The topological system with a twisting edge band: position-dependent   Hall resistance
  We study a $\nu=1$ topological system with one twisting edge-state band and one normal edge-state band. For the twisting edge-state band, Fermi energy goes through the band three times, thus, having three edge states on one side of the sample; while the normal edge band contributes only one edge state on the other side of the sample. In such a system, we show that it consists of both topologically protected and unprotected edge states, and as a consequence, its Hall resistance depends on the location where the Hall measurement is done even for a translationally invariant system. This unique property is absent in a normal topological insulator. 
Xuele Liu, Qing-feng Sun, X. C. Xie
cond-mat.mes-hall