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Register a new userWeyl and Dirac Semimetals in Three Dimensional Solids
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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. Here we review the theoretical foundations of these phases, their proposed realizations in solid state systems, recent experiments on candidate materials, as well as their relation to other states of matter.
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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.
We study the electronic contribution to the thermal conductivity and the thermopower of Weyl and Dirac semimetals using a semiclassical Boltzmann approach. We investigate the effect of various relaxation processes including disorder and interactions on the thermoelectric properties, and also consider doping away from the Weyl or Dirac point. We find that the thermal conductivity and thermopower have an interesting dependence on the chemical potential that is characteristic of the linear electronic dispersion, and that the electron-electron interactions modify the Lorenz number. For the interacting system, we also use the Kubo formalism to obtain the transport coefficients. We find exact agreement between the Kubo and Boltzmann approaches at high temperatures. We also consider the effect of electric and magnetic fields on the thermal conductivity in various orientations with respect to the temperature gradient. Notably, when the temperature gradient and magnetic field are parallel, we find a large contribution to the longitudinal thermal conductivity that is quadratic in the magnetic field strength, similar to the magnetic field dependence of the longitudinal electrical conductivity due to the presence of the chiral anomaly when no thermal gradient is present.
We numerically study the effect of short ranged potential disorder on massless noninteracting three-dimensional Dirac and Weyl fermions, with a focus on the question of the proposed quantum critical point separating the semimetal and diffusive metal phases. We determine the properties of the eigenstates of the disordered Dirac Hamiltonian ($H$) and exactly calculate the density of states (DOS) near zero energy, using a combination of Lanczos on $H^2$ and the kernel polynomial method on $H$. We establish the existence of two distinct types of low energy eigenstates contributing to the disordered density of states in the weak disorder semimetal regime. These are (i) typical eigenstates that are well described by linearly dispersing perturbatively dressed Dirac states, and (ii) nonperturbative rare eigenstates that are weakly-dispersive and quasi-localized in the real space regions with the largest (and rarest) local random potential. Using twisted boundary conditions, we are able to systematically find and study these two types of eigenstates. We find that the Dirac states contribute low energy peaks in the finite-size DOS that arise from the clean eigenstates which shift and broaden in the presence of disorder. On the other hand, we establish that the rare quasi-localized eigenstates contribute a nonzero background DOS which is only weakly energy-dependent near zero energy and is exponentially small at weak disorder. We find that the expected semimetal to diffusive metal quantum critical point is converted to an {it avoided} quantum criticality that is rounded out by nonperturbative effects, with no signs of any singular behavior in the DOS near the Dirac energy. We discuss the implications of our results for disordered Dirac and Weyl semimetals, and reconcile the large body of existing numerical work showing quantum criticality with the existence of the rare region effects.
We theoretically investigate the temperature-dependent static susceptibility and long-range magnetic coupling of three-dimensional (3D) chiral gapless electron-hole systems (semimetals) with arbitrary band dispersion [i.e., $varepsilon(k) sim k^N$, where $k$ is the wave vector and $N$ is a positive integer]. We study the magnetic properties of these systems in the presence of dilute random magnetic impurities. Assuming carrier-mediated Ruderman-Kittel-Kasuya-Yosida indirect exchange interaction, we find that the magnetic ordering of intrinsic 3D chiral semimetals in the presence of dilute magnetic impurities is ferromagnetic for all values of $N$. Using finite-temperature self-consistent field approximation, we calculate the ferromagnetic transition temperature ($T_{rm c}$). We find that $T_{rm c}$ increases with increasing $N$ due to the enhanced density of states, and the calculated $T_{rm c}$ is experimentally accessible assuming reasonable coupling between the magnetic impurities and itinerant carriers.
We numerically study the three-dimensional (3D) quantum Hall effect (QHE) and magnetothermoelectric transport of Weyl semimetals in the presence of disorder. We obtain a bulk picture that the exotic 3D QHE emerges in a finite range of Fermi energy near the Weyl points determined by the gap between the $n=-1$ and $n=1$ Landau levels (LLs). The quantized Hall conductivity is attributable to the chiral zeroth LLs traversing the gap, and is robust against disorder scattering for an intermediate number of layers in the direction of the magnetic field. Moreover, we predict several interesting characteristic features of the thermoelectric transport coefficients in the 3D QHE regime, which can be probed experimentally. This may open an avenue for exploring Weyl physics in topological materials.
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