Electric fields induced spin and/or valley polarization in Weiss oscillations of monolayer 1{\it T}$^{\prime}$-$\mathrm{MoS}_{2}$

TL;DR

This work demonstrates that Weiss oscillations in monolayer 1T'-MoS2 can be polarized in spin and/or valley degrees of freedom under uniform electric fields and a one-dimensional electrostatic modulation. The authors develop a low-energy $k\cdot p$ description with tilted Dirac cones, derive the Landau level spectrum under magnetic fields (including field-induced tilts), and compute the diffusive magnetoconductivity via the Kubo formalism, revealing how polarization arises in both amplitude and period. A vertical field induces spin–valley polarization, a transverse field induces valley polarization, and applying both fields yields four polarized branches with tunable switching via field directions. Crucially, period polarization originates from polarized effective Fermi energies or Landau level spacings, and its presence generally accompanies amplitude polarization, leading to measurable shifts and misalignments that can be probed experimentally. The results offer a pathway to control spin and valley transport in 2D TMDCs through modest external fields and periodic modulation, with potential applications in nanoelectronic spintronics and valleytronics.

Abstract

Monolayer 1{\it T}$^{\prime}$-$\mathrm{MoS}_{2}$ exhibits spin- and valley-dependent massive tilted Dirac cones with two velocity correction terms in low-energy effective Hamiltonian. We theoretically investigate the longitudinal diffusive magneto-conductivity of monolayer 1{\it T}$^{\prime}$-$\mathrm{MoS}_{2}$ by using the linear response theory. It is shown that the Weiss oscillations are polarized in spin and valley degrees of freedom, under uniform electric fields and a weak one-dimensional spatially-periodic electrostatic potential modulation. The spin polarization, the valley polarization and the spin-valley polarization can be switched by flipping the external electric fields. The polarization is found not only in the amplitudes but also in the periods of the Weiss oscillations. It is found that the period polarization in Weiss oscillations originates from the polarized effective Fermi energies or the polarized Landau level spacing scales. In Weiss oscillations, polarization in amplitude does not imply the presence of polarization in period, whereas polarization in period is accompanied by polarization in amplitude. The superposition of polarization in amplitude and polarization in period enables the appearance of considerable polarization in Weiss oscillations under relatively weak external electric fields.

Figures (9)

• Figure 1: The diffusive conductivities in different spin and valley channels versus the inverse magnetic field in the absence of both electric fields. The modulation period is $a_{0} = 350 \mathrm{nm}$, the system size is $L_{x} \times L_{y} = 10 a_{0} \times 10 a_{0}$, the temperature is $T = 3 \mathrm{K}$, and the Fermi energy is taken as 0.17 eV. $B_{0} = \frac{\hbar}{ea_{0}^{2}}$ is the characteristic magnetic field.
• Figure 2: The diffusive conductivities versus the inverse magnetic field in the presence of the uniform vertical electric field.
• Figure 3: The polarization rates versus the inverse magnetic field in the presence of the uniform vertical electric field.
• Figure 4: The diffusive conductivities versus the inverse magnetic field in the presence of the uniform transverse electric field.
• Figure 5: The velocity correction factor $1 - 2 \rho_{0}^{2}$ in different valleys versus the effective tilting velocity $v_{r}$.