Microwave frequency dependence of integer quantum Hall effect: Evidence for finite-frequency scaling

Abstract

We present ac measurements of the diagonal conductivity o xx , in the integer quantum Hall regime for frequency /between 0.2 and 14 GHz and temperature r>:50 mK. Re(cr xx ) was obtained from the measured attenuation of a coplanar transmission line on the sample surface. For/S; 1 GHz, a xx peaks between IQHE minima broaden as / increases, roughly as (AB)<xf 7 , where AB is the peak width. y^OAl ± 0.04 for spin-split peaks, and for spin-degenerate peaks 7=0.20 ± 0.05. We interpret our data in terms of dynamic scaling. Our y, when compared with existing estimates of the localization length exponent v, is consistent with assigning a dynamic exponent z = 1.PACS numbers: 73.40. Hm, 72.30.+q, 75.40.Gb Around integer Landau fillings / the integer quantum Hall effect (IQHE) produces wide regions of magnetic field B, in which the transverse resistivity p xy is a plateau with quantized value h/e 2 i, and the diagonal resistivity p xx , and conductivity a xx are a flat minimum with Pxx,<*xx vanishing. At low T these plateau regions of B are separated by comparatively narrow transition regions, where p xy rises sharply, and p xx , o xx exhibit peaks. The peaks are a manifestation of the derealization of the electrons in the 2D electron system (2DES), as B approaches B*, the field at which a Landau level lies on the Fermi energy. This derealization has been shown to be a critical phenomenon [1], where B* is a critical magnetic field, and at T = 0 the localization length % diverges as B-+B*. Quite generally, as criticality is approached, the internal dynamics of the system must slow down [2], so that as § diverges, a correlation time, r c , that characterizes the dynamics of the system, also diverges. In this work we present broadband microwave ac conductivity measurements that for the first time directly exhibit the slowing down of the internal dynamics as B* is approached, and allow us to determine the critical exponent associated with the divergence of T C .

High Frequency Conductivity in the Quantum Hall Regime

“…A similar analysis of Dn as a function of frequency has already been performed by Engel et al [10] and Balaban et al [11] with contradicting results concerning the validity of scaling. However, it is important to stress that although the plateau transition is a powerful tool for the test of scaling, it is only an indirect approach to the localization length.…”

“…Previous experiments by Engel et al [10] and Balaban et al [11] were restricted to a measurement of the real part of s xx , whereas our technique gives access to both the real and imaginary part. This allows an additional test of universal frequency scaling.…”

Integer quantum Hall effect in double-layer systems

“…21 . Experiments on the frequency, (f ), dependent conductivity have shown that σ xx peaks broadens as (∆B) ∼ f γ with γ = 0.41 ± 0.04 for the spin split transition and γ = 0.20 ± 0.05 for the spin-degenerate case 25 . This, tantalizing effect was explained in terms of an unstable critical point so that the enhancement of the exponent is understood as an artifact of crossover phenomena 27 (See Fig.…”

“…This work is motivated by recent experiments hinting at changes in localization properties when two different Landau levels are nearly degenerate [22][23][24][25][27][28][29] , by growing interest in the conditions necessary for the occurrence of the quantum Hall effect in three-dimensional electron systems, and by the need for improved understanding of the disappearance of the quantum Hall effect at weak magnetic fields in high mobility samples. In each case, we believe that double-layer quantum Hall systems offer advantages for both theoretical studies and for the experimental studies which we hope to motivate.…”

“…(Experiments in the fractional quantum Hall regime find similar values 24 for this exponent.) Recently the dynamical critical exponent, z, has been measured 25,26 to be z = 1.…”