounds where electrons occupy highly localized d orbitals. However, ferromagnetic order may also arise in low-density two-dimensional electron systems1-5. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene6 drive spontaneous ferromagnetic polarization of the electron system into one or more spin and valley flavours. Using capacitance and transport measurements, we observe a cascade of transitions tuned to the density and electronic displacement field between phases in which quantum oscillations have fourfold, twofold or onefold degeneracy, associated with a spin- and valley-degenerate normal metal, spin-polarized 'half-metal', and spin- and valley-polarized 'quarter-metal', respectively. For electron doping, the salient features of the data are well captured by a phenomenological Stoner model7 that includes valley-anisotropic interactions. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, we introduce a moiré superlattice using a rotationally aligned hexagonal boron nitride substrate5,8. Remarkably, we find that the isospin order is only weakly perturbed, with the moiré potential catalysing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter-metal states occur at half- or quarter-superlattice band filling. Our results show that rhombohedral graphene is an ideal platform for well-controlled tests of many-body theory, and reveal magnetism in moiré materials4,5,9,10 to be fundamentally itinerant in nature.

Nuclear spin effects in biological processes.

Traditionally, nuclear spin is not considered to affect biological processes. Recently, this has changed as isotopic fractionation that deviates from classical mass dependence was reported both in vitro and in vivo. In these cases, the isotopic effect correlates with the nuclear magnetic spin. Here, we show nuclear spin effects using stable oxygen isotopes (16O, 17O, and 18O) in two separate setups: an artificial dioxygen production system and biological aquaporin channels in cells. We observe that oxygen dynamics in chiral environments (in particular its transport) depend on nuclear spin, suggesting future applications for controlled isotope separation to be used, for instance, in NMR. To demonstrate the mechanism behind our findings, we formulate theoretical models based on a nuclear-spin-enhanced switch between electronic spin states. Accounting for the role of nuclear spin in biology can provide insights into the role of quantum effects in living systems and help inspire the development of future biotechnology solutions.

Topological Charges of Periodically Kicked Molecules.

We show that the simplest of existing molecules-closed-shell diatomics not interacting with one another-host topological charges when driven by periodic far-off-resonant laser pulses. A periodically kicked molecular rotor can be mapped onto a "crystalline" lattice in angular momentum space. This allows us to define quasimomenta and the band structure in the Floquet representation, by analogy with the Bloch waves of solid-state physics. Applying laser pulses spaced by 1/3 of the molecular rotational period creates a lattice with three atoms per unit cell with staggered hopping. Within the synthetic dimension of the laser strength, we discover Dirac cones with topological charges. These Dirac cones, topologically protected by reflection and time-reversal symmetry, are reminiscent of (although not equivalent to) that seen in graphene. They-and the corresponding edge states-are broadly tunable by adjusting the laser strength and can be observed in present-day experiments by measuring molecular alignment and populations of rotational levels. This paves the way to study controllable topological physics in gas-phase experiments with small molecules as well as to classify dynamical molecular states by their topological invariants.

Nonadiabatic Laser-Induced Alignment Dynamics of Molecules on a Surface.

We demonstrate that a sodium dimer, Na_{2}(1^{3}Σ_{u}^{+}), residing on the surface of a helium nanodroplet, can be set into rotation by a nonresonant 1.0 ps infrared laser pulse. The time-dependent degree of alignment measured, exhibits a periodic, gradually decreasing structure that deviates qualitatively from that expected for gas-phase dimers. Comparison to alignment dynamics calculated from the time-dependent rotational Schrödinger equation shows that the deviation is due to the alignment dependent interaction between the dimer and the droplet surface. This interaction confines the dimer to the tangential plane of the droplet surface at the point where it resides and is the reason that the observed alignment dynamics is also well described by a 2D quantum rotor model.

Spontaneous Gully-Polarized Quantum Hall States in ABA Trilayer Graphene.

Bernal-stacked multilayer graphene is a versatile platform to explore quantum transport phenomena and interaction physics due to its exceptional tunability via electrostatic gating. For instance, upon applying a perpendicular electric field, its band structure exhibits several off-center Dirac points (so-called Dirac gullies) in each valley. Here, the formation of Dirac gullies and the interaction-induced breakdown of gully coherence is explored via magnetotransport measurements in high-quality Bernal-stacked (ABA) trilayer graphene. At zero magnetic field, multiple Lifshitz transitions indicating the formation of Dirac gullies are identified. In the quantum Hall regime, the emergence of Dirac gullies is evident as an increase in Landau level degeneracy. When tuning both electric and magnetic fields, electron-electron interactions can be controllably enhanced until, beyond critical electric and magnetic fields, the gully degeneracy is eventually lifted. The arising correlated ground state is consistent with a previously predicted nematic phase that spontaneously breaks the rotational gully symmetry.

Unconventional Superconductivity in Systems with Annular Fermi Surfaces: Application to Rhombohedral Trilayer Graphene.

We show that in a two-dimensional electron gas with an annular Fermi surface, long-range Coulomb interactions can lead to unconventional superconductivity by the Kohn-Luttinger mechanism. Superconductivity is strongly enhanced when the inner and outer Fermi surfaces are close to each other. The most prevalent state has chiral p-wave symmetry, but d-wave and extended s-wave pairing are also possible. We discuss these results in the context of rhombohedral trilayer graphene, where superconductivity was recently discovered in regimes where the normal state has an annular Fermi surface. Using realistic parameters, our mechanism can account for the order of magnitude of T_{c}, as well as its trends as a function of electron density and perpendicular displacement field. Moreover, it naturally explains some of the outstanding puzzles in this material, that include the weak temperature dependence of the resistivity above T_{c}, and the proximity of spin singlet superconductivity to the ferromagnetic phase.

Light-Induced Fractional Quantum Hall Phases in Graphene.

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at nonzero relative angular momentum can become dominant, resembling a hollow-core pseudopotential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν=1/2 and ν=2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

Analytic Model of Chiral-Induced Spin Selectivity.

Organic materials are known to feature long spin-diffusion times, originating in a generally small spin-orbit coupling observed in these systems. From that perspective, chiral molecules acting as efficient spin selectors pose a puzzle that attracted a lot of attention in recent years. Here, we revisit the physical origins of chiral-induced spin selectivity (CISS) and propose a simple analytic minimal model to describe it. The model treats a chiral molecule as an anisotropic wire with molecular dipole moments aligned arbitrarily with respect to the wire's axes and is therefore quite general. Importantly, it shows that the helical structure of the molecule is not necessary to observe CISS and other chiral nonhelical molecules can also be considered as potential candidates for the CISS effect. We also show that the suggested simple model captures the main characteristics of CISS observed in the experiment, without the need for additional constraints employed in the previous studies. The results pave the way for understanding other related physical phenomena where the CISS effect plays an essential role.

Fractional quantum Hall effect in Hofstadter butterflies of Dirac fermions.

We report on the influence of a periodic potential on the fractional quantum Hall effect (FQHE) states in monolayer graphene. We have shown that for two values of the magnetic flux per unit cell (one-half and one-third flux quantum) an increase of the periodic potential strength results in a closure of the FQHE gap and appearance of gaps due to the periodic potential. In the case of one-half flux quantum this causes a change of the ground state and consequently the change of the momentum of the system in the ground state. While there is also crossing between low-lying energy levels for one-third flux quantum, the ground state does not change with the increase of the periodic potential strength and is always characterized by the same momentum. Finally, it is shown that for one-half flux quantum the emergent gaps are due entirely to the electron-electron interaction, whereas for the one-third flux quantum per unit cell these are due to both non-interacting electrons (Hofstadter butterfly pattern) and the electron-electron interaction.