Theory of Resonant Raman Scattering in One Dimensional Electronic systems

A theory of resonant Raman scattering spectroscopy of one dimensional electronic systems is developed on the assumptions that (i) the excitations of the one dimensional electronic system are described by the Luttinger Liquid model, (ii) Raman processes involve virtual excitations from a filled valence band to an empty state of the one dimensional electronic system and (iii) excitonic interactions between the valence and conduction bands may be neglected. Closed form analytic expressions are obtained for the Raman scattering cross sections, and are evaluated analytically and numerically for scattering in the polarized channel, revealing a "double-peak" structure with the lower peak involving multispinon excitations with total spin S=0 and the higher peak being the conventional plasmon. A key feature of our results is a nontrivial power law dependence, involving the Luttinger Liquid exponents, of the dependence of the Raman cross sections on the difference of the laser frequency from resonance. We find that near resonance the calculated ratio of intensity in the lower energy feature to the intensity in the higher energy feature saturates at a value of the order of unity (times a factor of the ratio of the velocities of the two modes). We explicate the differences between the 'Luttinger liquid' and 'Fermi liquid' calculations of RRS spectra and argue that excitonic effects, neglected in all treatments so far, are essential for explaining the intensity ratios observed in quantum wires. We also discuss other Luttinger liquid features which may be observed in future RRS experiments

Many skyrmion wave functions and skyrmion statistics in quantum Hall ferromagnets

We determine the charge and statistical angle of skyrmions in quantum Hall ferromagnets by performing Berry phase calculations based on the microscopic variational wave functions for many-skyrmion states. We find, in contradiction to a recent claim by Dziarmaga, that both the charge and the statistical angle of a skyrmion are independent of its spin (size), and are identical to those of Laughlin quasiparticles at the same filling factor. We discuss some subtleties in the use of these variational wave functions.Comment: 11 pages, RevTex, no figure. Accepted in Phys. Rev. B, Rapid Communication

Wave Function of the Largest Skyrmion on a Sphere

It has been clarified that charged excitation known as a skyrmion exists around the ferromagnetic ground state at the Landau level filling factor $\nu=1/q$, where $q$ is an odd integer. An infinite sized skyrmion is realized in the absence of the spin-Zeeman splitting or for double-layered systems. Analytical form of the wave function is identified at $\nu=1$ and $\nu=1/3$ through exact diagonalization of the Hamiltonian for finite sized spherical systems. It is clarified that the skyrmion wave functions at $\nu=1$ and $\nu=1/3$ are qualitatively different: they are not related by the composite fermion transformation. Long-range behavior of the skyrmion wave function around $\nu=1$ is shown to be consistent with the semiclassical picture of the skyrmion.Comment: 4 pages. to be published in J. Phys. Soc. Jpn. Vol.67 No.10. Three references are adde

Topological defects and Goldstone excitations in domain walls between ferromagnetic quantum Hall effect liquids

It is shown that the low-energy spectrum of a ferromagnetic quantum Hall effect liquid in a system with a multi-domain structure generated by an inhomogeneous bare Zeeman splitting $\epsilon_{Z}$ is formed by excitations localized at the walls between domains. For a step-like $\epsilon_Z(r)$, the domain wall spectrum includes a spin-wave with a linear dispersion and a small gap due to spin-orbit coupling, and a low-energy topological defects. The latter are charged and may dominate in the transport under conditions that the percolation through the network of domain walls is provided.Comment: 4 pages, 1 fi

Critical Behavior of Nuclear-Spin Diffusion in GaAs/AlGaAs Heterostructures near Landau Level Filling \nu=1

Thermal measurements on a GaAs/AlGaAs heterostructure reveal that the state of the confined two-dimensional electrons dramatically affects the nuclear-spin diffusion near Landau level filling factor \nu=1. The experiments provide quantitative evidence that the sharp peak in the temperature dependence of heat capacity near \nu=1 is due to an enhanced nuclear-spin diffusion from the GaAs quantum wells into the AlGaAs barriers. We discuss the physical origin of this enhancement in terms the possible Skyrme solid-liquid phase transition.Comment: 1 LateX file, 3 figures, submitte

Spin-isospin textured excitations in a double layer at filling factor ν=2\nu =2

We study the charged excitations of a double layer at filling factor 2 in the ferromagnetic regime. In a wide range of Zeeman and tunneling splittings we find that the low energy charged excitations are spin-isospin textures with the charge mostly located in one of the layers. As tunneling increases, the parent spin texture in one layer becomes larger and it induces, in the other layer, a shadow spin texture antiferromagnetically coupled to the parent texture. These new quasiparticles should be observable by measuring the strong dependence of its spin on tunneling and Zeeman couplings.Comment: 4 pages, 4 figure

Shape Deformation driven Structural Transitions in Quantum Hall Skyrmions

The Quantum Hall ground state away from $\nu = 1$ can be described by a collection of interacting skyrmions. We show within the context of a nonlinear sigma model, that the classical ground state away from $\nu = 1$ is a skyrmion crystal with a generalized N\'eel order. We show that as a function of filling $\nu$, the skyrmion crystal undergoes a triangle to square to triangle transition at zero temperature. We argue that this structural transition, driven by a change in the shape of the individual skyrmions, is stable to thermal and quantum fluctuations and may be probed experimentally.Comment: 4 pages (REVTEX) and 4 .eps figure

Skyrmions in quantum Hall ferromagnets as spin-waves bound to unbalanced magnetic flux quanta

A microscopic description of (baby)skyrmions in quantum Hall ferromagnets is derived from a scattering theory of collective (neutral) spin modes by a bare quasiparticle. We start by mapping the low lying spectrum of spin waves in the uniform ferromagnet onto that of free moving spin excitons, and then we study their scattering by the defect of charge. In the presence of this disturbance, the local spin stiffness varies in space, and we translate it into an inhomogeneus metric in the Hilbert space supporting the excitons. An attractive potencial is then required to preserve the symmetry under global spin rotations, and it traps the excitons around the charged defect. The quasiparticle now carries a spin texture. Textures containing more than one exciton are described within a mean-field theory, the interaction among the excitons being taken into account through a new renormalization of the metric. The number of excitons actually bound depends on the Zeeman coupling, that plays the same role as a chemical potencial. For small Zeeman energies, the defect binds many excitons which condensate. As the bound excitons have a unit of angular momentum, provided by the quantum of magnetic flux left unbalanced by the defect of charge, the resulting texture turns out to be a topological excitation of charge 1. Its energy is that given by the non-linear sigma model for the ground state in this topological sector, i.e. the texture is a skyrmion.Comment: 17 pages, 1 figur

Spin-orbit coupling effect on quantum Hall ferromagnets with vanishing Zeeman energy

We present the phase diagram of a ferromagnetic quantum Hall effect liquid in a narrow quantum well with vanishing single-particle Zeeman splitting, $\epsilon_{{\rm Z}}$ and pronounced spin-orbit coupling. Upon decreasing $\epsilon_{{\rm Z}}$, the spin-polarization field of a liquid takes, first, the easy-axis configuration, followed by the formation of a helical state, which affects the transport and NMR properties of a liquid and the form of topological defects in it. The analysis is extended over high odd integer filling factors.Comment: This revised version takes into account easy-axis terms in the energy and offers a corrected phase diagram of the ferromagnetic QHE liquid. Analysis is extended over higher filling factor

Simultaneous Excitation of Spins and Pseudospins in the Bilayer ν=1\nu=1 Quantum Hall State

The tilting angular dependence of the energy gap was measured in the bilayer quantum Hall state at the Landau level filling $\nu=1$ by changing the density imbalance between the two layers. The observed gap behavior shows a continuous transformation from the bilayer balanced density state to the monolayer state. Even a sample with 33 K tunneling gap shows the same activation energy anomaly reported by Murphy {\it et al.}. We discuss a possible relation between our experimental results and the quantum Hall ferromagnet of spins and pseudospins.Comment: 4 pages, 4 figure