  Quantum spin liquid (QSL) state in rare-earth triangular lattice has
attracted much attention recently due to its potential application in quantum
computing and communication. Here we report the single-crystal growth
synthesis, crystal structure characterizations and magnetic properties of
$A$YbSe$_{2}$ ($A$= K, Rb) compounds. The X-ray diffraction analysis shows that
$A$YbSe$_{2}$ ($A$ = K and Rb) crystallizes in a trigonal space group, $R$-3$m$
(No. 166) with Z = 3. $A$YbSe$_{2}$ possesses a two-dimensional (2D) Yb-Se-Yb
layered structure formed by edged-shared YbSe$_6$ octahedra. The magnetic
properties are highly anisotropic for both title compounds and no long-range
order is found down to 0.4 K, revealing the possible QSL ground state in these
compounds. The isothermal magnetization exhibits one-third magnetization
plateau when the magnetic fields are applied in $ab$-plane. Heat capacity is
performed along both $ab$-plane and $c$-axis, and features the characteristic
dome for triangular magnetic lattice compounds as a function of magnetic
fields. Due to the change of the interlayer and intralayer distance of
Yb$^{3+}$, the dome shifts to low fields from KYbSe$_2$ to RbYbSe$_2$. All
these results indicate the $A$YbSe$_2$ family presents unique frustrated
magnetism close to the possible QSL and noncolinear spin states.
