Quantum Spin Hall Effect — BHZ Model
Helical Edge States · Z₂ Topological Invariant · Spin-Momentum Locking
BHZ Model Parameters
Mass M (controls topology):
-1.0
Spin-orbit coupling λ
SO
:
0.5
B parameter (asymmetry):
1.0
Chemical potential μ:
0.0
Z₂ = 1 (Topological)
H(k) = ε(k)I + d(k)·σ
d
z
= M - B(k
x
²+k
y
²)
Z₂: ν = (1/2π)∮dk·A(k)
M/B < 0: trivial; 0 < M/B < 2: QSH
The BHZ (Bernevig-Hughes-Zhang) model describes HgTe quantum wells. When -2B < M < 0, the Z₂ invariant ν=1, producing helical edge states protected against backscattering by time-reversal symmetry.