Neutral Collective Excitations Research Articles

Evidence for chiral graviton modes in fractional quantum Hall liquids.

Exotic physics could emerge from interplay between geometry and correlation. In fractional quantum Hall (FQH) states1, novel collective excitations called chiral graviton modes (CGMs) are proposed as quanta of fluctuations of an internal quantum metric under a quantum geometry description2-5. Such modes are condensed-matter analogues of gravitons that are hypothetical spin-2 bosons. They are characterized by polarized states with chirality6-8 of +2 or -2, and energy gaps coinciding with the fundamental neutral collective excitations (namely, magnetorotons9,10) in the long-wavelength limit. However, CGMs remain experimentally inaccessible. Here we observe chiral spin-2 long-wavelength magnetorotons using inelastic scattering of circularly polarized lights, providing strong evidence for CGMs in FQH liquids. At filling factor v = 1/3, a gapped mode identified as the long-wavelength magnetoroton emerges under a specific polarization scheme corresponding to angular momentum S = -2, which persists at extremely long wavelength. Remarkably, the mode chirality remains -2 at v = 2/5 but becomes the opposite at v = 2/3 and 3/5. The modes have characteristic energies and sharp peaks with marked temperature and filling-factor dependence, corroborating the assignment of long-wavelength magnetorotons. The observations capture the essentials of CGMs and support the FQH geometrical description, paving the way to unveil rich physics of quantum metric effects in topological correlated systems.

Domain Textures in the Fractional Quantum Hall Effect.

Impacts of domain textures on low-lying neutral excitations in the bulk of fractional quantum Hall effect (FQHE) systems are probed by resonant inelastic light scattering. We demonstrate that large domains of quantum fluids support long-wavelength neutral collective excitations with well-defined wave vector (momentum) dispersion that could be interpreted by theories for uniform phases. Access to dispersive low-lying neutral collective modes in large domains of FQHE fluids such as long wavelength magnetorotons at filling factor v=1/3 offer significant experimental access to strong electron correlation physics in the FQHE.

Thermodynamics of free and bound magnons in graphene

Symmetry-broken electronic phases support neutral collective excitations. For example, monolayer graphene in the quantum Hall regime hosts a nearly ideal ferromagnetic phase at specific filling factors that spontaneously breaks the spin-rotation symmetry1–3. This ferromagnet has been shown to support spin-wave excitations known as magnons that can be electrically generated and detected4,5. Although long-distance magnon propagation has been demonstrated via transport measurements, important thermodynamic properties of such magnon populations—including the magnon chemical potential and density—have not been measured. Here we present local measurements of electron compressibility under the influence of magnons, which reveal a reduction in the gap associated with the ν = 1 quantum Hall state by up to 20%. Combining these measurements with the estimates of temperature, our analysis reveals that the injected magnons bind to electrons and holes to form skyrmions, and it enables the extraction of free magnon density, magnon chemical potential and average skyrmion spin. Our methods provide a means of probing the thermodynamic properties of charge-neutral excitations that are applicable to other symmetry-broken electronic phases.

Collective excitations of quantum Hall states under tilted magnetic field

We study the neutral excitations of fractional quantum Hall states in electronic systems of finite width where an external anisotropy is introduced by tilting the magnetic field. As in the isotropic case, the neutral collective excitation can be worked out through the conserving method of composite fermions in the Hamiltonian theory because the interaction potential has a natural cutoff due to the quantum well width. We show how such a computation can be carried out perturbatively for an anisotropic interaction. We find that unlike the charge gap, the neutral collective gap is much more sensitive to the tilt and can thus, for certain fractional quantum Hall states, be easily destroyed by the parallel component of the magnetic field. We also discuss the convergence of the collective spectrum to the activation gap in the large-momentum limit.

Chiral Gravitons in Fractional Quantum Hall Liquids.

We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum -2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the system's response to what is the fractional Hall analog of gravitational waves. The relation with existing and possible future experimental work that can detect these fractional quantum Hall gravitons and reveal their chirality is discussed.

Neutral collective excitation in fractional quantum Hall effect at Jain series

We have studied collective excitation almost all of the filling fraction, in the Jain series of positive flux attachment states. In this article we have presented excitation spectrum of all positive flux attachment states for a real two dimensional electron system to get the complete scenario. The fundamental roton energy becomes zero at the filling fractions associated with four pair of magnetic flux quanta attachment composite fermion, which suggest that there is a limitation of flux attachment to the electron to form a composite fermion in fractional quantum Hall effect. The roton energy and energy gap become zero at filling fraction ν=1/2, which shows that the gapless state ν=1/2 can be naturally obtained as an extrapolation of the collective excitation of the incompressible gaped states.

Incompressible states of the interacting composite fermions in negative effective magnetic fields atν=4/13,5/17, and 3/10

By developing an algorithm for evaluating the basis states for the composite fermions with negative effective magnetic field, we perform the composite-fermion-diagonalization study for the fully spin-polarized fractional quantum Hall states at the filling factors $\nu = 3/10$, 4/13, and 5/17 in the range $2/7 <\nu < 1/3$. These observed states correspond to partially filled second effective Landau level, for the composite fermions carrying four vortices, with filling factor $\bar{\nu} = 1/2$, 1/3, and 2/3 respectively, analogous to the previously studied states of composite fermions with two attached vortices in the range $1/3 <\nu <2/5$. We show that the character of these states in the range $2/7 <\nu < 1/3$ replicates the same for the states in the range $1/3 <\nu <2/5$ having identical $\bar{\nu}$: Chiral p-wave pairing with anti-Pfaffian correlation of composite fermions carrying six quantized vortices produces incompressible state at $\nu = 3/10$; an unconventional interaction between composite fermions, resulting from the suppression of fermion pairs with relative angular momentum three and producing fractional quantum Hall effect of composite fermions in the second effective Landau level with $\bar{\nu} =1/3$ and its particle-hole conjugate filling factor 2/3, reproduces incompressible states at $4/13$ and $5/17$ filling factors. We further estimate the thermodynamic limit of the ground state energies and calculate the lowest energy gap for neutral collective excitations of these states.

Energy Transport by Neutral Collective Excitations at the Quantum Hall Edge

We use the edge of the quantum Hall sample to study the possibility for counterpropagating neutral collective excitations. A novel sample design allows us to independently investigate charge and energy transport along the edge. We experimentally observe an upstream energy transfer with respect to the electron drift for the filling factors 1 and 1/3. Our analysis indicates that a neutral collective mode at the interaction-reconstructed edge is a proper candidate for the experimentally observed effect.

Magnetoplasmons and SU(4) symmetry in graphene

We study magnetoplasmons or neutral collective excitations of graphene in a strong perpendicular magnetic field, which can be modelled as bound electron-hole pairs. The SU(4) symmetry of graphene arising from spin and valley pseudospin degrees of freedom is explored using Young diagrams to correctly predict the degeneracies of these excitations. The multiplet structure of the states is identical to that of mesons composed of first and second generation quarks.

Neutral collective excitations in striped Hall states

In the striped Hall state, a magnetic translation in one direction is spontaneously broken to the discrete translation. The spectrum of the neutral collective excitation is obtained in the single mode approximation at half-filled third and fourth Landau levels. The spectrum is anisotropic and has a multiple line node structure. In one direction, the spectrum resembles the liquid Helium spectrum with the phonon and roton minimum.

Energy spectrum of neutral collective excitations in striped Hall states

We investigate neutral collective excitations in the striped Hall state. In the striped Hall state, the magnetic translation and rotation symmetries are spontaneously broken. Using the commutation relation between charges and currents corresponding to the broken and unbroken symmetry, the existence of the gapless neutral excitation is proved. The spectrum of the neutral collective excitation at the half-filled third Landau level is obtained in the single mode approximation. We find the periodic line nodes in the spectrum. The spectrum is compared with the particle-hole excitation spectrum in the Hartree-Fock approximation.