  Motivated by recent numerical discovery of a gapped spin liquid phase in
spin-$1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model, we classify
symmetric $Z_2$ spin liquids on triangular lattice in the Abrikosov-fermion
representation. We find 20 phases with distinct spinon symmetry quantum
numbers, 8 of which have their counterparts in the Schwinger-boson
representation. Among them we identify 2 promising candidates (#1 and #20),
which can realize a gapped $Z_2$ spin liquid with up to next nearest neighbor
mean-field amplitudes. We analyze their neighboring magnetic orders and valence
bond solid patterns, and find one state (#20) that is connected to 120-degree
Neel order by a continuous quantum phase transition. We also identify gapped
nematic $Z_2$ spin liquids in the neighborhood of the symmetric states and find
3 promising candidates (#1, #6 and #20).

Strongly Correlated Electrons