Composite Fermion Mass Research Articles

Composite fermion mass: Experimental measurements in ultrahigh quality two-dimensional electron systems

Composite fermions (CFs), exotic quasi-particles formed by pairing an electron and an even number of magnetic flux quanta emerge at high magnetic fields in an interacting electron system, and can explain phenomena such as the fractional quantum Hall state (FQHS) and other many-body phases. CFs possess an effective mass ($m_{CF}$) whose magnitude is inversely related to the most fundamental property of a FQHS, namely its energy gap. We present here experimental measurements of $m_{CF}$ in ultra-high quality two-dimensional electron systems confined to GaAs quantum wells of varying thickness. An advantage of measuring $m_{CF}$ over gap measurements is that mass values are insensitive to disorder and are therefore ideal for comparison with theoretical calculations, especially for high-order FQHS. Our data reveal that $m_{CF}$ increases with increasing well width, reflecting a decrease in the energy gap as the electron layer becomes thicker and the in-plane Coulomb energy softens. Comparing our measured masses with available theoretical results, we find significant quantitative discrepancies, highlighting that more rigorous and accurate calculations are needed to explain the experimental data.

Quantitative theory of composite fermions in Bose-Fermi mixtures at ν=1

Composite fermions provide a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level. Recently a low-energy noncommutative field theory for bosons at Landau-level filling factor $\nu=1$ has been formulated by Dong and Senthil. In the limit of long-wavelength and small-amplitude gauge fluctuation, they found it reduces to the celebrated Halperin-Lee-Read theory of composite fermion liquid. In this work we consider a Bose-Fermi mixture at total filling factor $\nu=1$. Different from previous work, the number density of composite fermions in the mixture and corresponding Fermi momentum can be tuned by changing the filling factor of bosons, $\nu_b = 1 -\nu_f$. This tunability enables us to study the dilute limit $\nu_b\ll 1$, which allows for a controlled and asymptotically exact calculation of the energy dispersion and effective mass of composite fermions. Furthermore, the approximation of the low-energy description by a commutative field theory is manifestly justified. Most importantly, we demonstrate gauge fluctuations acquire a Higgs mass due to the presence of a composite boson condensate, as a result of which the system behaves like a genuine Landau Fermi liquid. Combined with the irrelevance of four-fermion interaction in the dilute limit, we are able to obtain asymptotically exact properties of this composite fermion Fermi liquid. In the opposite limit of $\nu_f\ll 1$, the Higgs mass goes to zero and we find crossover between Fermi liquid and non-Fermi liquid as temperature increases. Observing these properties either experimentally or numerically provides unambiguous evidence of not only the composite fermions and the Fermi surface they form, but also the presence of emergent gauge fields and their fluctuations due to strong correlation.

Composite fermion mass enhancement and particle-hole symmetry of fractional quantum Hall states in the lowest Landau level under realistic conditions

Particle-hole symmetry breaking in the fractional quantum Hall effect has recently been studied both theoretically and experimentally with most works focusing on non-Abelian states in the second electronic Landau level. In this work, we theoretically investigate particle-hole symmetry breaking of incompressible fractional quantum Hall states in the lowest Landau level under the influence of the realistic effect of a finite magnetic field strength. A finite magnetic field induces Landau level and sub-band mixing which are known to break particle-hole symmetry at the level of the Hamiltonian. We analyze the Haldane pseudopotentials, energy spectra and energy gaps, and the wave functions themselves, under realistic conditions. We find that particle-hole symmetry is broken, as determined by energy gaps, between states related via particle-hole conjugation, however, we find that particle-hole symmetry is largely maintained as determined by the effective mass of composite fermions. Finally, we comment and make connection to recent experimental observations regarding particle-hole symmetry in the lowest Landau level fractional quantum Hall effect [Pan et al. Phys. Rev. Lett. 124, 156801 (2020)]

Phenomenology at the LHC of composite particles from strongly interacting Standard Model fermions via four-fermion operators of NJL type

A new physics scenario shows that four-fermion operators of Nambu-Jona-Lasinio (NJL) type have a strong-coupling UV fixed point, where composite fermions F (bosons Pi ) form as bound states of three (two) SM elementary fermions and they couple to their constituents via effective contact interactions at the composite scale Lambda approx {{{mathcal {O}}}} (TeV). We present a phenomenological study to investigate such composite particles at the LHC by computing the production cross sections and decay widths of composite fermions in the context of the relevant experiments at the LHC with pp collisions at sqrt{s}=13 TeV and sqrt{s}=14 TeV. Systematically examining all the different composite particles F and the signatures with which they can manifest, we found a vast spectrum of composite particles F that has not yet been explored at the LHC. Recasting the recent CMS results of the resonant channel pprightarrow e^+F rightarrow e^+e^- qbar{q}' (as F=E), we find that the composite fermion mass m_F below 4.25 TeV is excluded for Lambda /m_F = 1. We further highlight the region of parameter space where this specific composite particle F can appear using 3 hbox {ab}^{-1}, expected by the High-Luminosity LHC, computing 3 and 5 sigma contour plots of its statistical significance.

Spinless composite fermions in an ultrahigh-quality strained Ge quantum well

We report on an observation of a fractional quantum Hall effect in an ultra-high quality two-dimensional hole gas hosted in a strained Ge quantum well. The Hall resistance reveals precisely quantized plateaus and vanishing longitudinal resistance at filling factors $\nu = 2/3, 4/3$ and $5/3$. From the temperature dependence around $\nu = 3/2$ we obtain the composite fermion mass of $m^\star \approx 0.4\,m_e$, where $m_e$ is the mass of a free electron. Owing to large Zeeman energy, all observed states are spin-polarized and can be described in terms of spinless composite fermions.

Current-induced nuclear spin depolarization at Landau level filling factorν=1/2

Hyperfine interactions between electron and nuclear spins in the quantum Hall regime provide powerful means for manipulation and detection of nuclear spins. In this work we demonstrate that significant changes in nuclear spin polarization can be created by applying an electric current in a 2-dimensional electron system at Landau level filling factor nu=1/2. Electron spin transitions at nu= 2/3 and 1/2 are utilized for the measurement of the nuclear spin polarization. Consistent results are obtained from these two different methods of nuclear magnetometry. The finite thickness of the electron wavefunction is found to be important even for a narrow quantum well. The current induced effect on nuclear spins can be attributed to electron heating and the efficient coupling between the nuclear and electron spin systems at nu=1/2. The electron temperature, elevated by the current, can be measured with a thermometer based on the measurement of the nuclear spin relaxation rate. The nuclear spin polarization follows a Curie law dependence on the electron temperature. This work also allows us to evaluate the electron g-factor in high magnetic fields as well as the polarization mass of composite fermions.

Effective mass of composite fermions and the energy gaps of quantum Hall states

The effective mass of the quasi-particles in the fermion-Chern-Simons description of the quantum Hall state at half-filling is computed for electron-electron interactions $V(r)\sim r^{x-2}$, for $0<x<3/2$, following the previous work of Stern and Halperin, Phys. Rev. B {\bf 52}, 5890 (1995). The energy gap of quantum Hall states with filling factors $\nu=\frac{p}{2p+1}$ for $p\gg 1$ can then be obtained either from the effective mass at half-filling, as proposed by Halperin, Lee and Read, Phys. Rev. B {\bf 47}, 7312 (1993), or evaluated directly from the self-energy of the system in presence of the residual magnetic field; both results are shown to agree as $p\to \infty$. The energy gap is then given by a self-consistent equation, which asymptotic solution for $p\gg 1$ and short-range interactions is $E_g(p)\sim (2p+1)^{-\frac{3-x}{2}}$, in agreement with previous results by Kim, Lee and Wen, Phys. Rev. B {\bf 52}, 17275 (1995). The power law for the energy gap seems to be {\it exact} to all orders in the perturbative expansion. Moreover, the energy gap for systems with Coulomb interaction is recovered in the limit $x\to 1$.

Korringa-like nuclear spin–lattice relaxation in a 2DES at [formula omitted

Via a resistively detected NMR technique, the nuclear spin–lattice relaxation time T 1 of 71Ga has been measured in a GaAs/AlGaAs heterostructure containing two weakly coupled 2D electron systems (2DES) at low temperatures, each at Landau level filling ν = 1 2 . Incomplete electronic spin polarization, which has been reported previously for low density 2DESs at ν = 1 2 , should facilitate hyperfine-coupled nuclear spin relaxation owing to the presence of both electron spin states at the Fermi level. Composite fermion theory suggests a Korringa-law temperature dependence: T 1 T = constant is expected for temperatures T < 1 K . Our measurements show that for temperatures in the range 35 mK < T < 200 mK , T 1 rises less rapidly with falling temperature than this law predicts. This may suggest the existence of alternate nuclear spin relaxation mechanisms in this system. Also, our data allows for an estimate of the composite fermion mass.

Excitation gaps of incompressible composite fermion states: Approach to the Fermi sea

Activation gaps are determined for fractional quantum Hall states with up to seven filled Landau levels of composite fermions carrying two vortices, which correspond to electron filling factors of up to 7/15 along the sequence v=n/(2n+1). Systems with as many as 100 composite fermions are studied for this purpose. The relevance of the results to the issues of composite-fermion mass and the stability of fractional quantum Hall effect along the sequence n/(2n + 1) is discussed.

HIGH FIELD NMR IN STRONGLY CORRELATED LOW-DIMENSIONAL FERMIONIC SYSTEMS

We review some recent NMR results obtained in Grenoble High Magnetic Field Laboratory on magnetic field induced phenomena in strongly correlated low-dimensional fermionic systems: i) magnetic field dependence of the soliton lattice in the IC phase of the spin-Peierls system CuGeO3, ii) NMR study of the complete H-T phase diagram of the organo-metallic spin ladder Cu2(C5H12N2)2Cl4, and iii) the first "standard" NMR measurements (i.e., without optical pumping) on 2D electrons in Quantum wells, providing a detailed description of the fractional quantum Hall effect state at ν = 1/2 with the first determination of the corresponding effective polarization mass of composite fermions. Latest study of the ν = 2/3 state revealed, among other features, an unexpected phase transition.

The spin polarization of 2D electrons in the region 1< ν

We report a study of the spin polarization of the Composite Fermion system in the occupancy range 1< ν e<2 equivalent to the occupancy range 1> ν h>0 of Composite Fermion holes. Polarized magneto-reflectivity is used to measure the polarization of the unoccupied states in the lowest Landau level. We observe the existence of spin polarized and unpolarized states at ν e = 5 3 =2− 1 3 and ν e = 4 3 =2− 2 3 . We measure the polarization of the Composite Fermion gas at ν e = 3 2 =2− 1 2 from which we can deduce the Composite Fermion mass.

Phonon-drag thermopower of composite fermions at filling factor 3/2

We present, for the first time, a quantitative interpretation of the measured diagonal thermopower, S xx , for a 2DEG at filling factor ν=3/2. The S xx data span the temperature range 0.2⩽T⩽1.2 K and show that the phonon-drag thermopower, S xx g , is the dominant contribution at all T. S xx g is calculated by using the standard Cantrell–Butcher formalism within the composite fermion picture. The theoretical results for S xx g agree very well with the experimental data when the value 0.87 m e for the composite fermion mass at ν=3/2 is used. We also calculate the ratio S xx g ( ν=3/2)/ S xx g ( ν=1/2) and we find that it is unity for T⩽0.5 K which is in very good agreement with the experiment.

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.

Activation Gaps and Mass Enhancement of Composite Fermions

We compute the activation gaps for fractional quantum Hall states at filling fractions $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/(2n+1)$ incorporating modifications in the interaction potential due to the nonzero transverse width of the electron wave function and find good agreement with experiments in high-mobility samples with high density. The results also shed light on the mysterious enhancement of the composite fermion mass for fractions with large $n$.

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.

Temperature dependent scattering of composite fermions.

We have studied the temperature dependent resistivity at exactly half Landau level filling of a high-quality two-dimensional electron system in high magnetic field. The experimental data can be well described in terms of a standard degenerate system of fermions at zero magnetic field being scattered by impurities and acoustic phonons. The gauge-field-mediated phonon scattering contributes a ${T}^{\ensuremath{-}3}$ dependence to the composite fermion mobility. The effective mass of composite fermions is obtained from the temperature dependence of composite fermion-impurity scattering.

Drastic enhancement of composite fermion mass near Landau level filling v=1/2.

Drastic enhancement of composite fermion mass near Landau level filling v=1/2.

Masses and anomalous magnetic moments of composite fermions by non-renormalizable supersymmetric interactions

Characteristic features of supersymmetric models are examined in which quarks and leptons are composites in a singlet state of fermions and scalars of N-plets of the internal symmetry group O( N). It is shown that M( M 2)=1/ g R, M= mass of composite fermions, g R= “renormalized” coupling constant, in the all (leading) order of the 1/ N expansion in a model with non-renormalizable supersymmetric F (D)-type interactions, while their anomalous magnetic moment vanishes in the leading order of both types of models.