Renormalizing into the mesoscopic quantum Hall insula - tor

– Using the Chalker-Coddington network model as a drastically simplified, but universal model of integer quantum Hall physics, we investigate the plateau-to-insulator transition at strong magnetic field by means of a real-space renormalization approach. Our results suggest that for a fully quantum coherent situation, both the Hall insulator with diverging Hall resistance RH and the quantized Hall insulator with RH ≈ h/e 2 can be observed depending on the precise nature of the averaging procedure. Introduction. – The integer quantum Hall (QH) transitions are described well in terms of a series of delocalization-localization transitions of the electron wavefunction [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. These universal plateau-plateau transitions are accompanied by a power-law divergence ǫ of the electronic localization length ξ, where ǫ defines the distance to the transition for a suitable controlled parameter, e.g. the electron energy [8, 9, 10]. Similarly, it is now conclusively established that plateau-plateau and insulator-plateau transitions exhibit the same critical behavior [12, 13, 14, 15, 16, 17, 18, 19, 20,11, 21]. However, the value of the Hall resistivity RH in this insulating phase (at large magnetic field) is still rather controversial. Various experiments have found that RH remains very close to its quantized value h/e even deep in the insulating regime [12, 13, 14, 16, 17, 18, 21] with longitudinal resistance RL > h/e . This scenario has been dubbed the quantized Hall insulator. On the other hand, theoretical predictions show that a diverging RH should be expected, i.e., RH ∝ R α L [22, 23]. This Hall insulator is to be expected at strong disorder or strong magnetic fields. In fully quantum coherent transport measurements such as in mesoscopic devices at low temperature, the results clearly show the paramount influence of quantum interference and the measured quantities fluctuate strongly [24]. At magnetic field B = 0, the universal conductance fluctuations provide the most famous example [25]. For the QH situation, similarly reproducible and pronounced fluctuations have been observed previously [26,27,28,29,30,31, 32, 33, 34], although no complete understanding of their behavior has yet emerged. Thus for quantum coherent QH samples, the average values RL and RH become meaningless unless