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We investigate the effects of a nonuniform uniaxial strain and a triaxialstrain on the $\alpha-{\cal T}_3$ lattice. The analytical expressions of thepseudo-Landau levels (pLLs) are derived based on low-energy Hamiltonians, andare verified by tight-binding calculations. We find the pseudo-magnetic fieldleads to the oscillating density of states, and the first pLL is sublatticepolarized, which is distributed on only two of the three sets of sublattices.For the nonuniform uniaxial strain, we show that pLLs become dispersive due tothe renormalization of the Fermi velocity, and a valley polarized currentemerges. Our results generalize the study of pseudo-magnetic field to the$\alpha-{\cal T}_3$ lattice, which will not only deepen the understanding ofthe intriguing effects of mechanical strains, but also provide theoreticalfoundation for possible experimental studies of the effects of strain on the$\alpha-{\cal T}_3$ lattice.

Strain-induced pseudo-magnetic field in $\alpha-{\cal T}_3$ lattice