Two-flux composite fermion series of the fractional quantum Hall states in strained Si

Magnetotransport properties are investigated in a high-mobility two-dimensional electron system in the strained Si quantum well of a (100) Si(0.75)Ge(0.25)/Si/Si(0.75)Ge0.25 heterostructure, at temperatures down to 30 mK and in magnetic fields up to 45 T. We observe around nu=1/2 the two-flux composite fermion (CF) series of the fractional quantum Hall effect (FQHE) at nu=2/3, 3/5, 4/7, and at nu=4/9, 2/5, 1/3. Among these FQHE states, the nu=1/3, 4/7, and 4/9 states are seen for the first time in the Si/SiGe system. Interestingly, of the CF series, the 3/5 state is weaker than the nearby 4/7 state and the 3/7 state is conspicuously missing, resembling the observation in the IQHE regime that the nu=3 is weaker than the nearby nu=4 state. Our results can be quantitatively understood in the picture of CF's with the valley degree of freedom.     

Observation of collapse of pseudospin order in bilayer quantum Hall ferromagnets

The Hartree-Fock paradigm of bilayer quantum Hall states with finite tunneling at filling factor nu=1 has full pseudospin ferromagnetic order with all the electrons in the lowest symmetric Landau level. Inelastic light scattering measurements of low energy spin excitations reveal major departures from the paradigm at relatively large tunneling gaps. The results indicate the emergence of a novel correlated quantum Hall state at nu=1 characterized by reduced pseudospin order. Marked anomalies occur in spin excitations when pseudospin polarization collapses by application of in-plane magnetic fields.     

Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential

Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin–orbit coupling quantum number κ. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy between members of the pseudospin doublet is removed by tensor interaction. Furthermore, the radial node structure of the Dirac spinor is discussed.     

具有自旋轨道耦合项的Manning-Rosen势的赝自旋对称解

近似研究了具有任意自旋轨道耦合项的Manning-Rosen势的Dirac方程。在赝自旋对称的条件下获得了关联的二分量的旋量及相应的能量方程。最后,对 和Hulthén 势两类特殊情况进行了简单 讨论。     

Pseudospin soliton in the nu=1 bilayer quantum Hall state

We investigate a domain structure of pseudospins, a soliton lattice in the bilayer quantum Hall state at total Landau level filling factor nu = 1, in a tilted magnetic field, where the pseudospin represents the layer degree of freedom. An anomalous peak in the magnetoresistance Rxx appears at the transition point between the commensurate and incommensurate phases. The Rxx at the peak is highly anisotropic for the angle between the in-plain magnetic field B parallel and the current, and indicates a formation of the soliton lattice aligned parallel to B parallel. The temperature dependence of the Rxx peak reveals that the dissipation is caused by thermal fluctuations of pseudospin solitons. We also study a phase diagram of the bilayer nu = 1 system, and the effects of density imbalance between the two layers.     

Test of nuclear wave functions for pseudospin symmetry

Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.     

Conical Diffraction from Approximate Dirac Cone States in a Superhoneycomb Lattice

Superhoneycomb lattice is an edge‐centered honeycomb lattice that represents a hybrid fermionic and bosonic system. It contains pseudospin‐1/2 and pseudospin‐1 Dirac cones, as well as a flat band in its band structure. In this paper, we cut the superhoneycomb lattice along short‐bearded boundaries and obtain the corresponding band structure. The states very close to the Dirac points represent approximate Dirac cone states that can be used to observe conical diffraction during light propagation in the lattice. In comparison with the previous literature, this research is carried out using the continuous model, which brings new results and is simple, direct, accurate, and computationally efficient.     

Longitudinal conductivity in ABC-stacked trilayer graphene under irradiating of linearly polarized light

We study the effect of linearly polarized light on the band structure and longitudinal conductivity in ABC-stacked trilayer graphene. The linearly polarized light can induce a pair of additional points in ABC-stacked trilayer graphene, where conduct and valence bands touch. The locations of these points are determined by the amplitude of the light. Furthermore, the layer pseudospin polarization can be controlled by the light. When the Fermi energy locates at Dirac points, i.e., E_f=0, the longitudinal conductivity shows resonance phenomena when the light is present. Away from the Dirac points, the longitudinal conductivity is unchanged as varying E_f for weak light field at larger Fermi energy, and the amplitude of longitudinal conductivity can be controlled by tuning the light field amplitude. Moreover, the effect of linearly polarized light on resonance phenomena in k-cubic Rashba-Dresselhaus system under the irradiating of linearly polarized light is discussed.     

Dirac Equation with a New Tensor Interaction under Spin and Pseudospin Symmetries

The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method. Because a tensor interaction in the Dirac equation removes the energy degeneracy in the spin and pseudospin doublets that leads to atomic stability, we study the Dirac equation with a Hellmann-like tensor potential newly proposed in this study.The newly proposed tensor potential removes the degeneracy from both the spin symmetry and pseudospin symmetry completely. The proposed tensor potential seems better than the Coulomb and Yukawa-like tensor potentials.     

Dirac Equation with a New Tensor Interaction under Spin and Pseudospin Symmetries

The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method. Because a tensor interaction in the Dirac equation removes the energy degeneracy in the spin and pseudospin doublets that leads to atomic stability, we study the Dirac equation with a Hellmann-like tensor potential newly proposed in this study. The newly proposed tensor potential removes the degeneracy from both the spin symmetry and pseudospin symmetry completely. The proposed tensor potential seems better than the Coulomb and Yukawa-like tensor potentials.     

Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit

We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term κ. We also investigate the energy eigenvalues of the Dirac particles for the well-known Kratzer-Fues and modified Kratzer potentials which are Mie-type potentials.     

Spin and the honeycomb lattice: lessons from graphene

A model of electrons hopping from atom to atom in graphene's honeycomb lattice gives low-energy electronic excitations that obey a relation formally identical to a 2+1 dimensional Dirac equation. Graphene's spin equivalent, "pseudospin," arises from the degeneracy introduced by the honeycomb lattice's two inequivalent atomic sites per unit cell. Previously it has been thought that the usual electron spin and the pseudospin indexing the graphene sublattice state are merely analogues. Here we show that the pseudospin is also a real angular momentum. This identification explains the suppression of electron backscattering in carbon nanotubes and the angular dependence of light absorption by graphene. Furthermore, it demonstrates that half-integer spin like that carried by the quarks and leptons can derive from hidden substructure, not of the particles themselves, but rather of the space in which these particles live.     

Phase diagram for quantum hall bilayers at nu=1

We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at a total filling factor nu=1, based on exact numerical calculations of the topological Chern number matrix and the (interlayer) superfluid density. We find three phases: a quantized Hall state with pseudospin superfluidity, a quantized Hall state with pseudospin "gauge-glass" order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau, and vanishing Hall drag resistance, as well as the zero-bias conductance peak effect, and suggests some interesting points to pursue experimentally.     

New phase transition between partially and fully polarized quantum Hall states with charge and spin gaps at nu = 2/3

The average electron spin polarization Rho of a two-dimensional electron gas confined in GaAs/GaAlAs multiple quantum wells was measured by NMR near the fractional quantum Hall state with filling factor nu = 2/3. Above this filling factor (2/3< or = nu < 0.85), a strong depolarization is observed corresponding to two spin flips per additional flux quantum. The most remarkable behavior of the polarization is observed at nu = 2/3, where a quantum phase transition from a partially polarized (Rho approximately 3/4) to a fully polarized (Rho = 1) state can be driven by increasing the ratio between the Zeeman and the Coulomb energy above a critical value eta(c) = Delta(Z)/Delta(C) = 0.0185.     

Bound-state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry<Superscript>⋆</Superscript>

The energy spectra and the corresponding two-component spinor wave functions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The s -wave ( k \kappa = 0 state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wave functions for this potential and other special types of this potential are obtained. The extension of this result to the k \kappa 1 \neq 0 state is suggested.     

Spin and pseudospin symmetries of the Dirac equation with shifted Hulthén potential using supersymmetric quantum mechanics

In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthén potential within the framework of spin and pseudospin symmetry limits for arbitrary spin–orbit quantum number κ using the supersymmetry quantum mechanics. The energy eigenvalues and the corresponding Dirac wave functions are obtained in closed forms.     

Approximate <Emphasis Type="Italic">κ</Emphasis>-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C _s from the valence energy spectrum of particle and also for pseudospin symmetry constant C _ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.     

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.     

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.     

Electrically controlled nuclear spin polarization and relaxation by quantum-Hall states

We study interactions between electrons and nuclear spins by using the resistance ( Rxx) peak which develops near the Landau-level filling factor nu = 2/3 as a probe. Temporarily tuning nu to a different value, nu(temp), with a gate demonstrates that the Rxx peak regenerates even after complete depletion ( nu(temp) = 0), while it rapidly relaxes on either side of nu(temp) = 1. This indicates that the nu = 2/3 domain morphology is memorized by the nuclear spins which can be rapidly depolarized by Skyrmions. An additional enhancement in the nuclear spin relaxation around nu = 1/2 and 3/2 suggests a Fermi sea of partially polarized composite fermions.