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It is well known that quantum spin Hall (QSH) edge modes being helical areimmune to backscattering due to non-magnetic disorder within the sample. Thus,quantum spin Hall edge modes are non-localized and show a vanishing Hallresistance along with quantized 2-terminal, longitudinal and non-localresistances even in presence of sample disorder. However, this is not the casefor contact disorder. This paper shows that when all contacts are disordered inan N-terminal quantum spin Hall sample, then transport via these helical QSHedge modes can have a significant localization correction. All the resistancesin an N-terminal quantum spin Hall sample deviate from their values derivedwhile neglecting the phase acquired at disordered contacts, and this deviationis called the quantum localization correction. This correction term increaseswith the increase of disorderedness of contacts but decreases with the increasein the number of contacts in an N terminal sample. The presence of inelasticscattering, however, can completely destroy the quantum localizationcorrection.

Disordered contacts can localize helical edge electrons