Dimensional engineering of a topological insulating phase in Half-Heusler LiMgAs

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.

Figure 1

(a) Face Centered Cubic (FCC) structure of LiMgAs with; Li, Mg and As placed at, 4b, 4c and 4a Wyckoff positions respectively. (b) [111] plane of FCC LiMgAs. (c) Quantum confinement achieved by introducing 15 (Å) vacuum along z-direction of the [111] layer of LiMgAs which has structure similar to that of ${\text{1T-MoS}}_2$. (d and e) Side and Top views of the low-dimensional supercell. Figure (d) indicates the sandwich type structure with, Li atoms placed on top layer shifted towards right (red arrow) and Mg atom place in the bottom layer shifted towards left (green arrow) while the As atoms occupy the middle layer. (f) Irreducible first Brillouin Zones with the path for Electronic Band Structure indicated for the bulk and the low-dimensional [111] phase of LiMgAs.

Figure 2

Phonon Dispersion Curves (PDC) at 0% pressure alongside the Phonon Density of States (PHDOS) for the (a) bulk and (b) low-dimensional [111] phase of LiMgAs. The absence of negative phonon frequencies in the entire Brillouin Zone indicates the systems are dynamically stable. Electronic Band Structure (EBS) of the (c) bulk and (d) low-dimensional [111] phase of LiMgAs.

Figure 3

Density of States (DOS) for the bulk (top panel) and the low-dimensional [111] phase of LiMgAs (bottom panel) at (a − 0%, b − 8%, c − 15%) and (a − 0%, b − 8%, c − 10%) pressures respectively.

Figure 4

Electronic Band Structure (EBS) in the vicinity of Fermi level indicating the closing of band gap with band inversion in (a) bulk (inset, opening of the gap at 17% VEP) and (b) low-dimensional [111] phase of LiMgAs.

Figure 5

(a) Partial Density of States (PDOS) of the bulk phase of LiMgAs and (b) the low-dimensional [111] phase of LiMgAs (Top panel: without SOC, Bottom panel: with SOC) before and after critical pressure/strain indicating exchange of orbital contributions and orbital parity around Fermi.

Figure 6

(a) Electronic Band Structure (EBS) of [111] LiMgAs without and with SOC indicating a strong band inversion at 10% compressive strain. (b) Orbital mechanism of band inversion in [111] LiMgAs due to SOC at 0% and 10% strain.

Figure 7

Computational surface and edge states of the (a) Bulk and (b) Low dimensional [111] phase of HH LiMgAs respectively (alongside zoomed image of the edge states in a small energy range).