The energy band structure of quantum wires with both Rashba and Dresselhaus spin-orbit couplings in a magnetic field is studied theoretically. We find that the magnetic field strongly affects the subband structure of the wire. With both couplings we obtain a beating pattern in the magnetoresistance. Compared with the quantum wire with only Rashba spin-orbit coupling, the beating pattern can be suppressed even if the coupling strengths are large. This is due to the interplay of the two spin-orbit couplings. The disappearing threshold of the nodes depends on both coupling strengths. When the coupling strengths change, the number of nodes of the beating pattern also varies.

Two-dimensional (2D) materials have potential applications in nanoscale sensors and spintronic devices. Herein, motivated by experimental synthesis of a CrI${}_3$ monolayer possessing intrinsic magnetism and a Janus MoSSe monolayer with piezoelectricity, we propose a 2D Janus Cr${}_2$I${}_3$F${}_3$ monolayer as a multifunctional material exhibiting both piezoelectricity and ferromagnetism. Using density functional theory calculations, we systematically investigated the structural stability and the electronic, magnetic, and piezoelectric properties of the Janus Cr${}_2$I${}_3$F${}_3$ monolayer. We predicted that a vertical polarization of up to −0.155 × 10${}^{-10}$ C/m is induced in the Cr${}_2$I${}_3$F${}_3$ monolayer due to the breaking of symmetry. The origination mechanism of polarization was demonstrated in terms of a local dipole moment calculated by maximally localized Wannier functions. Meanwhile, it was found that a remarkable piezoelectric response can be produced under a uniaxial strain in the basal plane. The calculated piezoelectric coefficients of the Cr${}_2$I${}_3$F${}_3$ monolayer compare favorably with those of the frequently used bulk piezoelectric materials such as $\alpha$–quartz and wurtzite AlN. Particularly, the e${}_{31}$ and d${}_{31}$ values of the Cr${}_2$I${}_3$F${}_3$ monolayer are nearly 10 times as large as that of Mo-based transition metal dichalcogenides. We also found that the magnitude of e${}_{31}$ mainly arises from the ionic contribution, while the electronic contribution can be nearly neglected. The considerable piezoelectric response combined with the intrinsic magnetism make the Janus Cr${}_2$I${}_3$F${}_3$ monolayer a potential candidate for novel multifunctional devices integrating both piezoelectric and spintronic applications.

Utilizing a continuum model, this study systematically investigates the Fermi arcs of topological surface states in three-dimensional multi-Weyl semimetals. We analyzed the energy spectra and wave functions for bulk quadratic and cubic-Weyl semimetals, each with a single Weyl point. The Fermi arcs of the topological surface states in these multi-Weyl semimetals were derived analytically. Those results reveal a direct proportionality between the number of arcs emanating from a Weyl point and its winding number. Furthermore, we elucidate the topological Lifshitz transition of Fermi arcs, which depends on boundary condition parameters, and pinpoint the critical points associated with the Lifshitz transition in these semimetals. These findings highlight the evolution of Fermi arcs of topological surface states in multi-Weyl semimetals, potentially opening new avenues for modulating transport properties of topological quantum materials. Our study provides a robust analytic framework for understanding the behavior of Fermi arcs in multi-Weyl semimetals, offering valuable insights for developing topological quantum devices.

The effects of crack defects on electronic and magnetic properties of zigzag MoS ₂ nanoribbons are investigated systematically by first-principles calculations based on spin-polarized density functional theory. We find that not only the electronic and spin transport ability of zigzag MoS ₂ nanoribbons can be enhanced significantly by the armchair crack defects, but also their magnetism could be modulated flexibly by crack defects. Our study suggests that the introduction of crack defect is a feasible way to modulate the electronic and magnetic properties of zigzag MoS ₂ nanoribbons. We further propose that the crack defects may also provide a useful tool for improving the performance of devices.

We point out four mistakes in the symmetry classification of vibrational modes of the CrI₃ monolayer at the Γ point in Webster et al.'s paper [PCCP, 2018, 20, 23546]. The discrepancy of Raman activity of A_2g mode as well as the misidentification of two optical modes A_1u and A_2u have been clarified.