Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHall Viscosity of Composite Fermions
95
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Hall viscosity, also known as the Lorentz shear modulus, has been proposed as a topological property of a quantum Hall fluid. Using a recent formulation of the composite fermion theory on the torus, we evaluate the Hall viscosities for a large number of fractional quantum Hall states at filling factors of the form $ u=n/(2pnpm 1)$, where $n$ and $p$ are integers, from the explicit wave functions for these states. The calculated Hall viscosities $eta^A$ agree with the expression $eta^A=(hbar/4) {cal S}rho$, where $rho$ is the density and ${cal S}=2ppm n$ is the shift in the spherical geometry. We discuss the role of modular invariance of the wave functions, of the center-of-mass momentum, and also of the lowest-Landau-level projection. Finally, we show that the Hall viscosity for $ u={nover 2pn+1}$ may be derived analytically from the microscopic wave functions, provided that the overall normalization factor satisfies a certain behavior in the thermodynamic limit. This derivation should be applicable to a class of states in the parton construction, which are products of integer quantum Hall states with magnetic fields pointing in the same direction.
rate research
Read More
In 1929 Felix Bloch suggested that the paramagnetic Fermi sea of electrons should make a spontaneous transition to a fully-magnetized state at very low densities, because the exchange energy gained by aligning the spins exceeds the enhancement in the kinetic energy. We report here the observation of an abrupt, interaction-driven transition to full magnetization, highly reminiscent of Bloch ferromagnetism that has eluded experiments for the last ninety years. Our platform is the exotic two-dimensional Fermi sea of composite fermions at half-filling of the lowest Landau level. Via quantitative measurements of the Fermi wavevector, which provides a direct measure of the spin polarization, we observe a sudden transition from a partially-spin-polarized to a fully-spin-polarized ground state as we lower the composite fermions density. Our detailed theoretical calculations provide a semi-quantitative account of this phenomenon.
Motivated by recent experiments on the phonon contribution to the thermal Hall effect in the cuprates, we present an analysis of chiral phonon transport. We assume the chiral behavior arises from a non-zero phonon Hall vicosity, which is likely induced by the coupling to electrons. Phonons with a non-zero phonon Hall viscosity have an intrinsic thermal Hall conductivity, but Chen et al. (Phys. Rev. Lett. 124, 167601 (2020)) have argued that a significantly larger thermal Hall conductivity can arise from an extrinsic contribution which is inversely proportional to the density of impurities. We solve the Boltzmann equation for phonon transport and compute the temperature ($T$) dependence of the thermal Hall conductivity originating from skew scattering off point-like impurities. We find that the dominant source for thermal Hall transport is an interference between impurity skew scattering channels with opposite parity. The thermal Hall conductivity $sim T^{d+2}$ at low $T$ in $d$ dimensions, and has a window of $T$-independent behavior for $T > T_{rm imp}$, where $T_{rm imp}$ is determined by the ratio of scattering potentials with opposite parity. We also consider the role of non-specular scattering off the sample boundary, and find that it leads to negligible corrections to thermal Hall transport at low $T$.
Two-dimensional interacting electrons exposed to strong perpendicular magnetic fields generate emergent, exotic quasiparticles phenomenologically distinct from electrons. Specifically, electrons bind with an even number of flux quanta, and transform into composite fermions (CFs). Besides providing an intuitive explanation for the fractional quantum Hall states, CFs also possess Fermi-liquid-like properties, including a well-defined Fermi sea, at and near even-denominator Landau level filling factors such as $ u=1/2$ or $1/4$. Here, we directly probe the Fermi sea of the rarely studied four-flux CFs near $ u=1/4$ via geometric resonance experiments. The data reveal some unique characteristics. Unlike in the case of two-flux CFs, the magnetic field positions of the geometric resonance resistance minima for $ u<1/4$ and $ u>1/4$ are symmetric with respect to the position of $ u=1/4$. However, when an in-plane magnetic field is applied, the minima positions become asymmetric, implying a mysterious asymmetry in the CF Fermi sea anisotropy for $ u<1/4$ and $ u>1/4$. This asymmetry, which is in stark contrast to the two-flux CFs, suggests that the four-flux CFs on the two sides of $ u=1/4$ have very different effective masses, possibly because of the proximity of the Wigner crystal formation at small $ u$.
Topological pairing of composite fermions has led to remarkable ideas, such as excitations obeying non-Abelian braid statistics and topological quantum computation. We construct a $p$-wave paired Bardeen-Cooper-Schrieffer (BCS) wave function for composite fermions in the torus geometry, which is a convenient geometry for formulating momentum space pairing as well as for revealing the underlying composite-fermion Fermi sea. Following the standard BCS approach, we minimize the Coulomb interaction energy at half filling in the lowest and the second Landau levels, which correspond to filling factors $ u=1/2$ and $ u=5/2$ in GaAs quantum wells, by optimizing two variational parameters that are analogous to the gap and the Debye cut-off energy of the BCS theory. Our results show no evidence for pairing at $ u=1/2$ but a clear evidence for pairing at $ u=5/2$. To a good approximation, the highest overlap between the exact Coulomb ground state at $ u=5/2$ and the BCS state is obtained for parameters that minimize the energy of the latter, thereby providing support for the physics of composite-fermion pairing as the mechanism for the $5/2$ fractional quantum Hall effect. We discuss the issue of modular covariance of the composite-fermion BCS wave function, and calculate its Hall viscosity and pair correlation function. By similar methods, we look for but do not find an instability to $s$-wave pairing for a spin-singlet composite-fermion Fermi sea at half-filled lowest Landau level in a system where the Zeeman splitting has been set to zero.
We propose a (4+1) dimensional Chern-Simons field theoretical description of the fractional quantum Hall effect. It suggests that composite fermions reside on a momentum manifold with a nonzero Chern number. Based on derivations from microscopic wave functions, we further show that the momentum manifold has a uniformly distributed Berry curvature. As a result, composite fermions do not follow the ordinary Newtonian dynamics as commonly believed, but the more general symplectic one. For a Landau level with the particle-hole symmetry, the theory correctly predicts its Hall conductance at half-filling as well as the symmetry between an electron filling fraction and its hole counterpart.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
