Width-Tuned Magnetic Order Oscillation on Zigzag Edges of Honeycomb Nanoribbons.

Quantum confinement and interference often generate exotic properties in nanostructures. One recent highlight is the experimental indication of a magnetic phase transition in zigzag-edged graphene nanoribbons at the critical ribbon width of about 7 nm [ Magda , G. Z. et al. Nature 2014 , 514 , 608 ]. Here we show theoretically that with further increase in the ribbon width, the magnetic correlation of the two edges can exhibit an intriguing oscillatory behavior between antiferromagnetic and ferromagnetic, driven by acquiring the positive coherence between the two edges to lower the free energy. The oscillation effect is readily tunable in applied magnetic fields. These novel properties suggest new experimental manifestation of the edge magnetic orders in graphene nanoribbons and enhance the hopes of graphene-like spintronic nanodevices functioning at room temperature.

Multifarious topological quantum phase transitions in two-dimensional topological superconductors.

We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers.

Single-Spin Dirac Fermion and Chern Insulator Based on Simple Oxides.

It is highly desirable to combine recent advances in the topological quantum phases with technologically relevant materials. Chromium dioxide (CrO2) is a half-metallic material, widely used in high-end data storage applications. Using first-principles calculations, we show that a novel class of half semimetallic Dirac electronic phase emerges at the interface CrO2 with TiO2 in both thin film and superlattice configurations, with four spin-polarized Dirac points in momentum-space (k-space) band structure. When the spin and orbital degrees of freedom are allowed to couple, the CrO2/TiO2 superlattice becomes a Chern insulator without external fields or additional doping. With topological gaps equivalent to 43 K and a Chern number ±2, the ensuing quantization of Hall conductance to ±2e(2)/h will enable potential development of these highly industrialized oxides for applications in topologically high fidelity data storage and energy-efficient electronic and spintronic devices.

Topological quantum phase transitions on the kagomé and square-octagon lattices.

We study the topological quantum phase transitions of tight-binding electrons on two representative multi-band lattice models with superimposed staggered fluxes: the kagomé lattice and the square-octagon lattice. By considering the nearest-neighbor and next-nearest-neighbor hopping parameters (t1 and t2) and the staggered flux parameter φ, we obtain rich topological quantum phase transitions for both the lattices. The whole phase diagram for the kagomé lattice in the t2-φ parameter space is obtained. We also illustrate a series of topological quantum phase transitions as well as topological bands of high Chern numbers for the square-octagon lattice. Furthermore, interesting topological flat bands with high flatness ratios (e.g. of about 43) are found in the square-octagon lattice, especially when the next-next-nearest-neighbor hopping (t3) is included.

Topological phase transition induced by spin-orbit coupling in bilayer graphene.

We study the topological phase transition in biased bilayer graphene in the presence of intrinsic and Rashba spin-orbit couplings. The system exhibits a complicated topological phase transition depending on the given parameters. The topological phase transition between these phases is always accompanied by the bulk gap closing and reopening, and can be realized by tuning the bias voltage. The stability of these topological phases are also investigated. We find that the weak (strong) topological insulator phase remains stable under a finite exchange field provided that the effect of intrinsic (Rashba) spin-orbit coupling is dominant, and this also holds for the quantum valley Hall phase if the spatial inversion symmetry breaking overcomes the time-reversal symmetry breaking.

Pressure-induced crystal structure and spin-state transitions in magnetite (Fe3O4).

High pressure is an important dimension for the emergent phenomena in transition metal oxides, including high-temperature superconductivity, colossal magnetoresistance, and magnetoelectric coupling. In these multiply correlated systems, the interplay between lattice, charge, orbital, and spin is extremely susceptible to external pressure. Magnetite (Fe(3)O(4)) is one of the oldest known magnetic materials and magnetic minerals, yet its high pressure behaviors are still not clear. In particular, the crystal structure of the high-pressure phase has remained contentious. Here, we investigate the pressure-induced phase transitions in Fe(3)O(4) from first-principles density-functional theory. It is revealed that the net magnetic moment, arising from two ferrimagnetically coupled sublattices in Fe(3)O(4), shows an abrupt drop when entering into the high-pressure phase but recovers finite value when the pressure is beyond 65.1 GPa. The origin lies in the redistribution of Fe 3d orbital occupation with the change of crystal field, where successive structural transitions from ambient pressure phase Fd3[combining overline]m to high pressure phase Pbcm (at 29.7 GPa) and further to Bbmm (at 65.1 GPa) are established accurately. These findings not only explain the experimental observations on the structural and magnetic properties of the highly compressed Fe(3)O(4) but also suggest the existence of highly magnetized magnetite in the Earth's lower mantle.

Topological quantum phase transitions and topological flat bands on the kagomé lattice.

We investigate the topological properties of the tight-binding electrons on the two-dimensional kagomé lattice with two kinds of short-range hopping integral and two kinds of staggered magnetic flux. Considering the nearest-neighbor hopping (t(1)) with the staggered flux parameter φ(1) and the next nearest-neighbor hopping (t(2)) with the staggered flux parameter φ(2), we demonstrate a series of topological quantum phase transitions and find some topological bands with high Chern numbers, when tuning one parameter (t(2) or φ(2)) while the others are fixed. We have also found that, in some parameter regions, the system exhibits interesting topological flat bands with Chern number C =± 1 and a large gap above them, and the flatness ratio can reach a high value of about 170.

Non-abelian quantum Hall effect in topological flat bands.

Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable ν=1 bosonic non-abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read pfaffian state.

Quantized four-terminal resistances in a ferromagnetic graphene p-n junction.

The quantum Hall and longitudinal resistances in four-terminal ferromagnetic graphene p-n junctions under a perpendicular magnetic field are investigated. In the Hall measurement, the transverse contacts are assumed to be located at the p-n interface to avoid the mixing of edge states at the interface and the resulting quantized resistances are then topologically protected. According to the charge carrier type, the resistances in a four-terminal p-n junction can be naturally divided into nine different regimes. The symmetric Hall and longitudinal resistances are observed, with many new robust quantum plateaus revealed due to the competition between spin splitting and local potentials.

Fractional quantum Hall effect of hard-core bosons in topological flat bands.

Recent proposals of topological flat band models have provided a new route to realize the fractional quantum Hall effect without Landau levels. We study hard-core bosons with short-range interactions in two representative topological flat band models, one of which is the well-known Haldane model (but with different parameters). We demonstrate that fractional quantum Hall states emerge with signatures of an even number of quasidegenerate ground states on a torus and a robust spectrum gap separating these states from the higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases.

Tight-binding electrons on triangular and kagomé lattices under staggered modulated magnetic fields: quantum Hall effects and Hofstadter butterflies.

We consider the tight-binding models of electrons on a two-dimensional triangular lattice and kagomé lattice under staggered modulated magnetic fields. Such fields have two components: a uniform-flux part with strength φ, and a staggered-flux part with strength Δφ. Various properties of the Hall conductances and Hofstadter butterflies are studied. When φ is fixed, variation of Δφ leads to the quantum Hall transitions and Chern numbers of Landau subbands being redistributed between neighboring pairs. The energy spectra with nonzero Δφs have similar fractal structures but quite different energy gaps compared with the original Hofstadter butterflies of Δφ = 0. Moreover, the fan-like structure of Landau levels in the low magnetic field region is also modified appreciably by Δφ.

Tuning kinetic magnetism of strongly correlated electrons via a staggered flux.

An interplay between kinetic process and magnetic ordering is manifested when strong correlation and electronic frustration are present: tuning a staggered flux phi from 0 to pi makes the ground state (GS) of an infinite-U Hubbard model change abruptly from a Nagaoka-type ferromagnet to a Haerter-Shastry-type antiferromagnet at a phi_(c), with both states being metallic and of kinetic origin. Intraplaquette spin correlation, as well as nonanalyticity in the GS energy, signals such a novel quantum criticality. This tunable kinetic magnetism is generic and may be experimentally realized.

Redistributing Chern numbers of Landau subbands: tight-binding electrons under staggered modulated magnetic fields.

We investigate the magnetotransport properties of electrons on a square lattice under a magnetic field with the alternate flux strength phi+/-Deltaphi in neighboring plaquettes. A new peculiar behavior of the Hall conductance has been found and is robust against weak disorder: if phi=(p/2N)2pi (p and 2N are coprime integers) is fixed, the Chern numbers of Landau subbands will be redistributed between neighboring pairs and hence the total quantized Hall conductance exhibits a direct transition by +/-Ne2/h at critical fillings when Deltaphi is increased from 0 up to a critical value Deltaphi_{c}. This effect can be an experimental probe of the staggered-flux phase.

Coexistence of f-wave superconductivity, charge order, and spin antiferromagnetism around nonmagnetic impurities in Na0.33CoO2.1.3H2O.

To check whether charge dynamics is responsible for the superconductivity in NaxCoO2.yH2O, we investigate local electronic and magnetic structure around nonmagnetic impurities embedded in this material at x=0.33 in the vicinity of charge instability, by using a phenomenological model within the slave-boson framework including competitions among a square root of 3 x square root of 3 charge order, antiferromagnetism, and f-wave superconductivity. Around the repulsive impurities, it is found that both local charge and spin orders are induced. Furthermore, the f-wave pairing order parameter is decreased on one sublattice but increased on another honeycomb sublattice. If the charge dynamics is responsible for the superconductivity, the predicted local electronic and magnetic structure could be observed by the STM and spatial resolved NMR experiments.