Tuning quantum tunneling in WSe$_2$ via strain engineering

We present a comprehensive theoretical study of strain-engineered quantum transport in monolayer tungsten diselenide (WSe$_2$) in the presence of an electrostatic scalar potential. By incorporating strain effects within a low-energy Dirac framework, we analyze their impact on spin- and valley-resolved transmission, conductance, and polarization. The applied potential barrier partitions the system into three distinct regions, allowing for an analytical derivation of the wave functions in each domain. Enforcing continuity conditions at the interfaces yields exact expressions for the transmission and reflection amplitudes. The transmission probability is evaluated from the corresponding current densities, while the conductance is obtained using the Landauer-B\"uttiker formalism, enabling a quantitative determination of spin and valley polarizations. Our numerical analysis reveals that strain acts as a powerful tuning parameter that reshapes the electronic dispersion and strongly modifies transport characteristics. In particular, the transmission and conductance exhibit pronounced oscillatory behavior driven by quantum interference and resonant tunneling mechanisms. More importantly, both spin and valley polarizations display substantial and highly controllable variations as functions of strain, barrier height, and incident energy. These results demonstrate that strain and electrostatic engineering provide an efficient and versatile platform for manipulating spin-valley degrees of freedom in WSe$_2$. The ability to tailor polarization and interference effects suggests promising opportunities for the design of next-generation spintronic, valleytronic, and optoelectronic devices based on two-dimensional transition-metal dichalcogenides.