Sarmal kenar elekronlarının nükleer spinlerden eşevreli saçılımı

Topological insulators (TIs) are symmetry-protected states of matter characterized by a topological index, featuring gapless edge or surface states that are topologically protected, hence robust to weak disorder as long as the relevant anti-unitary symmetry is preserved. In this thesis, we focus on a particular TI, namely the quantum spin Hall insulator, where the relevant symmetry is the time-reversal (TR) symmetry. However, most topological insulators contain nuclear spins, which interact with the helical edge states via hyperfine coupling, breaking the TR symmetry and thus destroying the topological protection of the edge states. We perform numerical simulations to calculate the hyperfine-enabled backscattering probabilities of the helical edge electrons for edges containing up to 10 nuclear spins. We presented the plots of total reflection probabilities for a range of single-nucleus reflection amplitudes and discuss how our results apply to dynamic nuclear polarization. We also propose a universal extremum of the total reflection probability curves, independent of the system size, and expose which particular arrangements of nuclear spins cause the universal extremum.