  The vacuum expectation value (VEV) of the fermionic current density is
investigated in the geometry of two parallel branes in locally AdS spacetime
with a part of spatial dimensions compactified to a torus. Along the toral
dimensions quasiperiodicity conditions are imposed with general phases and the
presence of a constant gauge field is assumed. Different types of boundary
conditions are discussed on the branes, including the bag boundary condition
and the conditions arising in $Z_{2}$-symmetric braneworld models. Nonzero
vacuum currents appear along the compact dimensions only. In the region between
the branes they are decomposed into the brane-free and brane-induced
contributions. Both these contributions are periodic functions of the magnetic
flux enclosed by compact dimensions with the period equal to the flux quantum.
Depending on the boundary conditions, the presence of the branes can either
increase or decrease the vacuum current density. For a part of boundary
conditions, a memory effect is present in the limit when one of the branes
tends to the AdS boundary. Unlike to the fermion condensate and the VEV of the
energy-momentum tensor, the VEV of the current density is finite on the branes.
Applications are given to higher-dimensional generalizations of the
Randall-Sundrum models with two branes and with toroidally compact subspace.
The features of the fermionic current are discussed in odd-dimensional parity
and time-reversal symmetric models. The corresponding results for
three-dimensional spacetime are applied to finite length curved graphene tubes
threaded by a magnetic flux. It is shown that a nonzero current density can
also appear in the absence of the magnetic flux if the fields corresponding to
two different points of the Brillouin zone obey different boundary conditions
on the tube edges.
