One-dimensional quantum waveguide theory of Rashba electrons

The ballistic spin transport in one-dimensional waveguides with the Rashba effect is studied. Due to the Rashba effect, there are two electron states with different wave vectors for the same energy. The wave functions of two Rashba electron states are derived, and it is found that their phase depend on the direction of the circuit and the spin directions of two states are perpendicular to the circuit, with the +pi/2 and -pi/2 angles, respectively. The boundary conditions of the wave functions and their derivatives at the intersection of circuits are given, which can be used to investigate the waveguide transport properties of Rashba spin electron in circuits of any shape and structure. The eigenstates of the closed circular and square loops are studied by using the transfer matrix method. The transfer matrix M(E) of a circular arc is obtained by dividing the circular arc into N segments and multiplying the transfer matrix of each straight segment. The energies of eigenstates in the closed loop are obtained by solving the equation det[M(E)-I]=0. For the circular ring, the eigenenergies obtained with this method are in agreement with those obtained by solving the Schrodinger equation. For the square loop, the analytic formula of the eigenenergies is obtained first The transport properties of the AB ring and AB square loop and double square loop are studied using the boundary conditions and the transfer matrix method In the case of no magnetic field, the zero points of the reflection coefficients are just the energies of eigenstates in closed loops. In the case of magnetic field, the transmission and reflection coefficients all oscillate with the magnetic field; the oscillating period is Phi(m)=hc/e, independent of the shape of the loop, and Phi(m) is the magnetic flux through the loop. For the double loop the oscillating period is Phi(m)=hc/2e, in agreement with the experimental result. At last, we compared our method with Koga's experiment. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3253752]

Quantum mechanical simulation of nanosized metal-oxide-semiconductor field-effect transistor using empirical pseudopotentials: A comparison for charge density occupation methods

The atomistic pseudopotential quantum mechanical calculations are used to study the transport in million atom nanosized metal-oxide-semiconductor field-effect transistors. In the charge self-consistent calculation, the quantum mechanical eigenstates of closed systems instead of scattering states of open systems are calculated. The question of how to use these eigenstates to simulate a nonequilibrium system, and how to calculate the electric currents, is addressed. Two methods to occupy the electron eigenstates to yield the charge density in a nonequilibrium condition are tested and compared. One is a partition method and another is a quasi-Fermi level method. Two methods are also used to evaluate the current: one uses the ballistic and tunneling current approximation, another uses the drift-diffusion method. (C) 2009 American Institute of Physics. [doi:10.1063/1.3248262]

Mode characteristics for equilateral triangle optical resonators

Mode characteristics of equilateral triangle resonators (ETRs) are analyzed based on the symmetry operation of the point group C-3v. The results show that doubly degenerate eigenstates can be reduced to the A(1) and A(2) representations of C-3v, if the longitudinal mode number is a multiple of 6; otherwise, they form the E irreducible representation Of C-3v. And the one-period length for the mode light ray is half of the perimeter of the ETR. Mode Q-factors are calculated by the finite-difference time-domain (FDTD) technique and compared with those calculated from far-field emission based on the analytical near-field pattern for TE and TM modes. The results show that the far-field emission based on the analytical field distribution can be used to estimate the mode Q-factor, especially for TM modes. FDTD numerical results also show that Q-factor of TE modes reaches maximum value as the longitudinal mode number is a multiple of 7. In addition, photoluminescence spectra and measured Q-factors are presented for fabricated ETR with side lengths of 20 and 30 mu m, and the mode wavelength intervals are compared with the analytical results.

Magnetotransport in two-dimensional electron gas: The interplay between spin-orbit interaction and Zeeman splitting

We investigate theoretically the interplay between Zeeman splitting, Rashba spin-orbit interaction (RSOI), and Dresselhaus spin-orbit interaction (DSOI) and its influence on the magnetotransport property of two-dimensional electron gas (2DEG) at low temperature. Our theoretical results show that the nodes of the beating patterns of the magnetoresistivity rho(xx) for 2DEG with RSOI or DSOI alone depend sensitively on the total spin splitting induced by these three spin splitting mechanisms. It is interesting to find that the eigenstates in the presence of RSOI alone are connected with those in the presence of DSOI alone but with opposite Zeeman splitting by a time-reversal transformation. Consequently, the magnetoresistivities exhibit exactly the same oscillation patterns for these two cases. For strong RSOI or DSOI alone, the magneto-oscillation of rho(xx) shows two distinct periods. For 2DEG with both RSOI and DSOI, the beating patterns vanish for equal RSOI and DSOI strengths and vanishing Zeeman splitting. They will appear again, however, when Zeeman splitting or the difference between RSOI and DSOI strengths increases.

Influence of mode symmetry on quality factors of degenerate states in microlasers with an equilateral triangle resonator

Modes in equilateral triangle resonator (ETR) are analyzed and classified according to the irreducible representations of the point group C-3v., Both the analytical method based on the far field emission and the numerical method by FDTD technique are used to calculate the quality factors (Q-factors) of the doubly degenerate states in ETR. Results obtained from the two methods are in reasonable agreement. Considering the different symmetry properties of the doubly degenerate eigenstates, we also discuss the ETR joined with an output waveguide at one of the vertices by FDTD technique and the Pade approximation. The variation of Q-factors versus width of output waveguide is analyzed. The numerical results show that doubly degenerate eigenstates of TM0.36 and TM0.38 whose wavelengths are around 1.5 mu m in the resonator with side-length of 5 mu m have the Q-factors larger than 1000 when the width of the output waveguide is smaller than 0.4 mu m. When the width of the output waveguide is set to 0.3 mu m, the symmetrical states that are more efficiently coupled to output waveguide have Q-factors about 8000, which are over 3 times larger than those of asymmetric state.

Unified theory for Goos-Hanchen and imbert-fedorov effects

A unified theory is advanced to describe both the lateral Goos-Hanchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a three-dimensional light beam in terms of a two-form angular spectrum consisting of its two orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the two orthogonal linear polarizations in this two-form representation, and the eigenstates of the IF displacement are the two orthogonal circular polarizations. The theoretical predictions are found to be in agreement with recent experimental results.

CALCULATION OF SPIN-REORIENTATION TEMPERATURE IN ND2FE14B

The spin-reorientation phenomenon in Nd2Fe14B has been investigated using an angular dependent free energy approach. A magnetic Hamiltonian which includes the crystal electric field term and the exchange term has been established using realistic band structure results. The temperature dependence of the molecular field is accounted for by introducing the Brillouin function and the magnetic Hamiltonian is diagonalized within the ground state multiplet of the Nd ion. The eigenstates are then used to form the partition function for the free energy. At each temperature, the direction of the molecular field is obtained by searching for the minimum in the angular parameter space of the free energy. Our calculations show that for Nd2Fe14B, the net magnetic anisotropy direction is canted away from the c axis at a temperature close to the experimentally reported spin-reorientation temperature of 150 K. The temperature dependence of the magnetic structure is found to be very sensitive to the size of the second order crystal field parameter B20.

Mieszanie stanów magnetycznych w skończonych układach spinowych opisywanych modelem Heisenberga

Wydział Fizyki: Zakład Fizyki Komputerowej

Spatial and energetic mode dynamics of cold atomic systems

In this thesis we relate the formal description of various cold atomic systems in the energy eigenbasis, to the observable spatial mode dynamics. Herein the `spatial mode dynamics' refers to the direction of photon emission following the spontaneous emission of an excited fermion in the presence of a same species and spin ideal anisotropic Fermi sea in its internal ground state. Due to the Pauli principle, the presence of the ground state Fermi sea renders the phase space, anisotropic and only partially accessible, thereby a ecting the direction of photon emission following spontaneous emission. The spatial and energetic mode dynamics also refers to the quantum `tunneling' interaction between localised spatial modes, synonymous with double well type potentials. Here we relate the dynamics of the wavefunction in both the energetic and spatial representations. Using this approach we approximate the relationship between the spatial and energetic representations of a wavefunction spanning three spatial and energetic modes. This is extended to a process known as Spatial Adiabatic Passage, which is a technique to transport matter waves between localised spatial modes. This approach allows us to interpret the transport of matter waves as a signature of a geometric phase acquired by the one of the internal energy eigenstates of the system during the cyclical evolution. We further show that this geometric phase may be used to create spatial mode qubit and qutrit states.

Two-stage Kondo effect and Kondo-box level spectroscopy in a carbon nanotube

The concept of the "Kondo box" describes a single spin, antiferromagnetically coupled to a quantum dot with a finite level spacing. Here, a Kondo box is formed in a carbon nanotube interacting with a localized electron. We investigate the spins of its first few eigenstates and compare them to a recent theory. In an "open" Kondo-box, strongly coupled to the leads, we observe a nonmonotonic temperature dependence of the nanotube conductance, which results from a competition between the Kondo-box singlet and the "conventional" Kondo state that couples the nanotube to the leads. © 2010 The American Physical Society.

Positronium scattering by lithium

We report cross sections for Ps(1s)-Li(2s) scattering in the energy range up to 30 eV. The calculations have been carried out in a coupled state approximation. The Ps states consist of both eigenstates and pseudostates. the latter to allow for ionization of the Ps. The atom is treated as a frozen core represented by it model potential which supports the valence orbitals. The coupled state expansion includes only the 2s and 2p states of the atom as well as in unphysical Is state which exists in the model potential. The inclusion of this Is state is necessary in order to avoid pronounced false pseudostructure. Results are presented for excitation and ionization of the Ps as well as collisions in which the Ps(1s) remains unchanged. These results also differentiate between the case where the Li(2s) remains unexcited and where it is excited to the 2p level. (c) 2005 Published by Elsevier B.V.

Electron recombination with multicharged ions via chaotic many-electron states

We show that a dense spectrum of chaotic multiply excited eigenstates can play a major role in collision processes involving many-electron multicharged ions. A statistical theory based on chaotic properties of the eigenstates enables one to obtain relevant energy-averaged cross sections in terms of sums over single-electron orbitals. Our calculation of low-energy electron recombination of Au25+ shows that the resonant process is 200 times more intense than direct radiative recombination, which explains the recent experimental results of Hoffknecht [J. Phys. B 31, 2415 (1998)].

Time operator for diffusion

Volume: 11 Issue: 4 Pages: 465-477 Published: MAR 2000 Times Cited: 9 References: 15 Citation MapCitation Map beta Abstract: We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion. (C) 2000 Elsevier Science Ltd. All rights reserved.

Effective collision strengths for electron-impact excitation of S X

Effective collision strengths computed by the R-matrix method are presented for the electron-impact excitation of nitrogen-like S X. The total wave function used in the expansion includes the lowest 11 eigenstates of S X which arise from the 2s(2)2p(3), 2s2p(4), 2p(5) and 2s(2)2p(2)3s configurations. These 11 LS target states correspond to 22 fine-structure levels, giving 231 possible transitions. All the effective collision strengths for these transitions are tabulated in the range log T(K) = 4.6 to log T(K) = 6.7. The energy level values and oscillator strengths for allowed transitions are also tabulated. The effective collision strengths were calculated by averaging the electron collision strengths over a Maxwellian distribution of velocities. The present effective collision strengths are the only results currently available for these fine-structure transition rates. (C) 2000 Academic Press.

Mixing of dielectronic and multiply-excited states in electron-ion recombination: a study of Au24+

It has been suggested (Gribakin et al 1999 Aust. J. Phys. 52 443–57, Flambaum et al 2002 Phys. Rev. A 66 012713) that strongly enhanced low-energy electron recombination observed in Au25+ (Hoffknecht et al 1998 J. Phys. B: At. Mol. Opt. Phys. 31 2415–28) is mediated by complex multiply excited states, while simple dielectronic excitations play the role of doorway states for the electron capture process. We present the results of an extensive study of con?guration mixing between doubly excited (doorway) states and multiply excited states which account for the large electron recombination rate on Au25+ . A detailed analysis of spectral statistics and statistics of eigenstate components shows that the dielectronic doorway states are virtually ‘dissolved’ in complicated chaotic multiply excited eigenstates. This work provides a justi?cation for the use of statistical theory to calculate the recombination rates of Au25+ and similar complex multiply charged ions. We also investigate approaches which allow one to study complex chaotic many-body eigenstates and criteria of strong con?guration mixing, without diagonalizing large Hamiltonian matrices.