15 research outputs found
Symmetry and Quantum Kinetics of the Non-linear Hall Effect
We argue that the static non-linear Hall conductivity can always be
represented as a vector in two-dimensions and as a pseudo-tensor in
three-dimensions independent of its microscopic origin. In a single band model
with a constant relaxation rate this vector or tensor is proportional to the
Berry curvature dipole \cite{Sodemann_2015}. Here, we develop a quantum
Boltzmann formalism to second order in electric fields. We find that in
addition to the Berry Curvature Dipole term, there exist additional disorder
mediated corrections to the non-linear Hall tensor that have the same scaling
in impurity scattering rate. These can be thought of as the non-linear
counterparts to the side-jump and skew-scattering corrections to the Hall
conductivity in the linear regime. We illustrate our formalism by computing the
different contributions to the non-linear Hall conductivity of two-dimensional
tilted Dirac fermions.Comment: 5 pages, 1 figure, Phys Rev. B versio
Theoretical investigations on Kerr and Faraday rotations in topological multi-Weyl Semimetals
Motivated by the recent proposal of giant Kerr rotation in WSMs, we
investigate the Kerr and Faraday rotations in time-reversal broken multi-Weyl
semimetals (mWSMs) in the absence of an external magnetic field. Using the
framework of Kubo response theory, we find that both the longitudinal and
transverse components of the optical conductivity in mWSMs are modified by the
topological charge (). Engendered by the optical Hall conductivity, we show
in the thin film limit that, while the giant Kerr rotation and corresponding
ellipticity are independent of , the Faraday rotation and its ellipticity
angle scale as and , respectively. In contrast, the polarization
rotation in semi-infinite mWSMs is dominated by the axion field showing
dependence. In particular, the magnitude of Kerr (Faraday) angle decreases
(increases) with increasing in Faraday geometry, whereas in Voigt geometry,
it depicts different -dependencies in different frequency regimes. The
obtained results on the behavior of polarization rotations in mWSMs could be
used in experiments as a probe to distinguish single, double, and triple WSMs,
as well as discriminate the surfaces of mWSMs with and without hosting Fermi
arcs.Comment: 12 Pages, 5 Figures, Submission to SciPos
Signature of nodal topology in nonlinear quantum transport across junctions in Weyl and multi-Weyl semimetals
We investigate quantum transport through a rectangular potential barrier in
Weyl semimetals (WSMs) and multi-Weyl semimetals (MSMs), within the framework
of Landauer-B\"uttiker formalism. Our study uncovers the role of nodal topology
imprinted in the electric current and the shot noise. We find that, in contrast
to the finite odd-order conductance and noise power, the even-order
contributions vanish at the nodes. Additionally, depending on the topological
charge (), the linear conductance () scales with the Fermi energy
() as . We demonstrate that the
-dependence of the second-order conductance and shot noise power could
quite remarkably distinguish an MSM from a WSM depending on the band topology,
and may induce several smoking gun experiments in nanostructures made out of
WSMs and MSMs. Analyzing shot noise and Fano factor, we show that the transport
across the rectangular barrier follows the sub-Poissonian statistics.
Interestingly, we obtain universal values of Fano factor at the nodes unique to
their topological charges. The universality for a fixed , however, indicates
that only a fixed number of open channels participate in the transport through
evanescent waves at the nodes. The proposed results can serve as a potential
diagnostic tool to identify different topological systems in experiments.Comment: 11 pages, 4 figure