  It is well known that quantum spin Hall (QSH) edge modes being helical are
immune to backscattering due to non-magnetic disorder within the sample. Thus,
quantum spin Hall edge modes are non-localized and show a vanishing Hall
resistance along with quantized 2-terminal, longitudinal and non-local
resistances even in presence of sample disorder. However, this is not the case
for contact disorder. This paper shows that when all contacts are disordered in
an N-terminal quantum spin Hall sample, then transport via these helical QSH
edge modes can have a significant localization correction. All the resistances
in an N-terminal quantum spin Hall sample deviate from their values derived
while neglecting the phase acquired at disordered contacts, and this deviation
is called the quantum localization correction. This correction term increases
with the increase of disorderedness of contacts but decreases with the increase
in the number of contacts in an N terminal sample. The presence of inelastic
scattering, however, can completely destroy the quantum localization
correction.
