Spin liquids in graphene

Understand

We reveal that local interactions in graphene allow novel spin liquids between the semi-metal and antiferromagnetic Mott insulating phases, identified with algebraic spin liquid and Z$_{2}$ 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.
• Nature of the Z$_{2}$ spin liquid turns out to be $d + i d'$ singlet pairing, but time reversal symmetry is preserved, taking $d + i d'$ in one valley and $d - i d'$ in the other valley.
• We propose the quantized thermal valley Hall effect as an essential feature of this gapped spin liquid state.