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Exchange bias, a shift in the hysteresis loop of a ferromagnet arising from interfacial exchange coupling between adjacent ferromagnetic and antiferromagnetic layers, is an integral part of spintronic devices. Here, we show that spin–orbit torque generated from spin current, a promising approach to switch the ferromagnetic magnetization of next-generation magnetic random access memory, can also be used to manipulate the exchange bias. Applying current pulses to a Pt/Co/IrMn trilayer causes concurrent switching of ferromagnetic magnetization and exchange bias, but with different underlying mechanisms. This implies that the ferromagnetic magnetization and exchange bias can be manipulated independently. Our work demonstrates that spin–orbit torque in ferromagnet/antiferromagnet heterostructures facilitates independent manipulations of distinct magnetic properties, motivating innovative designs for future spintronics devices. Spin–orbit torque is used to control the magnetic exchange bias in a Pt/Co/IrMn trilayer.

This study demonstrates a mathematical description of a point-like nanocontact model, which is developed to simulate electron transport through a nanoconstriction between magnetic or non-magnetic contact sides. The theory represents a solution to the quasi-(semi)-classical transport equations for charge current, which takes into account second-order derivatives of the related quasi-classical Green functions along the transport direction. The theoretical approach also enables the creation of an I-V model for a heterojunction with embedded objects, where the initial condition, a conduction band minimum profile of the system, is well-defined. The presented spin-resolved current approach covers a complete range of the scales including quantum, ballistic, quasi-ballistic (intermediate), and diffusive classical transport conditions, with a smooth transition between them without residual terms or any empirical variables. The main benefit of the mathematical solution is its novel methodology, which is an alternative candidate to the well-known Boltzmann technique.

The work represents the theoretical modeling of the electrical conductance in the nanoscale interconnects within approach of the extended point-like contact (PC) model. The approach describes a diffusive, quasi-ballistic, ballistic and quantum regimes of the spinresolved conductance, that is important for the development of the heterojunction models, including 2D -3D interconnects. As a benefit, the model provides a unified description of the contact resistance from Maxwell diffusive through the ballistic to a purely quantum transport regimes without residual terms. The model of the PC assumes that the contact area can be replaced by a complex quantum device, e.g. single tunnel junction, narrow magnetic domain wall (DW), vacuum gap between tip and surface, source to drain transistor’s channel, etc. The potential energy landscape of the device determines its electrical properties.

We investigate pairing mechanism in multiband superconductors. To put our feet on firm ground, unbiased renormalization group analysis is carried out for iron-based superconductors. It is quite remarkable that, after integrating out quantum fluctuations, the renormalization-group flows agree exceedingly well with a mean-field Hamiltonian where interband pair hopping plays an essential role. Through interband pair hopping, electrons can overcome the repulsive interaction between them and form resonating Cooper pairs between different bands. Unlike the conventional superconductors, the pairing mechanism in multiband superconductors is resonating pair hopping between different bands, just like the resonating chemical bonds in benzene. The effective mean-field Hamiltonian spots a small parameter dictating the critical temperature and also explains how interband pair hopping always enahnces spin fluctuations at the nesting momentum connecting the Fermi surfaces. In short, no attractive glue is needed and resonating interband pair hopping is the key to Cooper pair formation in unconventional superconductors. Implications to cuprates and related issues are also discussed at the end., Comment: 4 pages, 4 figures, major revision

Error threshold is the upper bound of the mutation rate such that the genetic information can pass on during reproduction. In Eigen’s original proposal, the fitness landscape consists of a single peak along with other background sequences. However, realistic fitness landscapes are far more complicated and thus obstruct deeper understanding from either analytic or numerical approaches. Here we propose a variational approach to derive the error thresholds in generic fitness landscapes. When applying to the Eigen model, it delivers the correct error threshold and reveals the scaling relations between relevant parameters. For the fitness landscape with a peak–mesa profile, the two-dimensional phase diagram in the mesa fitness and the mutation rate can be computed with minimal cost. When the mesa fitness is larger than some critical value, upon increasing the mutation rate, the quasispecies changes from the peak to the mesa and then dissolves into the random background. The phase boundaries can be computed analytically within the effective-fitness approximation. At the end, the universal phase diagram in terms of the rescaled variables is explained in detail.

The role of electron-phonon interactions in iron-based superconductor is currently under debate with conflicting experimental reports on the isotope effect. To address this important issue, we employ the renormalization-group method to investigate the competition between electron-electron and electron-phonon interactions in these materials. The renormalization-group analysis shows that the ground state is a phonon-dressed unconventional superconductor: the dominant electronic interactions account for pairing mechanism while electron-phonon interactions are subdominant. Because of the phonon dressing, the isotope effect of the critical temperature can be normal or reversed, depending on whether the retarded intra- or inter-band interactions are altered upon isotope substitutions. The connection between the anomalous isotope effect and the unconventional pairing symmetry is discussed at the end.

Competitions between different interactions in strongly correlated electron systems often lead to exotic phases. Renormalization group is one of the powerful techniques to analyze the competing interactions without presumed bias. It was recently shown that the renormalization group transformations to the one-loop order in many correlated electron systems are described by potential flows. Here we prove several rigorous theorems in the presence of renormalization-group potential and find the complete classification for the potential flows. In addition, we show that the relevant interactions blow up at the maximal scaling exponent of unity, explaining the puzzling power-law Ansatz found in previous studies. The above findings are of great importance in building up the hierarchy for relevant couplings and the complete classification for correlated ground states in the presence of generic interactions.

The work represents the extended theoretical model of the electrical conductance in nanoscale magnetic point-like contacts. The developed approach describes diffusive, quasi-ballistic, ballistic and quantum regimes of the spin-resolved conductance that is important for further development of the contact Andreev reflection spectroscopy, heterojunction models, scanning tunnel microscopy techniques. As a benefit, the model provides a unified description of the contact resistance from Maxwell diffusive through the ballistic to purely quantum transport regimes without residual terms. The model of the point contact assumes that the contact area can be replaced by a complicated object (i.e. the tunnel barrier or complicated one with nanoparticles, narrow domain wall, etc.), where the potential energy profile determines its electrical properties. The model can be easily adapted to particular contact materials, its physical properties and species of the contact area.

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Simulation results are given for electron tunneling through the insulating layer of a magnetic tunnel junction with embedded nonmagnetic nanoparticles (NPs). The size dispersion of the NPs was an important part of the solution for tunnel magnetoresistance, which was calculated on the basis of the double-barrier model. Theoretical agreement with experimental data was achieved by adjusting the NP dispersion and quantization. A step-like quantization related to the initial distribution of the electrons over quantum-well states was considered for different size NPs.

The problem of the ballistic electron tunneling is considered in magnetic tunnel junction with embedded non-magnetic nanoparticles (NP-MTJ), which creates additional conducting middle layer. The strong temperature impact was found in the system with averaged NP diameter dav dav ≈ 1.8 nm) between quantum well and bulk-assisted states of the middle layer.

In our previous study, a single-branch of ferromagnetic magnon with linear dispersion is shown to exist near the (uncompensated) zigzag edge for Heisenberg model on honeycomb lattice. Here we develop a field-theory description for the edge magnon and find its dynamics is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart, described by the two-dimensional Klein-Gordon equation. Furthermore, we also reveal how the parity symmetry relates evanescent modes on opposite edges in a honeycomb nanoribbon. By employing alternative methods, including Schwinger bosons and density-matrix renormalization group, we also demonstrate that the relativistic edge magnon is robust even when the Neel order in the bulk is destroyed by quantum fluctuations. The edge magnon is a direct consequence of uncompensated edge and may be verified in realistic materials by experimental probes., Comment: 4 pages, 3 figures

The simulation is done for electron tunneling through the insulating layer of the magnetic tunnel junction with non-magnetic embedded nanoparticles (npMTJs). The distribution of the nanoparticles by size (DNPS) was important part of the solution for tunnel magnetoresistance (TMR) which was calculated on the basement of the double barrier tunneling model. It was found that theoretical agreement with experimental data can be influenced not only from DNPS but also due to different cases of the quantization. A few cases of the quantization related with a redistribution over quantum well (QW) states of the nanoparticles (NPs) (with diameter d) were considered (one of the possible DNPS and related TMR is shown in Fig. 1a and Fig. 1b).

By engineering multidomain formation in Co/Pt multilayers, it is demonstrated how multilevel storage can be achieved by spin-orbit torque switching. It is rather remarkable that, by modulating the writing pulse conditions, the final magnetization states can be controlled, independent of the initial configurations. The initialization-free multilevel memory advances the spin-orbit-torque magnetic random access memory to higher storage density for practical applications.

We investigate the carrier-mediated exchange coupling between two ferromagnets, sandwiching an intermediate thin layer with Rashba interaction. The effective exchange coupling is obtained by integrating out the itinerant carriers. It turns out that the magnetic trends depend sensitively upon the topology of the Fermi surface. As the topology changes from “wedding cake” to “donut”, the mediated exchange goes from the oscillatory Ruderman-Kittel-Kasuya-Yosida to the non-collinear spiral interactions accordingly. It is rather surprising that the Fermi surface topology determines which type of magnetic interaction becomes dominant. Finally, we also discuss potential applications for carrier-mediated exchange coupling across the junction.

Magnetic patterning, with designed spatial profile of the desired magnetic properties, has been a rising challenge for developing magnetic devices at nanoscale. Most existing methods rely on locally modifying magnetic anisotropy energy or saturation magnetization and thus post stringent constraints on the adaptability in diverse applications. We propose an alternative route for magnetic patterning: by manipulating the local intergranular exchange coupling to tune lateral magnetic properties. As demonstration, the grain boundary structure of Co/Pt multilayers is engineered by thermal treatment, where the stress state of the multilayers and thus the intergranular exchange coupling can be modified. With Ag passivation layers on top of the Co/Pt multilayers, we can hinder the stress relaxation and grain boundary modification. Combining the pre-patterned Ag passivation layer with thermal treatment, we can design spatial variations of the magnetic properties by tuning the intergranular exchange coupling, which diversifies the magnetic patterning process and extends its feasibility for varieties of new devices.

Evolutionary dynamics is captured by replicator equations when populations are well mixed. However, in realistic ecosystems, competitions often occur between neighbors and the spatial structure of the system is of significant importance. In most evolutionary algorithms, the dynamics of local death/birth processes often relies on the effective fitness: a global knowledge of the whole ecosystem. To make the spatial game theory logically consistent, it is desirable to introduce an algorithm where only local information is necessary. Here we resolve the challenge by introducing the three-party Reference-Gamble-Birth (RGB) algorithm. For the well-mixed case, the RGB algorithm reproduces the replicator equations in the large population limit. We also apply the RGB algorithm on the rock-paper-scissor game to demonstrate how the ecological stability sensitively depends on the spatial structures. The proposed RGB algorithm is not limited to cyclically competing systems and can be applied to various spatial games with different network structures.

We study the Andreev edge state on the semi-infinite triangular lattice with different pairing symmetries and boundary topologies. We find a rich phase diagram of zero energy Andreev edge states that is a unique fingerprint of each of the possible pairing symmetries. We propose to pin down the pairing symmetry in recently discovered Na_xCoO_2 material by the Fourier-transformed scanning tunneling spectroscopy for the edge state. A surprisingly rich phase diagram is found and explained by a general gauge argument and mapping to 1D tight-binding model. Extensions of this work are discussed at the end.

We present a theory of carrier-induced ferromagnetism in diluted magnetic semiconductors (III,Mn)V which allows for arbitrary itinerant-carrier spin polarization and dynamic correlations. Both ingredients, which are absent in an RKKY description, are essential in identifying the system's elementary excitations and describing their properties. We find a branch of gapped collective modes, in addition to the spin waves and Stoner continuum which occur in metallic ferromagnets. We determine the low-temperature spin stiffness and derive, in different regimes, its dependence on the exchange coupling between magnetic ions and free carriers, as well as on the effective band mass.

We study the Andreev bound states with different pairing symmetries and boundary topologies on semi-infinite triangular lattice of the sodium cobalt oxide. A general mapping from the two dimensional lattice to the one-dimensional tight-binding model is developed. Due to the hidden structure of these effective one-dimensional models, the Andreev bound states can be categorized into the positive and negative Witten parity states in supersymmetric algebra. By solving these parity states, the momentum-resolved local density of states near the edge is revealed and can be used to predict the position of the sharp peaks that can be observed in FT-STS experiments.

We analyze a model of resonant point-contact tunneling between multiple Luttinger-liquid leads. The model is a variant of the multichannel Kondo model and can be related to the quantum Brownian motion of a particle on lattices with $\ensuremath{\pi}$ flux through each plaquette (in the three-lead case, it is a honeycomb lattice with $\ensuremath{\pi}$ flux). By comparing the perturbative and instanton gas expansions, we find a duality property of the model. At the boundary, this duality exchanges Neumann and Dirichlet boundary conditions on the Tomonaga-Luttinger bosons, which describe the leads; in the bulk, it exchanges the ``momentum'' and ``winding'' modes of these bosons. Over a certain range of Luttinger-liquid parameter g, a nontrivial intermediate coupling fixed-point controls the low-energy physics. The finite conductance at this fixed point can be exactly computed for two special values of g. For larger values of g, there is a stable fixed point at strong coupling that has enhanced conductance resulting from an analogue of Andreev reflection at the point contact.

We study the non-collinear exchange coupling across the trilayer magnetic junction composed of an intermediate layer with Rashba interaction and two sandwiching ferromagnetic ones. To compute the mediated exchange coupling between the ferromagnetic layers, one needs to go beyond the single-particle argument and numerically integrates over contributions from the whole Fermi surface. We found interesting competition between the oscillatory Ruderman–Kittel–Kasuya–Yosida and the non-collinear spiral interactions. Surprisingly, the Fermi surface topology determines which type of magnetic interaction becomes dominant. Finally, we also discuss potential applications for the non-collinear exchange coupling across the junction.

Single-wall carbon nanotubes with on-site interaction $U \ll t$ are studied by a controlled renormalization group method. When formulated as a system of $N_{f}$ flavors of interacting Dirac fermions, the effective model at generic filling resembles a set of quasi-1D Hubbard chains. For the undoped $(N_{y}, N_{y})$-armchair and the $(N_{x}, -N_{x})$-zigzag with $N_x=3n$, specific mappings to the 2-chain Hubbard model at half filling with effective interaction $u_{eff}=U/N_{y}$ and $2U/N_{x}$ are found from this more general equivalence. The phase diagrams of the (3, 3)-armchair and the (6, -6)-zigzag at generic fillings are studied and compared as an example., Comment: 9 pages, 5 figures, title changed

We study the effect of an ac drive on the current-voltage (I-V) characteristics of a tunnel junction between two fractional Quantum Hall fluids at filling $\nu ^{-1}$ an odd integer. Within the chiral Luttinger liquid model of edge states, the point contact dynamics is described by a driven damped quantum mechanical pendulum. In a semi-classical limit which ignores electron tunnelling, this model exhibits mode-locking, which corresponds to current plateaus in the I-V curve at integer multiples of $I= e\omega /2\pi$, with $\omega$ the ac drive angular frequency. By analyzing the full quantum model at non-zero $\nu$ using perturbative and exact methods, we study the effect of quantum fluctuation on the mode-locked plateaus. For $\nu=1$ quantum fluctuations smear completely the plateaus, leaving no trace of the ac drive. For $\nu \ge 1/2$ smeared plateaus remain in the I-V curve, but are not centered at the currents $I=n e \omega /2\pi$. For $\nu < 1/2$ rounded plateaus centered around the quantized current values are found. The possibility of using mode locking in FQHE point contacts as a current-to-frequency standard is discussed., Comment: 12 pages, 8 figures, minor changes

To address thermal stability issues for spintronic devices with a reduced size, we investigate spin-orbit torque in Co/Pt multilayers with strong perpendicular magnetic anisotropy. Note that the spin-orbit torque arises from the global imbalance of the spin currents from the top and bottom interfaces for each Co layer. By inserting Ta or Cu layers to strengthen the top-down asymmetry, the spin-orbit torque efficiency can be greatly modified without compromised perpendicular magnetic anisotropy. Above all, the efficiency builds up as the number of layers increases, realizing robust thermal stability and high spin-orbit-torque efficiency simultaneously in the multilayers structure.

We study correlation effects due to the short-range interactions in the single-wall carbon nanotube. Detailed phase diagrams in weak coupling for (un-)doped nanotubes are obtained and compared to the phases in strong coupling. If the range of the interaction is much larger than the circumference of the nanotube, a new phase arises with the power-law correlations of the kinetic energy across the rungs between different sublattices of the honeycomb.

In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the divergent logarithmic length $l_d$ and a set of renormalization-group exponents, also works rather well. The superconducting phases in a doped two-leg ladder are studied and classified by these renormalization-group exponents as demonstration. Finally, non-trivial constraints among the exponents are derived and explained., 4 pages, 3 figures; minor revisions with references added

The phase diagram for the interacting fermions in weak coupling is described by the perturbative renormalization group equations. Due to the lack of analytic solutions for these coupled non-linear differential equations, it is rather subtle to tell which couplings are relevant or irrelevant. We propose a powerful classification scheme to build up the hierarchy of the relevant couplings by a scaling Ansatz found numerically. To demonstrate its superiority over the conventional classification for the relevant couplings, we apply this scheme to a controversial phase transition in the two-leg ladder and show that it should be a non-trivial crossover instead. The scaling Ansatz we propose here can classify the relevant couplings in hierarchical order without any ambiguity and can improve significantly how we interpret the numerical outcomes in general renormalization group methods., 5 pages, 3 figures

Defects in graphene give rise to zero modes that are often related to the sharp peak in the local density of states near the defect site. Here we solved all zero modes induced by a single defect in the finite-size graphene and show that their contributions to the local density of states vanish in the thermodynamic limit. Instead, lots of resonant states emerge at low energies and eventually lead to a power-law singularity in the local density of states. Our findings show that the impurity problem in graphene should be treated as a collective phenomenon rather than a single impurity state.

Carrier-mediated exchange coupling, known as Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a fundamental role in itinerant ferromagnetism and has great application potentials in spintronics. A recent theorem based on the imaginary-time method shows that the oscillatory RKKY interaction becomes commensurate on bipartite lattice and predicts that the effective exchange coupling is always ferromagnetic for the same sublattice but antiferromagnetic for opposite sublattices. We revisit this important problem by real- and imaginary-time methods and find that the theorem misses important contributions from zero modes. To illustrate the importance of zero modes, we study the spin susceptibility in graphene nanoribbons numerically. The effective exchange coupling is largest on the edges but does not follow the predictions from the theorem.

We derive a Hamiltonian for a two-leg ladder which includes an arbitrary number of charge and spin interactions which must be weak but are otherwise of arbitrary strength. To illustrate this Hamiltonian we consider two examples and use a renormalization-group technique to evaluate the ground-state phases. The first example is a two-leg ladder with zigzagged legs. We find that increasing the number of interactions in such a two-leg ladder may result in a richer phase diagram, particularly at half-filling where a few exotic phases are possible when the number of interactions are large and the angle of the zigzag is small. In the second example we determine under which conditions a two-leg ladder at quarter-filling is able to support a Tomanaga-Luttinger liquid phase. We show that this is only possible when the spin interactions across the rungs are ferromagnetic. In both examples we focus on lithium purple bronze, a two-leg ladder with zigzagged legs which is thought to support a Tomanaga-Luttinger liquid phase.

We investigate transport through a single impurity in metallic zigzag carbon nanotube and find the conductance sensitively depends on the impurity strength and the bias voltage. It is rather interesting that interplay between the current-carrying scattering state and evanescent modes leads to rich phenomena including resonant backward scattering, perfect tunneling and charge accumulations. In addition, we also find a dual relation between the backscattered conductance and the charge accumulation. At the end, relevance to the experiments is discussed., 3 pages, 3 figures

We revisit correlation effects in doped metallic zigzag carbon nanotubes by using both the one-loop renormalization group and non-perturbative bosonization techniques. Note that, if a nanotube is placed near a conducting plate, the long-range Coulomb interactions are screened and the resulting short-range interactions can be modelled by on-site and nearest-neighbor repulsive interactions $U$, $V$ and $V_{\perp}$ respectively. Using both analytic and numeric means, we determine the phase diagram of the ground states. For $U/t, 7 pages, 4 figures

Due to the weak spin-orbit interaction and the peculiar relativistic dispersion in graphene, there are exciting proposals to build spin qubits in graphene nanoribbons with armchair boundaries. However, the mutual interactions between electrons are neglected in most studies so far and thus motivate us to investigate the role of electronic correlations in armchair graphene nanoribbon by both analytical and numerical methods. Here we show that the inclusion of mutual repulsions leads to drastic changes and the ground state turns ferromagnetic in a range of carrier concentrations. Our findings highlight the crucial importance of the electron-electron interaction and its subtle interplay with boundary topology in graphene nanoribbons. Furthermore, since the ferromagnetic properties sensitively depends on the carrier concentration, it can be manipulated at ease by electric gates. The resultant ferromagnetic state with metallic conductivity is not only surprising from an academic viewpoint, but also has potential applications in spintronics at nanoscale., Comment: 10 pages, 5 figures

We study the exchange coupling mediated by itinerant carriers with spin-orbit interaction by both analytic and numeric approaches. The mediated exchange coupling is non-collinear and its spatial trends depend on the Fermi surface topology of the itinerant carriers. Taking Rashba interaction as an example, the exchange coupling is similar to the conventional Ruderman-Kittel-Kasuya-Yosida type in weak coupling. On the other hand, in the strong coupling, the spiral interaction dominates. In addition, inclusion of finite spin relaxation always makes the non-collinear spiral exchange interaction dominant. Potential applications of our findings are explained and discussed., Comment: 9 pages, 7 figures

Ferromagnetism above room temperature was observed in Cr-doped hydrogenated amorphous silicon films deposited by rf magnetron-sputtering. Structure analysis reveals that films are amorphous without any detectable precipitates up to the solubility limit 16 atomic percentages of Cr. Experimental results suggest that hydrogenation has a dramatic influence on magnetic properties, electrical conductivity and carrier concentration in the thin films. Pronounced anomalous Hall effect and magnetization curve both suggest the origin of the ferromagnetism may arises from percolation of magnetic polarons., Comment: 3 pages, 4 figures

Recently, Andreev bound states in iron pnictide have been proposed as an experimental probe to detect the relative minus sign in the $s_\pm$-wave pairing. While previous theoretical investigations demonstrated the feasibility of the approach, the local density of states in the midgap regime is small, making the detection hard in experiments. We revisit this important problem from the Bogoliubov-de Gennes Hamiltonian on the square lattice with appropriate boundary conditions. Significant spectral weights in the midgap regime are spotted, leading to easy detection of the Andreev bound states in experiments. Peaks in the momentum-resolved local density of states appear and lead to enhanced quasiparticle interferences at specific momenta. We analyze the locations of these magic spots and propose they can be verified in experiments by the Fourier-transformed scanning tunneling spectroscopy., Comment: 5 pages, 3 figures

We study the Andreev edge states with different pairing symmetries and boundary topologies on semi-infinite triangular lattice of ${\text{Na}}_{x}{\text{CoO}}_{2}\ensuremath{\cdot}y{\text{H}}_{2}\text{O}$. A general mapping from the two-dimensional lattice to the one-dimensional tight-binding model is developed. It is shown that the phase diagram of the Andreev edge states depends on the pairing symmetry and also on the boundary topology. Surprisingly, the structure of the phase diagram crucially relies on the nodal points on the Fermi surface and can be explained by an elegant gauge argument. We compute the momentum-resolved local density of states near the edge and predict the hot spots which are measurable in Fourier-transformed scanning tunneling spectroscopy.

We study the spin-wave excitations near the zigzag edge of graphene. It is rather interesting that we obtain a single branch of relativistic ferromagnetic magnon due to the presence of the open boundary. Note that magnons in antiferomagnets appear in pairs, while the single brach magnon in ferromagnets does not have relativistic dispersion. Thus, the magnon near the zigzag edge of graphene is a hybrid of both, signaling its intrinsic property as a boundary excitation that must be embedded in a higher dimensional bulk system., 4 pages, 3 figures

We investigate a metallic zigzag carbon nanotube by means of a Hubbard model which includes both on-site and nearest neighbour interactions. Assuming weak interactions, a renormalization group analysis of the equivalent two-leg ladder followed by bosonization and refermionization results in a Gross-Neveu model with an enlarged symmetry relative to the original Hamiltonian. For the undoped case the symmetry of the Gross-Neveu model is SO(8), but for the doped case the particle-hole symmetry is broken and the symmetry reduces to SO(6). Four ground state phases are found in the undoped carbon nanotube with repulsive interactions, a d-wave Mott insulator, an s-wave Mott insulator, a p-density wave and a charge density wave. The doped case has two ground state phases, a d-wave superconductor and a phase where a p-density wave and a charge density wave co-exist. We also explore the global phase diagram with a general interaction profile and find several additional states, including a chiral current phase where current flows around the nanotube along the zigzag bonds., 16 pages, 9 figures

Employing the self-consistent Green's function approach, we studied the temperature dependence of the spin-wave stiffness in diluted magnetic semiconductors. Note that the Green's function approach includes the spatial and temperature fluctuations simultaneously which was not possible within conventional Weiss mean-field theory. It is rather interesting that we found the stiffness becomes dramatically softened as the critical temperature is approached, which seems to explain the mysterious sharp drop of magnetization curves in samples within diffusive regime., 4 pages, 1 figure

We studied the interlayer coupling in the quadrilayer consisting of IrMn/CoFe (bottom layer)/NiFeOx/ CoFe (top layer). The in-plane perpendicular interlayer coupling is observed between CoFe layers at room temperature. An anisotropy transition from uniaxial to unidirectional in the perpendicular direction is observed around Tt = 55 K. The nano-oxide layer NiFeOx shows no distinguishable ferromagnetic signal in the high-temperature (uniaxial) phase, while a strong signal appeared in the low-temperature (unidirectional) phase. A possible two-component scenario, that the nano-oxide layer may contain both amorphous short-range antiferromagnetic domains and superparamagneitc clusters, is proposed to explain the phase transition., final version to appear in Applied Physics Letters