Spin liquids in graphene

Abstract

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 $d+i{d}^{\prime }$ singlet pairing, but time reversal symmetry is preserved, taking $d+i{d}^{\prime }$ in one valley and $d-i{d}^{\prime }$ 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 semi-metal, algebraic spin liquid, and Z${}_2$ spin liquid are shown to be continuous while the transition from the Z${}_2$ spin liquid to the antiferromagnetic Mott insulator turns out to be the first order. We emphasize that both algebraic spin liquid and $d\pm i{d}^{\prime }$ Z${}_2$ 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 Z${}_2$ spin liquid.

References in corpus (17)

• The electronic properties of graphene
• "Deconfined" quantum critical points
• Valley Dependent Optoelectronics from Inversion Symmetry Breaking
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The Quantum Spin Hall Effect: Theory and Experiment
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• On the stability of U(1) spin liquids in two dimensions
• Density waves and Cooper pairing on the honeycomb lattice
• Algebraic spin liquid as the mother of many competing orders
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Disorder and Electronic Transport in Graphene
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice
• SU(2) gauge theory of the Hubbard model: Emergence of an anomalous metallic phase near the Mott critical point
• Quantum spin Hall phases
• How to control pairing fluctuations: SU(2) slave-rotor gauge theory of the Hubbard model

Cited by in corpus (17)

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• Helical fluctuations in the Raman response of the topological insulator Bi2Se3
• Chiral d-wave superconductivity on the honeycomb lattice close to the Mott state
• A phase diagram for a topological Kondo insulating system
• Phase diagram of the strongly correlated Kane-Mele-Hubbard model
• Topological Superconductivity in Two Dimensions with Mixed Chirality
• Correlated metallic state in honeycomb lattice: Orthogonal Dirac semimetal
• Nambu-Eliashberg theory for multi-scale quantum criticality : Application to ferromagnetic quantum criticality in the surface of three dimensional topological insulators
• Evidence of electron fractionalization in the Hall coefficient at Mott criticality
• Emergent gauge fields and their nonperturbative effects in correlated electrons
• Stoner instability revisited: Emergence of local quantum criticality?
• Spin-liquid Mott quantum criticality in two dimensions: Destabilization of a spinon Fermi surface and emergence of one-dimensional spin dynamics
• Role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal
• Orthogonal Dirac semimetal on honeycomb lattice and the electron spectral function in orthogonal metallic states