Scaling Collapse of Longitudinal Conductance near the Integer Quantum Hall Transition

Dresselhaus, Elizabeth; Sbierski, Björn; Gruzberg, Ilya A.

doi:10.1103/physrevlett.129.026801

Cited by 13 publications

(6 citation statements)

References 31 publications

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“…First, we look for a temperature-independent conductance/resistance at the critical point x = x c . Although several experimental and theoretical works report critical resistance values equal to the h / e 2 in quantum Hall systems 17 , 19 , whether this value is universal or bears larger significance remains a subject of debate 29 . The second behavior we look for is a power-law temperature dependence of the tuning parameter derivative of the conductance/resistance when evaluated at the critical point x c , i.e., , where κ = p /2 ν .…”

Section: Resultsmentioning

confidence: 99%

Quantized resistance revealed at the criticality of the quantum anomalous Hall phase transitions

Deng,

Zhang,

Eckberg

et al. 2023

Nat Commun

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In multilayered magnetic topological insulator structures, magnetization reversal processes can drive topological phase transitions between quantum anomalous Hall, axion insulator, and normal insulator states. Here we report an examination of the critical behavior of two such transitions: the quantum anomalous Hall to normal insulator (QAH-NI), and quantum anomalous Hall to axion insulator (QAH-AXI) transitions. By introducing a new analysis protocol wherein temperature dependent variations in the magnetic coercivity are accounted for, the critical behavior of the QAH-NI and QAH-AXI transitions are evaluated over a wide range of temperature and magnetic field. Despite the uniqueness of these different transitions, quantized longitudinal resistance and Hall conductance are observed at criticality in both cases. Furthermore, critical exponents were extracted for QAH-AXI transitions occurring at magnetization reversals of two different magnetic layers. The observation of consistent critical exponents and resistances in each case, independent of the magnetic layer details, demonstrates critical behaviors in quantum anomalous Hall transitions to be of electronic rather than magnetic origin. Our finding offers a new avenue for studies of phase transition and criticality in QAH insulators.

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Section: Resultsmentioning

confidence: 99%

Quantized resistance revealed at the criticality of the quantum anomalous Hall phase transitions

Deng,

Zhang,

Eckberg

et al. 2023

Nat Commun

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“…The recent proposal of a conformal field theory [14,15] with marginal scaling, i.e., with ν ¼ ∞, has stimulated further numerical study of this problem. [16,17] A major difficulty in finite size scaling analyses of the quantum Hall transition is the presence of slow irrelevant corrections that complicate the estimation of the critical exponent. In ref.…”

Section: Introductionmentioning

confidence: 99%

“…In ref. [17], the energy x and system size L dependence of two terminal conductance gðx, LÞ of the Chalker-Coddington model [18,19] was calculated and a finite size scaling analysis performed. In that article, Dresselhaus et al proposed a method for taking into account the irrelevant correction based on a factorization ansatz for the scaling function.…”

Section: Introductionmentioning

confidence: 99%

“…The recent proposal of a conformal field theory [ 14,15 ] with marginal scaling, i.e., with

\nu = \infty

, has stimulated further numerical study of this problem. [ 16,17 ]…”

Section: Introductionmentioning

confidence: 99%

“…In ref. [17], the energy x and system size L dependence of two terminal conductance

g \left(\right. x , L \left.\right)

of the Chalker–Coddington model [ 18,19 ] was calculated and a finite size scaling analysis performed.…”

Section: Introductionmentioning

confidence: 99%

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Irrelevant Corrections at the Quantum Hall Transition

Slevin

Ohtsuki

2023

Physica Rapid Research Ltrs

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The quantum Hall effect is one of the most extensively studied topological effects in solid‐state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous numerical finite size scaling studies have focused on the critical exponent ν for the correlation length. In such studies, it is important to take proper account of irrelevant corrections to scaling. Recently, Dresselhaus et al. proposed a new scaling ansatz, which they applied to the two terminal conductance of the Chalker–Coddington model. Herein, their proposal is applied to the previously reported data for the Lyapunov exponents of that model using both polynomial fitting and Gaussian process fitting.

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