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Unidirectional transport and localized cyclotron motion are two opposite physical phenomena. Here, we study the interplay effects between them on nonreciprocal lattices subject to a magnetic field. We show that, in the long-wavelength limit, the trajectories of the wave packets always form closed orbits in four-dimensional (4D) complex space. Therefore, the semiclassical quantization rules persist despite the nonreciprocity, which preserves real Landau levels. We predict a different type of non-Hermitian spectral transition induced by the spontaneous breaking of the combined mirror-time reversal ($\mathcal{MT}$) symmetry, which generally exists in such systems. An order parameter is proposed to describe the $\mathcal{MT}$ phase transition, not only to determine the $\mathcal{MT}$ phase boundary but also to quantify the degree of $\mathcal{MT}$-symmetry breaking. Such an order parameter can be generally applied to all types of non-Hermitian phase transitions., 18 pages, including supplemental material, major revision, the version to be published in PRB Letter

In the presence of a magnetic field $\mathbf{B}$, the negative transverse magnetoconductivity (TMC) for $\mathbf{E}\ensuremath{\perp}\mathbf{B}$, with $\mathbf{E}$ being the applied electric field, and anomalous positive longitudinal magnetoconductivity (LMC) for $\mathbf{E}\ensuremath{\parallel}\mathbf{B}$ of a three-dimensional (3D) Weyl semimetal (WSM) both exhibit periodic-in-$1/B$ quantum oscillations. We develop a semiclassical theory of the magnetoconductivities of a 3D WSM, taking into account the effect of the Landau level broadening and finite temperatures. We find that if one fixes the direction of $\mathbf{B}$ and switches the direction of $\mathbf{E}$ to be perpendicular and parallel to $\mathbf{B}$, there exists an interesting peak-valley correspondence, or, say, a relative $\ensuremath{\pi}$ oscillation phase shift, between the oscillating TMC and LMC. This can serve as unambiguous measurable evidence manifesting the distinct underlying physical mechanisms of the TMC and LMC in WSMs, which has so far not been reported in theories or experiments.

Proximity-effect-induced superconductivity is studied for high-quality ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}/\mathrm{Fe}{\mathrm{Se}}_{0.5}{\mathrm{Te}}_{0.5}$ (FST) thin-film heterostructures with atomically sharp interfaces and for ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}/{\mathrm{TiO}}_{2}$/FST heterostructures where ${\mathrm{TiO}}_{2}$ is the ultrathin buffer layer. Adjusting the buffer layer thickness from zero to several nanometers is used to simulate different interface conditions: strongly, weakly, and zero-coupled interfaces. It is found that, for the strongly coupled interface, both the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ thin film and the FST have almost the same magnitude as the superconducting pair potential; for the weakly coupled interface, the pairing potential of the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ thin film exhibits an approximately exponential decay with the ${\mathrm{TiO}}_{2}$ buffer layer thickness. Our experimental results can be explained qualitatively by several theories under different interface conditions.

The chiral edge state (CES) at zero magnetic field has already been realized in the magnetically doped topological insulator (TI). However, this scheme strongly relies on material breakthroughs, and in fact, most of the TIs cannot be driven into a Chern insulator in this way. Here, we propose to achieve the CESs in two-dimensional TI/ferromagnetic insulator/TI sandwiched structures through spin-selective coupling between the helical edge states of the two TIs. Due to this coupling, the edge states of one spin channel are gapped and those of the other spin channel remain almost gapless, so that the helical edge states of each isolated TI are changed into the CESs. Such CESs can be hopefully achieved in all TI materials, which are immune to magnetic-disorder-induced backscattering. We propose to implement our scheme in the van der Waals heterostructures between monolayer $1{T}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{WTe}}_{2}$ and bilayer ${\mathrm{CrI}}_{3}$. The electrical control of magnetism in bilayer ${\mathrm{CrI}}_{3}$ switches the transport direction of the CESs, which can realize a low-consumption transistor.

We study the effect of inhomogeneous strain on transition-metal dichalcogenides with a large intrinsic gap in their spectrum. It is found that, by tuning the chemical potential, superconductivity can preserve within the strain-induced discrete pseudo Landau levels (LLs), which introduce interesting topological properties to these systems. As we show, the superconductivity for integer fillings is quantum critical, and the quantum critical coupling strength is determined by the spacing between the two LLs closest to the Fermi level. For partial fillings, the superconducting gap is scaled linearly with the coupling strength, and decreases rapidly when the chemical potential shifts away from the middle of each LL. In the presence of a Zeeman field, a pair of Majorana modes emerge simultaneously in the two valleys of strained dichalcogenides. When valley symmetry is further destroyed, a single Majorana mode can be expected to emerge at the edges of the strained monolayer dichalcogenides., Accepted by Phys. Rev. B

We theoretically study the effect of impurity scattering in a magnetically doped Dirac semimetal. It is found that the magnetic impurity potential can split a Dirac point into a pair of Weyl nodes, due to the broken time-reversal symmetry, and the DSM undergoes a topological phase transition to a Weyl semimetal (WSM). The Chern numbers on a cross section between the Weyl nodes in the Brillouin zone are integer quantized. As a consequence, open Fermi arcs emerge, which connect the projections of the Weyl nodes on the surface Brillouin zone. However, a relatively strong magnetic potential, in addition to separating the Weyl nodes, will introduce some localized states to the system. These localized states smear the Weyl nodes, and the anomalous Hall conductivity deviates from the linear dependence on the momentum distance of the Weyl nodes. Interestingly, though the nonmagnetic charge potential of the impurities is shown to be irrelevant to the topological phase transition, it can modify the Berry curvature and anomalous Hall conductivity of the impurity-induced WSM phase, by redistribution of the energies of the localized states.

We present an experimental study of the local and collective magnetism of ${\mathrm{EuFe}}_{2}{\mathrm{As}}_{2}$ that is isostructural with the high-temperature superconductor parent compound ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$. In contrast to ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$, where only Fe spins order, ${\mathrm{EuFe}}_{2}{\mathrm{As}}_{2}$ has an additional magnetic transition below 20 K due to the ordering of the ${\mathrm{Eu}}^{2+}$ spins $(J=7/2$, with $L=0$ and $S=7/2)$ in an $A$-type antiferromagnetic texture (ferromagnetic layers stacked antiferromagnetically). This may potentially affect the FeAs layer and its local and correlated magnetism. $\mathrm{Fe}\phantom{\rule{0.16em}{0ex}}K\ensuremath{\beta}$ x-ray emission experiments on ${\mathrm{EuFe}}_{2}{\mathrm{As}}_{2}$ single crystals reveal a local magnetic moment of $1.3\ifmmode\pm\else\textpm\fi{}0.15{\ensuremath{\mu}}_{B}$ at 15 K that increases slightly to $1.45\ifmmode\pm\else\textpm\fi{}0.15{\ensuremath{\mu}}_{B}$ at 300 K. Resonant inelastic x-ray scattering experiments performed on the same crystals show dispersive broad (in energy) magnetic excitations along $(0,0)\ensuremath{\rightarrow}(1,0)$ and $(0,0)\ensuremath{\rightarrow}(1,1)$ with a bandwidth on the order of 170--180 meV. These results on local and collective magnetism are in line with other parent compounds of the ${\mathrm{AFe}}_{2}{\mathrm{As}}_{2}$ series $(A=\mathrm{Ba}$, Ca, and Sr), especially the well-characterized ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$. Thus, our experiments lead us to the conclusion that the effect of the high magnetic moment of Eu on the magnitude of both the Fe local magnetic moment and spin excitations is small and confined to low-energy excitations.

We consider the Dirac electron scattering off a pointlike impurity absorbed on the surface of a topological insulator, which is irradiated by a beam of circularly polarized light. It is found that the Dirac electron backscattering is allowed even for a nonmagnetic impurity due to the reshuffled spectrum caused by the light, and so exhibits interesting spin texture and Friedel oscillation in the real space. Furthermore, in the charge density of states, the interplay of the light irradiation and impurity scattering can lead to an in-gap bound state around the Dirac point, heavily modulating the Dirac dispersion. We discuss the different scenarios for resonant and off-resonant lights in detail. The impurity scattering feature is sensitive to the parameters of the polarized light, which suggests a possibility to optically manipulate the topological surface states.

We investigate the anomalous Hall effect (AHE) on the surface of a topological insulator induced by a finite concentration of magnetic impurities, and find topologically nontrivial and trivial mechanisms simultaneously contributing to the Hall conductivity. In the topologically nontrivial mechanism, the impurities gap the surface spectrum and result in a half-integer quantized intrinsic Hall conductivity in units ${e}^{2}/h$, while in the topologically trivial mechanism, the half-integer quantized plateau is modified by impurity-induced localized states via a gap-filling process. The nonmagnetic charge potential itself, though participating in the gap-filling process, cannot induce the AHE. In the presence of a finite magnetic potential, the charge potential would destroy the symmetric distribution of the Hall conductivity by redistributing the localized levels. More interestingly, the sign of the Hall conductivity is tunable by changing the strength of the charge potential.

A great deal of attention has been paid to the topological phases engineered by photonics over the past few years. Here, we propose a topological quantum phase transition to a quantum anomalous Hall (QAH) phase induced by off-resonant circularly polarized light in a two-dimensional system that is initially in a quantum spin Hall phase or a trivial insulator phase. This provides an alternative method to realize the QAH effect, other than magnetic doping. The circularly polarized light effectively creates a Zeeman exchange field and a renormalized Dirac mass, which are tunable by varying the intensity of the light and drive the quantum phase transition. Both the transverse and longitudinal Hall conductivities are studied, and the former is consistent with the topological phase transition when the Fermi level lies in the band gap. A highly controllable spin-polarized longitudinal electrical current can be generated when the Fermi level is in the conduction band, which may be useful for designing topological spintronics.

In iron-based superconductors (FeSCs), orbital differentiation is an important phenomenon, whereby correlations stronger on the ${d}_{xy}$ orbital than on the ${d}_{xz}/{d}_{yz}$ orbital yield quasiparticles with a ${d}_{xy}$ orbital character having larger mass renormalization and an abnormal temperature evolution. However, the physical origin of this orbital differentiation is debated between the Hund's coupling-induced unbinding of spin and orbital degrees of freedom and the Hubbard interaction instigated orbital-selective Mott transition. Here we use angle-resolved photoemission spectroscopy to identify an orbital-dependent correlation-induced quasiparticle (QP) anomaly in LiFeAs. The excellent agreement between our photoemission measurements and first-principles many-body theory calculations shows that the orbital-differentiated QP lifetime anomalies in LiFeAs are controlled by the Hund's coupling.

We synthesized a series of V-doped LiFe$_{1-x}$V$_x$As single crystals. The superconducting transition temperature $T_c$ of LiFeAs decreases rapidly at a rate of 7 K per 1\% V. The Hall coefficient of LiFeAs switches from negative to positive with 4.2\% V doping, showing that V doping introduces hole carriers. This observation is further confirmed by the evaluation of the Fermi surface volume measured by angle-resolved photoemission spectroscopy (ARPES), from which a 0.3 hole doping per V atom introduced is deduced. Interestingly, the introduction of holes does not follow a rigid band shift. We also show that the temperature evolution of the electrical resistivity as a function of doping is consistent with a crossover from a Fermi liquid to a non-Fermi liquid. Our ARPES data indicate that the non-Fermi liquid behavior is mostly enhanced when one of the hole $d_{xz}/d_{yz}$ Fermi surfaces is well nested by the antiferromagnetic wave vector to the inner electron Fermi surface pocket with the $d_{xy}$ orbital character. The magnetic susceptibility of LiFe$_{1-x}$V$_x$As suggests the presence of strong magnetic impurities following V doping, thus providing a natural explanation to the rapid suppression of superconductivity upon V doping., Comment: 7 pages, 5 figures. See published version for the latest update

We study the effects of electron-electron interaction in a Floquet topological superconducting chain using the exact diagonalization and the dynamics simulation of quenching process. It is found that a weak interaction can lead to a multitude of tiny avoided crossings in quasienergy spectra, indicating the emergence of chaos, and that the Floquet topological superconducting state can be robust against the weak chaos. With increasing the interaction strength, there is a crossover from weak to strong chaos. On the other hand, the survival probability of Majorana edge modes vanishes and so the Floquet system is transformed into a topologically trivial phase.

We used x-ray magnetic circular dichroism (XMCD) to probe the ferromagnetic properties of As $p$-symmetric ($4p$) states in the recently synthesized diluted magnetic semiconductor $(\mathrm{B}{\mathrm{a}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}){(\mathrm{Z}{\mathrm{n}}_{1\ensuremath{-}y}\mathrm{M}{\mathrm{n}}_{y})}_{2}\mathrm{A}{\mathrm{s}}_{2}$ system under ambient- and high-pressure conditions. The As $K$-edge XMCD signal scales with the sample magnetization (dominated by Mn) and scales with the ferromagnetic ordering temperature $T\mathrm{c}$, and hence it is representative of the bulk magnetization. The XMCD intensity gradually decreases upon compression and vanishes at around 25 GPa, indicating quenching of ferromagnetism at this pressure. Transport measurements show a concomitant increase in conductivity with pressure, leading to a nearly metallic state at about the same pressure where magnetic order collapses. High-pressure x-ray diffraction shows an absence of structural transitions to 40 GPa. The results indicate that the mobility of doped holes, probed by both transport and x-ray absorption spectroscopy ($4p$ band broadening), is intimately connected with the mechanism of magnetic ordering in this class of compounds and that its control using external pressure provides an alternative route for tuning the magnetic properties in diluted magnetic semiconductor materials.

We present a theory for the inverse spin Hall effect in a thin film of topological insulator (TI) ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, connected to a reservoir with applied spin bias, in the ballistic regime. In the case that either the spin polarization of the spin bias is along the longitudinal direction, or the hybridization gap $\mathrm{\ensuremath{\Delta}}$ of the surface states vanishes, the spin Hall angle ${\mathrm{\ensuremath{\Theta}}}_{\mathrm{sh}}$ tends to infinity, indicating that the spin bias is perfectly converted into a measurable transverse charge current, essentially without generating a longitudinal spin current in the TI. In other cases, with increasing the Fermi energy ${E}_{\mathrm{F}}$ from the bottom of the conduction band of surface states, ${\mathrm{\ensuremath{\Theta}}}_{\mathrm{sh}}$ grows continuously from zero and exhibits an interesting linear dependence on ${E}_{\mathrm{F}}/\mathrm{\ensuremath{\Delta}}$ for ${E}_{\mathrm{F}}\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$. We also find that the inverse Edelstein effect occurs, when the in-plane transverse component of the spin polarization vector is nonzero. The spin-to-charge conversion becomes complete, when the spin polarization vector is along the transverse direction, or the hybridization gap $\mathrm{\ensuremath{\Delta}}$ vanishes.

Using first-principles calculations, we find a dynamically stable structure of Li-intercalated bilayer ${\mathrm{MoS}}_{2}$, of which two monolayers are mirror images of each other. It is shown that the stable Li-intercalated bilayer ${\mathrm{MoS}}_{2}$ can become a BCS superconductor with superconducting transition temperature ${T}_{c}$ evaluated over 10 K. The partial charge transfer from Li atoms to inner S planes of two ${\mathrm{MoS}}_{2}$ monolayers leads to a semiconductor-metal transition and an ionic interlayer interaction so as to increase the screening effect within the layers, soften phonon modes, and enhance electron-phonon couplings. Our finding suggests further experimental efforts directed toward an understanding of quasi-two-dimensional superconductivity.

In copper-oxide and iron-based high-temperature (high-${T}_{\mathrm{c}})$ superconductors, many physical properties exhibit in-plane anisotropy, which is believed to be caused by a rotational symmetry-breaking nematic order, whose origin and its relationship to superconductivity remain elusive. In many iron pnictides, a tetragonal-to-orthorhombic structural transition temperature ${T}_{\mathrm{s}}$ coincides with the magnetic transition temperature ${T}_{\mathrm{N}}$, making the orbital and spin degrees of freedom highly entangled. NaFeAs is a system where ${T}_{\mathrm{s}}=54$ K is well separated from ${T}_{\mathrm{N}}=42$ K, which helps simplify the experimental situation. Here we report nuclear magnetic resonance (NMR) measurements on ${\mathrm{NaFe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}\mathrm{As}$ $(0\ensuremath{\le}x\ensuremath{\le}0.042)$ that revealed orbital and spin nematicity occurring at a temperature ${T}^{*}$ far above ${T}_{\mathrm{s}}$ in the tetragonal phase. We show that the NMR spectra splitting and its evolution can be explained by an incommensurate orbital order that sets in below ${T}^{*}$ and becomes commensurate below ${T}_{\mathrm{s}}$, which brings about the observed spin nematicity.

We investigate the effect of spin-inelastic scattering of Dirac electrons off a high-spin nanomagnet adsorbed on a topological insulator (TI) surface, in which transitions of the nanomagnet between its internal magnetic levels are taken into account, beyond the classic spin theory. It is found that the presence of magnetic anisotropy of nanomagnets can result in a Dirac-point resonance peak in local density of states. It can significantly modify the topologically protected Dirac surface-state spectrum at the Dirac point, quite different from previously reported low-energy resonances. Furthermore, we propose to tune electrically the appearance of the Dirac-point resonance peak and its height by use of the spin-flip torque effect. This provides an approach to engineer the Dirac cone and tune the Dirac electron properties on the TI surface in the absence of an external magnetic field.

The quantum Hall (QH) effect discovered in 1980 (1) is the first example of topological state in the field of condensed matter physics. Since then, there has been continuously strong interest in topological phenomena of condensed matter systems. Laughlin (2) interpreted the integer QH effec as a quantum charge pump. In- creasing the magnetic flux by a single flux quantum that threads a looped QH ribbon constitutes a cycle of the pump due to gauge invariance, transferring an integer- quantized amount of charge from one edge of the rib- bon to the other. Thouless, Kohmoto, Nightingale, and Nijs (3) showed that the QH state can be classified by a topological invariant, the Chern number. Thouless and Niu (4, 5) also established a general relation between the Chern number and the charge pumped during a period of slow variation of potential in the Schrodinger equation. Recently, an important discovery was the topological insulator, (6-9) a new quantum state of matter existing in nature. Different from the QH systems, the topolog- ical insulators preserve the time-reversal (TR) symme- try. Two-dimensional topological insulators, also called the quantum spin Hall (QSH) systems, have a bulk band gap and a pair of gapless helical edge states traversing the bulk gap. When electron spin is conserved, the topo- logical properties of the QSH systems can be easily un- derstood, as a QSH system can be viewed as two inde- pendent QH systems without Landau levels. (10) When the spin conservation is destroyed, unconventional topo- logical invariants are needed to classify the QSH systems. The Z2 index (11) and the spin Chern numbers (12-14) have been proposed to describe the QSH systems. While the two different invariants are found to be equivalent to each other for TR-invariant systems, (13, 14) they lead to controversial predictions when the TR symmetry is bro- ken. The definition of the Z2 index explicitly relies on the presence of TR symmetry, suggesting that the QSH state turns into a trivial insulator once the TR symme- try is broken. However, calculations (15) based upon the spin Chern numbers showed that the nontrivial topolog- ical properties of the QSH systems remain intact when the TR symmetry is broken, as long as the band gap and spin spectrum gap stay open. The nonzero spin Chern numbers guarantee that the edge states must appear on the sample boundary, (16) which could be either gaped or gapless, depending on symmetries or spatial distributions of the edge states. (17) This prediction was supported by the recent experimental observation of the QSH effect in InAs/GaSb bilayers under broken TR symmetry. (18) Spin pumps promise broad applications in spintronics

By using the unrestricted Hartree-Fock approximation and the real-space recursion method, we have investigated various magnetic structures in an enlarged double cell of layered perovskite ${\mathrm{LaSrCoO}}_{4}.$ These include the low-spin state ${(t}_{2g}^{6}{e}_{g}^{0}),$ the intermediate-spin state ${(t}_{2g}^{5}{e}_{g}^{1}),$ and the high-spin state ${(t}_{2g}^{4}{e}_{g}^{2})$ as well as all possible combinations among these three states. The densities of states are computed and stabilities of various states are analyzed as functions of the model parameters. For a fixed Hund's coupling $j,$ it is shown that the ground state of ${\mathrm{LaSrCoO}}_{4}$ transforms first from the antiferromagnetic high-spin state to the ferromagnetically ordered high-spin low-spin state, and then to the nonmagnetic low-spin state as the crystal-field splitting $\mathrm{Dq}$ increases. The intermediate-spin state never becomes the ground state of ${\mathrm{LaSrCoO}}_{4}.$ In view of the measured effective magnetic moment of ${\ensuremath{\mu}}_{\mathrm{eff}}\ensuremath{\sim}2.6{\ensuremath{\mu}}_{B},$ we conclude that the most probable ground state of ${\mathrm{LaSrCoO}}_{4}$ lies in the regime of ferromagnetically ordered high-spin low-spin state, this state is also consistent with the optical conductivity spectra and neutron-diffraction experiment.

We take the Andreev reflection into account and apply a quantum-mechanical approach to studying spin-polarized transport in a ferromagnet/superconductor/ferromagnet double tunnel junction and its effect on superconductivity in the superconductor. It is found that in the presence of the Andreev reflection the tunneling magnetoresistance in the double tunnel junction depends strongly on barrier strength. In the antiferromagnetic alignment of the magnetizations, an increase in bias voltage will give rise to a first-order transition from the superconducting state to a normal one.

The density-of-states (DOS) near Fermi level of a single-wall carbon nanotube is studied in the presence of a magnetic field (B) parallel to the nanotube axis. Expressions of the band gap and the DOS near the Fermi level are derived in the case of with and without spin-$B$ interaction. A magnetic-field-induced metal-insulator transition is indicated in the variation of the band gap and the DOS. Zeeman effect on the band gap and the DOS is obvious from the derived expressions. These results may be observed by scanning tunneling spectroscopy measurements.

Taking into account pinning, thermal fluctuations, and vortex-vortex interactions, we develop a unified theory to explain the sign reversal of the mixed-state Hall resistivity rho(xy) in both high-T(c) and low-T(c) superconductors. Molecular dynamics simulations show that besides the pinning forces, either the thermal fluctuations in the high-T(c) superconductors or the vortex-vortex interactions in the low-T(c) ones play an important role in the sign reversal of rho(xy). From a calculated phase diagram for vortex motion, we find that the abnormal Hall effect always occurs in the plastic flow state of vortices. [S0163-1829(99)11629-1].

Based on an extended Slonczewski model with double $\ensuremath{\delta}$-type potential barriers, we study spin-dependent resonant tunneling conductances in a double-tunnel-junction structure, in which two ferromagnetic electrodes are separated from a middle nonmagnetic layer of thickness a by two thin insulating layers, respectively. It is shown that as the thickness a is increased, the tunneling magnetoresistance, along with the tunneling conductance for parallel and antiparallel magnetization configurations, exhibits amplitude-varying oscillating behavior with a period of $a=\ensuremath{\pi}{/k}_{F} {(k}_{F}$ being the Fermi wave vector). This abnormal phenomenon is found to stem from the spin-dependent resonant transmission of electrons passing through the double-tunnel-junction structure.

In contrast to the traditional viewpoint that a metal-insulator transition (MIT) occurs just at the resistivity peak temperature ${T}_{p},$ we propose that in perovskite manganites with temperature-dependent disorder, ${T}_{\mathrm{MI}}$ at which the MIT occurs may be well below the Curie temperature ${T}_{C}(\ensuremath{\simeq}{T}_{p}).$ At temperatures between ${T}_{\mathrm{MI}}$ and ${T}_{C},$ due to a decrease in localization length upon heating, the resistivity of the localized electrons behaves with metallic temperature dependence. Only above ${T}_{C}$ does the resistivity exhibit semiconductorlike temperature behavior. Such an idea that the MIT occurs below ${T}_{C}$ can account for the anomalous resistivity behavior in the layered manganite crystal ${\mathrm{La}}_{2\ensuremath{-}2x}{\mathrm{Sr}}_{1+2x}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ with $x=0.3.$

Using the extended Hubbard model and sum-over-state method, we have calculated the linear polarizability $\ensuremath{\alpha}$ and the third-order nonlinear polarizability $\ensuremath{\gamma}$ for carbon nanotubes with finite lengths. We find that the chiral symmetry of nanotubes with finite length has a great effect on their optical properties. For example, the finite length $(n,m)$ tubes with $n\ensuremath{-}m$ being not a multiple of 3, will have smaller $\ensuremath{\alpha}$ and much smaller $\ensuremath{\gamma}$ values than other finite length tubes.

From the Dyson equation of the nonequilibrium Green's functions, we derive a Boltzmann equation for the spin-dependent electronic transport, in which the electron distribution function is in general a $2\ifmmode\times\else\texttimes\fi{}2$ off-diagonal matrix in spin space. This equation is applicable to the transport in magnetic inhomogeneous systems, such as the magnetic layered structures and granular solids, with arbitrary magnetization configurations. For the parallel transport in the magnetic multilayers, it recovers the phenomenological Boltzmann equation proposed previously. It is shown that, as a consequence of continuity of the currents, the current density distribution depends only on the voltage drop between the ends of the sample. This allows us to determine the measurable physical quantities without calculating the actual internal electric field.

Using the Slonczewski model with a $\ensuremath{\delta}$-type potential barrier, we study spin-dependent tunneling conductances in a tunnel junction composed of two ferromagnetic layers (FM's) separated by an insulating barrier (I). In the high barrier case, the expression for the tunneling magnetoresistance is found to have the same form as that proposed by Julliere, but the electron-spin polarizations in both models have different definitions. We suggest that the spin dependence of the transmission coefficient should be taken into account in a FM/I/FM tunnel junction, and so the present formula can better describe its tunneling magnetoresistance.

We numerically solve the overdamped equation of vortex motion in a twin-boundary (TB) superconductor, in which the applied Lorentz force ${F}_{L},$ the pinning forces due to TB's and point defects, and the intervortex interacting force are taken into account. Our simulations show that TB's act as easy flow channels for the vortex motion parallel to the TB's and obstructive barriers for that normal to the TB's. Due to the barrier effect, the transverse velocity of vortices increases with ${F}_{L},$ but if ${F}_{L}$ is strong enough, the vortices can cross through the TB's so that the transverse velocity vs ${F}_{L}$ curve exhibits peak behavior.

It is found that the sharp resistivity peak observed near the Curie temperature TC in the manganites R12xAxMnO3 is closely correlated to the residual resistivity r 0 of the sample, suggesting that nonmagnetic randomness plays an important role in determining their anomalous properties. Using the one-parameter scaling theory to study the electronic localization due to both the nonmagnetic randomness and the double exchange spin disorder, we show that the sharp resistivity peak is caused by the Anderson metal-insulator ~M-I! transition and that r 0.r c ~a critical value! is a prerequisite to the occurrence of the M-I transition. TC as a function of r 0 has also been calculated. These results are in good agreement with experimental measurements. @S0163-1829~97!51836-4# The mixed-valence oxides R12xAxMnO3 ~where R5La, Nd, Pr; A5Ca, Sr, Ba, Pb! have recently been subjected to intense experimental 1‐10 and theoretical 11‐18 investigations because of a huge negative magnetoresistance ~colossal magnetoresistance or CMR! exhibited in samples of 0.2,x,0.5. For such a range of doping, the resistivity r vs temperature T curve usually exhibits a sharp peak at a certain temperature T p , indicating a crossover from metallic behavior (dr/dT.0) below T p to activated behavior ( dr/dT,0) above T p . The application of an external magnetic field strongly suppresses r and moves the resistivity peak to higher temperatures, thereby producing a CMR near T p .I t is generally accepted that the anomalous transport phenomena in these R 12x A x MnO 3 systems are closely related to their magnetic properties, in particular the paramagnetic ~PM!ferromagnetic ~FM! phase transition upon cooling. Most experimental measurements 1‐10 indicate that T p is very close to the Curie temperature TC , which is reminiscent of the double exchange ~DE! model 19 based on the exchange of electrons between Mn 31 and Mn 41 ions. For the Mn oxides, metallic ferromagnetism occurs in the composition range 0.2,x,0.5, where it is associated with the simultaneous presence of Mn 31 and Mn 41 ions. Each Mn 31 ion has four 3d electrons, three in the t 2g state and the fourth in the e g state. The Hund’s rule coupling is very strong so that spins of all the d electrons on a given site must be parallel. Three t 2g electrons are localized on the Mn site and give rise to a local spin S of magnitude 3/2, while the eg electron may hop into the vacant eg states of surrounding Mn 41 ions. Owing to the strong Hund’s rule coupling, the hopping of an eg electron between Mn 31 and Mn 41 sites is affected by the relative alignment of the local spins, being maximal when the localized spins are parallel and minimal when they are antiparallel. The sharp drop in r below TC can be attributed to the fact that an increase in the magnetization M upon cooling should reduce spin disorder scattering and thus increase the carrier conductivity. However, whether DE alone can account for the anomalous transport behavior is a question at issue. 13,16,17

The single-cluster coherent potential approximation (CPA) including off-diagonal coherent potential is applied to interdiffusional interfaces with correlated impurities. It is assumed that atoms on two monolayers nearest the interface may exchange between the two monolayers and within each monolayer so that there exist four kinds of atomic configurations in a two-atom cluster. In the presence of correlation the interfacial scattering rate is found to depend not only on the diagonal part of the coherent potential, but also on the off-diagonal part. Calculated results show that the correlation produces interfacial scattering which is more strongly spin dependent than the scattering in the bulk.

The conventional quasiclassical approach to magnetotransport in magnetic multilayers and magnetic granular solids is found to be suitable only for collinear magnetization configurations. A quantum treatment of electron spin is proposed to improve the quasiclassical theory to be applicable to arbitrary magnetization alignments, in which the electron distribution functions, as well as the electric fields and currents, need to be regarded as spinor matrices which are off-diagonal in spin space of conduction electrons. An extended Boltz- mann equation has been used to derive the two-point spinor conductivity in magnetic inhomogeneous systems. The result obtained is found to be identical to that obtained from the real-space Kubo formula, indicating a close link between the reformed quasiclassical approach and the quantum theory. Angular dependence of the current-in-plane magnetoresistance in magnetic superlattices is discussed.

We design a spintronic quantum eraser to quantitatively probe the two-electron entanglement. It is shown that the concurrence of two spin-entangled electrons is directly given by the Aharonov-Bohm oscillation amplitude of the Fano factor, a measurable current-current correlation, making it rather promising to experimentally quantify the two-electron entanglement. The singlet and triplet entangled states are distinguished by the opposite signs in the Fano factor. Since the main building blocks in the designed setup, an electronic Mach-Zehnder interferometer and a spin filter, have already been implemented, our proposal is particularly pertinent to experiments.

Using the quantum-statistical approach, we have developed a unified transport theory of metallic films. A general description for the conductivity in metallic films has been rigorously formulated in the presence of both impurity scattering and surface roughness. An explicit connection between the quasiclassical and present quantum approaches is also presented. We show that the quasiclassical theory by Fuchs [Proc. Cambridge Philos. Soc. 34, 100 (1938)] and Sondheimer [Adv. PHys. 1, 1 (1952)] can be reformed to be applicable to ultrathin metallic films by introducing a treatment of the surface via angle-dependent specularity parameters and including the quantum size effect. Moreover, to the lowest-order approximation in the theory, the previous quantum-approach results and discussions have naturally been recovered.

The molecules C{sub 59}{ital X} ({ital X}=B,N) are investigated by the extended Su-Schrieffer-Heeger model. The obtained results for the energy levels and molecular structures are compared with those from a self-consistent-field molecular-orbital (SCF-MO) method. We have found that by choosing suitable empirical parameters, most of the features included in the results of the SCF-MO method can be well reproduced. Other structural and electronic properties such as the excess electron density and the amplitude of the midgap states have also been studied.