Effect of position-dependent mass on dynamical breaking of type B and type X2 N-fold supersymmetry

We investigate effect of position-dependent mass profiles on dynamical breaking of N-fold supersymmetry in several type B and type X2 models. We find that N-fold supersymmetry in rational potentials in the constant-mass background is steady against the variation of mass profiles. On the other hand, some physically relevant mass profiles can change the pattern of dynamical N-fold supersymmetry breaking in trigonometric, hyperbolic and exponential potentials of both type B and type X2. The latter results open the possibility of detecting experimentally the phase transition of N-fold as well as ordinary supersymmetry at a realistic energy scale. (paper)