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Register a new userWeyl-Kondo semimetals in nonsymmorphic systems
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There is considerable current interest to explore electronic topology in strongly correlated metals, with heavy fermion systems providing a promising setting. Recently, a Weyl-Kondo semimetal phase has been concurrently discovered in theoretical and experimental studies. The theoretical work was carried out in a Kondo lattice model that is time-reversal invariant but inversion-symmetry breaking. In this paper, we show in some detail how nonsymmorphic space-group symmetry and strong correlations cooperate to form Weyl nodal excitations with highly reduced velocity and pin the resulting Weyl nodes to the Fermi energy. A tilted variation of the Weyl-Kondo solution is further analyzed here, following the recent consideration of such effect in the context of understanding a large spontaneous Hall effect in Ce$_3$Bi$_4$Pd$_3$ (Dzsaber et al., arXiv:1811.02819). We discuss the implications of our results for the enrichment of the global phase diagram of heavy fermion metals, and for the space-group symmetry enforcement of topological semimetals in other strongly correlated settings.
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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.
The surface of a Weyl semimetal famously hosts an exotic topological metal that contains open Fermi arcs rather than closed Fermi surfaces. In this work, we show that the surface is also endowed with a feature normally associated with strongly interacting systems, namely, Luttinger arcs, defined as zeros of the electron Greens function. The Luttinger arcs connect surface projections of Weyl nodes of opposite chirality and form closed loops with the Fermi arcs when the Weyl nodes are undoped. Upon doping, the ends of the Fermi and Luttinger arcs separate and the intervening regions get filled by surface projections of bulk Fermi surfaces. For bilayered Weyl semimetals, we prove two remarkable implications: (i) the precise shape of the Luttinger arcs can be determined experimentally by removing a surface layer. We use this principle to sketch the Luttinger arcs for Co and Sn terminations in Co$_{3}$Sn$_{2}$S$_{2}$; (ii) the area enclosed by the Fermi and Luttinger arcs equals the surface particle density to zeroth order in the interlayer couplings. We argue that the approximate equivalence survives interactions that are weak enough to leave the system in the Weyl limit, and term this phenomenon weak Luttingers theorem.
We consider the effect of the Coulomb interaction in a nonsymmorphic Dirac semimetal, leading to collective charge oscillation modes (plasmons), focusing on the model originally predicted by Young and Kane [Phys. Rev. Lett. 115, 126803 (2015)]. We model the system in a two-dimensional square-lattice and evaluate the density-density correlation function within the random-phase approximation (RPA) in presence of the Coulomb interaction. The non-interacting band-structure consists of three band-touching points, near which the electronic states follow Dirac equations. Two of these Dirac nodes, at the momentum points $X_1$ and $X_2$ are anisotropic, i.e, disperses with different velocities in different directions, whereas the third Dirac point at $M$ is isotropic. Interestingly we find that, the system of these three Dirac nodes hold a single low-energy plasmon mode, within its particle-hole gap, that disperses in isotropic manner, in the case when the nodes at $X_1$ and $X_2$ are related by symmetry. We also show this analytically using a long-wavelength approximation. We discuss effects of perturbations that can give rise to anisotropic plasmon dispersions and comment on possible experimental observation of our prediction.
We present an analytical low-energy theory of piezoelectric electron-phonon interactions in undoped Weyl semimetals, taking into account also Coulomb interactions. We show that piezoelectric interactions generate a long-range attractive potential between Weyl fermions. This potential comes with a characteristic angular anisotropy. From the one-loop renormalization group approach and a mean-field analysis, we predict that superconducting phases with either conventional s-wave singlet pairing or nodal-line triplet pairing could be realized for sufficiently strong piezoelectric coupling. For small couplings, we show that the quasi-particle decay rate exhibits a linear temperature dependence where the prefactor vanishes only in a logarithmic manner as the quasi-particle energy approaches the Weyl point. For practical estimates, we consider the Weyl semimetal TaAs.
Energy transfer from electrons to phonons is an important consideration in any Weyl or Dirac semimetal based application. In this work, we analytically calculate the cooling power of acoustic phonons, i.e. the energy relaxation rate of electrons which are interacting with acoustic phonons, for Weyl and Dirac semimetals in a variety of different situations. For cold Weyl or Dirac semimetals with the Fermi energy at the nodal points, we find the electronic temperature, $T_e$, decays in time as a power law. In the heavily doped regime, $T_e$ decays linearly in time far away from equilibrium. In a heavily doped system with short-range disorder we predict the cooling power of acoustic phonons is drastically increased because of an enhanced energy transfer between electrons and phonons. When an external magnetic field is applied to an undoped system, the cooling power is linear in magnetic field strength and $T_e$ has square root decay in time, independent of magnetic field strength over a range of values.
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