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Register a new userGiant orbital diamagnetism of three-dimensional Dirac electrons in Sr$ _3$PbO antiperovskite
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In Dirac semimetals, inter-band mixing has been known theoretically to give rise to a giant orbital diamagnetism when the Fermi level is close to the Dirac point. In Bi$ _{1-x}$Sb$ _x$ and other Dirac semimetals, an enhanced diamagnetism in the magnetic susceptibility $chi$ has been observed and interpreted as a manifestation of such giant orbital diamagnetism. Experimentally proving their orbital origin, however, has remained challenging. Cubic antiperovskite Sr$ _3$PbO is a three-dimensional Dirac electron system and shows the giant diamagnetism in $chi$ as in the other Dirac semimetals. $ ^{207}$Pb NMR measurements are conducted in this study to explore the microscopic origin of diamagnetism. From the analysis of the Knight shift $K$ as a function of $chi$ and the relaxation rate $T_1^{-1}$ for samples with different hole densities, the spin and the orbital components in $K$ are successfully separated. The results establish that the enhanced diamagnetism in Sr$ _3$PbO originates from the orbital contribution of Dirac electrons, which is fully consistent with the theory of giant orbital diamagnetism.
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Novel topological phenomena are anticipated for three-dimensional (3D) Dirac electrons. The magnetotransport properties of cubic ${rm Sr_{3}PbO}$ antiperovskite, theoretically proposed to be a 3D massive Dirac electron system, are studied. The measurements of Shubnikov-de Haas oscillations and Hall resistivity indicate the presence of a low density ($sim 1 times 10^{18}$ ${rm cm^{-3}}$) of holes with an extremely small cyclotron mass of 0.01-0.06$m_{e}$. The magnetoresistance $Deltarho_{xx}(B)$ is linear in magnetic field $B$ with the magnitude independent of temperature. These results are fully consistent with the presence of 3D massive Dirac electrons in ${rm Sr_{3}PbO}$. The chemical flexibility of the antiperovskites and our findings in the family member, ${rm Sr_{3}PbO}$, point to their potential as a model system in which to explore exotic topological phases.
The three-dimensional topological semimetals represent a new quantum state of matter. Distinct from the surface state in the topological insulators that exhibits linear dispersion in two-dimensional momentum plane, the three-dimensional semimetals host bulk band dispersions linearly along all directions, forming discrete Dirac cones in three-dimensional momentum space. In addition to the gapless points (Weyl/Dirac nodes) in the bulk, the three-dimensional Weyl/Dirac semimetals are also characterized by topologically protected surface state with Fermi arcs on their specific surface. The Weyl/Dirac semimetals have attracted much attention recently they provide a venue not only to explore unique quantum phenomena but also to show potential applications. While Cd3As2 is proposed to be a viable candidate of a Dirac semimetal, more experimental evidence and theoretical investigation are necessary to pin down its nature. In particular, the topological surface state, the hallmark of the three-dimensional semimetal, has not been observed in Cd3As2. Here we report the electronic structure of Cd3As2 investigated by angle-resolved photoemission measurements on the (112) crystal surface and detailed band structure calculations. The measured Fermi surface and band structure show a good agreement with the band structure calculations with two bulk Dirac-like bands approaching the Fermi level and forming Dirac points near the Brillouin zone center. Moreover, the topological surface state with a linear dispersion approaching the Fermi level is identified for the first time. These results provide strong experimental evidence on the nature of topologically non-trivial three-dimensional Dirac cones in Cd3As2.
A Dirac electron system in solids mimics a relativistic quantum physics that is compatible with Maxwells equations, by which we anticipate unified electromagnetic responses. We find a large orbital diamagnetism only along the interplane direction and the nearly temperature-independent conductance of the order of e2/h for the new 2D Dirac organic conductor, a-(BETS)2I3. Distinct from conventional electrons in solids whose nonrelativistic effects bifurcate electric and magnetic responses, the observed orbital diamagnetism scales the electrical conductivity for a wide temperature range. This demonstrates that an electromagnetic duality that is valid only within the relativistic framework is revived in solids.
Bismuth crystal is known for its remarkable properties resulting from particular electronic states, e. g., the Shubnikov-de Haas effect and the de Haas-van Alphen effect. Above all, the large diamagnetism of bismuth had been a long-standing puzzle soon after the establishment of quantum mechanics, which had been resolved eventually in 1970 based on the effective Hamiltonian derived by Wolff as due to the interband effects of a magnetic field in the presence of a large spin-orbit interaction. This Hamiltonian is essentially the same as the Dirac Hamiltonian, but with spatial anisotropy and an effective velocity much smaller than the light velocity. This paper reviews recent progress in the theoretical understanding of transport and optical properties, such as the weak-field Hall effect together with the spin Hall effect, and ac conductivity, of a system described by the Wolff Hamiltonian and its isotropic version with a special interest of exploring possible relationship with orbital magnetism. It is shown that there exist a fundamental relationship between spin Hall conductivity and orbital susceptibility in the insulating state on one hand, and the possibility of fully spin-polarized electric current in magneto-optics. Experimental tests of these interesting features have been proposed.
Dirac fermions display a singular response against magnetic and electric fields. A distinct manifestation is large diamagnetism originating in the interband effect of Bloch bands, as observed in bismuth alloys. Through $^{209}$Bi NMR spectroscopy, we extract diamagnetic orbital susceptibility inherent to Dirac fermions in the semiconducting bismuth alloys Bi$_{1-x}$Sb$_x$ ($x = 0.08 - 0.16$). The $^{209}$Bi hyperfine coupling constant provides an estimate of the effective orbital radius. In addition to the interband diamagnetism, Knight shift includes an anomalous temperature-independent term originating in the enhanced intraband diamagnetism under strong spin-orbit coupling. The nuclear spin-lattice relaxation rate $1/T_1$ is dominated by orbital excitation and follows cubic temperature dependence in the extensive temperature range. The result demonstrates the robust diamagnetism and low-lying orbital excitation against the small gap opening, whereas $x$-dependent spin excitation appears at low temperatures.
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