Figure 4. Temperature dependence and illustrative schematics of the QHE and v=0 state in TI.

(a) R_xx and (b) R_nl measured in sample ‘A' as functions of V_tg for different temperatures at B=18 T, where V_bg is chosen to set ν_b at 1/2 (dashed lines) and −1/2 (solid lines), respectively. (c) The R_nl value at (ν_t, ν_b)=(−1/2, 1/2) and (1/2, −1/2) shows approximately linear dependence on temperature. (d) σ_xx versus V_tg (with the same two values of V_bg chosen in a and b) at T=0.3 K as an example, with each highlighted circle corresponding to a state in e plotted with corresponding coloured symbols. (e) σ_xx and (f) σ_xy of ν=+1, −1 and 0 states as functions of temperature. In e, we also plot Δσ_xx (difference between averaged ν=0 states' σ_xx and averaged ν=±1 states' σ_xx), which barely changes with T. (g,h) Schematics of surface band structure (energy spectrum) in high magnetic field, showing LLs from top and bottom surfaces (blue and red) in the middle of the sample transitioning into side surface sub-bands at sample edge, and (i,j) edge states in a slab-shaped sample for ν=1 and ν=0 states. The dashed line indicates a representative Fermi level E_f and circles in g label chiral edge modes.