We develop a Fermionic Chern-Simons (CS) theory for the fractional quantum Hall effect in monolayer graphene with SU(4) symmetry, arising from the spin and the valley degrees of freedom, which involves four distinct CS gauge fields. We choose the corresponding elements of the CS coupling matrix such that an even number of spin and valley quantum number dependent flux quanta is attached to all electrons and that any electron with a given spin and valley quantum number sees an integer number of flux attached to other electrons with different (spin and valley) quantum numbers. Using this CS matrix, we obtain a list of possible fractional quantum Hall states that might occur in graphene and propose wavefunctions for those states. Our analysis also applies to fractional quantum Hall states of both bilayer quantum Hall systems without spin polarization and bilayer spin polarized graphene.

We study a junction of a topological insulator with a thin two-dimensional (2D) non-magnetic or partially polarized ferromagnetic metallic film deposited on a 3D insulator. We show that such a junction leads to a finite spin current injection into the film whose magnitude can be controlled by tuning a voltage $V$ applied across the junction. For ferromagnetic films, the direction of the component of the spin current along the film magnetization can also be tuned by tuning the barrier potential $V_0$ at the junction. We point out the role of the chiral spin-momentum locking of the Dirac electrons behind this phenomenon and suggest experiments to test our theory.Comment: Revised version with supplemental material

We study the zero temperature non-equilibrium dynamics of a fermionic superfluid in the BCS limit and in the presence of a drive leading to a time-dependent chemical potential μ(t). We choose a periodic driving protocol characterized by a frequency ω and compute the fermion density, the wavefunction overlap, and the residual energy of the system at the end of N periods of the drive. We demonstrate that the BCS self-consistency condition is crucial in shaping the long time behaviour of the fermions subjected to the drive and provide an analytical understanding of the behaviour of the fermion density nkF (where kF is the Fermi momentum vector) after a drive period and for large ω. We also show that the momentum distribution of the excitations generated due to such a drive bears the signature of the pairing symmetry and can be used, for example, to distinguish between s- and d-wave superfluids. We propose experiments to test our theory.

We study a mixture of ultracold spin-half fermionic and spin-one bosonic atoms in a shallow optical lattice where the bosons are coupled to the fermions via both density-density and spin-spin interactions. We consider the parameter regime where the bosons are in a superfluid ground state, integrate them out, and obtain an effective action for the fermions. We carry out a renormalization group analysis of this effective fermionic action at low temperatures, show that the presence of the spinor bosons may lead to a separation of Fermi surfaces of the spin-up and spin-down fermions, and investigate the parameter range where this phenomenon occurs. We also calculate the susceptibilities corresponding to the possible superfluid instabilities of the fermions and obtain their possible brokensymmetry ground states at low temperatures and weak interactions.