Disorder dependence of helical edge states in HgTe/CdTe quantum wells

Abstract

In recent years, extensive attention has been focused on a new topological phase induced by nonmagnetic disorder, known as the topological Anderson insulator (TAI). In this work, we study the disorder strength dependence of the edge states in TAI phase in disordered HgTe/CdTe quantum wells. It is shown clearly that the disorder-induced edge states appear above a critical disorder strength after a gap-closing phase transition. These edge states are then found to decline with an increase of disorder strength in a stepwise pattern due to the finite-width effect, where the opposite edges couple to each other through the localized bulk states. This is in sharp contrast with the localization of the edge states themselves by time-reversal symmetry breaking. The size-independent phase boundaries are further obtained through scaling analysis, where a metallic phase is found separating two topologically distinct phases, which is due to the Fermi energy and mass renormalization. A. The complete dependence of the energy spectrum on disorder strength in disordered HgTe/CdTe quantum wells (QWs) 13 Appendix B. Comparison of the energy spectrum in disordered HgTe/CdTe QWs between periodic and open boundary conditions in the y-direction 14 Appendix C. Spin-momentum locking of the edge states in disordered HgTe/CdTe QWs in the topological Anderson insulator phase 14 References 15

Phase structure of the topological Anderson insulator

“…Line eg2 represents a quantized-to-insulator transition, and separates the localized phase in region II from the conductance plateau. Contrary to Chen et al, 14 we see no evidence of an intervening metallic phase along eg2; we will discuss this further in Sec. III B.…”

“…Chen et al 14 calculated the logarithmic average of the bulk conductance at system sizes 70a × 70a, 100a × 100a, 130a × 130a. They used periodic boundary conditions and did not include the conductance of edge states.…”

“…Moreover, Guo et al 16 and Chen et al 14 plotted the region where the CPA predicts a bulk gap, and demonstrated that this region is much smaller than the conductance plateau which has been determined numerically. Outside the gapped region Chen et al 14 found numerical evidence that robust edge states coexist with bulk states, and they also reported a metallic phase lying between the quantized and insulating phases. These results reveal ongoing questions about the precise nature of the TAI conductance plateau and about the overall phase diagram.…”

“…The maximum value of L x until now has been L x = 300a, in a paper which used L x = 130a data to determine the TAI phase diagram (Ref. 14). Other studies have considered 13), and L x = 150a (Ref.…”

Effects of disorder on electron tunneling through helical edge states

“…On the one hand, various studies have tested such robustness to disorder when inelastic scattering is included [1,[5][6][7][8], possibly in interplay with Rashba impurities [9][10][11][12][13], or when time-reversal symmetry is broken either by magnetic impurities [14][15][16][17] or by applied magnetic fields [18][19][20]. On the other hand, it also been realized that disorder itself can cause an ordinary insulator to undergo a phase transition to a topological insulator (topological Anderson insulator) [21][22][23][24]. In turn, such a transition may be strongly modified when disorder exhibits spatial correlations [25].…”