  Microscopic-level understanding of the separation mechanism for
two-dimensional (2D) membranes is an active area of research due to potential
implications of this class of membranes for various technological processes.
Helium (He) purification from the natural resources is of particular interest
due to the shortfall in its production. In this work, we applied the ring
polymer molecular dynamics (RPMD) method to graphdiyne (Gr2) and graphtriyne
(Gr3) 2D membranes having variable pore sizes for the separation of He
isotopes. We found that the transmission rate through Gr3 is many orders of
magnitude greater than Gr2. The selectivity of either isotope at low
temperatures is a consequence of a delicate balance between the zero-point
energy effect and tunneling of $^4$He and $^3$He. RPMD provides an efficient
approach for studying the separation of He isotopes, taking into account
quantum effects of light nuclei motions at low temperatures, which classical
methods fail to capture.
