Thermohydrodynamics in Quantum Hall Systems

Akera, Hiroshi; Suzuura, Hidekatsu

doi:10.1143/jpsj.74.997

Cited by 12 publications

(15 citation statements)

References 48 publications

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“…The observed polarity of the spin current, which is opposite to the heat flow around ν = 3, is consistent with the calculation of the electron temperature gradient in Ref. [7].…”

supporting

confidence: 91%

“…In Ref. [7], Akera and Suzuura have shown theoretically that the electron temperature gradient perpendicular to the electric current exhibits quantum oscillations as a function of the position of µ within the LL structure where the spin splitting is neglected. It crosses zero when µ lies near the center of the Landau gap.…”

mentioning

confidence: 99%

“…The majority carriers, which determine the polarity of the total spin current, are electrons in the LL(↓, 1) for ν > 3 but are holes in the LL(↑, 1) for ν < 3. For the consideration of the heat flow, the Landau level energy of the majority carriers measured from µ is important [7]. The polarity of the heat flow is expected to change when µ crosses the LLs at ν ≈ 5/2 and 7/2.…”

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confidence: 99%

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Ettingshausen Effect around a Landau Level Filling Factorν=3Studied by Dynamic Nuclear Polarization

Komori¹,

Sakuma²,

Okamoto³

2007

Phys. Rev. Lett.

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A spin current perpendicular to the electric current is investigated around a Landau level filling factor ν = 3 in a GaAs/AlGaAs two-dimensional electron system. Measurements of dynamic nuclear polarization in the vicinity of the edge of a specially designed Hall bar sample indicate that the direction of the spin current with respect to the Hall electric field reverses its polarity at ν = 3, where the dissipative current carried by holes in the spin up Landau level is replaced with that by electrons in the spin down Landau level.PACS numbers: 72.25.Pn, 73.50.Jt, A two-dimensional electron system (2DES) at low temperatures and in a strong magnetic field shows the quantum Hall (QH) effect, in which the longitudinal resistance vanishes and the Hall resistance is quantized as R H = h/ie 2 for an integer i [1,2]. While the electric current does not involve energy dissipation in the QH state, it can cause heat flow in the transition region between QH states and in the current-induced breakdown regime. Heat flow parallel to the electric current has been studied in the current-induced breakdown regime by measuring the longitudinal resistance with a set of voltage probes along the current channel [3,4,5]. On the other hand, Akera predicted that the heat flow in the current-induced breakdown regime can have a component perpendicular to the electric current [6]. In general, this phenomenon is known as the Ettingshausen effect. His calculation shows that the heat flow across the current channel causes an increase (decrease) of the electron temperature T e in the vicinity of one edge (the other edge) while T e is approximately uniform in the middle of the current channel. Furthermore a recent calculation for the transition region shows that the sign of the electron temperature gradient perpendicular to the electric current exhibits quantum oscillations as a function of the position of the chemical potential µ with respect to the Landau levels (LLs) [7]. Evidence of the Ettingshausen effect is observed in the current-induced breakdown regime at Landau level filling factor ν = 2 by Komori and Okamoto, who used microHall bars attached to both edges of the current channel as electron temperature indicators [8]. However, they were not able to extend their work to the transition region owing to the strong current-dependence of the background at ν = integer.In a strong magnetic field, the spin degeneracy is lifted due to the Zeeman energy and the many body effect. When µ lies between spin-split Landau levels, electron spin polarization strongly depends on T e and the heat flow is dominated by the spin current. One of the advantages of using the spin degree of freedom in the study of heat flow is that the flip of electron spin can be memorized by dynamic nuclear polarization (DNP) owing to the contact hyperfine interaction [9,10,11,12,13,14,15,16],where A (> 0) is the hyperfine constant, and I and S are the nuclear spin and electron spin, respectively. The first term causes the electron-nucleus flip-flop process and the second term...

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“…The observed polarity of the spin current, which is opposite to the heat flow around ν = 3, is consistent with the calculation of the electron temperature gradient in Ref. [7].…”

supporting

confidence: 91%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Ettingshausen Effect around a Landau Level Filling Factorν=3Studied by Dynamic Nuclear Polarization

Komori¹,

Sakuma²,

Okamoto³

2007

Phys. Rev. Lett.

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“…where j n el is the number flux density and j ε is the energy flux density. P L is the energy loss per unit area due to the heat transfer between electrons and phonons 15 . The thermal flux density is given by…”

Section: Thermo-hydrodynamic Theorymentioning

confidence: 99%

Theoretical investigation of local electron temperature in quantum Hall systems

Yurdaşan¹,

Akgüngör²,

Siddiki³

et al. 2012

Physica E: Low-dimensional Systems and Nanostructures

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The local electron temperature distribution is calculated considering a two dimensional electron system in the integer quantum Hall regime in presence of disorder and uniform perpendicular magnetic fields. We solve thermal-hydrodynamical equations to obtain the spatial distribution of the local electron temperature in the linear-response regime. It is observed that, the variations of electron temperature exhibit an antisymmetry regarding the center of the sample in accordance with the location of incompressible strips. To understand the effect of sample mobility on the local electron temperature we impose a disorder potential calculated within the screening theory. Here, long range potential fluctuations are assumed to simulate cumulative disorder potential depending on the impurity atoms. We observe that the local electron temperature strongly depends on the number of impurities in narrow samples. arXiv:1908.06791v1 [cond-mat.mes-hall]

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“…As for the µ eq dependence of σ 0 yx and σ 0 yy , we employ a model [16] which retains the observed features of σ 0 yx (B) and σ 0 yy (B):…”

Section: Model and Equationsmentioning

confidence: 99%

Hall-potential distribution in AC quantum Hall effect

Akera

2011

J. Phys.: Conf. Ser.

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Abstract. The distribution of the Hall voltage induced by low-frequency AC current is studied theoretically in the incoherent linear transport of quantum Hall systems with slowly-varying confining potential. It is shown that in the low-frequency limit the Hall potential has a steeper slope where the diagonal conductivity is smaller, while at higher frequencies it exhibits a peak or a dip where the Hall conductivity has a slope. IntroductionIn the quantum Hall effect [1, 2] observed in two-dimensional electron systems (2DES) in strong magnetic fields, the Hall voltage V H divided by the current I is quantized as V H /I = h/(ie 2 ) with i an integer. The distribution of this quantized Hall voltage along the width of the 2DES has been studied theoretically [3,4,5,6,7,8,9,10,11,12,13] and experimentally [14], but has problems that remain to be solved. One of the problems is the distribution in the AC current. In this paper we study theoretically the Hall-voltage distribution in low-frequency AC current with the angular frequency ω in the incoherent linear transport in a system with slowly-varying confining potential. The Hall-voltage distribution in a uniform 2DES with sharp edges has been studied elsewhere [15].

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Thermohydrodynamics in Quantum Hall Systems

Cited by 12 publications

References 48 publications

Ettingshausen Effect around a Landau Level Filling Factorν=3Studied by Dynamic Nuclear Polarization

Ettingshausen Effect around a Landau Level Filling Factorν=3Studied by Dynamic Nuclear Polarization

Theoretical investigation of local electron temperature in quantum Hall systems

Hall-potential distribution in AC quantum Hall effect

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