Two copies of spin helices with stretching pitch and compensating helicity

Persistent spin helix (PSH) manifests itself as an effective knob to tackle spin decay inevitably occurring in disordered two-dimensional electron gases. Here, for ordinary (110)-oriented two-subband GaInAs wells subjected to top and back gate voltages, we theoretically achieve adjusting the Dresselhaus terms of the two bands while meanwhile consistently pinning the system at symmetric configuration [i.e., locking the Rashba spin-orbit (SO) terms to zero], thus enabling simultaneous formation of two copies of PSHs of flexible control. Strikingly, we are able to stretch the pitch---spin density wave length---of PSH by far more than one period, enabling helix-stretch functional spin field-effect transistor (FET), with both on and off states protected by the PSH symmetry. Moreover, we attain a scenario in which the helicities of the two copies of PSHs are sufficiently compensated. This makes possible a new concept: ``orbit (band) filter,'' which resembles spin FET while with novel functionality of orbit filtering, opening up a new route towards spintronic and orbitronic combined applications.