Quantum spin liquid emerging in two-dimensional correlated Dirac fermions

Abstract

At sufficiently low temperatures, condensed-matter systems tend to develop order. A notable exception to this behaviour is the case of quantum spin liquids, in which quantum fluctuations prevent a transition to an ordered state down to the lowest temperatures. There have now been tentative observations of such states in some two-dimensional organic compounds, yet quantum spin liquids remain elusive in microscopic two-dimensional models that are relevant to experiments. Here we show, by means of large-scale quantum Monte Carlo simulations of correlated fermions on a honeycomb lattice (a structure realized in, for example, graphene), that a quantum spin liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence-bond liquid, akin to the one proposed for high-temperature superconductors: the possibility of unconventional superconductivity through doping therefore arises in our system. We foresee the experimental realization of this model system using ultra-cold atoms, or group IV elements arranged in honeycomb lattices.

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

“…For limiting cases, we have performed unrestricted Hartree-Fock calculations for multi-orbital Hubbard models defined on (111) bilayers. We found that the TI states are rather robust for e g 2 systems and become unstable against antiferromagnetic insulating states when the interaction strength is comparable to the full bandwidth as in the 2D Hubbard model on the honeycomb lattice 52 . For e g 1 or e g 3 systems, the QAH-insulating states could be generated dynamically by correlation effects without the SOC 53,54 , yet trivial-insulating states due to the Jahn-Teller effect would also be stabilized depending on the relative balance between the Coulomb interaction and the Jahn-Teller coupling.…”

Artificial honeycomb lattices for electrons, atoms and photons

“…The findings of Ref. [82] have been recently addressed in Ref. [83], by QMC simulations of the same model in larger clusters (containing up to 2592 sites), finding very weak evidence of a spin liquid phase.…”

“…Early on it was shown that at half filling and for U/t > ∼ 5 a semimetal-Mott insulator transition occurs [81]. Recently, a QMC calculation has demonstrated [82] the existence of a gapped antiferromagnetic phase for U/t > 4.3 and presented evidence for a gapped spin liquid phase in the range of couplings 3.5 < U/t < 4.3. The findings of Ref.…”

Chirald-wave superconductivity in doped graphene

“…For example, magnetism has experimentally been reported both in nanographene [58,59,60], and in graphite in the presence of disorder [61] or grain boundaries [62], although pristine graphene has not been found to be either magnetic [63] or gapped [64,20]. Theoretically, on-site Coulomb repulsion exceeding U > 3.9t has been found to give an antiferromagnetic state in undoped graphene in quantum Monte Carlo simulations [15,17]. This relatively large value of U is a consequence of undoped graphene being a semimetal with only a point-like Fermi surface.…”

“…A large number of exotic states of matter has been proposed theoretically, see e.g. [4,5,6,7,8,9,10,11,12,13,14,15,16,17], but most have not been experimentally observed as of yet. One exception is multi-layer graphene systems where there are now experimental reports of an energy gap opening at low temperatures, which has been ascribed to interactions effects [18,19,20,21,22,23,24,25].…”