Low-frequency behavior of the kinetic coefficients in localization regimes in strong magnetic fields

Viehweger, O.; Efetov, K. B.

doi:10.1103/physrevb.44.1168

Cited by 29 publications

(18 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently it has been stated [1][2][3] that the zero-temperature Hall resistivity ρ xy (ω) of noninteracting electrons in the insulating regime remains finite as the frequency ω → 0. This result was derived from the Kubo formula for the frequency-dependent conductivity.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Hall Resistance in the Hopping Regime: A "Hall Insulator"?

et al. 1995

View full text Add to dashboard Cite

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and at small magnetic fields are obtained. It is found that the results depend on whether the conductivity or the resistivity tensors are averaged to obtain the macroscopic Hall resistivity. In the second case the Hall resistivity always diverges exponentially as the temperature tends to zero. But when the Hall resistivity is derived from the averaged conductivity, the resulting temperature dependence is sensitive to the disorder configuration. Then the Hall resistivity may approach a constant value as T → 0. This is the Hall insulating behavior. It is argued that for strictly dc conditions, the transport quantity that should be averaged is the resistivity.72.20. My, 71.50+t Recently it has been stated [1][2][3] that the zero-temperature Hall resistivity ρ xy (ω) of noninteracting electrons in the insulating regime remains finite as the frequency ω → 0. This result was derived from the Kubo formula for the frequency-dependent conductivity. It was found that at zero temperature the disorder-averaged σ xy (ω) of the Anderson insulator vanishes at low frequencies proportionally to ω 2 . Since to leading order in ω the longitudinal conductivity σ xx ∼ iωε 0 , where ε 0 is the dielectric constant, this yielded that the Hall resistivity ρ xy ∼ σ xy /(σ 2 xx + σ 2 xy ) approaches a constant in the small-frequency, zero-temperature limit.Obviously one would like to examine the Hall resistance at finite temperatures. Here we address this question for strongly localized electrons. We consider the problem using the Holstein model [4] for the Hall effect in a system with localized states. The conductivity tensor for a triangle of three sites is obtained first. To get the macroscopic Hall resistivity one may attempt to apply two averaging procedures. We find that the result strongly depends on whether the conductivity tensor is averaged before inverting it or vice versa. In the first case a Hall insulator behavior is possible, while in the second the macroscopic Hall resistivity increases with decreasing temperature. The latter is similar to the finding of Friedman and Pollak [5]. The two behaviors are argued to be related with "ac" and "dc" conditions.The previous [1-3] discussions of the zero-temperature Hall resistivity were all based on the ensemble averaged Kubo formula, which yields thatσ xx =σ yy and thatσ xy vanishes proportionally to the magnetic field (the bar above the quantity indicates ensemble averaging). However, before averaging, σ xy includes a field-independent term. We show that in the strongly localized regime this term is comparable in magnitude to σ xx and σ yy . This leads to delicate cancellations when the local (unaveraged) conductivity tensor is inverted to obtain the resistivity, and consequently to the very different temperature dependences described above.It is convenient to investigate the transport properties of electrons in the hopping regime by constructing the rate equations for the electron distribu...

show abstract

mentioning

confidence: 99%

“…This is because of the factors n xy and ρ (2) xy are independent of the strength of the coupling to the phonons. This is in analogy with the "classical" (Boltzmann equation) result for the Hall coefficient, which does not contain the mean free path.…”

mentioning

confidence: 99%

Hall Resistance in the Hopping Regime: A "Hall Insulator"?

et al. 1995

View full text Add to dashboard Cite

show abstract

“…We can now check this theory quantitatively. To do this we need to know the values of Oxy and <Jxx at/=/EMP and the value of e. The frequency dependence of (Jxy in the QHE regime has been shown [16,18] to be negligible up to -10 GHz, so we can use Oxy obtained from dc measurements. The frequency dependence of Oxx is so far not known for the studied / range at low T, But from the strong nonmonotonic behavior of 7EMP(V) at low T in our experiments we conclude that there is a small frequency dependence.…”

Section: Nonlocal Dispersion Of Edge Magnetoplasma Excitations In a Tmentioning

confidence: 99%

Nonlocal dispersion of edge magnetoplasma excitations in a two-dimensional electron system

1991

View full text Add to dashboard Cite

Edge magnetoplasma excitations in a two-dimensional electron system have been studied in radiofrequency experiments which exhibit a strong nonlocal behavior of the plasmon dispersion. The nonlocality is shown to be caused by the diagonal conductivity GXX, which, via a length IOZCTXX, governs the spatial distribution of the plasma charge oscillations in the direction perpendicular to the plasmon wave vector, i.e., to the edge of the two-dimensional layer.PACS numbers: 7I.45.Gm, 73.20.Dx, 73.20.Mf The collective excitation spectrum of an electronic system at large wave vectors q is governed by well-known nonlocal effects [1]. Nonlocal effects are of the order (qvf/cop)^, where Vf is the Fermi velocity and cOp is the "local" plasmon frequency, and are usually rather small. Here we report on a very different, large nonlocal effect on the plasmon dispersion which is a unique property of a finite-size two-dimensional electron system (2DES) when the edges become important. We have observed this nonlocal effect in magnetic-field experiments on two-dimensional electron systems of macroscopic size (1x1 cm^) for the low-frequency {l7if<^cOc) branch of the plasma excitations, i.e., the edge magnetoplasmons (EMP). The nonlocal effect arises from a significant influence of the diagonal conductivity Oxx on the EMP excitation which has not previously been observed. It can be characterized by a length l^^Oxxy which is related to the spatial extent of the plasma charge oscillations in the direction perpendicular to the plasmon wave vector, i.e., to the edge of a 2DES. It represents a kind of "transverse" nonlocality in contrast to the "longitudinal" nonlocality discussed above and also occurs for very small values of q.EMP excitations have recently attracted much attention due to their unique properties, in particular, a surprisingly small damping which also occurs for the condition 2;r/T <^ 1, where r is the B =0 momentum relaxation time [2][3][4][5][6][7][8][9][10]. The EMP frequency/EMP has been calculated by different authors [10][11][12][13] and is shown to be essentially proportional to the Hall conductivity Oxy and the wave vector q=^l7tn/P, where AZ = 1,2, ..., is the mode index and P is the perimeter of the finite-size 2DES. The theories in Refs. [10,11] include nonlocal efitects and, in spite of their different underlying physical models, give practically the same form for /EMP which is, if we neglect single-particle effects, density oscillations are concentrated in a very small region close to the edge. The interesting point for a 2DES is that the oscillating charge cannot be concentrated in a local ^-function "line" (which would lead to logarithmic divergences in the potential and electrostatic energy) [11]. This is a unique property of a 2DES and in contrast to surface plasmons at the surface of a 3DES (neglecting the spatial dispersion). Thus the oscillating charges of edge plasmons are inherently distributed over a certain region perpendicular to the edge and respond in a nonlocal manner. The calculation of this ...

show abstract

“…A number of theoretical studies [1][2][3][4][5] have argued that a Hall insulating behavior, where ρ xy ∼ B as in a Drude conductor, is actually a quite generic property of disordered non-interacting electron systems. These correspond to electronic states where the insulating character is a consequence of Anderson localization; the behavior of ρ xy possibly marks their distinction from band insulators or Mott (interaction-dominated) insulators.…”

Section: The Concept Of "Hall Insulator"mentioning

confidence: 99%

The Quantized Hall Insulator: A "Quantum" Signature of a "Classical" Transport Regime?

Shimshoni

2004

Mod. Phys. Lett. B

View full text Add to dashboard Cite

Experimental studies of the transitions from a primary quantum Hall (QH) liquid at filling factor ν = 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/e 2 . 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 ν. 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. Keywords: Quantum Hall transitions; quantized Hall insulator; localization; dephasing. 923 Mod. Phys. Lett. B 2004.18:923-943. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ DAVIS on 02/07/15. For personal use only.

show abstract

Low-frequency behavior of the kinetic coefficients in localization regimes in strong magnetic fields

Cited by 29 publications

References 16 publications

Hall Resistance in the Hopping Regime: A "Hall Insulator"?

Hall Resistance in the Hopping Regime: A "Hall Insulator"?

Nonlocal dispersion of edge magnetoplasma excitations in a two-dimensional electron system

The Quantized Hall Insulator: A "Quantum" Signature of a "Classical" Transport Regime?

Contact Info

Product

Resources

About