Table 1 Comparison of chiral(topological) QAH edge modes, chiral(topological) QAH edge mode with trivial QSH edge modes and chiral(trivial) QAH edge mode with trivial QSH edge modes. Note: In the 2T, 3T and 4T QAH samples depicted in Figs. 1,2, and 4 the magnetization direction is (↑) implying the QAH edge mode shown by black solid or dashed line is spin-up polarized. The conductance matrices depicted in Eqs. 2–6 and 14 as well as the calculations shown in Eqs. 7–13, 15–16 and the 2T, Hall and non-local resistances derived and plotted in Figs. 3, 5 are therefore for magnetization (↑). We follow similar procedure to calculate the resistances for magnetization direction (↓) in which case the QAH edge modes shown by black solid or dashed lines in Figs. 1, 2 and 4 will be spin-down polarized and mention the results in this table.
From: Role of helical edge modes in the chiral quantum anomalous Hall state
QAH(topological) | QAH(topological) + Trivial QSH | QAH(trivial) + Trivial QSH | ||
|---|---|---|---|---|
R H | Ideal (zero disorder) | Quantized \(\frac{{e}^{2}}{h}\) (R H (↑) = −R H (↓)) | Not quantized (R H (↑) = −R H (↓)) | Not quantized (R H (↑) = −R H (↓)) |
Finite disorder | Quantized \(\frac{{e}^{2}}{h}\) (R H (↑) = −R H (↓)) | Not quantized (R H (↑) = −R H (↓)) | Not quantized (R H (↑) = −R H (↓)) | |
Disorder + Inelastic scattering | Quantized \(\frac{{e}^{2}}{h}\) (R H (↑) = −R H (↓)) | Not quantized (Fig. 5(a)) (R H (↑) ≠ −R H (↓)) | Quantized e2/h (Fig. 5(a)) (R H (↑) = −R H (↓)) | |
R 2T | Ideal (zero disorder) | Quantized \(\frac{{e}^{2}}{h}\) (R2T(↑) = R2T(↓)) | Not quantized (R2T(↑) = R2T(↓)) | Not quantized (R2T(↑) = R2T(↓)) |
Finite disorder | Quantized \(\frac{{e}^{2}}{h}\) (R2T(↑) = R2T(↓)) | Not quantized (Fig. 3(b)) (R2T(↑) = R2T(↓)) | Not quantized (Fig. 3(b)) (R2T(↑) = R2T(↓)) | |
Disorder + Inelastic scattering | Quantized \(\frac{{e}^{2}}{h}\) (R2T(↑) = R2T(↓)) | Not quantized (Fig. 5(b)) (R2T(↑) ≠ R2T(↓)) | Quantized e2/h (Fig. 5(b)) (R2T(↑) = R2T(↓)) | |
R NL | Ideal (zero disorder) | 0 (R NL (↑) = R NL (↓)) | Finite (R NL (↑) = R NL (↓)) | Finite (R NL (↑) = R NL (↓)) |
Finite disorder | 0 (R NL (↑) = R NL (↓)) | Finite (Fig. 3(c)) (R NL (↑) = R NL (↓)) | Finite (Fig. 3(c)) (R NL (↑) = R NL (↓)) | |
Disorder + Inelastic scattering | 0 (R NL (↑) = R NL (↓)) | Finite (Fig. 5(c,d)) (R NL (↑) ≠ R NL (↓)) | 0 (Fig. 5(d)) (R NL (↑) = R NL (↓)) |
