Composite Fermion States Research Articles

Half-Integer Filling-Factor States in Quantum Dots

The emergence of half-integer filling-factor states, such as upsilon=5/2 and 7/2, is found in quantum dots by using numerical many-electron methods. These states have interesting similarities and differences with their counterstates found in the two-dimensional electron gas. The upsilon=1/2 states in quantum dots are shown to have high overlaps with the composite fermion states. The lower overlap of the Pfaffian state indicates that electrons might not be paired in quantum dot geometry. The predicted upsilon=5/2 state has a high spin polarization, which may have an impact on the spin transport through quantum dot devices.

Ground states of interacting composite fermions with spin at total filling factor one

The effects of interactions in a 2D electron system of two degenerate Landau levels with opposite spins and at total filling factor one are studied. Using the Chern-Simons gauge transformation, the system is mapped to composite fermions. The fluctuations of the gauge field induce an effective interaction between fermions which can be attractive in both the particle-particle and the particle-hole channel. As a consequence, a spin-singlet ($s$-wave) ground state of composite fermions can exist with a finite pair-breaking energy gap for particle-particle or particle-hole pairs. The competition between these two possible ground states is discussed. For long-range Coulomb interaction the particle-particle state is favored if the interaction strength is small. With increasing interaction strength there is a crossover towards the particle-hole state. If the interaction is short range, only the particle-particle state is possible.

Status of the Fermi surface in mixed composite-boson–composite-fermion quantum Hall states

We argue that the naively expected singularities of the Fermi surface, in the mixed composite boson-composite fermion states proposed [S.H. Simon et al., Phys. Rev. Lett. 91, 046803 (2003)] for the evolution of $\ensuremath{\nu}=1$ bilayer quantum Hall system with distance, are obliterated. Our conclusion is based on a careful analysis of the momentum distribution in $\ensuremath{\nu}=\frac{1}{2}$ single-layer composite-fermion state. We point out to a possibility of the phenomenon hitherto unknown outside Kondo lattice systems when, in a translationally invariant system, Fermi-liquid-like portion of electrons enlarges its volume.

Fractional quantum Hall states of clustered composite fermions

The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high density the QE's form pairs or larger clusters. This behavior, opposite to Laughlin correlations, invalidates the (sometimes invoked) reapplication of the composite fermion picture to the individual QE's. The series of finite-size incompressible ground states are identified at the QE filling factors nu_QE=1/2, 1/3, 2/3, corresponding to the electron fillings nu=3/8, 4/11, 5/13. The equivalent quasihole (QH) states occur at nu_QH=1/4, 1/5, 2/7, corresponding to nu=3/10, 4/13, 5/17. All these six novel FQH states were recently discovered experimentally. Detailed analysis indicates that QE or QH correlations in these states are different from those of well-known FQH electron states (e.g., Laughlin or Moore-Read states), leaving the origin of their incompressibility uncertain. Halperin's idea of Laughlin states of QP pairs is also explored, but is does not seem adequate.

Nodal correlations in the incompressible composite fermion liquid

To search for possible correlations in the system of interpenetrating liquids of zeroes and electrons in the fractional quantum Hall effect, this paper studies several ground state correlation functions involving particles and zeroes in the incompressible states of composite fermions at filling factors $\ensuremath{\nu}=2/5,$ 3/7, and 4/9. It is found that the zeroes form a liquid of their own in which they repel one another at short distances, and also repel particles (with the obvious exception of the Pauli zeroes that are tied to the particles). For certain states, it is found that three body configurations containing two nearby electrons and a zero in the middle are highly probable, indicating that the zeroes tend to insert themselves between nearby particles in an effort to keep them apart.

Search for particles and forces beyond the standard model in high energy lepton-hadron and hadron-hadron collisions

A review of searches for physics beyond the Standard Model carried out at high energy leptonhadron and hadron-hadron facilities is presented, with emphasis on topics of interest for future data taking at the upgraded Tevatron p p and HERA ep colliders. The status and discovery prospects are discussed for leptoquarks, Technicolour and supersymmetry, forbidden lepton and quark flavour-changing processes, extra gauge bosons, excited states of composite fermions, generic contact interactions and extra compactified dimensions.

Theoretical search for the nested quantum Hall effect of composite fermions

Almost all quantum Hall effect to date can be understood as {\em integral} quantum Hall effect of appropriate particles, namely electrons or composite fermions. This paper investigates theoretically the feasibility of nested states of composite fermions which would lead to a quantum Hall effect that cannot be understood as integral quantum Hall effect of composite fermions. The weak residual interaction between composite fermions will play a crucial role in the establishment of such quantum Hall states by opening a gap in a partially filled composite-fermion level. To treat the problem of interacting composite fermions, we develop a powerful method that allows us to obtain the low energy spectra at composite fermion fillings of $\nu^*=n+\bar \nu$ without making any assumption regarding the structure of composite fermions in the topmost partially filled level. The method is exact aside from neglecting the composite-fermion Landau level mixing, and enables us to study rather large systems, for example, 24 particles at a total flux of 62 $hc/e$, for which the dimension of the lowest Landau level Hilbert space is $\sim 10^{17}$. We have investigated, for fully spin polarized composite fermions, several filling factors between 1/3 and 2/5 using this approach. The results indicate that any possible incompressibility at these fractions is likely to have a fundamentally different origin than that considered earlier.

POSSIBLE NEW PHASES OF COMPOSITE FERMIONS

When the effective filling factor of composite fermions is an integer, the residual interaction between them can often be neglected because the ground state of the non-interacting model is unique and incompressible. However, at non-integer composite fermion (CF) filling factors the ground state of composite fermions is enormously degenerate if the interaction between them is neglected, and consideration of the inter composite fermion interaction is necessary for determining the true ground state. In this article, we summarize certain results regarding what new states the inter composite fermion interaction can possibly produce. More details can be found in Refs. [11] and [12].

Transition from an electron solid to the sequence of fractional quantum Hall states at very low Landau level filling factor.

At low Landau level filling of a two-dimensional electron system, typically associated with the formation of an electron crystal, we observe local minima in Rxx at filling factors nu = 2/11, 3/17, 3/19, 2/13, 1/7, 2/15, 2/17, and 1/9. Each of these developing fractional quantum Hall (FQHE) states appears only above a filling-factor-specific temperature. This can be interpreted as the melting of an electron crystal and subsequent FQHE liquid formation. The observed sequence of FQHE states follows the series of composite fermion states emanating from nu = 1/6 and nu = 1/8.

Stripe formation in the fractional quantum Hall regime.

An understanding of the physics of the half-filled lowest Landau level has been achieved in terms of a Fermi sea of composite fermions, but the nature of the state at other even-denominator fractions has remained unclear. We investigate theoretically Landau level fillings of the form nu = (2n + 1)/(4n + 4), which correspond to composite-fermion fillings nu* = n + 1/2. By considering various plausible candidate states with complete spin polarization, we rule out the composite-fermion Fermi sea and paired composite-fermion state at these filling factors, and predict that the system phase separates into stripes of n and n + 1 filled Landau levels of composite fermions.

Phase diagram of bilayer composite fermion states

We construct a class of composite fermion states for bilayer electron systems in a strong transverse magnetic field, and determine quantitatively the phase diagram as a function of the layer separation, layer thickness, and electron density. We find, in general, that there are several transitions, and that the incompressible phases are separated by compressible ones. The paired states of composite fermions, described by Pfaffian wave functions, are also considered.

Mixed states of composite fermions carrying two and four vortices

There now exists preliminary experimental evidence for some fractions, such as $\nu$ = 4/11 and 5/13, that do not belong to any of the sequences $\nu=n/(2pn\pm 1)$, $p$ and $n$ being integers. We propose that these states are mixed states of composite fermions of different flavors, for example, composite fermions carrying two and four vortices. We also obtain an estimate of the lowest-excitation dispersion curve as well as the transport gap; the gaps for 4/11 are smaller than those for 1/3 by approximately a factor of 50.

Girvin–MacDonald–Platzman collective mode at general filling factors: magneto-roton minimum at half-filled Landau level

The single mode approximation has proved useful for the excitation spectrum at ν=1/3. We apply it to general fractions and find that it predicts n magneto-roton minima in the dispersion of the Girvin–MacDonald–Platzman collective mode for the fractional quantum Hall states at ν= n/(2 n+1), and one magneto-roton minimum for both the composite Fermi sea and the paired composite fermion state. Experimental relevance of the results will be considered.

Spin Polarization of Composite Fermions: Measurements of the Fermi Energy

From the degree of circular polarization of the time-resolved radiative recombination of 2D electrons with photoexcited holes bound to acceptors we have measured the magnetic field dependencies of the electron spin polarization for various fractional ( $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2/3$, $3/5$, $4/7$, $2/5$, $3/7$, $4/9$, $8/5$, $4/3$, and $7/5$) and composite fermions ( $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$, $1/4$, and $3/2$) states. The Fermi energies of these composite fermion states are measured for the first time and the corresponding value of the composite fermion density of states mass at $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ is found to be about 4 times heavier than the previously reported values of the ``activation'' mass.

Quantum Hall Effect at Half-Filled Landau Level: Pairing of Composite Fermions

We discuss the possibility of the quantum Hall effect at half-filled Landau level in terms of the pairing of the composite fermions. In the absence of Coulomb energy, we show that the ground state of the system is described by the {\it p}-wave BCS pairing state of composite fermions. When the ratio $\alpha \equiv (e^2/\epsilon \ell_B)/\epsilon_F$ ($\ell_B$ : the magnetic length, $\epsilon_F$ : Fermi energy of the composite fermions) is larger than a critical value $\alpha_c \sim 8.2$ the gap of the pairing state vanishes. However, $\alpha$ remains less than $\alpha_c$ if $\hbar \omega_c \gg e^2/\epsilon \ell_B$ holds. Then in this situation it is possible that the pairing state which results in the quantum Hall effect occurs. The effect of the real spin degrees of freedom and the Zeeman energy is also discussed.

Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field

We propose a new ground state trial wavefunction for a two-dimensional Wigner crystal in a strong perpendicular magnetic field. The wavefunction includes Laughlin-Jastrow correlations between electron pairs, and may be interpreted as a crystal state of composite fermions or composite bosons. Treating the power $m$ of the Laughlin-Jastrow factor as a variational parameter, we use quantum Monte Carlo simulations to compute the energy of these new states. We find that our wavefunctions have lower energy than existing crystalline wavefunctions in the lowest Landau level. Our results are consistent with experimental observations of the filling factor at which the transition between the fractional quantum Hall liquid and the Wigner crystal occurs for electron systems. Exchange contributions to the wavefunctions are estimated quantitatively and shown to be negligible for sufficiently small filling factors.

On the Collective Mode Spectrum for Composite Fermions at 1/3 Filling Factor

The collective mode spectrum of the composite fermion state at 1/3 filling factor is evaluated. The conductivity at zero momentum, the result coincides with the cyclotron energy at the external magnetic field value, and not at the effective field, in spite of the fact that only the former enter in the equations, thus, the Kohn theorem is satisfied. In place of a magneto-roton minimum, the collective mode gets a threshold indicating the instability of the mean field composite fermion state under the formation of crystalline structures. However, the question about if this outcome only appears within the mean field approximation should be further considered.

Incompressible, metallic and insulating states of two-dimensional systems: Recent experiments

This paper provides a brief summary of some recent experimental results regarding the states of two-dimensional electron systems at high magnetic fields. The states include the incompressible, quantum Hall liquid at integer and fractional Landau-level fillings, the metallic-like state of the flux-particle composite Fermions at half-filling and the insulating phase at low fillings. Some unifying features of these states and their interrelation are also discussed.

Understanding the dynamics of fractional edge states with composite fermions

Fractional edge states can be viewed as integer edge states of composite fermions. We exploit this to discuss the conductance of the fractional quantized Hall states and the velocity of edge magnetoplasmons.

Broken symmetry of two-component nu =1/2 quantum Hall states.

We show that the recently discovered $\nu=1/2$ quantum Hall states in bilayer systems are triplet p-wave pairing states of composite Fermions, of exactly the same form as $^{3}$He superfluids. The observed persistence (though weakening) of the $\nu=1/2$ state in the two- to one-component crossover region corresponds to a continuous deformation of the so-called (331) state towards the ``Pfaffian" state, identical to the well known A to A$_{1}$ transition in $^{3}$He. This deformation also demonstrates the remarkable fact that electrons can release and capture ``vortices" in a continuous and incompressible manner through spin rotations. The broken symmetry of the triplet pairing state is a ``pairing" vector ${\bf d}$. It also implies a (pseudo-spin) magnetization $\propto i{\bf d}\times {\bf d}^{\ast}$. In the presence of layer tunneling, the (331) state ({\bf d} real) is unstable against other states with a magnetization ({\bf d} complex). The recently observed persistence of the $\nu=5/2$ state in single layer systems in the two- to one-component crossover region is also consistent with triplet pairing interpretation.