132 research outputs found
Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials
Quantum transport close to a critical point is a fundamental, but enigmatic
problem due to fluctuations, persisting at all length scales. We report the
scaling of optical conductivity (OC) in the \emph{collisionless} regime () in the vicinity of a relativistic quantum critical point,
separating two-dimensional () massless Dirac fermions from a fully gapped
insulator or superconductor. Close to such critical point gapless fermionic and
bosonic excitations are strongly coupled, leading to a \emph{universal}
suppression of the inter-band OC as well as of the Drude peak (while
maintaining its delta function profile) inside the critical regime, which we
compute to the leading order in - and -expansions, where
counts fermion flavor number and . Correction to the OC at such a
non-Gaussian critical point due to the long-range Coulomb interaction and
generalizations of these scenarios to a strongly interacting three-dimensional
Dirac or Weyl liquid are also presented, which can be tested numerically and
possibly from non-pertubative gauge-gravity duality, for example.Comment: Published version in PRL: 5+epsilon Pages, 2 Figures (Supplementary
Materials as Ancillary file: 4 pages
Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling
We propose a general framework for constructing a large set of nodal-point
semimetals by tuning the number of linearly () and (at most) quadratically
() dispersing directions. By virtue of such a unifying scheme, we identify
a new perturbative route to access various strongly interacting non-Dirac
semimetals with . As a demonstrative example, we relate a two
dimensional anisotropic semimetal with , describing the topological
transition between a Dirac semimetal and a normal insulator, and its three
dimensional counterparts with , . We address the quantum critical
phenomena and emergence of non-Fermi liquid states with unusual dynamical
structures within the framework of an expansion, where
, when these systems reside at the brink of charge- or
spin-density-wave orderings, or an -wave pairing. Our results can be germane
to two-dimensional uniaxially strained optical honeymcomb lattice,
-(BEDT-TTF).Comment: 5 pages, 3 figures; Published versio
Unconventional superconductivity in nearly flat bands in twisted bilayer graphene
Flat electronic bands can accommodate a plethora of interaction driven
quantum phases, since kinetic energy is quenched therein and electronic
interactions therefore prevail. Twisted bilayer graphene, near so-called the
"magic angles", features \emph{slow} Dirac fermions close to the
charge-neutrality point that persist up to high-energies. Starting from a
continuum model of slow, but strongly interacting Dirac fermions, we show that
with increasing chemical doping away from the charge-neutrality point, a
time-reversal symmetry breaking, valley pseudo-spin-triplet, topological
superconductor gradually sets in, when the system resides at the brink of an
anti-ferromagnetic ordering (due to Hubbard repulsion), in qualitative
agreement with recent experimental findings. The paired state exhibits
quantized spin and thermal Hall conductivities, polar Kerr and Faraday
rotations. Our conclusions should also be applicable for other correlated
two-dimensional Dirac materials.Comment: 5 Pages, 2 Figures: Published Version in PRB (Supplementary
Materials: 4 Pages, Ancillary file
Optical conductivity of an interacting Weyl liquid in the collisionless regime
Optical conductivity (OC) can serve as a measure of correlation effects in a
wide range of condensed matter systems. We here show that the long-range tail
of the Coulomb interaction yields a universal correction to the OC in a
three-dimensional Weyl semimetal , where of is
the OC in the non-interacting system, with as the actual (renormalized)
Fermi velocity of Weyl quasiparticles at frequency , and is the
electron charge in vacuum. Such universal enhancement of OC, which depends only
on the number of Weyl nodes near the Fermi level (), is a remarkable
consequence of an intriguing conspiracy among the quantum-critical nature of an
interacting Weyl liquid, marginal irrelevance of the long-range Coulomb
interaction and the violation of hyperscaling in three dimensions, and can
directly be measured in recently discovered Weyl as well as Dirac materials. By
contrast, a local density-density interaction produces a non-universal
correction to the OC, stemming from the non-renormalizable nature of the
corresponding interacting field theory.Comment: 21 Pages, 1 Figure: Published Version in PR
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