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[en] Using a transformation of hyperbolic function, the Schroedinger equation with reflectionless potential well is transformed into an associated-Legendre equation. Then both bound and scattering state eigenfunctions are expressed in terms of associated-Legendre polynomials and functions respectively. The exact solutions obtained in this paper are more general and systematic than some asymptotic solutions or solutions of reflectionless potential with special parameters in literatures. The normalization of the scattering state is discussed in detail
[en] By considering the nodal characteristic of radial wavefunction for valence electron of multi-electron atoms and spectrum experimental data, we suggest a method of determination and inspection for the parameters in model potential theory of atomic structure, with which the collapse due to mixing of inner electron wavefunction can be avoided
[en] We study the effect of an electric potential well on the Landau level (LL) spectrum for surface states of a three-dimensional (3D) topological insulator (TI) by using a method of numerical diagonalization for the Hamiltonian in a truncated Hilbert space. It is found that the dispersivity of energy is dependent on the position of electron cyclotron orbit center (COC). A dispersionless energy spectrum like flat LLs appeared as if without the confining potential when the electron COC is far away from the well boundaries (corners). When the electron COC is near the boundaries, however, there exist some interesting interface states propagating along the well due to the presence of electric confinement which causes quantized subband mixing. Moreover, the probability density and the spin polarization of interface states in conduction band oscillate mainly inside the well and decay outside, while those in valence band oscillate outside and decay inside. These findings here may provide a further understanding of 3D TI surface states.
[en] Highlights: • First report for molecular junction of oligothiophenes contact graphene electrodes. • Obvious difference in transport between molecules with and without amino. • Coexisted negative differential resistance and dual spin-filtering. • Ideal dual spin-filtering effect for molecule with NH2 side group. - Abstract: The influence of chemical side groups is significant in physical or chemical understanding the transport through the single molecular junction. Motivated by the recent successful fabrication and measurement of a single organic molecule sandwiched between graphene electrodes (Prins et al., 2011), here we study the spin-dependent transport properties through a junction of a fused oligothiophenes molecule embedded between two zigzag-edged graphene nanoribbon (ZGNR) electrodes. The molecule with and without an attached amino NH2 side group is considered, respectively, and external magnetic fields or FM stripes are applied onto the ZGNRs to initially orient the magnetic alignment of the electrodes for the spin-dependent consideration. By the ab initio calculations based on the density functional theory combined with nonequilibrium Green’s function formalism, we have demonstrated the remarkable difference in the spin-charge transport property between the junctions of the molecule with and without NH2 side group. In particular, the junction with side group shows more obvious NDR. In addition, it exhibits an interesting dual spin-filtering effect when the magnetic alignment in electrodes is initially antiparallel-oriented. The mechanisms of the results are revealed and discussed in terms of the spin-resolved transmission spectrum associated with the frontier molecular orbitals evolution, the molecular projected self-consistent Hamiltonian eigenvalues, and the local density of states.
[en] We study the penetration depth (PD) of surface state into the bulk, the local density of states (LDOS) and the spin-polarized STM tip tunneling conductance (TG) for a smoothly varying step described by an asymptotic model, on the surface of a three-dimensional (3D) topological insulator (TI). Using curvilinear coordinates for calculation, we find that the PD shows two peaks near step edges with maximum surface curvature and a dip value of flat surface at step middle with zero curvature. In contrast, the LDOS exhibits a double valley (dip) pattern, in which it rapidly declines from the highest value for flat surface to the dip value near step edges, and then shows a small peak at step middle. This interesting small peak is in good agreement with experimentally observed LDOS peak within a step of definite span on a 3D TI surface. Moreover, the calculated surface spin-polarized STM tip TG also confirms the LDOS qualitatively. The findings here may provide a further understanding of 3D TI surface with step line defects
[en] We investigate theoretically the spin current in a quantum wire with weak Dresselhaus spin-orbit coupling connected to two normal conductors. Both the quantum wire and conductors are described by a hard-wall confining potential. Using the electron wave-functions in the quantum wire and a new definition of spin current, we have calculated the elements of linear spin current density js,xiT and js,yiT (i = x, y, z). We find that the elements jTs,xx and jTs,yy have a antisymmetrical relation and the element jTs,yz has the same amount level as js,xxT and js,yyT. We also find a net linear spin current density, which has peaks at the center of quantum wire. The net linear spin current can induce a linear electric field, which may imply a way of spin current detection.
[en] We investigate theoretically the spin accumulation in a Rashba spin-orbit coupling (SOC) nanoribbon nonadiabatically connected to a normal conductor. Both the nanoribbon and conductor are described by a hard-wall confining potential. Using the scattering matrix approach within the effective free-electron approximation, we have calculated the out-of-plane spin accumulation in the nanoribbon. It is found that the spin accumulation shifts toward the two edges of nanoribbon with the increasing of propagation modes. Specifically, as the Rashba SOC strength increases the spin accumulation in the nanoribbon will be enhanced and this result may suggest us a simple method to control the spin accumulation of the system by Rashba SOC strength.
[en] We investigate theoretically the electronic structure and transport for a two-level quantum wire with Rashba spin-orbit coupling (SOC) under the irradiation of an external laser field at low temperatures. The photon-induced transitions between SOC-split subbands with the same lateral confinement quantum number and between subbands with different confinement quantum numbers are expected. Using the method of equation of motion (EOM) for Keldysh nonequilibrium Green's functions (NGF), we examine the time-averaged density of states (DOS) and the spin-polarized conductance for the system with photon polarization perpendicular to the wire direction. Through the analytical analysis and some numerical examples, the interplay effects of the external laser field and the Rashba SOC on both the DOS and the conductance of the system are demonstrated and discussed. It is found that the external laser field can adjust the spin polarization rate and the transport of the quantum wire system with some appropriate Rashba SOC strengths
[en] We study the transport properties for a Luttinger liquid (LL) quantum wire in the presence of both Rashba spin-orbit coupling (SOC) and a weak external in-plane magnetic field. The bosonized Hamiltonian of the system with an externally applied longitudinal electric field is established. Then the equations of motion for the bosonic phase fields are solved in Fourier space, with which both the charge and spin conductivities for the system are calculated analytically, based on linear response theory. Generally, the ac conductivity is an oscillation function of the strengths of electron-electron interaction, Rashba SOC and magnetic field, as well as the driving frequency and the measurement position in the wire. Through analysis with some examples it is demonstrated that the modification of the conductivity due to electron-electron interactions is more remarkable than that due to SOC, while the effects of SOC and Zeeman splitting on the conductivity are very similar. The spin-polarized conductivities for the system in the absence of Zeeman effect or SOC are also discussed. The ratio of the spin-polarized conductivities σ↑/σ↓ is dependent on the electron-electron interactions for a system without SOC, while it is independent of the electron-electron interactions for a system without Zeeman splitting
[en] To increase the accuracy and reliability of the transmissibility function evaluation, a combined crosstalk cancellation method based on wavelet packet denoising and Welch’s method for operational transfer path analysis (OTPA) is proposed. Firstly, prior tests are carried out with pulsed excitation, and the signals at reference points are measured concurrently. Secondly, wavelet packet denoising is adopted to process the measured signals, which can effectively reduce the effects of measurement noises and other random errors. Thirdly, Welch’s method is adopted to evaluate auto-power spectrums and cross-power spectrums, and thus the prior transmissibility functions can be accurately obtained. Fourthly, a crosstalk cancellation method is proposed and the signals at reference points without crosstalk are obtained. Finally, the crosstalk problem is solved and an efficient and accurate OTPA is obtained. Furthermore, numerical case studies and experimental case studies on a test bed with shell structures are carried out to study comparatively the performances of the proposed method. Generally, this study provides an effective crosstalk cancellation method for OTPA, which can increase the accuracy and reliability of transfer path identification and contribution evaluation, and thus benefit vibration and noise monitoring, reduction and control. (paper)