Valleytronics beyond valley flavor

In 2D hexagonal materials, two types of atomic sites (A, B) are alternately located on vertices of hexagons, leading to intriguing topological aspect in association with the binary degree of freedom (DOF) known as valley flavor^1-4. Here, a useful field quantity called local valley magnetic moment (LVMM) is introduced and operationally defined by the response of an electron to local magnetic field. The study of LVMM enables insight into the local magnetic control of valley DOF. Surprisingly, for some valley states LVMM shows an oscillation with sign variation, which demonstrates the necessity to include LVMM in addition to the global, valley flavor, in the study of valleytronics. As illustrated, LVMM reflects the local difference ρ_A – ρ_B (ρ_A(B) = local probability on site A (B)). Thus, LVMM and the sum ρ_A + ρ_B form a comparatively complete yet insightful, real-space set of key state variables, for viewing the general valley-involved physics. A study along this line is given in the case of carrier transport.

 

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