Physical Review B 83, 125416 (2011)

SCI

Spin liquid in graphene

Minh-Tien Tran and Ki-Seok Kim

We reveal that local interactions in graphene allow novel spin liquids between the semimetal and antiferromagnetic Mott insulating phases, identified with algebraic spin liquid and Z2 spin liquid, respectively. We argue that the algebraic spin liquid can be regarded as the two-dimensional realization of one-dimensional spin dynamics, where antiferromagnetic correlations show exactly the same power-law dependence as valence bond correlations. The nature of the Z2 spin liquid turns out to be d+id′ singlet pairing, but time-reversal symmetry is preserved, taking d+id′ in one valley and d-id′ in the other valley. We propose the quantized thermal valley Hall effect as an essential feature of this gapped spin liquid state. Quantum phase transitions among the semimetal, algebraic spin liquid, and Z2 spin liquid are shown to be continuous while the transition from the Z2 spin liquid to the antiferromagnetic Mott insulator turns out to be first order. We emphasize that both algebraic spin liquid and d±id′ Z2 spin liquid can be verified by the quantum Monte Carlo simulation, showing the enhanced symmetry in the algebraic spin liquid and the quantized thermal valley Hall effect in the Z2 spin liquid.