Drag force on a moving impurity in a spin-orbit-coupled Bose-Einstein condensate

We investigate the drag force on a moving impurity in a spin-orbit-coupled Bose-Einstein condensate. We prove rigorously that the superfluid critical velocity is zero when the impurity moves in all directions but one, in contrast to the case of liquid helium and superconductor, where it is finite in all directions. We also find that when the impurity moves in all directions except the two special ones, the drag force has nonzero transverse component with a small velocity. When the velocity becomes large and the states of the upper band are also excited, the transverse force becomes very small due to opposite contributions of the two bands. The characteristics of the superfluid critical velocity and the transverse force are results of the order-by-disorder mechanism in spin-orbit-coupled boson systems.