  Landau quantization associated with the quantized cyclotron motion of
electrons under magnetic field provides the effective way to investigate
topologically protected quantum states with entangled degrees of freedom and
multiple quantum numbers. Here we report the cascade of Landau quantization in
a strained type-II Dirac semimetal NiTe2 with spectroscopic-imaging scanning
tunneling microscopy. The uniform-height surfaces exhibit single-sequence
Landau levels (LLs) at a magnetic field originating from the quantization of
topological surface state (TSS) across the Fermi level. Strikingly, we reveal
the multiple sequence of LLs in the strained surface regions where the rotation
symmetry is broken. Firstprinciples calculations demonstrate that the multiple
LLs attest to the remarkable lifting of the valley degeneracy of TSS by the
in-plane uniaxial or shear strains. Our findings pave a pathway to tune
multiple degrees of freedom and quantum numbers of TMDs via strain engineering
for practical applications such as high-frequency rectifiers, Josephson diode
and valleytronics.
