Room temperature magnetic order on zigzag edges of narrow graphene nanoribbons

Magnetic order emerging in otherwise non-magnetic materials as carbon is a paradigmatic example of a novel type of s-p electron magnetism predicted to be of exceptional high-temperature stability. It has been demonstrated that atomic scale structural defects of graphene can host unpaired spins. However, it is still unclear under which 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 only from one sub-lattice of the bipartite graphene lattice, can give rise to a robust magnetic order. We employ a nanofabrication technique based on Scanning Tunneling Microscopy to define graphene nanoribbons with nanometer precision and well-defined crystallographic edge orientations. While armchair ribbons display quantum confinement gap, zigzag ribbons narrower than 7 nm reveal a bandgap of about 0.2 - 0.3 eV, which can be identified as a signature of interaction induced spin ordering along their edges. Moreover, a semiconductor to metal transition is revealed upon increasing the ribbon width, indicating the switching of the magnetic coupling between opposite ribbon edges from antiferromagnetic to ferromagnetic configuration. We found that the magnetic order on graphene edges of controlled zigzag orientation can be stable even at room temperature, raising hope for graphene-based spintronic devices operating under ambient conditions

Bound on quantum computation time: Quantum error correction in a critical environment

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user. © 2010 The American Physical Society

Quantized conductance of a suspended graphene nanoconstriction

One of the most promising characteristics of graphene(1) is the ability of charge carriers to travel through it ballistically over hundreds of nanometres. Recent developments in the preparation of high mobility graphene(2-4) should make it possible to study the effects of quantum confinement in graphene nanostructures in the ballistic regime. Of particular interest are those effects that arise from edge states, such as spin polarization at zigzag edges(5) of graphene nanoribbons(6,7) and the use of graphene's valley-degeneracy for 'valleytronics'(8). Here we present the observation of quantized conductance(9,10) at integer multiples of 2e(2)/h at zero magnetic field in a high mobility suspended graphene ballistic nanoconstriction. This quantization evolves into the typical quantum Hall effect for graphene at magnetic fields above 60mT. Voltage bias spectroscopy reveals an energy spacing of 8meV between the first two subbands. A pronounced feature at 0.6 x 2e(2)/h present at a magnetic field as low as similar to 0.2 T resembles the '0.7 anomaly' observed in quantum point contacts in a GaAs-AlGaAs two-dimensional electron gas, possibly caused by electron-electron interactions(11)