  Recently, the chiral-induced spin selectivity in molecular systems has
attracted extensive interest among the scientific communities. Here, we
investigate the effect of the gate voltage on spin-selective electron transport
through the $\alpha$-helical peptide/protein molecule contacted by two
nonmagnetic electrodes. Based on an effective model Hamiltonian and the
Landauer-B\"uttiker formula, we calculate the conductance and the spin
polarization under an external electric field which is perpendicular to the
helix axis of the $\alpha$-helical peptide/protein molecule. Our results
indicate that both the magnitude and the direction of the gate field have a
significant effect on the conductance and the spin polarization. The spin
filtration efficiency can be improved by properly tuning the gate voltage,
especially in the case of strong dephasing regime. And the spin polarization
increases monotonically with the molecular length without the gate voltage,
which is consistent with the recent experiment, and presents oscillating
behavior in the presence of the gate voltage. In addition, the spin selectivity
is robust against the dephasing, the on-site energy disorder, and the space
angle disorder under the gate voltage. Our results could motivate further
experimental and theoretical works on the chiral-based spin selectivity in
molecular systems.
