[Paper Review] The Quantized Hall Insulator: A New Insulator in Two-Dimensions

Michael Hilke, D. Shahar+4 more|eScholarship (California Digital Library)|Oct 15, 1998

Quantum and electron transport phenomena39 citations

TL;DR

This paper experimentally demonstrates the existence of a new insulating phase in two-dimensional electron systems under high magnetic fields, termed the quantized Hall insulator (QHI), where the Hall resistivity remains approximately quantized at h/e² even in the insulating regime. The QHI emerges at high magnetic fields beyond the quantum Hall plateau, confirmed by temperature-dependent measurements showing ρxy saturates at h/e² below 2 K, and is further validated by a semicircle relation between σxx and σxy, indicating universal transport behavior in the insulating phase.

ABSTRACT

Quite generally, an insulator is theoretically defined by a vanishing conductivity tensor at the absolute zero of temperature. In classical insulators, such as band insulators, vanishing conductivities lead to diverging resistivities. In other insulators, in particular when a high magnetic field (B) is added, it is possible that while the magneto-resistance diverges, the Hall resistance remains finite, which is known as a Hall insulator. In this letter we demonstrate experimentally the existence of another, more exotic, insulator. This insulator, which terminates the quantum Hall effect series in a two-dimensional electron system, is characterized by a Hall resistance which is approximately quantized in the quantum unit of resistance h/e^2. This insulator is termed a quantized Hall insulator. In addition we show that for the same sample, the insulating state preceding the QHE series, at low-B, is of the HI kind.

Motivation & Objective

• To identify and characterize a new insulating phase in two-dimensional electron systems under strong magnetic fields.
• To determine whether the Hall resistivity remains quantized in the insulating phase, distinct from conventional Hall insulators.
• To investigate the transport behavior in the insulating regime, particularly the interplay between ρxx and ρxy, and their temperature dependence.
• To test the validity of the semicircle relation between σxx and σxy in the insulating phase.
• To clarify the nature of the insulating state beyond the quantum Hall effect, including the role of disorder and localization.

Proposed method

• Measurement of diagonal (ρxx) and Hall (ρxy) resistivities as functions of magnetic field B and temperature T in a high-mobility 2D electron system.
• Use of field-symmetrization technique by reversing B-field direction to cancel symmetric contributions from ρxx and isolate ρxy.
• Low-frequency lock-in technique with 1 nA current to minimize heating and improve accuracy in ρxy measurements.
• Extrapolation of ρxx(T) to T=0 K to identify insulating behavior via exponential divergence.
• Analysis of the semicircle relation σxx² + (σxy - e²/(2h))² = (e²/(2h))² using matrix inversion of resistivity tensors.
• Comparison of experimental data with theoretical models, including KLZ global phase diagram and semi-classical network models for QHI.

Experimental results

Research questions

• RQ1 Does the Hall resistivity remain quantized in the insulating phase beyond the quantum Hall plateau?
• RQ2 What distinguishes the quantized Hall insulator (QHI) from the conventional Hall insulator (HI) in terms of transport properties?
• RQ3 How does the semicircle relation between σxx and σxy hold in the insulating regime, particularly at low temperatures?
• RQ4 What is the role of temperature and current in reducing measurement inaccuracy for ρxy in high-resistivity regimes?
• RQ5 Can the QHI phase be described by a semi-classical network model with localized quantum Hall liquids and coherent tunneling?

Key findings

• The Hall resistivity ρxy remains approximately quantized at h/e² over a broad range of magnetic fields (2.7–10 T) and Landau level filling factors ν from 1.5 to 0.4, indicating the existence of a new insulating phase.
• At temperatures below 2 K, ρxy saturates at the quantized value h/e² within 2% accuracy, confirming the QHI state deep in the insulating regime.
• With increased current (up to 400 nA), the experimental error in ρxy is reduced from 20% to 6%, improving measurement fidelity.
• The semicircle relation σxx² + (σxy - e²/(2h))² = (e²/(2h))² is clearly observed across all measured temperatures, confirming universal transport behavior in the QHI phase.
• The insulating state at low B-fields is identified as a conventional Hall insulator (HI), where ρxy remains finite but not quantized, contrasting with the QHI at high B-fields.
• The transition from HI to QHI occurs at νc = 0.75, with ρxx showing T-independent behavior at the critical field, confirming the phase boundary.