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Layered narrow band gap semiconductor Bi2Se3 is composed of heavy elements with strong spin-orbital coupling (SOC), which has been identified both as a good candidate of thermoelectric material of high thermoelectric figure-of-merit (ZT) and a topological insulator of Z2-type with a gapless surface band in Dirac cone shape. The existence of a conjugated pi-bond system on the surface of each Bi2Se3 quintuple layer is proposed based on an extended valence bond model having valence electrons distributed in the hybridized orbitals. Supporting experimental evidences of a 2D conjugated pi-bond system on each quintuple layer of Bi2Se3 are provided by electron energy-loss spectroscopy (EELS) and electron density (ED) mapping through inverse Fourier transform of X-ray diffraction data. Quantum chemistry calculations support the pi-bond existence between partially filled 4pz orbitals of Se via side-to-side orbital overlap positively. The conjugated pi-bond system on the surface of each quintuple Bi2Se3 layer is proposed being similar to that found in graphite (graphene) and responsible for the unique 2D conduction mechanism. The van der Waals (vdW) attractive force between quintuple layers is interpreted being coming from the anti-ferroelectrically ordered effective electric dipoles which are constructed with pi-bond trimer pairs on Se-layers across the vdW gap of minimized Coulomb repulsion., Comment: 12 pages, 9 figures, to be published in Phys. Rev. Materials

The nature of Na ion distribution, diffusion path, and the spin structure of $P2$-type Na$_2$Ni$_2$TeO$_6$ with a Ni honeycomb network has been explored. The nuclear density distribution of Na ions reveals a 2D chiral pattern within Na layers without breaking the original 3D crystal symmetry, which has been achieved uniquely via an inverse Fourier transform (iFT)-assisted neutron diffraction technique. The Na diffusion pathway described by the calculated iso-surface of Na ion bond valence sum (BVS) map is found consistent to a chiral diffusion mechanism. The Na site occupancy and Ni$^{2+}$ spin ordering were examined in detail with the electron density mapping, neutron diffraction, magnetic susceptibility, specific heat, thermal conductivity and transport measurements. Signatures of both strong incommensurate (ICM) and weak commensurate (CM) antiferromagnetic (AFM) spin ordering were identified in the polycrystalline sample studied, and the CM-AFM spin ordering was confirmed by using a single crystal sample through the $k$-scan in the momentum space corresponding to the AFM peak of ($\frac{1}{2}$, 0, 1)., 9 pages, 8 figures

The peculiar field-dependent magnetism of Na0.82CoO2 has been investigated through an analysis of its DC and AC spin susceptibilities. To account for the easily activated narrow b2g-a1g gap of the crystal field for Co in the cobalt oxide layer, the spin-state transition of Co3+ (3d6) between the low spin (LS) state b2g^2-a1g^0 of S=0 and the intermediate spin (IS) state b2g^1-a1g^1 of S=1 is thus seen as thermally activated and exhibits a Boltzmann distribution. The IS state of Co3+ within each sqrt(13a) hexagonal superlattice formed by the S=1/2 state of the Co4+ ions appears randomly within each supercell and shows significant temperature and field dependence. The magnetic field is found to assist in pinning down the thermally activated state of Co3+ and swings the Boltzmann distribution weight toward a higher fraction of the IS state. The field dependence of the in-plane magnetic moment from the added number of S=1 spins is used to explain the origin of A-type antiferromagnetic (AF) ordering, particularly that the ferromagnetic (FM)-like behavior below TN at low field is actually a ferrimagnetic IS spin ordering of Co3+., Comment: 5 pages, 4 figures, to be published in PRB

The B20 magnets with the Dzyaloshinskii-Moriya (D-M) interaction exhibit spin helix and Skyrmion spin textures unattainable in traditional Heisenberg ferromagnets. We have determined the intrinsic resistivity of the spin helix, which is a macroscopic Bloch domain wall, in B20 (Fe-Co)Si magnets. We found a universal resistance ratio of gamma = 1.35 with current parallel and perpendicular to the helix, independent of composition and temperature. This gamma value is much smaller than 3, the well-known minimum value for domain wall resistivity in traditional ferromagnets, due to the significant spin-orbit coupling in the B20 magnets.

The B20 chiral magnets with broken inversion symmetry and C4 rotation symmetry have attracted much attention. The broken inversion symmetry leads to the Dzyaloshinskii-Moriya that gives rise to the helical and Skyrmion states. We report the unusual magnetoresistance (MR) of B20 chiral magnet Fe0.85Co0.15Si that directly reveals the broken C4 rotation symmetry. We present a microscopic theory, a minimal theory with two spin-orbit terms, that satisfies all the symmetry requirements and accounts for the transport experiments.

The magnetic moment per Co4+ of P2(gamma)-type NaxCoO2 in Curie-Weiss metal regime is revisited and examined under a newly proposed modification of the octahedral crystal electric field (CEF). The proposed model explains the origin of the existence of the intermediate state S=1 for Co3+ through an exciton-like elementary excitation of the narrow gap between the split eg and t2g groups. The CoO2 layer is proposed to be constructed from the tilted edge-sharing square-planar CoO2 chains with inter-chain coupling. The square-planar CEF of CoO2 requires covalent bond formation between Co and the four in-plane neighboring oxygens, while the oxygens sitting in the neighboring chains can be viewed as apical oxygens of low effective charge for a CoO6 pseudo-octahedron. The reason why angle-resolved photoemission spectroscopy (ARPES) failed to observe the local-density approximation (LDA) predicted e'g hole pockets at kz=0 and the reversed order of the t2g splittings between LDA and CEF calculations can also be resolved using the proposed model., 5 pages, 6 figures, to be published in PRB

Chemical bond analysis for the topological insulator (TI) Bi2Se3 following valence bond theory and VSEPR rule is proposed and compared to that of graphene. The existence of pi-bond trimers on surface Se-layer is revealed to be responsible for the unusual 2D surface conduction found in the prototype Z2 topological insulator Bi2Se3, which shows great similarity to the ideal "surface-only" 2D material graphene with surface band in Dirac cone shape. The pi-bond trimers on the surface of TI form a dynamic pi-bond conjugated system of implicit chirality. Local pi-bond energy exchange in cross-bridge model is proposed responsible for the unique 2D surface conduction for topological insulator Bi2Se3, and the similar low dimensional conduction mechanism can also be identified in graphene and conductive polymers. Preliminary supporting evidence for the existence of pi-bonds is provided by the commonly assigned pi plasmon for the spectral feature near 7 eV in graphite and Bi2Se3 using electron energy-loss spectroscopy (EELS)., 5 pages, 5 figures

Plasmons dispersion and nonvertical interband transitions in Bi2Se3 single crystals were investigated by electron energy-loss spectroscopy in conjunction with (scanning) transmission electron microscopy, (S)TEM-EELS. Both volume plasmons ({\pi} plasmon at 7 eV and {\pi}+{\sigma} plasmon at 17 eV) and surface plasmons (~5.5 and 10 eV) were demonstrated in STEM-EELS spectra and the corresponding spectral imaging in real space. In the further EELS experiments in reciprocal space, the momentum-dependent spectra reveal very different dispersion behavior between {\pi} and {\pi}+{\sigma} plasmons, with {\pi}+{\sigma} plasmons showing a typical quadratic dependence whereas the {\pi} plasmon exhibiting a linear dispersion analogous to what was reported for graphene. Furthermore, a low energy excitation 0.7~1.6 eV was also observed which is attributed to direct nonvertical interband transitions along the gamma-F direction.

In the spin ladder compound BiCu$_2$PO$_6$ there exists a decisive dynamics of spin excitations that we classify and characterize using inelastic light scattering. We observe low-energy singlets and a broad triplon continuum extending from 36 cm$^{-1}$ to 700 cm$^{-1}$ in ($aa$), ($bb$), and ($cc$) light scattering polarizations. Though isolated spin ladder physics can roughly account for the observed excitations at high energies, frustration and interladder interactions need to be considered to fully describe the spectral distribution and scattering selection rules at low and intermediate energies. More significantly, an interladder singlet bound mode at 24 cm$^{-1}$, lying below the continuum, shows its largest scattering intensity in interladder ($ab$) polarization. In contrast, two intraladder bound states at 62 cm$^{-1}$ and 108 cm$^{-1}$ with energies comparable to the continuum are observed with light polarization along the leg ($bb$) and the rung ($cc$). We attribute the rich spectrum of singlet bound modes to a melting of a dimer crystal. Our study provides evidence for a Z$_2$ quantum phase transition from a dimer to a resonating valence bond state driven by singlet fluctuations., Comment: 14 pages, 4 figures, Accepted for publication in PRL

Electronic phase diagram of LixCoO2 has been re-examined using potentiostatically de-intercalated single crystal samples. Stable phases of x ~ 0.87, 0.72, 0.53, 0.50, 0.43, and 0.33 were found and isolated for physical property studies. A-type and chain-type antiferromagnetic orderings have been suggested from magnetic susceptibility measurement results in x ~ 0.87 and 0.50 below ~ 10 K and 200 K, respectively, similar to those found in NaxCoO2 system. There is no Li vacancy superlattice ordering observed at room temperature for the electronically stable phase Li0.72CoO2 as revealed by synchrotron X-ray Laue diffraction. The peculiar magnetic anomaly near ~ 175 K as often found in powder samples of x ~ 0.46-0.78 cannot be isolated through this single crystal potentiostatic method, which supports the previously proposed explanation to be surface stabilized phase of significant thermal hysteresis and aging character., 9 pages, 9 figures, 1 table

A hybrid orbital model for the topological insulator Bi2Se3 is proposed and compared to that of graphene. The existence of a pi-bond trimer on the Se1 layer at the van der Waals gap and on the surface is thought to be responsible for the unusual surface conduction mechanism found in Bi2Se3 as a topological insulator. The three pi-bonds are locked as permanent electric dipoles between the Se1 layers in the van der Waals gap as an attractive force for the bulk as a gapped semiconductor. In contrast, the pi-bond trimers on the surface are unlocked and exhibit two degenerate quantum states, creating a local charge transfer mechanism in the cross-bridge model that is responsible for the surface conduction. The role of pi-bonds on the Bi2Se3 surface is compared with that in graphene for a similar 2D band structure containing Dirac cones., Comment: 6pages, 6figures

The existence of pi-bonds on topological insulator surfaces is found to be closely related to the phenomena of surface conduction and surface band spin polarization. A pi-bond trimer or pi-bond dimer on the surface can form open conjugated systems that are responsible for the unique surface conduction mechanism of a topological insulator. Parity operation in 2D is identified for a pi-bond trimer within a six-fold symmetry coordination and a pi-bond dimer within a four-fold symmetry coordination. Spontaneous 2D parity symmetry breaking is found to be closely related to the theoretically predicted pi Berry's phase and the observed surface band spin polarization. The role of pi-bonds on a cleaved Bi2Se3 surface is compared to that for graphene with a 2D band structure containing Dirac cones. Similar pi-bond dimers within a four-fold 2D symmetry coordination can also be identified in strained alpha-Sn of diamond structure as a theoretically predicted topological insulator., Comment: 5pages, 6figures

The impact of oxygen deficiency on physical properties of Na2/3CoO2-x has been investigated. From the combined thermogravimetric, magnetic susceptibility and synchrotron X-ray Laue diffraction studies, it is demonstrated that Na2/3CoO2 shows no superlattice ordering due to Na ions; however Na2/3CoO1.98, which has the same Co valence as that of Na0.71CoO2, shows nearly identical magnetic and transport properties and the same simple hexagonal superlattice ordering of sqrt(12)a. It is proposed that the Na ion ordering found in Na2/3CoO1.98 is identical to the ideal Na0.71CoO2 of large sqrt(12)a x sqrt(12)a x 3c superlattice but with additional Na vacancies which are bound to the oxygen defects at room temperature. We conclude that oxygen vacancies play a key role in stabilizing the superlattice structure and must be accounted for in its modeling., This paper has been withdrawn by the author due to we can directly change our old version of 1005.2529

The impact of oxygen deficiency on physical properties of Na2/3CoO2-x has been investigated. From the combined thermogravimetric, magnetic susceptibility and synchrotron X-ray Laue diffraction studies, it is demonstrated that Na2/3CoO2 shows no superlattice ordering due to Na ions; however Na2/3CoO1.98, which has the same Co valence as that of Na0.71CoO2, shows nearly identical magnetic and transport properties and the same simple hexagonal superlattice ordering of sqrt(12)a. It is proposed that the Na ion ordering found in Na2/3CoO1.98 is identical to the ideal Na0.71CoO2 of large sqrt(12)a x sqrt(12)a x 3c superlattice but with additional Na vacancies which are bound to the oxygen defects at room temperature. We conclude that oxygen vacancies play a key role in stabilizing the superlattice structure and must be accounted for in its modeling., Comment: 5 pages, 4 figures

Hexagonal superlattice formed by sodium multi-vacancy cluster ordering in Na$_{0.77}$CoO$_2$ has been proposed based on synchrotron X-ray Laue diffraction study on electrochemically fine-tuned single crystals. The title compound sits closely to the proposed lower end of the miscibility gap of x ~ 0.77-0.82 phase separated range. The average sodium vacancy cluster size is estimated to be 4.5 Na vacancies per layer within a large superlattice size of sqrt{19}a*sqrt{19}a*3c. The exceptionally large Na vacancy cluster size favors large twinned simple hexagonal superlattice of sqrt{19}a, in competition with the smaller di-, tri- and quadri-vacancy clusters formed superlattices of sqrt{12}a and sqrt{13}a. Competing electronic correlations are revealed by the observed spin glass-like magnetic hysteresis below ~ 3K and the twin, triple and mono domain transformations during thermal cycling between 273-373K., 7 pages, 6 figures

Phase diagram of Na$_x$CoO$_2$ (x $\gtrsim$ 0.71) has been reinvestigated using electrochemically fine tuned single crystals. Both phase separation and staging phenomena as a result of sodium multi-vacancy cluster ordering have been found. Phase separation phenomenon is observed in the narrow ranges of 0.76 $\lesssim$ x $\lesssim$ 0.82 and 0.83 $\lesssim$ x $\lesssim$ 0.86. While x = 0.820 shows A-type antiferromagnetic (A-AF) ordering below 22K, x = 0.833 is confirmed to have a magnetic ground state of A-AF ordering below $\sim$8K and is only reachable through slow cooling. In addition, x = 0.859 is found to be responsible for the highest A-AF transition temperature at about 29K. Staging model based on ordered stacking of multi-vacancy layers is proposed to explain the hysteretic behavior and A-AF correlation length for x $\sim$ 0.82-0.86., 6 pages, 6 figures, to be published in PRB

The sodium cobaltate family (NaxCoO2) is unique among transition metal oxides because the Co sits on a triangular lattice and its valence can be tuned over a wide range by varying the Na concentration x. Up to now detailed modeling of the rich phenomenology (which ranges from unconventional superconductivity to enhanced thermopower) has been hampered by the difficulty of controlling pure phases. We discovered that certain Na concentrations are specially stable and are associated with superlattice ordering of the Na clusters. This leads naturally to a picture of co-existence of localized spins and itinerant charge carriers. For x = 0.84 we found a remarkably small Fermi energy of 87 K. Our picture brings coherence to a variety of measurements ranging from NMR to optical to thermal transport. Our results also allow us to take the first step towards modeling the mysterious ``Curie-Weiss'' metal state at x = 0.71. We suggest the local moments may form a quantum spin liquid state and we propose experimental test of our hypothesis., 16 pages, 5 figures

We report on the preparation and characterization of single crystal gamma phase NaxCoO2 with 0.25 < x < 0.84 using a non-aqueous electrochemical chronoamperemetry technique. By carefully mapping the overpotential versus x (for x < 0.84), we find six distinct stable phases with Na levels corresponding to x ~ 0.75, 0.71, 0.50, 0.43, 0.33 and 0.25. The composition with x ~0.55 appears to have a critical Na concentration which separates samples with different magnetic behavior as well as different Na ion diffusion mechanisms. Chemical analysis of an aged crystal reveals different Na ion diffusion mechanisms above and below x_c ~ 0.53, where the diffusion process above x_c has a diffusion coefficient about five times larger than that below x_c. The series of crystals were studied with X-ray diffraction, susceptibility, and transport measurements. The crystal with x = 0.5 shows a weak ferromagnetic transition below T=27 K in addition to the usual transitions at T = 51 K and 88 K. The resistivity of the Curie-Weiss metallic Na0.71CoO2 composition has a very low residual resistivity, which attests to the high homogeneity of the crystals prepared by this improved electrochemical method. Our results on the various stable crystal compositions point to the importance of Na ion ordering across the phase diagram., 9 pages, 9 figures

Here we report the observation of Fermi surface (FS) pockets via the Shubnikov de Haas effect in Na$_x$CoO$_2$ for $x = 0.71$ and 0.84, respectively. Our observations indicate that the FS expected for each compound intersects their corresponding Brillouin zones, as defined by the previously reported superlattice structures, leading to small reconstructed FS pockets, but only if a precise number of holes per unit cell is \emph{localized}. For $0.71 \leq x < 0.75$ the coexistence of itinerant carriers and localized $S =1/2$ spins on a paramagnetic triangular superlattice leads at low temperatures to the observation of a deviation from standard Fermi-liquid behavior in the electrical transport and heat capacity properties, suggesting the formation of some kind of quantum spin-liquid ground state., 4 pages, 4 figures