Spontaneous Spin and Valley Symmetry-Broken States of Interacting Massive Dirac Fermions in a Bilayer Graphene Quantum Dot

We predict the existence of spontaneous spin and valleysymmetry-brokenstates of interacting massive Dirac Fermions in a gated bilayer graphenequantum dot based on the exact diagonalization of the many-body Hamiltonian.The dot is defined by a vertical electric field and lateral gates,and its single-particle (SP) energies, wave functions, and Coulombmatrix elements are computed by using the atomistic tight-bindingmodel. The effect of the Coulomb interaction is measured by the ratioof Coulomb elements to the SP level spacing. As we increase the interactionstrength, we find the electrons in a series of spin and valley symmetry-brokenphases with increasing valley and spin polarizations. The phase transitionsresult from the competition of the SP, exchange, and correlation energyscales. A phase diagram for N = 1-6 electronsis mapped out as a function of the Coulomb interaction strength.