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Register a new userClassification of emergent Weyl spinors in multi-fermion systems
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Authors
M.A. Zubkov
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In the fermionic systems with topologically stable Fermi points the emergent two - component Weyl fermions appear. We propose the topological classification of these fermions based on the two invariants composed of the two - component Green function. We define these invariants using Wigner - Weyl formalism also in case of essentially non - homogeneous systems. In the case when values of these invariants are minimal ($pm 1$) we deal with emergent relativistic symmetry. The emergent gravity appears, and our classification of Weyl fermions gives rise to the classification of vierbein. Transformations between emergent relativistic Weyl fermions of different types correspond to parity conjugation, time reversal, and charge conjugation.
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Weyl fermions are massless chiral particles first predicted in 1929 and once thought to describe neutrinos. Although never observed as elementary particles, quasiparticles with Weyl dispersion have recently been experimentally discovered in solid-state systems causing a furore in the research community. Systems with Weyl excitations can display a plethora of fascinating phenomena and offer great potential for improved quantum technologies. Here we show that Weyl excitations generically exist in three-dimensional systems of dipolar particles with weakly broken time-reversal symmetry (for example, by a magnetic field). They emerge as a result of dipolar-interaction-induced transfer of angular momentum between the $J=0$ and $J=1$ internal particle levels. We also discuss momentum-resolved Ramsey spectroscopy methods for observing Weyl quasiparticles in cold alkaline-earth-atom systems. Our results provide a pathway for a feasible experimental realisation of Weyl quasiparticles and related phenomena in clean and controllable atomic systems.
We report the discovery of Weyl semimetal NbAs featuring topological Fermi arc surface states.
Insulating states can be topologically nontrivial, a well-established notion that is exemplified by the quantum Hall effect and topological insulators. By contrast, topological metals have not been experimentally evidenced until recently. In systems with strong correlations, they have yet to be identified. Heavy fermion semimetals are a prototype of strongly correlated systems and, given their strong spin-orbit coupling, present a natural setting to make progress. Here we advance a Weyl-Kondo semimetal phase in a periodic Anderson model on a noncentrosymmetric lattice. The quasiparticles near the Weyl nodes develop out of the Kondo effect, as do the surface states that feature Fermi arcs. We determine the key signatures of this phase, which are realized in the heavy fermion semimetal Ce$_3$Bi$_4$Pd$_3$. Our findings provide the much-needed theoretical foundation for the experimental search of topological metals with strong correlations, and open up a new avenue for systematic studies of such quantum phases that naturally entangle multiple degrees of freedom.
Disorder such as impurities and dislocations in Weyl semimetals (SMs) drives a quantum critical point (QCP) where the density of states at the Weyl point gains a non-zero value. Near the QCP, the asymptotic low energy singularities of physical quantities are controlled by the critical exponents $ u$ and $z$. The nuclear spin-lattice relaxation rate, which originates from the hyperfine coupling between a nuclear spin and long-range orbital currents in Weyl fermion systems, shows intriguing critical behavior. Based on the self-consistent Born approximation for impurities, we study the nuclear spin-lattice relaxation rate $1/T_1$ due to the orbital currents in disordered Weyl SMs. We find that $(T_1T)^{-1}sim E^{2/z}$ at the QCP where $E$ is the maximum of temperature $T$ and chemical potential $mu(T)$ relative to the Weyl point. This scaling behavior of $(T_1T)^{-1}$ is also confirmed by the self-consistent $T$-matrix approximation, where a remarkable temperature dependence of $mu(T)$ could play an important role. We hope these results of $(T_1T)^{-1}$ will serve as an impetus for exploration of the disorder-driven quantum criticality in Weyl materials.
The Weyl semimetal phase is a recently discovered topological quantum state of matter characterized by the presence of topologically protected degeneracies near the Fermi level. These degeneracies are the source of exotic phenomena, including the realization of chiral Weyl fermions as quasiparticles in the bulk and the formation of Fermi arc states on the surfaces. Here, we demonstrate that these two key signatures show distinct evolutions with the bulk band topology by performing angle-resolved photoemission spectroscopy, supported by first-principle calculations, on transition-metal monophosphides. While Weyl fermion quasiparticles exist only when the chemical potential is located between two saddle points of the Weyl cone features, the Fermi arc states extend in a larger energy scale and are robust across the bulk Lifshitz transitions associated with the recombination of two non-trivial Fermi surfaces enclosing one Weyl point into a single trivial Fermi surface enclosing two Weyl points of opposite chirality. Therefore, in some systems (e.g. NbP), topological Fermi arc states are preserved even if Weyl fermion quasiparticles are absent in the bulk. Our findings not only provide insight into the relationship between the exotic physical phenomena and the intrinsic bulk band topology in Weyl semimetals, but also resolve the apparent puzzle of the different magneto-transport properties observed in TaAs, TaP and NbP, where the Fermi arc states are similar.
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