TY - JOUR

T1 - The quantized Hall insulator

T2 - A "quantum" signature of a "classical" transport regime?

AU - Shimshoni, Efrat

PY - 2004/8/10

Y1 - 2004/8/10

N2 - Experimental studies of the transitions from a primary quantum Hall (QH) liquid at filling factor v = 1/k (with k an odd integer) to the insulator have indicated a "quantized Hall insulator" (QHI) behavior: while the longitudinal resistivity diverges with decreasing temperature and current bias, the Hall resistivity remains quantized at the value kh/e2. We review the experimental results and the theoretical studies addressing this phenomenon. In particular, we discuss a theoretical approach which employs a model of the insulator as a random network of weakly coupled puddles of QH liquid at fixed v. This model is proved to exhibit a robust quantization of the Hall resistivity, provided the electron transport on the network is incoherent. Subsequent theoretical studies have focused on the controversy whether the assumption of incoherence is necessary. The emergent conclusion is that in the quantum coherent transport regime, quantum interference destroys the QHI as a consequence of localization. Once the localization length becomes much shorter than the dephasing length, the Hall resistivity diverges. We conclude by mentioning some recent experimental observations and open questions.

AB - Experimental studies of the transitions from a primary quantum Hall (QH) liquid at filling factor v = 1/k (with k an odd integer) to the insulator have indicated a "quantized Hall insulator" (QHI) behavior: while the longitudinal resistivity diverges with decreasing temperature and current bias, the Hall resistivity remains quantized at the value kh/e2. We review the experimental results and the theoretical studies addressing this phenomenon. In particular, we discuss a theoretical approach which employs a model of the insulator as a random network of weakly coupled puddles of QH liquid at fixed v. This model is proved to exhibit a robust quantization of the Hall resistivity, provided the electron transport on the network is incoherent. Subsequent theoretical studies have focused on the controversy whether the assumption of incoherence is necessary. The emergent conclusion is that in the quantum coherent transport regime, quantum interference destroys the QHI as a consequence of localization. Once the localization length becomes much shorter than the dephasing length, the Hall resistivity diverges. We conclude by mentioning some recent experimental observations and open questions.

KW - Dephasing

KW - Localization

KW - Quantized Hall insulator

KW - Quantum Hall transitions

UR - http://www.scopus.com/inward/record.url?scp=12544258709&partnerID=8YFLogxK

U2 - 10.1142/S021798490400730X

DO - 10.1142/S021798490400730X

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AN - SCOPUS:12544258709

SN - 0217-9849

VL - 18

SP - 923

EP - 943

JO - Modern Physics Letters B

JF - Modern Physics Letters B

IS - 18

ER -