Phonon Excitations of Composite-Fermion Landau Levels

Schulze-Wischeler, F.; Hohls, Frank; Zeitler, U.; Reuter, D.; Wieck, A. D.; Haug, Rolf J.

doi:10.1103/physrevlett.93.026801

Cited by 4 publications

(14 citation statements)

References 23 publications

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“…We find that the results are largely independent on the magnetic field in the range studied. This is consistent with the proposed presence of magnetic domains [4,11,12,13].The experiments were done in a dilution fridge with optical windows at a base temperature of 70 mK, and a magnetic field applied along the growth axis of the wafer. Two experimental techniques were implemented to measure the absorption spectrum.…”

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confidence: 50%

Absorption in the Fractional Quantum Hall Regime: Trion Dichroism and Spin Polarization

et al. 2007

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We present measurements of optical interband absorption in the fractional quantum Hall regime in a GaAs quantum well in the range 0 < ν ≤ 1. We investigate the mechanism of singlet trion absorption, and show that its circular dichroism can be used as a probe of the spin polarization of the ground state of the two-dimensional electron system (2DES). We find that at ν ≤ 1/3 the 2DES is fully spin-polarized. Increasing the filling factor results in a gradual depolarization, with a sharp minimum in the dichroism near ν = 2/3. We find that in the range 0.5 ≤ ν < 0.85 the 2DES remains partially polarized for the broad range of magnetic fields from 2.75 to 11 Tesla. This is consistent with the presence of a mixture of polarized and depolarized regions.The electron-electron Coulomb interaction plays an important role in determining the spin polarization (P) of a two-dimensional electron system (2DES) in a perpendicular magnetic field B. The effect of the interactions on the spin is most readily seen in in the filling factor range ν ≤ 1, where the level degeneracy exceeds the number of electrons. The exchange part of the Coulomb interactions favors a ferromagnetic state. However, a manybody wavefunction in which all electrons have the same spin is restricted by the Pauli principle and may not constitute in general an optimal spatial distribution that minimizes the total Coulomb energy. Inclusion of components of the opposite spin in the wavefunction opens a larger phase space for the electrons and may result in a lower Coulomb repulsion. Thus, the ground state of the 2DES in this regime is determined by the competition between the gain in Coulomb energy and the cost in Zeeman energy.Several methods have been used to determine the 2DES spin polarization in the fractional quantum Hall regime. The direct method is measuring the shift in the nuclear magnetic resonance (NMR) caused by the 2DES magnetization. Indeed, NMR measurements have yielded quantitative measurements of P throughout a broad range of filling factors [1,2]. Transport experiments have also been used and were successful in identifying transitions in the spin polarization, although are less effective in providing a quantitative value of P [3, 4].An alternative approach for measuring P is using optical spectroscopy: photoluminescence [5], reflectivity [6], and absorption spectroscopy [7]. In these techniques, the occupation of each spin levels are obtained from measurements of the circular dichroism of the interband transitions. In quantum wells (QW), however, establishing the relation between the optical oscillator strengths (OS) and P presents a major difficulty. As a result of the strong interaction between the photo-created valence hole and the electrons, the spectrum in QWs is dominated by resonance peaks, associated with the neutral exciton, and charged excitons (trions). A further complication is introduced by the fact that in a trion, the two electrons can form a singlet or triplet wavefunctions [8,9]. Hence, it is essential to take into account the nat...

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Absorption in the Fractional Quantum Hall Regime: Trion Dichroism and Spin Polarization

et al. 2007

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“…In this chapter, we describe phonon absorption measurements to deduce the relative specific heat of a 2DES ( ) C T at fractional states with an energy gap [10,13,14] and at 1 2 ν = / [12,13,23], the state with zero effective magnetic field in the CF-picture. The states with an energy gap show an exponential function of ( ) C T as predicted by Chakraborty [24].…”

Section: Phonon Experiments: Relative Specific Heatmentioning

confidence: 99%

“…gaps [14,15]. These measurements are motivated by the fact that the phonons probe the 2DES only within their wavelength and therefore all measured gaps are nearly unaffected by disorder.…”

Section: Introductionmentioning

confidence: 98%

Phonon and transport measurements in the fractional quantum Hall effect

Schulze-Wischeler¹,

Dethlefsen

Hohls

et al. 2008

Physica Status Solidi (b)

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IntroductionThe Coulomb interaction in a twodimensional electron system (2DES) subjected to a quantizing magnetic field leads to the formation of new, fractionally charged quasi-particles at Landau level filling factors p q ν = / (q is an odd-integer) [1][2][3]. This fractional quantum Hall (FQH) effect was very effectively described in the framework of composite fermions (CFs) [4][5][6], new quasi particles with an effective mass m * originating from the Coulomb interaction [7]. In this picture the FQH effect is regarded as an integer quantum Hall effect of these new quasi particles. In particular, at a filling factor 1 2 ν = / these composite fermions can be described as a quasi-free Fermi sea in an effective zero-magnetic field. One of the most important features of the FQH effect are energy gaps ∆. In a simple (noninteracting) CF picture, these gaps originate from the level structure of composite fermions in the form of spin-split Landau levels and can thus be interpreted as either Landau level transitions or spin-excitations. This simple model of CF Landau levels with interaction-dependent cyclotron gap ( B µ ) and Zeeman spin-splitting (µ B) is suitable to describe the main structure of the CF Landau levels.

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“…In order to heat up the 2DES on short time scales of a few nanoseconds, it is bombarded with ballistic-phonon pulses emitted from a heater on the back side of the 2 mm thick GaAs substrate; a more detailed description of this phonon absortion technique can be found elsewhere. 17,18,20 The temperature change inside the 2DES is measured by converting its time-dependent resistance R to a temperature T using the equilibrium calibration for R͑T͒. In order to maximize the signal to noise ratio, the 2DES is patterned into a long meander, see Ref.…”

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“…In order to maximize the signal to noise ratio, the 2DES is patterned into a long meander, see Ref. 20 for more details. Figure 1͑a͒ shows a typical phonon signal for a 2DES at filling factor =1/2 at different equilibrium temperatures T 0 between 75 and 500 mK.…”

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Measurement of the specific heat of a fractional quantum Hall system

et al. 2007

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Using a time-resolved phonon absorption technique, we have measured the relative specific heat of a two-dimensional electron system in the fractional quantum Hall effect regime. For filling factors =5/3, 4/3, 2 / 3, 3 / 5, 4 / 7, 2 / 5, and 1 / 3 the specific heat displays a strong exponential temperature dependence in agreement with excitations across a quasiparticle gap. At filling factor =1/2 we were able to measure the relative specific heat of a composite fermion system. The observed nearly linear temperature dependence on temperature down to T = 0.14 K agrees well with early predictions for a Fermi liquid of composite fermions. DOI: 10.1103/PhysRevB.76.153311 PACS number͑s͒: 73.43.Ϫf, 72.10.Di, 73.20.Mf In the fractional quantum Hall ͑FQH͒ effect the Coulomb interaction induces the formation of new quasiparticle states characterized by a fractional charge and a finite excitation gap.1-4 A nice description of the FQH effect is given by the composite fermion ͑CF͒ theory 5 where the FQH effect is regarded as an integer quantum Hall effect of new quasiparticles. In particular, at a filling factor =1/2 these composite fermions can be described as a quasi-free Fermi sea in an effective zero-magnetic field. 6One of the experimental challenges lies in accessing the ground state properties of a two-dimensional electron system ͑2DES͒ by means of thermodynamic quantities such as magnetization, [7][8][9] thermal conductivity, 10,11 thermopower, 12,13 or specific heat. 14,15 It is, however, far from being straightforward to measure the specific heat C of a 2DES directly. In general C is strongly dominated by the contribution of the surrounding substrate, and, in order to obtain a reasonable signal from the 2DES, multilayer structures have to be used. 14,15 An alternative method lies in the use of time-resolved phonon-spectroscopy experiments. 16,17,26 Here, a defined amount of energy is dissipated inside the 2DES in a short period of time ͑typically a few nanoseconds͒. Measuring the temperature of the 2DES long before it reaches equilibrium with the substrate then allows us to determine its specific heat directly. 18In this Brief Report we will show how we can use phonon-absorption experiments to deduce the temperature dependence of C of a 2DES in the FQH regime. Results at fractional filling factors suggest the excitation across a quasiparticle gap in quantitative agreement with theoretical predictions.19 At filling factor =1/2 we essentially find a linear temperature dependence predicted for a Fermi liquid of composite fermions.6 Slight deviations from linearity will be tracked down to spin splitting in the CF system.The sample used in this experiment is a 2DES embedded in a modulation-doped AlGaAs/ GaAs heterostructure. Using its persistent photoconductivity the electron concentration n e inside the 2DES can be tuned be means of an infrared photodiode. The sample is mounted on the cold finger of a dilution refrigerator and inserted into a 13 T superconducting magnet. In order to heat up the 2DES on short time sc...

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Phonon Excitations of Composite-Fermion Landau Levels

Cited by 4 publications

References 23 publications

Absorption in the Fractional Quantum Hall Regime: Trion Dichroism and Spin Polarization

Absorption in the Fractional Quantum Hall Regime: Trion Dichroism and Spin Polarization

Phonon and transport measurements in the fractional quantum Hall effect

Measurement of the specific heat of a fractional quantum Hall system

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