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Spin--valley--resolved tunneling through magnetic barriers in WSe$_2$

Rachid El Aitouni, Clarence Cortes, David Laroze, Ahmed Jellal

Abstract

We investigate the influence of a magnetic field on the electronic properties of WS$e_2$ with a focus on spin-orbit coupling, spin and valley polarization, and conductance. We solve the eigenvalue equation analytically and use the continuity equation to determine the transmission probability based on current densities. We calculate the conductance using Büttiker formula. Our numerical results indicate that transmission through the $K$ valley is more likely than through the $K'$ valley. For both valleys, the Klein tunneling effect is clearly observed. The conductance is affected by an increase in the magnetic field because it alters the energy levels of fermions via the Zeeman effect. These modifications enable the confinement of fermions within the barrier. Spin and valley polarization are also influenced by the magnetic field. As the field intensity increases, it steers the fermions and determines which channel can cross the barrier. This adds another tool of controlling fermions, paving the way for relevant applications in valleytronics and valley filtering for information storage.

Spin--valley--resolved tunneling through magnetic barriers in WSe$_2$

Abstract

We investigate the influence of a magnetic field on the electronic properties of WS with a focus on spin-orbit coupling, spin and valley polarization, and conductance. We solve the eigenvalue equation analytically and use the continuity equation to determine the transmission probability based on current densities. We calculate the conductance using Büttiker formula. Our numerical results indicate that transmission through the valley is more likely than through the valley. For both valleys, the Klein tunneling effect is clearly observed. The conductance is affected by an increase in the magnetic field because it alters the energy levels of fermions via the Zeeman effect. These modifications enable the confinement of fermions within the barrier. Spin and valley polarization are also influenced by the magnetic field. As the field intensity increases, it steers the fermions and determines which channel can cross the barrier. This adds another tool of controlling fermions, paving the way for relevant applications in valleytronics and valley filtering for information storage.

Paper Structure

This paper contains 5 sections, 18 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Theoritical Model
  3. Transmission and conductance
  4. NUMERICAL RESULT
  5. Conclusion

Figures (6)

  • Figure 1: A schematic illustration of two ferromagnetic strips separated by a distance $D$ and deposited on a WSe$_2$ monolayer, defining three distinct regions due to the presence of the magnetic barrier.
  • Figure 2: Transmissions as a function of incident angle for $B=6$ T and $E=0.95$ eV. (a): Spin-up and spin-down transmission for the $K$ and $K'$ valleys with $D = 5$ nm, (b): Spin-up transmission for the $K$ valley, (c): Spin-down transmission for the $K'$ valley.
  • Figure 3: Spin-up and spin-down transmission as a function of the magnetic field $B$ for the $K$ and $K'$ valleys with $E = 1.2$ eV, $D=15$ nm, and three incident angles (a): $\phi=0$, (b): $\phi=15^\circ$, (c): $\phi=30^\circ$.
  • Figure 4: Transmission as a function of the incident energy $E$ for oblique incidence $\phi = 30^\circ$ with $D=5$ nm. (a): Spin-up and spin-down transmission for the $K$ and $K'$ valleys with $B = 15$ T, (b): Spin-up transmission, and (c) Spin-down transmission for the $K$ valley and four values of $B$.
  • Figure 5: Conductance as a function of the barrier width $D$. (a): $E=0.95$ eV and $B=15$ T, (b): $E=0.95$ eV and four values of $B$, (c): $B=15$ T and four values of $E$.
  • ...and 1 more figures