[Paper Review] Topological semimetals and topological insulators in rare earth monopnictides

Minggang Zeng, Chen Fang+6 more|arXiv (Cornell University)|Apr 14, 2015

Topological Materials and Phenomena111 citations

TL;DR

This study predicts that rare earth monopnictides LaX (X = N, P, As, Sb, Bi) host distinct topological phases: LaN is a nodal ring semimetal that evolves into a 3D Dirac semimetal upon inclusion of spin-orbit coupling, while LaP, LaAs, LaSb, and LaBi are 3D topological insulators with three surface Dirac cones at the M̄ points on the (111) surface. The topological transition is driven by lattice expansion and orbital reordering, with surface states observable only on specific surfaces due to symmetry-protected band inversion.

ABSTRACT

We use first principles calculations to study the electronic properties of rock salt rare earth monopnictides La$X$ ($X=$N, P, As, Sb, Bi). A new type of topological band crossing termed `linked nodal rings' is found in LaN when the small spin-orbital coupling (SOC) on nitrogen orbitals is neglected. Turning on SOC gaps the nodal rings at all but two points, which remain gapless due to $C_4$-symmetry and leads to a 3D Dirac semimetal. Interestingly, unlike LaN, compounds with other elements in the pnictogen group are found to be topological insulators (TIs), as a result of band reordering due to the increased lattice constant as well as the enhanced SOC on the pnictogen atom. These TI compounds exhibit multi-valley surface Dirac cones at three $\bar{M}$-points on the $(111)$-surface.

Motivation & Objective

• To identify topological electronic phases in rock-salt-structured rare earth monopnictides LaX (X = N, P, As, Sb, Bi).
• To determine the role of spin-orbit coupling and lattice expansion in driving topological phase transitions.
• To explain why topological surface states are only observable on certain surfaces, such as (111), and not on (001).
• To establish the connection between orbital character changes and topological invariants in these materials.

Proposed method

• First-principles density functional theory (DFT) calculations using the VASP package with GGA and PAW method.
• Incorporation of DFT+U to account for electron correlation, particularly for d-electrons.
• Use of a 11×11×11 Monkhorst-Pack k-mesh for Brillouin zone sampling.
• Calculation of mirror Chern numbers and Z2 invariants to characterize topological order.
• Analysis of band inversion at X-points and its impact on topological invariants via the Fu-Kane formula.
• Construction of thick (111) slabs (up to 20 layers) to simulate surface states and observe Dirac cones.

Experimental results

Research questions

• RQ1 What topological phases emerge in rare earth monopnictides LaX with rock-salt structure, and how do they vary across the pnictogen group?
• RQ2 How does spin-orbit coupling transform the nodal ring semimetal phase in LaN into a 3D Dirac semimetal?
• RQ3 Why do LaP, LaAs, LaSb, and LaBi exhibit topological insulator behavior despite similar band inversion at X-points?
• RQ4 What determines the surface termination dependence of observable topological surface states?
• RQ5 How does lattice expansion influence orbital character and induce a topological phase transition from semimetal to insulator?

Key findings

• LaN is a nodal ring semimetal with three intersecting nodal rings protected by mirror symmetries and spin rotation symmetry when spin-orbit coupling is neglected.
• Upon inclusion of spin-orbit coupling, the nodal rings are gapped except at two points per X-point, forming a 3D Dirac semimetal with six Dirac points in the Brillouin zone.
• LaP, LaAs, LaSb, and LaBi are 3D topological insulators due to band inversion at X-points and a change in valence band orbital character from px to py,pz mixtures.
• The topological transition is driven by increasing lattice constant, which alters orbital hybridization and enables a strong Z2 invariant.
• Surface Dirac cones in these topological insulators are only observable on the (111) surface, where three Dirac cones appear at the three M̄ points, as confirmed by slab calculations.
• On the (001) surface, no isolated Dirac cone is observable due to band inversion at multiple X-points and projection into the bulk continuum.