Twisted bilayer graphene is an exciting platform for exploring correlated quantum phases, extremely tunable with respect to both the single-particle bands and the interaction profile of electrons. Here, we investigate the phase diagram of twisted bilayer graphene as described by an extended Hubbard model on the honeycomb lattice with two fermionic orbitals (valleys) per site. Besides the special extended cluster interaction
Q, we incorporate the effect of gating through an on-site Hubbard-interaction
U. Within quantum Monte Carlo, we find valence-bond solid, Nel-valley antiferromagnetic or charge-density wave phases. Further, we elucidate the competition of these phases by noticing that the cluster interaction induces an exotic constraint on the Hilbert space, which we dub the cluster rule, in analogy to the famous pyrochlore spin-ice rule. Formulating the perturbative Hamiltonian by projecting into the cluster-rule manifold, we perform exact diagonalization and construct the fixed-point states of the observed phases. Finally, we compute the local electron density patterns as signatures distinguishing these phases, which could be observed with scanning tunneling microscopy. Our paper capitalizes on the notion of cluster constraints in the extended Hubbard model of twisted bilayer graphene and suggests a scheme towards realization of several symmetry-breaking insulating phases in a twisted-bilayer graphene sheet.
We investigate even-denominator fractional quantum Hall (EDFQH) states in monolayer graphene, focusing on the experimentally observed filling fractions
ν=1/2 and
ν=1/4. Owing to the approximate SU(4) symmetry arising from spin and valley degrees of freedom, graphene hosts a rich variety of multi-component fractional quantum Hall states with different polarization configurations. Using the Chern-Simons composite fermion framework for SU(4) systems, we construct candidate variational wave functions corresponding to distinct spin, valley, and mixed polarization states. The ground-state energies of these states are evaluated numerically using the Coulomb interaction in spherical geometry. By comparing energies across different polarization sectors, we identify the energetically favored configurations at
ν=1/2 and
ν=1/4. Our variational energy comparison suggests that the energetically favored candidate states correspond to multi-component correlated quantum Hall liquids. Within the restricted family of trial states considered here, these states differ from a simple composite-fermion Fermi-sea description. These findings provide insight into the role of valley polarization and SU(4) symmetry in stabilizing even-denominator fractional quantum Hall states in graphene.
We investigate ergotropy dynamics in a graphene-based quantum battery modeled as a four-level spin--valley system under different dissipative environments. The battery is charged via a Gaussian pulse and subsequently evolves under amplitude damping, dephasing, and both Markovian and non-Markovian reservoirs. We find that amplitude damping, while inducing energy loss, can stabilize non-passive steady states with finite ergotropy, whereas pure dephasing suppresses coherence and eliminates work extraction. On the other hand, non-Markovian memory slows ergotropy loss and enables partial recovery through information backflow. These results identify coherence and reservoir memory as essential resources for enhancing the long-time performance of graphene quantum batteries.