Strain Effects on Electronic Properties of Cobalt-Based Coordination Nanosheets

TL;DR

Problem: understanding how strain and crystal structure affect electronic, magnetic, and topological properties of CoBHT coordination nanosheets. Approach: first-principles DFT for HDS and LDS with SOC, plus Wannier-based tight-binding model to capture Berry curvature and anomalous Hall conductivity; uniaxial strain used to study tunability. Key findings: HDS is metallic with ferromagnetic moments; LDS is semiconducting with a finite gap; SOC opens gaps at K points and Berry curvature drives intrinsic anomalous Hall conductivity; a tight-binding model reproduces the DFT bands and clarifies topological features; strain modulates magnetic moments and DOS, and enhances anomalous Hall conductivity under hole doping. Significance: strain engineering can tailor electronic, magnetic, and catalytic properties of CoBHT for next-generation devices.

Abstract

We theoretically study the strain effects on the electronic properties of cobalt-based benzenehexathiol (CoBHT) coordination nanosheets using first-principles calculations. Two distinct crystal structures, high-density structure (HDS) and low-density structure (LDS), are explored. Our results reveal that HDS behaves as a metal, while LDS exhibits semiconducting. Spin-polarized electronic band structures highlight the presence of energy band structures of Kagome lattice, and the inclusion of spin-orbit coupling (SOC) results in band gap openings at high-symmetric K points. Furthermore, we construct the tight-binding model to investigate the topological properties of CoBHT, demonstrating anomalous Hall conductivity driven by the intrinsic Berry curvature. The impact of uniaxial strain on the electronic and magnetic properties of CoBHT is also studied. Strain induces significant modifications in magnetic moments and density of states, particularly in the HDS. Anomalous Hall conductivity is enhanced under hole-doping conditions, suggesting that strain can be used to tailor the electronic properties of CoBHT for specific applications. Our findings underscore the potential of CoBHT nanosheets for use in next-generation electronic, optoelectronic, and catalytic devices with tunable properties through strain engineering.

Figures (5)

• Figure 1: Crystal structures of CoBHT: (a) high-density structure (HDS) and (b) low-density structure (LDS). The gray rhombus is unit cell. CoBHT consists of Co (blue), S (yellow), and C (gray) atoms. Here, $\bm{a_1}=(a,0)$ and $\bm{a_2}=a(1/2,\sqrt{3}/2)$ are primitive vectors, where $a$ is lattice constant. For HDS and LDS, $a=8.45$ and $14.52$Å, respectively. (c) The corresponding 1st Brillouin zone. (BZ). Here, $\bm{b}_1=\frac{2\pi}{a}(1,-\frac{1}{\sqrt{3}})$ and $\bm{b}_2=\frac{2\pi}{a}(0,\frac{2}{\sqrt{3}})$.
• Figure 2: Spin density plots of CoBHT in the unit cell for (a) HDS and (b) LDS, respectively. CoBHT has finite magnetic moments originating from Co atoms. The magnetic moment of HDS is 1.85 $\mu_B$, while that of LDS is 4.07 $\mu_B$. Spin-polarized electronic band structures for (c) HDS and (d) LDS, respectively. Red and blue lines represent up and down spin states, respectively. Figures (e) and (f) depict the electronic band structures and density of states (DOS) considering SOC for HDS and LDS, respectively. The band gap openings at the K point are marked by red ellipses. In the DOS plots, the blue lines represent the cobalt atoms, yellow lines represent sulfur atoms, gray lines represent carbon atoms, and black lines represent the total DOS. LDS exhibits semiconductor behavior with a band gap of $0.265$ eV.
• Figure 3: (a) Comparison of the band structures of CoBHT for HDS with SOC as calculated by DFT (the black line) and the WTB Hamiltonian (the blue circles). The WTB Hamiltonian consists of all $d$-orbitals of the cobalt atoms. (b) Contour plot of Berry curvature ($-\Omega_{z \bm{k}}$) in the first BZ. (c) Energy band structure and corresponding Berry curvature ($-\Omega_{z\bm{k}}$) along the path through the high-symmetric points in the first BZ. (d) Fermi energy dependence of anomalous Hall conductivity of CoBHT for HDS.
• Figure 4: Strain effect of CoBHT for HDS on the electronic energy band structures. (Upper panels) Elongation strain along $x$-axis with the strain $1.0$, $5.0$, and $10.0$%. (Lower panels) Elongation strain along $y$-axis.
• Figure 5: (a) Strain dependence of magnetic moment for (lower) HDS and (upper) LDS, respectively. Here $E_F$ is fixed at $0$ eV, i.e., non-doping case. (b) The strain effect of DOS at $E_F$ for HDS is for several different electron or hole doping cases. (c) Strain effect of anomalous Hall conductivity of HDS. (d) Fermi energy dependence of anomalous Hall conductivity for HDS with several different strains.