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We test the valley-filtering capabilities of a quantum dot inscribed bylocally straining an $\alpha$-$\mathcal{T}_3$ lattice. Specifically, weconsider an out-of-plane Gaussian bump in the center of a four-terminalconfiguration and calculate the generated pseudomagnetic field having anopposite direction for electrons originating from different valleys, theresulting valley-polarized currents, and the conductance between the injectorand collector situated opposite one another. Depending on the quantum dot'swidth and width-to-height ratio, we detect different transport regimes with andwithout valley filtering for both the $\alpha$-$\mathcal{T}_3$ and dice latticestructures. In addition, we analyze the essence of the conductance resonanceswith a high valley polarization in terms of related (pseudo-) Landau levels,the spatial distribution of the local density of states, and the local currentdensities. The observed local charge and current density patterns reflect thelocal inversion symmetry breaking by the strain, besides the global inversionsymmetry breaking due to the scaling parameter $\alpha$. By this way we canalso filter out different sublattices.

Valley filtering in strain-induced $\alpha$-$\mathcal{T}_3$ quantum dots