  Helical edge states are the hallmark of the quantum spin Hall insulator.
Recently, several experiments have observed transport signatures contributed by
trivial edge states, making it difficult to distinguish between the
topologically trivial and nontrivial phases. Here, we show that helical edge
states can be identified by the random-gate-voltage induced $\Phi_0/2$-period
oscillation of the averaged electron return probability in the interferometer
constructed by the edge states. The random gate voltage can highlight the
$\Phi_0/2$-period Al'tshuler-Aronov-Spivak oscillation proportional to
$\sin^2(2\pi\Phi/\Phi_0)$ by quenching the $\Phi_0$-period Aharonov-Bohm
oscillation. It is found that the helical spin texture induced $\pi$ Berry
phase is key to such weak antilocalization behavior with zero return
probability at $\Phi=0$. In contrast, the oscillation for the trivial edge
states may exhibit either weak localization or antilocalization depending on
the strength of the spin-orbit coupling, which have finite return probability
at $\Phi=0$. Our results provide an effective way for the identification of the
helical edge states. The predicted signature is stabilized by the time-reversal
symmetry so that it is robust against disorder and does not require any fine
adjustment of system.
