Nonmetallic left-handed material by assembly of low-dimensional quantum structures is theoretically proposed. Specifically, we predict relatively wideband, tunable left-handed material by employing structures comprised of semiconductor quantum wells and quantum dots. Well established epitaxial growth of semiconductor material allows a feasible composition of such metamaterials. The advantages of the proposed scheme is the potential ability to invert the material losses to gain by electrical pumping and the possibility to switch the material regime from left-handed to right-handed by applying external voltage, which are not affordable in the recently proposed left-handed material configurations.