arXiv subjects

S. -R. Eric Yang

Publications and source records attributed to S. -R. Eric Yang.

64 records · Page 4Linked to original sources

arXiv1998

Ground State Wavefunctions of General Filling Factors in the Lowest Landau Level

We present a set of explicit trial wavefunctions for the filling factors ν=n/(2n\pm 1) and ν=1/2 in the symmetric gauge. We show that the zeroes of the wavefunction, except those dictated by the Fermi statistics, are detached from the particles. The evolution of zeroes as the filling factor is varied is examined. We show that the wavefunction at half-filling exhibits a 2k_F-like oscillation in its occupation number profile. The center-of-mass motion of the ground state droplet is described in terms of the intra-Landau- level excitations of composite fermions.

cond-mat.mes-hall↗

arXiv1998

Edge of a Half-Filled Landau Level

We have investigated the electron occupation number of the edge of a quantum Hall (QH) droplet at $ν=1/2$ using exact diagonalization technique and composite fermion trial wavefunction. We find that the electron occupation numbers near the edge obey a scaling behavior. The scaling result indicates the existence of a well-defined edge corresponding to the radius of a compact droplet of uniform filling factor 1/2. We find that the occupation number beyond this edge point is substantial, which is qualitatively different from the case of odd-denominator QH states. We relate these features to the different ways in which composite fermions occupy Landau levels for odd and even denominator states.

cond-mat.mes-hall↗

arXiv1997

Anomalous Exponent of the Spin Correlation Function of a Quantum Hall Edge

The charge and spin correlation functions of partially spin-polarized edge electrons of a quantum Hall bar are studied using effective Hamiltonian and bosonization techniques. In the presence of the Coulomb interaction between the edges with opposite chirality we find a different crossover behavior in spin and charge correlation functions. The crossover of the spin correlation function in the Coulomb dominated regime is characterized by an anomalous exponent, which originates from the finite value of the effective interaction for the spin degree of freedom in the long wavelength limit. The anomalous exponent may be determined by measuring nuclear spin relaxation rates in a narrow quantum Hall bar or in a quantum wire in strong magnetic fields.

cond-mat.mes-hall↗

arXiv1997

Spin-charge separation in Quantum Hall Liquids

We have investigated chiral edges of a quantum Hall(QH) liquid at filling factor ν=2. We find that spin and charge separate in the presence of the long-range Coulomb interaction, and the tunneling density of states(DOS) is given by D(ω)\sim [-1/\lnω]^{1/2}. The measurement of the temperature and voltage dependences of the tunneling current should reveal the presence spin-charge separation.

cond-mat.mes-hall↗

arXiv1997

Linear Chain of Coupled Quantum Dots

A linearly coupled chain of spin-polarized quantum dots is investigated under the condition that the number of electrons is equal to or less than the number of the dots. The chemical potential of the system, $μ_{N}=E(N)-E(N-1)$, satisfies, $(μ_{N}+μ_{N_{\ell}+2-N)}/2 \approx V+2t (N, N_{\ell}, V, E(N)$ and $t$ are the number of electrons, the number of dots, and the strength of nearest neighbor electron-electron interactions, the total groundstate energy and the hopping integral between two adjacent dots). This property will be reflected in the spacing between the conductance peaks. The electron density structures are determined using a quantum Monte Carlo method. As the number of electrons is varied several correlated structures are found that are commensurate/incommensurate with the periodic dot system. Hartree-Fock theory fails to predict the correct electronic structures of this system because several nearly degenerate solutions exist.

cond-mat.mes-hall↗

arXiv1996

Coulomb Gaps in One-Dimensional Spin-Polarized Electron Systems

We investigate the density of states (DOS) near the Fermi energy of one-dimensional spin-polarized electron systems in the quantum regime where the localization length is comparable to or larger than the inter-particle distance. The Wigner lattice gap of such a system, in the presence of weak disorder, can occur precisely at the Fermi energy, coinciding with the Coulomb gap in position. The interplay between the two is investigated by treating the long-range Coulomb interaction and the random disorder potential in a self-consistent Hartree-Fock approximation. The DOS near the Fermi energy is found to be well described by a power law whose exponent decreases with increasing disorder strength.

cond-mat↗

arXiv1996

Weak and Strong Localization in Low-Dimensional Semiconductor Structures

The dependence of the localization length on the number of occupied subbands $N$ in low-dimensional semiconductors is investigated. The localization length is shown to be proportional to the number of occupied subbands in quasi-one-dimensional quantum wires while it grows exponentially with $N$ in quasi-two-dimensional systems. Also a weak localization theory is developed for large N with a well-defined small expansion parameter $1/N$. The temperature dependence of the conductivity deduced using this perturbation theory agrees with the experimentally observed dependence.

cond-mat↗

arXiv1995

Interactions, Localization, and the Integer Quantum Hall Effect

We report on numerical studies of the influence of Coulomb interactions on localization of electronic wavefunctions in a strong magnetic field. Interactions are treated in the Hartree-Fock approximation. Localization properties are studied both by evaluating participation ratios of Hartree-Fock eigenfunctions and by studying the boundary-condition dependence of Hartree-Fock eigenvalues. We find that localization properties are independent of interactions. Typical energy level spacings near the Fermi level and the sensitivity of those energy levels to boundary condition show similar large enhancements so that the Thouless numbers of the Hartree-Fock eigenvalues are similar to those of non-interacting electrons.

cond-mat↗

arXiv1993

Addition Spectra of Quantum Dots in Strong Magnetic Fields

We consider the magnetic field dependence of the chemical potential for parabolically confined quantum dots in a strong magnetic field. Approximate expressions based on the notion that the size of a dot is determined by a competition between confinement and interaction energies are shown to be consistent with exact diagonalization studies for small quantum dots. Fine structure is present in the magnetic field dependence which cannot be explained without a full many-body description and is associated with ground-state level crossings as a function of confinement strength or Zeeman interaction strength. Some of this fine structure is associated with precursors of the bulk incompressible states responsible for the fractional quantum Hall effect.

cond-mat↗

arXiv1993

Quantum Dots in Strong Magnetic Fields: Stability Criteria for the Maximum Density Droplet

In this article we discuss the ground state of a parabolically confined quantum dots in the limit of very strong magnetic fields where the electron system is completely spin-polarized and all electrons are in the lowest Landau level. Without electron-electron interactions the ground state is a single Slater determinant corresponding to a droplet centered on the minimum of the confinement potential and occupying the minimum area allowed by the Pauli exclusion principle. Electron-electron interactions favor droplets of larger area. We derive exact criteria for the stability of the maximum density droplet against edge excitations and against the introduction of holes in the interior of the droplet. The possibility of obtaining exact results in the strong magnetic field is related to important simplifications associated with broken time-reversal symmetry in a strong magnetic field.

cond-mat↗