  We study the one-dimensional tight-binding models which include a slowly
varying, incommensurate off-diagonal modulation on the hopping amplitude.
Interestingly, we find that the mobility edges can appear only when this
off-diagonal (hopping) disorder is included in the model, which is different
from the known results induced by the diagonal disorder. We further study the
situation where the off-diagonal and diagonal disorder terms (the
incommensurate potential) are both included and find that the locations of
mobility edges change significantly and the varying trend of the mobility edge
becomes nonsmooth. We first identify the exact expressions of mobility edges of
both models by using asymptotic heuristic argument, and then verify the
conclusions by utilizing several numerical diagnostic techniques, including the
inverse participation ratio, the density of states and the Lyapunov exponent.
This result will perspectives for future investigations on the mobility edge in
low dimensional correlated disordered system.
