Observation of competing, correlated ground states in the flat band of rhombohedral graphite.

In crystalline solids, the interactions of charge and spin can result in a variety of emergent quantum ground states, especially in partially filled, topological flat bands such as Landau levels or in "magic angle" graphene layers. Much less explored is rhombohedral graphite (RG), perhaps the simplest and structurally most perfect condensed matter system to host a flat band protected by symmetry. By scanning tunneling microscopy, we map the flat band charge density of 8, 10, 14, and 17 layers and identify a domain structure emerging from a competition between a sublattice antiferromagnetic insulator and a gapless correlated paramagnet. Our density matrix renormalization group calculations explain the observed features and demonstrate that the correlations are fundamentally different from graphene-based magnetism identified until now, forming the ground state of a quantum magnet. Our work establishes RG as a platform to study many-body interactions beyond the mean-field approach, where quantum fluctuations and entanglement dominate.

Possible Inversion Symmetry Breaking in the S=1/2 Pyrochlore Heisenberg Magnet.

We address the ground-state properties of the long-standing and much-studied three-dimensional quantum spin liquid candidate, the S=1/2 pyrochlore Heisenberg antiferromagnet. By using SU(2) density-matrix renormalization group (DMRG), we are able to access cluster sizes of up to 128 spins. Our most striking finding is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments. We also determine the ground-state energy, E_{0}/N_{sites}=-0.490(6)J, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. These findings suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.

Room-temperature magnetic order on zigzag edges of narrow graphene nanoribbons.

The possibility that non-magnetic materials such as carbon could exhibit a novel type of s-p electron magnetism has attracted much attention over the years, not least because such magnetic order is predicted to be stable at high temperatures. It has been demonstrated that atomic-scale structural defects of graphene can host unpaired spins, but it remains unclear under what conditions long-range magnetic order can emerge from such defect-bound magnetic moments. Here we propose that, in contrast to random defect distributions, atomic-scale engineering of graphene edges with specific crystallographic orientation--comprising edge atoms from only one sub-lattice of the bipartite graphene lattice--can give rise to a robust magnetic order. We use a nanofabrication technique based on scanning tunnelling microscopy to define graphene nanoribbons with nanometre precision and well-defined crystallographic edge orientations. Although so-called 'armchair' ribbons display quantum confinement gaps, ribbons with the 'zigzag' edge structure that are narrower than 7 nanometres exhibit an electronic bandgap of about 0.2-0.3 electronvolts, which can be identified as a signature of interaction-induced spin ordering along their edges. Moreover, upon increasing the ribbon width, a semiconductor-to-metal transition is revealed, indicating the switching of the magnetic coupling between opposite ribbon edges from the antiferromagnetic to the ferromagnetic configuration. We found that the magnetic order on graphene edges of controlled zigzag orientation can be stable even at room temperature, raising hopes of graphene-based spintronic devices operating under ambient conditions.