Valley-contrasting physics in a two-dimensional ${p}_{x,y}$-orbital honeycomb lattice

Valley-contrasting physics in a two-dimensional $p_{x, y}$ -orbital honeycomb lattice

Yuanyuan Wang, Chengwang Niu, Baibiao Huang, Ying Dai, and Wei Wei

Phys. Rev. B 105, 075421 – Published 22 February 2022

Abstract

In valley physics, large spin-orbit coupling (SOC) is the key, which is however rather weak for many materials with two-dimensional (2D) hexagonal honeycomb lattice. In contrast to conventional materials such as graphene with active $p_{z}$ orbitals, we proposed that large SOC splitting could be realized in $p_{x, y}$ -orbitals active honeycomb lattice, i.e., the $X Y H$ lattice. In particular, our model analysis confirmed that dynamically and magnetically induced valley polarizations are experimentally accessible. In accordance to the first-principles calculation and many-body perturbation theory, quaternary-layer ${BiSbC}_{3}$ proves our proposed physics, with extremely large SOC splitting of 567.9 meV, excitonic energy difference of 496 meV for characteristic $A$ and $B$ excitons, and valley polarization of 168.7 meV by V doping.

Received 24 August 2021
Revised 18 January 2022
Accepted 31 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.075421

Physics Subject Headings (PhySH)

Electronic structure Excitons Spin-orbit coupling Valleytronics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuanyuan Wang, Chengwang Niu , Baibiao Huang, Ying Dai^*, and Wei Wei^*

School of Physics, State Key Laboratory of Crystal Materials, Shandong University, 250100 Jinan, China

^*Corresponding authors: daiy60@sdu.edu.cn; weiw@sdu.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 105, Iss. 7 — 15 February 2022

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Sketch of the $p_{x, y}$ -orbitals honeycomb lattice with sublattice asymmetry, $a$ and $δ_{i}$ are the lattice constant and the length of the nearest neighbor bond, respectively. Without loss of generality, the convention $a = 1$ is adopted throughout the rest of this article. (b) Hexagonal Brillouin zone with edge length of 4π/ $3 a$ . (c) Energy dispersion in three dimensions, and (d) Berry curvature of $p_{x, y}$ -orbitals model in the presence of the π bonding $t_{⊥}$ without considering the SOC effect. 2D band structure from model Hamiltonian (e) without and (f) with a uniform Zeeman field when SOC is considered. Parameters used are $λ = 0.4, t_{⊥} = 0.8, t_{∥} = - 0.02, γ = 0.06$ and $μ = 0.05$ . $t_{∥}$ and $t_{⊥}$ are the corresponding σ- and π-hopping strengths, respectively. $λ$ , γ, and μ represent the strength of staggered sublattice potential, SOC and Zeeman fields, respectively. The energy unit for these parameters is set to 1.
Reuse & Permissions
Figure 2
(a) Valley-selective optical selection rules: $σ_{+} / σ_{-}$ circularly polarized light couples only to band edge transitions in $K / K^{'}$ valley. (b) Schematic of phase winding in the $X Y H$ lattice that gives rise to the chiral optical selectivity, blue and yellow vectors represent the phase winding contribution from Bloch lattice phase, and red and gray axes indicate the rotation of local atomic coordinates that leads to the azimuth desynchronization, that is, the phase winding under a threefold rotation. Total phase winding of the Bloch function of valence and conduction bands in (c) $K$ and (d) $K^{'}$ valley.
Reuse & Permissions
Figure 3
(a) Top and side view of QL ${BiSbC}_{3}$ , rhombus indicates the unit cell. (b) Spin-resolved and (c) orbital-resolved band structure, the Fermi level is set to zero. Inset to (b) is the Berry curvature of QL ${BiSbC}_{3}$ over the full Brillouin zone. (d) Optical absorption spectrum of QL ${BiSbC}_{3}$ by means of GW+Bethe–Salpeter calculations. Inset defines the relevant energy, GW quasiparticle band gap $E_{g}$ , exciton binding energy $E_{b}$ , SOC spin splitting $E_{SOC}$ . $E_{g} - E_{b}$ denotes the vertical optical transition energy. (e) Exciton wave functions for $A$ and $B$ excitons plotted with a $21 \times 21 \times 1$ supercell, red dots represent the fixed holes.
Reuse & Permissions
Figure 4
(a) Sketch of possible ferromagnetic, Néel and strip antiferromagnetic spin orders in the 2D triangular lattice. (b) Spin charge density of V-doped QL ${BiSbC}_{3}$ , where the $2 \times 2 \times 1$ supercell is indicated by a rhombus, blue and yellow isosurfaces correspond to the spin-down and spin-up states, respectively. Spin-polarized band structure of V-doped QL ${BiSbC}_{3}$ (c) without and (d) with SOC, the Fermi level is set to zero.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics