Abstract
We propose a novel technique of dimensional engineering to realize low dimensional topological insulator from a trivial three dimensional parent. This is achieved by confining the bulk system to one dimension along a particular crystal direction, thus enhancing the quantum confinement effects in the system. We investigate this mechanism in the Half-Heusler compound LiMgAs with face-centered cubic (FCC) structure. At ambient conditions the bulk FCC structure exhibits a semi-conducting nature. But, under the influence of high volume expansive pressure (VEP) the system undergoes a topological phase transition (TPT) from semi-conducting to semi-metallic forming a Dirac cone. At a critical VEP we observe that, spin-orbit coupling (SOC) effects introduce a gap of [Formula: see text] 1.5 meV in the Dirac cone at high symmetry point [Formula: see text] in the Brillouin zone. This phase of bulk LiMgAs exhibits a trivial nature characterized by the [Formula: see text] invariants as (0,000). By further performing dimensional engineering, we cleave [111] plane from the bulk FCC structure and confine the system in one dimension. This low-dimensional phase of LiMgAs has structure similar to the two dimensional [Formula: see text] system. Under a relatively lower compressive strain, the low-dimensional system undergoes a TPT and exhibits a non-trivial topological nature characterized by the SOC gap of [Formula: see text] 55 meV and [Formula: see text] invariant [Formula: see text] = 1. Although both, the low-dimensional and bulk phase exhibit edge and surface states, the low-dimensional phase is far more superior and exceptional as compared to the bulk parent in terms of the velocity of Fermions ([Formula: see text]) across the surface states. Such a system has promising applications in nano-electronics.