First-principles Study On Magnetic Tuning Of The Valleytronic Properties Of WSe₂

Exploring the electron freedoms and their applications is a core issue in modern condensed matter physics.Traditional electronics processes information by manipulating charge degree of freedom,and its development is approaching its limits.Spintronics is based on electron spin degree of freedom for more efficient information processing.Recently,it has been found that electrons in some crystals have a new quantum degree of freedom—the valley pseudospin.In analogy to the Zeeman effect of electron spin in a magnetic field,these materials have a valley Zeeman effect in the magnetic field due to the pseudospin.In recent years,the valley Zeeman effect has been experimentally confirmed,but there are still some basic questions unclear.The response of the band structure,the spin state,the orbital magnetic moment and the Berry curvature to the external magnetic field remains to be studied.Based on first-principles calculation,we studied the valleytronic properties of WSe₂ monolayer in the magnetic field.The main findings are as follows:Our calculations show that the external magnetic field breaks the time-reversal symmetry of the system and hence lifts the energy degeneracy of the valleys and makes the energy gap at the inequivalent valleys different from each other,resulting in the valley Zeeman effect.We calculated the band structure under different magnetic fields.It is found that the valley Zeeman splitting varies linearly with the magnetic field B with a rate of 0.21 meV/Tesla,in good agreement with the experiment.The calculation of the orbital magnetic moment shows that the orbital magnetic moment of the inequivalent valleys is opposite to each other,which gives rise to opposite band shift and causes the valley Zeeman splitting.The valley Zeeman splitting is mainly contributed by the atomic orbital magnetic moment of the W atom,but the contribution of the valley magnetic orbital magnetic moment cannot be ignored;Our calculations found that the Berry curvatures of the inequivalent valleys of the WSe₂monolayer layer are opposite.We calculated the Berry curvatures of the highest valence band and the lowest conduction band.It is found that without magnetic field,the Berry curvatures are of the same magnitude with opposite sign at the inequivalent valleys.In the external magnetic field,the magnitude of their Berry curvature is no longer the same,and the difference is also linearly dependent on the magnetic field B;We calculate the circular dichroism and the dielectric function of the system and find that in the external magnetic field,the valley dependent selection rule still holds.The inequivalent valleys absorb light with opposite circular polarization.Therefore,selective excitation of the energy valley can still be achieved by circularly polarized light of different polarities in magnetic field.Without magnetic field,the calculated dielectric function indicates that the absorption peaks of the left-and right-handed circularly polarized light overlap.After the application of the magnetic field,the absorption peaks of opposite circular polarization are split,which is in good agreement with the experimental photoluminescence spectra.In addition,we also explained the broadening of the photoluminescence spectra and the relative intensity of the peaks by calculating the joint density of states.Our study reveals the mechanism of the valley Zeeman effect,confirms and explains the experimental results,which can help for further studies and applications of the valley Zeeman effect.