Composite Fermion Effective Mass Research Articles

Composite fermion nonlinear sigma models

We study the integer quantum Hall plateau transition using composite fermion mean-field theory. We show that the topological $\theta = \pi$ term in the associated nonlinear sigma model [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] is stable against a certain particle-hole symmetry violating perturbation, parameterized by the composite fermion effective mass. This result, which applies to both the Halperin, Lee, and Read and Dirac composite fermion theories, represents an emergent particle-hole symmetry. For a disorder ensemble without particle-hole symmetry, we find that $\theta$ can vary continuously within the diffusive regime. Our results call for further study of the universality of the plateau transition.

Temperature-Dependent Magnetotransport aroundν=1/2in ZnO Heterostructures

The sequence of prominent fractional quantum Hall states up to ν=5/11 around ν=1/2 in a high-mobility two-dimensional electron system confined at oxide heterointerface (ZnO) is analyzed in terms of the composite fermion model. The temperature dependence of R(xx) oscillations around ν=1/2 yields an estimation of the composite fermion effective mass, which increases linearly with the magnetic field. This mass is of similar value to an enhanced electron effective mass, which in itself arises from strong electron interaction. The energy gaps of fractional states and the temperature dependence of R(xx) at ν=1/2 point to large residual interactions between composite fermions.

Thermopower of two-dimensional electrons at filling factorsν=3/2and 5/2

The longitudinal thermopower of ultrahigh mobility two-dimensional (2D) electrons has been measured at both zero magnetic field and at high fields in the compressible metallic state at filling factor $\ensuremath{\nu}=3/2$ and the incompressible fractional quantized Hall state at $\ensuremath{\nu}=5/2$. At zero field our results demonstrate that the thermopower is dominated by electron diffusion for temperatures below about $T=150\text{ }\text{mK}$. A diffusion-dominated thermopower is also observed at $\ensuremath{\nu}=3/2$ and allows us to extract an estimate of the composite fermion effective mass. At $\ensuremath{\nu}=5/2$ both the temperature and magnetic field dependence of the observed thermopower clearly signal the presence of the energy gap of this fractional quantized Hall state. We find that the thermopower in the vicinity of $\ensuremath{\nu}=5/2$ exceeds that recently predicted under the assumption that the entropy of the 2D system is dominated by non-Abelian quasiparticle exchange statistics.

Phonon and transport measurements in the fractional quantum Hall effect

AbstractThe properties of a fractional quantum Hall system has been investigated with phonon experiments and with transport experiments. A detailed description of the phonon absorption technique is given. We measure the relative specific heat in the fractional quantum Hall effect regime at various filling factors. We use phonons to measure the activation gap Δ of the fractional quantum Hall states at constant fillings as a function of the perpendicular magnetic field B. At a given filling factor nearly all gaps measured show a square‐root dependence on the magnetic field and can be described by one single fit parameter related to the composite fermion effective mass. In addition, we present transport experiments to deduce energy gaps. Here, an astonish linear dependence of Δ on B is observed for a number of fractional filling factors. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

PHONON EXCITATIONS OF COMPOSITE FERMION LANDAU LEVELS

Energy gaps in the fractional quantum Hall regime are measured with phonon spectroscopy for various electron densities and filling factors ν=1/3, 2/5, 4/7, 3/5, 2/3, 4/3, and 5/3. At a given filling factor nearly all gaps measured show a square-root dependence on the magnetic field. The measured gaps can be described well with composite fermion theory: They are transitions between composite fermion Landau levels that are not affected by disorder on phonon wavelength. All transitions can be described by one single fit parameter related to the composite fermion effective mass. In contrast, the gaps at filling factor ν=2/3 in the high fields regime show a linear field dependence. This hints onto an only partially polarized ground state of 2/3.

Time and current dependencies of transport at the [formula omitted] phase transition in narrow quantum wells

The spin unpolarised to spin polarised ν= 2 3 phase transition is studied in narrow quantum wells. The phase transition is mapped in the filling factor ( ν), density ( n)-plane and is well described assuming a n dependence of the Composite Fermion effective mass. At high currents the huge longitudinal resistance anomaly appears along the phase boundary. A model is presented that treats the current induced nuclear spin polarisation as an additional source of disorder, which drastically alters the initial domain structure present at the phase boundary. Time and current dependent measurements at constant magnetic field indicate that a large alternating Hall field is necessary to maintain the high resistance state.

Systematic study of thermal transport of composite fermions around filling factorsν=1±12m

The thermopower is calculated for a two-dimensional electron and hole gas at low temperatures in the fractional quantum Hall-effect regime around filling factors $\ensuremath{\nu}=1\ifmmode\pm\else\textpm\fi{}\frac{1}{2m},$ $2m$ being the number of flux quanta attached to each carrier in the composite fermion (CF) picture. The general expressions obtained are applied to the $2m=2$ (i.e., $\ensuremath{\nu}=\frac{1}{2}$ and $\ensuremath{\nu}=\frac{3}{2})$ and $2m=4$ (i.e., $\ensuremath{\nu}=\frac{3}{4}$ and $\ensuremath{\nu}=\frac{5}{4})$ cases. The analysis leads to the determination, on a firm theoretical base, of the actual number of carriers involved in the expression of the thermopower of the system. We demonstrate the significance of the contribution of the nondiagonal component of the composite fermion thermopower to the diagonal component of the total thermopower of the system around $\ensuremath{\nu}=\frac{3}{2}.$ We investigate the dependence of the CF's effective mass on the magnetic field analyzing the ratios ${S}_{xx,\ensuremath{\nu}=3/2}{/S}_{xx,\ensuremath{\nu}=1/2}$ and ${S}_{xx,\ensuremath{\nu}=3/4}{/S}_{xx,\ensuremath{\nu}=1/2},$ together with the available experimental data, for the diffusion case. We also analyze the phonon-drag case. Our theoretical results are in agreement with the experimental data.

Cyclotron resonance of composite fermions

It is occasionally possible to interpret strongly interacting many-body systems within a single-particle framework by introducing suitable fictitious entities, or 'quasi-particles'. A notable recent example of the successful application of such an approach is for a two-dimensional electron system that is exposed to a strong perpendicular magnetic field. The conduction properties of the system are governed by electron-electron interactions, which cause the fractional quantum Hall effect. Composite fermions, electrons that are dressed with magnetic flux quanta pointing opposite to the applied magnetic field, were identified as apposite quasi-particles that simplify our understanding of the fractional quantum Hall effect. They precess, like electrons, along circular cyclotron orbits, but with a diameter determined by a reduced effective magnetic field. The frequency of their cyclotron motion has hitherto remained enigmatic, as the effective mass is no longer related to the band mass of the original electrons and is entirely generated from electron-electron interactions. Here we demonstrate enhanced absorption of a microwave field in the composite fermion regime, and interpret it as a resonance with the frequency of their circular motion. From this inferred cyclotron resonance, we derive a composite fermion effective mass that varies from 0.7 to 1.2 times that of the electron mass in vacuum as their density is tuned from 0.6 x 10(11) cm(-2) to 1.2 x 10(11) cm(-2).

Phonon-mediated drag at ν=1/2: A test of the Chern-Simons composite-fermion theory

We report on a study of the phonon-mediated frictional drag between two-dimensional electron layers at the Landau level filling factor $\nu=1/2$ predicted by Chern-Simons composite-fermion theory. Frictional drag between widely spaced layers is dominated by the phonon-mediated interaction and is altered from its zero-field form because of the large composite-fermion effective mass and, less strongly, by magnetic local-field effects. We find that the reduced drag resistance $\rho(T)/T^2$ peaks at a larger temperature and has a different density dependence than at zero field. We compare these results with recent experimental findings.

Fermi surface of composite fermions and one-particle excitations atν=12:Effect of band-mass anisotropy

We study the ground state and one-particle excitations in the half-filled Landau level when a two-dimensional electron gas is characterized by an anisotropic band-mass tensor. Using asymptotic Ward identities of the Chern-Simons theory for $\ensuremath{\nu}=\frac{1}{2},$ we show that a composite fermion Fermi surface is not renormalized by infrared gauge fluctuations so that its form is identical to that of an anisotropic electron Fermi surface in the absence of the magnetic field. It appears, however, that, despite the anisotropy of the Fermi surface, the composite fermion effective mass is almost isotropic. Possible experimental consequences of these effects are considered.

Effective mass of composite fermions: A phenomenological fit to the anomalous propagation of a surface acoustic wave

We calculate the conductivity associated with the anomalous propagation of a surface acoustic wave above a two-dimensional electron gas at $\ensuremath{\nu}=1/2.$ Murthy-Shankar's middle representation is adopted, and a contribution to the response functions beyond the random-phase approximation is taken into account. We give a phenomenological fit for the effective mass of a composite fermion, with experimental data for the anomalous propagation of surface acoustic wave at $\ensuremath{\nu}=1/2,$ and find that the phenomenological value of the effective mass is several times larger than the theoretical value ${m}_{\mathrm{th}}^{*}=6\ensuremath{\varepsilon}{/e}^{2}{l}_{1/2}$ derived from the Hartree-Fock approximation. We compare the phenomenological value of the composite fermion effective mass with that measured in experiments for the activation energy and the Shubnikov-de Haas oscillations. It is found that the comparison is fairly good.

Dynamical properties of a two-dimensional electron gas in a magnetic field within the composite fermion model

We investigate the response of a two-dimensional electron gas, in the fractional quantum Hall regime, to the sudden appearance of a localized charged probe using the Chern-Simons theory of composite fermions. The dynamic structure factor of the electron gas is found to have a major influence on the spectral function of the probe. In particular, there is an orthogonality catastrophe when the filling factor is an even-denominator filling fraction due to the compressibility of the state, but there is no catastrophe at odd-denominator filling factors because these states have a gap to excitations. The catastrophe is found to be more severe for composite fermions in zero effective magnetic field than it is for electrons in zero real magnetic field. Oscillations in the spectral function, arising when the composite fermions are at integer filling, have a period equal to the composite fermion cyclotron energy. We propose a tunneling experiment which directly measures the spectral function from which one could determine the composite fermion effective mass.

Experimental evidence for composite fermions

Abstract The study of correlated two-dimensional (2D) electron systems in the extreme quantum limit has been advanced by development of a field-theoretic model and associated experimental findings. The fundamental theoretical construction transforms the interacting 2D electrons into quasiparticles referred to as composite fermions. The properties of such an interacting particle system have recently been described, with the principal hypothesis that Fermi surfaces should form from the quasiparticle seas at specific ratios of the electron density to applied magnetic field. This model serves to provide an explanation for an extensive body of experimental data, including a description of the fractional quantum Hall effect as the integer quantum Hall effect for the quasiparticles. This review will present the experimental findings which both motivated and subsequently have verified aspects of this model. Following a brief introduction to 2D systems, early experimental findings pre-dating and influencing the composite fermion theory are examined. The theoretical construction and in particular the hypothesis of Fermi surface formation at high magnetic fields are briefly reviewed with respect to their experimental predictions. Experiments subsequent to the main theoretical developments are then presented. Emphasized are surface acoustic wave experiments which were responsible for measuring the composite fermion Fermi wave-vector and mean free path. Further demonstrations of semiclassical motion of the quasiparticles at the Fermi surface are also reviewed, including antidot experiments, magnetic focusing measurements, and transport studies through nanostructures. Experimental determination of the composite fermion effective mass is examined, considering results from measurements in dc transport, surface acoustic waves and thermopower. Extension of the theory and experi-ments to multiple filling factors in the magnetic field spectrum is also reviewed. Experimental findings are summarized and potential future studies are finally discussed.

Interaction dependence of composite-fermion effective masses

We estimate the composite fermion effective mass for a general two particle potential r^{-\alpha} using exact diagonalization for polarized electrons in the lowest Landau level on a sphere. Our data for the ground state energy at filling fraction \nu=1/2 as well as estimates of the excitation gap at \nu=1/3, 2/5 and 3/7 show that m_eff \sim \alpha^{-1}.

On the dependence on the magnetic field orientation of the composite fermion effective mass

The composite fermion (CF) model has been strikingly successful in describing many aspects of the fractional quantum Hall effect (FQHE) observed in two-dimensional electron systems (2DES). In the CF picture, the FQHE is the integer quantum Hall effect of the CFs. In order to assess the effect of an in-plane magnetic field on the CFs we have examined the temperature dependence of the oscillations in in a high-mobility GaAs - (Ga, Al)As heterojunction close to Landau level filling factors and for many different values of , the angle between the normal to the 2DES and the magnetic field. The CF energy gaps were evaluated at each angle using a variant of the Lifshitz - Kosevich approach. Close to , it was found that the CF gaps at each angle could be fitted to within experimental errors using a constant CF effective mass. However, the CF effective mass was found not to follow the -dependence expected for a purely 2D system; i.e. the CF energy gap at fixed grows markedly with increasing in-plane field. Around the situation is more complex, and the oscillations of the energy gaps at and as varied were interpreted using a recent model of two independent CF Landau fans separated by the Pauli spin splitting (Du R R, Yeh A S, Stormer H L, Tsui D C, Pfeiffer L N and West K W 1995 Phys. Rev. Lett. 75 3926). However, whilst the model qualitatively predicts some of the behaviour of the -minima, it is unable to account for the absolute sizes of the energy gaps. In order to reproduce the gaps at and quantitatively, an angle-dependent CF mass (as observed close to ) is required. The data suggest that the compression of the electronic wave function due to the in-plane field and exchange effects both play a role in determining the size of the CF gaps and cast doubts on the supposed `universal' behaviour of the CF mass.

Composite fermions in tilted magnetic fields and the effect of the confining potential width on the composite-fermion effective mass.

The temperature dependence (40 mK\ensuremath{\le}T\ensuremath{\le}1 K) of the oscillations in ${\mathrm{\ensuremath{\rho}}}_{\mathit{xx}}$ in a high-mobility GaAs-(Ga,Al)As heterojunction close to Landau-level filling factor \ensuremath{\nu}=1/2 has been examined for many different values of \ensuremath{\theta}, the angle between the normal to the sample and the magnetic field. It was found that the energy gaps associated with the fractional quantum Hall effect could be interpreted using the composite-fermion (CF) approach with a fixed CF effective mass \ensuremath{\mu} at each \ensuremath{\theta}. However, \ensuremath{\mu} was found not to follow the \ensuremath{\theta} dependence expected for a purely 2D system; i.e., the CF energy gaps at fixed \ensuremath{\nu} grow markedly with increasing in-plane field. Comparisons with models based on the Fang-Howard variational wave function show that this effect is due to the compression of the electronic wave function caused by the in-plane component of the magnetic field. \textcopyright{} 1996 The American Physical Society.

The dependence of the Composite Fermion effective mass on carrier density and Zeeman energy

Measurements of the temperature-dependent resistivity of high-mobility GaAs/GaAlAs heterojunctions are used to measure the effective mass of Composite Fermions (CF). The CF effective mass is found to increase approximately linearly with the effective field up to effective fields of 14 T. Data from all fractions around are unified by the single parameter for samples studied over a wide range of temperature. The energy gap is found to increase as at high fields. Hydrostatic pressure is used to reduce the value of the electron g-factor, and this is shown to have a large effect on the relative strengths of different fractions. By 13.4 kbar, where the Zeeman energy is only 1/4 of its value at 0 bar, fractions with odd numerators are found to be strongly suppressed, and new features with even numerators appear. The energy gaps measured for 5/3 as a function of carrier density and pressure are consistent with a g-factor equal to the bulk value enhanced by a factor of two due to exchange interactions.