다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

The MN+1AXN phases: A new class of solids

In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial insulators or superconductors in five out of ten symmetry classes introduced in seminal work by Altland and Zirnbauer within the context of random matrix theory, more than a decade ago. One of these is the recently introduced ${\mathbb{Z}}_{2}$ topological insulator in the symplectic (or spin-orbit) symmetry class. We show that there exist precisely four more topological insulators. For these systems, all of which are time-reversal invariant in three dimensions, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topological sectors that are separated by quantum phase transitions. Three of the above five topologically nontrivial phases can be realized as time-reversal invariant superconductors. In these the different topological sectors are characterized by an integer winding number defined in momentum space. When such 3D topological insulators are terminated by a two-dimensional surface, they support a number (which may be an arbitrary nonvanishing even number for singlet pairing) of Dirac fermion (Majorana fermion when spin-rotation symmetry is completely broken) surface modes which remain gapless under arbitrary perturbations of the Hamiltonian that preserve the characteristic discrete symmetries, including disorder. In particular, these surface modes completely evade Anderson localization from random impurities. These topological phases can be thought of as three-dimensional analogs of well-known paired topological phases in two spatial dimensions such as the spinless chiral $({p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y})$-wave superconductor (or Moore-Read Pfaffian state). In the corresponding topologically nontrivial (analogous to ``weak pairing'') and topologically trivial (analogous to ``strong pairing'') 3D phases, the wave functions exhibit markedly distinct behavior. When an electromagnetic U(1) gauge field and fluctuations of the gap functions are included in the dynamics, the superconducting phases with nonvanishing winding number possess nontrivial topological ground-state degeneracies.

Classification of topological insulators and superconductors in three spatial dimensions

Phase equilibria in the ternary system Pr--Fe--Al have been established in an isothermal section at 800 {degree}C from room temperature x-ray powder diffraction analysis of about 50 alloys, which were melted, annealed at 800 {degree}C, and quenched. Phase equilibria are characterized by the formation of rather extended homogeneous regions, i.e., by a random substitution of Fe/Al in Pr(Al{sub 1{minus}{ital x}}Fe{sub {ital x}}){sub 2}, 0{le}{ital x}{le}0.15, in Pr{sub 2}(Fe{sub 1{minus}{ital x}}Al{sub {ital x}}){sub 17}, 0{le}{ital x}{le}0.65, as well as by the formation of at least four ternary compounds. Whereas the existence of PrFe{sub 4}Al{sub 8} with the CeMn{sub 4}Al{sub 8}-type structure has been confirmed, there were no indications for a compound PrFe{sub 6}Al{sub 6}'' earlier claimed to crystallize with the ThMn{sub 12}-type structure. Pr{sub 6}(Fe{sub 1{minus}{ital x}}Al{sub {ital x}}){sub 14}, 0.16{le}{ital x}{le}0.36 with a homogeneous region parallel to the Fe--Al binary, was found to be isotypic with the La{sub 6}Co{sub 11}Ga{sub 3}-type of structure. Pr-rich alloys are liquid at 800 {degree}C, and all the alloys Pr{sub 2}(Fe{sub 1{minus}{ital x}}Al{sub {ital x}}){sub 17} with aluminium concentrations less than 5 at. % Al ({ital x}{similar to}0.07) enter a two-phase equilibrium with the Pr-rich liquid. At temperatures below 800 {degree}C, alloys with compositions closemore » to 30 at. % Pr and 5 at. % Al show a further ternary phase on solidification, whose crystal structure is related to the La{sub 6}Co{sub 11}Ga{sub 3}-type. PrFe{sub 2}Al{sub 8} is a new representative of the CeFe{sub 2}Al{sub 8}-type structure. The crystal structure of the ternary compound richest in Al, PrFe{sub 2}Al{sub 10}, has not been solved yet.« less

The ternary system:Aluminum-iron-praseodymium

The crystal structure of LaIr4B4 has been refined from single crystal counter data. LaIr4B4 is tetragonal,P42/n,Z=2, isotypic with NdCo4B4, Σ|ΔF|/Σ|Fo|=0.039 for 312 independent reflections [|Fo|>2 σ (Fo)]. ThIr4B4 and ThOs4B4 also belong to the NdCo4B4-type structure. URu4B4 and UOs4B4 were found to crystallize with LuRu4B4-type structure. The crystal chemistry of (RE)T4B4-phases is discussed and simple geometric relations are shown to exist between them.

The crystal structure of LaIr4B4, ThOs4B4, ThIr4B4 (NdCo4B4-type) and URu4B4, UOs4B4 (LuRu4B4-type)

TiAl-based alloys with nickel

New ternary metal borides with compositionR. E. T4B4 (R. E.=rare earth metal,T=transition metal) have been synthesized within the systems [La,Ce,Pr,Nd,Sm]−Os−B and [Y, La, Ce, Pr, Nd, Sm, Gd, Tb]−Ir−B. All compounds were found to be crystallizing with NdCo4B4-type structure. Magnetic measurements (80–300 K,Curie-Weiss behaviour, θ p ~ 16K and µeff=9.94µB for TbIr4B4) indicate Y andR. E. elements (except Ce) to be trivalent in these compounds. The crystal chemistry of the isotypic series [Y,R. E.] [Os,Ir]4B4 is discussed.

Peter Rogl

Papers

The ternary system:Aluminum-iron-praseodymium

The crystal structure of LaIr4B4, ThOs4B4, ThIr4B4 (NdCo4B4-type) and URu4B4, UOs4B4 (LuRu4B4-type)

TiAl-based alloys with nickel

Ternary metal borides [La,Ce,Pr,Nd,Sm] Os4B4 and [Y,La,Ce,Pr,Nd,Sm,Gd,Tb] Ir4B4 with NdCo4B4-type structure

On the Intermediate Valence of Ternary Silicides CeRhSi2 and CeIrSi2