Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHigh-Dimensional Disorder-Driven Phenomena in Weyl Semimetals, Semiconductors and Related Systems
372
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
It is commonly believed that a non-interacting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions distinct from Anderson localisation that have manifestations in the disorder-averaged density of states, conductivity and other observables. Such transitions have received particular attention in the context of recently discovered 3D Weyl and Dirac materials but have also been predicted in cold-atom systems with long-range interactions, quantum kicked rotors and all sufficiently high-dimensional systems. Moreover, such systems exhibit unconventional behaviour of Lifshitz tails, energy-level statistics and ballistic-transport properties. Here we review recent progress and the status of results on non-Anderson disorder-driven transitions and related phenomena.
rate research
Read More
Systems with the power-law quasiparticle dispersion $epsilon_{bf k}propto k^alpha$ exhibit non-Anderson disorder-driven transitions in dimensions $d>2alpha$, as exemplified by Weyl semimetals, 1D and 2D arrays of ultracold ions with long-range interactions, quantum kicked rotors and semiconductor models in high dimensions. We study the wavefunction structure in such systems and demonstrate that at these transitions they exhibit fractal behaviour with an infinite set of multifractal exponents. The multifractality persists even when the wavefunction localisation is forbidden by symmetry or topology and occurs as a result of elastic scattering between all momentum states in the band on length scales shorter than the mean free path. We calculate explicitly the multifractal spectra in semiconductors and Weyl semimetals using one-loop and two-loop renormalisation-group approaches slightly above the marginal dimension $d=2alpha$.
Disordered non-interacting systems in sufficiently high dimensions have been predicted to display a non-Anderson disorder-driven transition that manifests itself in the critical behaviour of the density of states and other physical observables. Recently the critical properties of this transition have been extensively studied for the specific case of Weyl semimetals by means of numerical and renormalisation-group approaches. Despite this, the values of the critical exponents at such a transition in a Weyl semimetal are currently under debate. We present an independent calculation of the critical exponents using a two-loop renormalisation-group approach for Weyl fermions in $2-varepsilon$ dimensions and resolve controversies currently existing in the literature.
We study dc conductivity of a Weyl semimetal with uniaxial anisotropy (Fermi velocity ratio $xi= v_bot/v_parallel eq1$) considering the scattering of charge carriers by a wide class of impurity potentials, both short- and long-range. We obtain the ratio of transverse and longitudinal (with respect to the anisotropy axis) conductivities as a function of both $xi$ and temperature. We find that the transverse and longitudinal conductivities exhibit different temperature dependence in the case of short-range disorder. For general long-range disorder, the temperature dependence ($sim T^4$) of the conductivity turns out to be insensitive of the anisotropy in the limits of strong ($xigg$ and $ll1$) and weak ($xiapprox1$) anisotropy.
The chiral anomaly in Weyl semimetals states that the left- and right-handed Weyl fermions, constituting the low energy description, are not individually conserved, resulting, for example, in a negative magnetoresistance in such materials. Recent experiments see strong indications of such an anomalous resistance response; however, with a response that at strong fields is more sharply peaked for parallel magnetic and electric fields than expected from simple theoretical considerations. Here, we uncover a mechanism, arising from the interplay between the angle-dependent Landau level structure and long-range scalar disorder, that has the same phenomenology. In particular, we ana- lytically show, and numerically confirm, that the internode scattering time decreases exponentially with the angle between the magnetic field and the Weyl node separation in the large field limit, while it is insensitive to this angle at weak magnetic fields. Since, in the simplest approximation, the internode scattering time is proportional to the anomaly-related conductivity, this feature may be related to the experimental observations of a sharply peaked magnetoresistance.
Internodal dynamics of quasiparticles in Weyl semimetals manifest themselves in hydrodynamic, transport and thermodynamic phenomena and are essential for potential valleytronic applications of these systems. In an external magnetic field, coherent quasiparticle tunnelling between the nodes modifies the quasiparticle dispersion and, in particular, opens gaps in the dispersion of quasiparticles at the zeroth Landau level. We study magnetotransport in a Weyl semimetal taking into account mechanisms of quasiparticle scattering both affected by such gaps and independent of them. We compute the longitudal resistivity of a disordered Weyl semimetal with two nodes in a strong magnetic field microscopically and demonstrate that in a broad range of magnetic fields it has a strong angular dependence $rho(eta)propto C_1+C_2 cos^2eta$, where $eta$ is the angle between the field and the separation between the nodes in momentum space. The first term is determined by the coherent internodal tunnelling and is important only at angles $eta$ close to $pi/2$. This contribution depends exponentially on the magnetic field, $propto expleft(-B_0/Bright)$. The second term is weakly dependent on the magnetic field for realistic concentrations of the impurities in a broad interval of fields.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
