[Show abstract][Hide abstract] ABSTRACT: The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being self-interaction free and having the correct −1/r asymptotics. In this paper we extend the localized Hartree-Fock potential to fractional particle numbers and observe that it yields derivative discontinuities in the energy as required by the exact theory. The discontinuities are numerically close to those of the computationally more demanding Hartree-Fock method. Our potential enjoys a “direct-energy” property, whereby the energy of the system is given by the sum of the single-particle eigenvalues multiplied by the corresponding occupation numbers. The discontinuities c
↑ and c
↓ of the spin-components of the potential at integer particle numbers N
↑ and N
↓ satisfy the condition c
↑
N
↑ + c
↓
N
↓ = 0. Thus, joining the family of effective potentials which support a derivative discontinuity, but being considerably easier to implement, the localized Hartree-Fock potential becomes a powerful tool in the broad area of applications in which the fundamental gap is an issue.
The Journal of Chemical Physics 07/2015; 143(6). DOI:10.1063/1.4928514 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The Wiedemann-Franz law, connecting the electronic thermal conductivity to the electrical conductivity of a disordered metal, is generally found to be well satisfied even when electron-electron (e-e) interactions are strong. In ultraclean conductors in the hydrodynamic regime, however, large deviations from the standard form of the law are expected, due to the fact that e-e interactions affect the two conductivities in radically different ways. Thus, the standard Wiedemann-Franz ratio between the thermal and the electric conductivity is reduced by a factor 1+τ/τ_{th}^{ee}, where 1/τ is the momentum relaxation rate and τ_{th}^{ee} is the relaxation time of the thermal current due to e-e collisions. Here we study the density and temperature dependence of 1/τ_{th}^{ee} of two-dimensional electron liquids. We show that at low temperature 1/τ_{th}^{ee} is 8/5 of the quasiparticle decay rate; remarkably, the same result is found in doped graphene and in conventional electron liquids in parabolic bands.
[Show abstract][Hide abstract] ABSTRACT: It is well known that a current driven through a two-dimensional electron gas
with Rashba spin-orbit coupling induces a spin polarization in the
perpendicular direction (Edelstein effect). This phenomenon has been
extensively studied in the linear response regime, i.e., when the average drift
velocity of the electrons is a small fraction of the Fermi velocity. Here we
investigate the phenomenon in the nonlinear regime, meaning that the average
drift velocity is comparable to, or exceeds the Fermi velocity. This regime is
realized when the electric field is very large, or when electron-impurity
scattering is very weak. The quantum kinetic equation for the density matrix of
noninteracting electrons is exactly and analytically solvable, reducing to a
problem of spin dynamics for "unpaired" electrons near the Fermi surface. The
crucial parameter is $\gamma=eEL_s/E_F$, where $E$ is the electric field, $e$
is the absolute value of the electron charge, $E_F$ is the Fermi energy, and
$L_s = \hbar/(2m\alpha)$ is the spin-precession length in the Rashba spin-orbit
field with coupling strength $\alpha$. If $\gamma\ll1$ the evolution of the
spin is adiabatic, resulting in a spin polarization that grows monotonically in
time and eventually saturates at the maximum value $n(\alpha/v_F)$, where $n$
is the electron density and $v_F$ is the Fermi velocity. If $\gamma \gg 1$ the
evolution of the spin becomes strongly non-adiabatic and the spin polarization
is progressively reduced, and eventually suppressed for $\gamma\to \infty$. We
also predict an inverse nonlinear Edelstein effect, in which an electric
current is driven by a magnetic field that grows linearly in time. The
"conductivities" for the direct and the inverse effect satisfy generalized
Onsager reciprocity relations, which reduce to the standard ones in the linear
response regime.
[Show abstract][Hide abstract] ABSTRACT: Hydrodynamic flow occurs in an electron liquid when the mean free path for
electron-electron collisions is the shortest length scale in the problem. In
this regime, transport is described by the Navier-Stokes equation, which
contains two fundamental parameters, the bulk and shear viscosities. In this
Article we present extensive results for these transport coefficients in the
case of the two-dimensional massless Dirac fermion liquid in a doped graphene
sheet. Our approach relies on microscopic calculations of the viscosities up to
second order in the strength of electron-electron interactions and in the
high-frequency limit, where perturbation theory is applicable. We then use
simple interpolation formulae that allow to reach the low-frequency
hydrodynamic regime where perturbation theory is no longer directly applicable.
The key ingredient for the interpolation formulae is the "viscosity transport
time" $\tau_{\rm v}$, which we calculate in this Article. The transverse nature
of the excitations contributing to $\tau_{\rm v}$ leads to the suppression of
scattering events with small momentum transfer, which are inherently
longitudinal. Therefore, contrary to the quasiparticle lifetime, which goes as
$-1/[T^2 \ln(T/T_{\rm F})]$, in the low temperature limit we find $\tau_{\rm v}
\sim 1/T^2$.
[Show abstract][Hide abstract] ABSTRACT: We study the collective charge excitations (plasmons) in spin polarized
graphene, and derive explicit expressions for their dispersion in the undamped
regime. From this, we are able to calculate the critical wave vector beyond
which the plasmon enters the electron-hole continuum, its quality factor
decreasing sharply. We find that the value of the critical wave vector is
strongly spin polarization-dependent, in a way that has no analogue in ordinary
two-dimensional electron gases. The origin of this effect is in the coupling
between the plasmon and the inter-band electron-hole pairs of the minority spin
carriers. We show that the effect is robust with respect to the inclusion of
disorder and we suggest that it can be exploited to experimentally determine
the spin polarization of graphene.
Physical Review B 05/2015; 91(24). DOI:10.1103/PhysRevB.91.245407 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Graphene plasmons were predicted to possess ultra-strong field confinement and very low damping at the same time, enabling new classes of devices for deep subwavelength metamaterials, single-photon nonlinearities, extraordinarily strong light-matter interactions and nano-optoelectronic switches. While all of these great prospects require low damping, thus far strong plasmon damping was observed, with both impurity scattering and many-body effects in graphene proposed as possible explanations. With the advent of van der Waals heterostructures, new methods have been developed to integrate graphene with other atomically flat materials. In this letter we exploit near-field microscopy to image propagating plasmons in high quality graphene encapsulated between two films of hexagonal boron nitride (h-BN). We determine dispersion and particularly plasmon damping in real space. We find unprecedented low plasmon damping combined with strong field confinement, and identify the main damping channels as intrinsic thermal phonons in the graphene and dielectric losses in the h-BN. The observation and in-depth understanding of low plasmon damping is the key for the development of graphene nano-photonic and nano-optoelectronic devices.
Nature Material 04/2015; 14(4):421-425. DOI:10.1038/nmat4169 · 36.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We explore the collective density oscillations of a collection of charged massive Dirac particles, in one, two and three dimensions and their one dimensional superlattice. We calculate the long wavelength limit of the dynamical polarization function analytically, and use the random phase approximation to obtain the plasmon dispersion. The density dependence of the long wavelength plasmon frequency in massive Dirac systems is found to be different as compared to systems with parabolic, and gapless Dirac dispersion. We also calculate the long wavelength plasmon dispersion of a 1d metamaterial made from 1d and 2d massive Dirac plasma. Our analytical results will be useful for exploring the use of massive Dirac materials as electrostatically tunable plasmonic metamaterials and can be experimentally verified by infrared spectroscopy as in the case of graphene [Nat. Nanotechnol. 6, 630 (2011)].
Physical Review B 02/2015; 91:205426. DOI:10.1103/PhysRevB.91.205426 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We explore the collective density oscillations of a collection of charged
massive Dirac particles, in one, two and three dimensions and their one
dimensional superlattice. We calculate the long wavelength limit of the
dynamical polarization function analytically, and use the random phase
approximation to obtain the plasmon dispersion. The density dependence of the
long wavelength plasmon frequency in massive Dirac systems is found to be
different as compared to systems with parabolic, and gapless Dirac dispersion.
We also calculate the long wavelength plasmon dispersion of a 1d metamaterial
made from 1d and 2d massive Dirac plasma. Our analytical results will be useful
for exploring the use of massive Dirac materials as electrostatically tunable
plasmonic metamaterials and can be experimentally verified by infrared
spectroscopy as in the case of graphene [Nat. Nanotechnol. 6, 630 (2011)].
[Show abstract][Hide abstract] ABSTRACT: We analyze the effect known as "spin current swapping" due to
electron-impurity scattering in a two-dimensional electron gas. In this effect
a primary spin current $J_i^a$ (lower index for spatial direction, upper index
for spin direction) generates a secondary spin current $J_a^i$ if $i \neq a$,
or $J_j^j$ with $j\ne i$ if $i= a$. By employing microscopic diagrammatic
calculations, as well as spin-dependent drift-diffusion equations, we show
that, contrary to naive expectation, the homogeneous spin current associated
with the uniform drift of the spin polarization in the presence of an electric
field does not act a source of spin current swapping. On the other hand, the
inhomogeneous spin current associated with spin diffusion is a legitimate
source of spin current swapping and does generate a transverse spin current. An
experimental setup for the observation of the effect is therefore proposed.
Physical Review B 02/2015; 92:035301. DOI:10.1103/PhysRevB.92.035301 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We provide a heuristic derivation of the "Inverse Edelstein Effect" (IEE), in which a non-equilibrium spin accumulation in the plane of a two-dimensional (interfacial) electron gas drives an electric current perpendicular to its own direction. The drift-diffusion equations that govern the effect are derived and applied to the interpretation of recent experiments. A brief analysis based on the Kubo formula shows that the result is valid also outside the diffusive regime, i.e. when spin and momentum relaxation become comparable.
Acta Physica Polonica Series a 02/2015; 127(2):454-456. DOI:10.12693/APhysPolA.127.454 · 0.53 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The experimental availability of ultra-high-mobility samples of graphene
opens the possibility to realize and study experimentally the "hydrodynamic"
regime of the electron liquid. In this regime the rate of electron-electron
collisions is extremely high and dominates over the electron-impurity and
electron-phonon scattering rates, which are therefore neglected. The system is
brought to a local quasi-equilibrium described by a set of smoothly varying (in
space and time) functions, {\it i.e.} the density, the velocity field and the
local temperature. In this paper we calculate the charge and spin
conductivities of doped graphene due solely to electron-electron interactions.
We show that, in spite of the linear low-energy band dispersion, graphene
behaves in a wide range of temperatures as an effectively Galilean invariant
system: the charge conductivity diverges in the limit $T \to 0$, while the spin
conductivity remains finite. These results pave the way to the description of
charge transport in graphene in terms of Navier-Stokes equations.
Physical Review B 01/2015; 91(20). DOI:10.1103/PhysRevB.91.205423 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the Kondo effect in three-dimensional (3D) Dirac materials and Weyl
semimetals. We find the scaling of the Kondo temperature with respect to the
doping $n$ and the coupling $J$ between the moment of the magnetic impurity and
the carriers of the semimetal. We find that when the temperature is much
smaller than the Kondo temperature the resistivity due to the Kondo effect
scales as the $n^{-4/3}$.We also study the effect of the interplay of
long-range scalar disorder and Kondo effect. In the presence of
disorder-induced long-range carrier density inhomogeneities the Kondo effect is
not characterized by a Kondo temperature but by a distribution of Kondo
temperatures. We obtain the expression of such distribution and show that its
features cause the appearance of strong non-Fermi liquid behavior. Finally we
compare the properties of the Kondo effect in 3D Dirac materials and 2D Dirac
systems like graphene and topological insulators.
Physical Review B 10/2014; 92(4). DOI:10.1103/PhysRevB.92.041107 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The broken inversion symmetry at the surface of a metallic film (or, more
generally, at the interface between a metallic film and a different metallic or
insulating material) greatly amplifies the influence of the spin-orbit
interaction on the surface properties. The best known manifestation of this
effect is the momentum-dependent splitting of the surface state energies
(Rashba effect). Here we show that the same interaction also generates a
spin-polarization of the bulk states when an electric current is driven through
the bulk of the film. For a semi-infinite jellium model, which is
representative of metals with a closed Fermi surface, we prove as a theorem
that, regardless of the shape of the confinement potential, the induced surface
spin density at each surface is given by ${\bf S} =-\gamma \hbar {\bf \hat
z}\times {\bf j}$, where ${\bf j}$ is the particle current density in the bulk,
${\bf \hat z}$ the unit vector normal to the surface, and
$\gamma=\frac{\hbar}{4mc^2}$ contains only fundamental constants. For a general
metallic solid $\gamma$ becomes a material-specific parameter that controls the
strength of the interfacial spin-orbit coupling. Our theorem, combined with an
{\it ab initio} calculation of the spin polarization of the current-carrying
film, enables a determination of $\gamma$, which should be useful in modeling
the spin-dependent scattering of quasiparticles at the interface.
Physical Review B 10/2014; 91(3). DOI:10.1103/PhysRevB.91.035403 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Graphene sheets encapsulated between hexagonal Boron Nitride (hBN) slabs
display superb electronic properties due to very limited scattering from
extrinsic disorder sources such as Coulomb impurities and corrugations. Such
samples are therefore expected to be ideal platforms for highly-tunable
low-loss plasmonics in a wide spectral range. In this Article we present a
theory of collective electron density oscillations in a graphene sheet
encapsulated between two hBN semi-infinite slabs (hBN/G/hBN). Graphene plasmons
hybridize with hBN optical phonons forming hybrid plasmon-phonon (HPP) modes.
We focus on scattering of these modes against graphene's acoustic phonons and
hBN optical phonons, two sources of scattering that are expected to play a key
role in hBN/G/hBN stacks. We find that at room temperature the scattering
against graphene's acoustic phonons is the dominant limiting factor for
hBN/G/hBN stacks, yielding theoretical inverse damping ratios of hybrid
plasmon-phonon modes of the order of $50$-$60$, with a weak dependence on
carrier density and a strong dependence on illumination frequency. We confirm
that the plasmon lifetime is not directly correlated with the mobility: in
fact, it can be anti-correlated.
Physical Review B 10/2014; 90(16):165408. DOI:10.1103/PhysRevB.90.165408 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Spin-orbit interactions in two-dimensional electron liquids are responsible
for many interesting transport phenomena in which particle currents are
converted to spin polarizations and spin currents and viceversa. Prime examples
are the spin Hall effect, the Edelstein effect, and their inverses. By similar
mechanisms it is also possible to partially convert an optically induced
electron-hole density wave to a spin density wave and viceversa. In this paper
we present a unified theoretical treatment of these effects based on quantum
kinetic equations that include not only the intrinsic spin-orbit coupling from
the band structure of the host material, but also the spin-orbit coupling due
to an external electric field and a random impurity potential. The
drift-diffusion equations we derive in the diffusive regime are applicable to a
broad variety of experimental situations, both homogeneous and non-homogeneous,
and include on equal footing "skew scattering" and "side-jump" from
electron-impurity collisions. As a demonstration of the strength and usefulness
of the theory we apply it to the study of several effects of current
experimental interest: the inverse Edelstein effect, the spin-current swapping
effect, and the partial conversion of an electron-hole density wave to a spin
density wave in a two-dimensional electron gas with Rashba and Dresselhaus
spin-orbit couplings, subject to an electric field.
Physical Review B 09/2014; DOI:10.1103/PhysRevB.90.245302 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate the effects of inhomogeneities on spin entanglement in
many-electron systems from an ab-initio approach. The key quantity in our
approach is the local spin entanglement length, which is derived from the local
concurrence of the electronic system. Although the concurrence for an
interacting systems is a highly nonlocal functional of the density, it does
have a simple, albeit approximate expression in terms of Kohn-Sham orbitals. We
show that the electron localization function -- well known in quantum chemistry
as a descriptor of atomic shells and molecular bonds -- can be reinterpreted in
terms of the ratio of the local entanglement length of the inhomogeneous system
to the entanglement length of a homogenous system at the same density. We find
that the spin entanglement is remarkably enhanced in atomic shells and
molecular bonds.
Physical Review B 09/2014; 91(7). DOI:10.1103/PhysRevB.91.075109 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Thermoelectric transport in nanoscale conductors is analyzed in terms of the
response of the system to a thermo-mechanical field, first introduced by
Luttinger, which couples to the electronic energy density. While in this
approach the temperature remains spatially uniform, we show that a spatially
varying thermo-mechanical field effectively simulates a temperature gradient
across the system and allows us to calculate the electric and thermal currents
that flow due to the thermo-mechanical field. In particular, we show that, in
the long-time limit, the currents thus calculated reduce to those that one
obtains from the Landauer-B{\"u}ttiker formula, suitably generalized to allow
for different temperatures in the reservoirs, if the thermo-mechanical field is
applied to prepare the system, and subsequently turned off at ${t=0}$.
Alternately, we can drive the system out of equilibrium by switching the
thermo-mechanical field after the initial preparation. We compare these two
scenarios, employing a model noninteracting Hamiltonian, in the linear regime,
in which they coincide, and in the nonlinear regime in which they show marked
differences. We also show how an operationally defined local effective
temperature can be computed within this formalism.
Physical Review B 07/2014; 90(11). DOI:10.1103/PhysRevB.90.115116 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The Wiedemann-Franz law, connecting the electronic thermal conductivity to
the electrical conductivity of a disordered metal, is generally found to be
well satisfied even when electron-electron (e-e) interactions are strong. In
ultra-clean conductors, however, large deviations from the standard form of the
law are expected, due to the fact that e-e interactions affect the two
conductivities in radically different ways. Thus, the standard Wiedemann-Franz
ratio between the thermal and the electric conductivity is reduced by a factor
$1+\tau/\tau_{\rm th}^{\rm ee}$, where $1/\tau$ is the momentum relaxation
rate, and $1/\tau_{\rm th}^{\rm ee}$ is the relaxation time of the thermal
current due to e-e collisions. Here we study the density and temperature
dependence of $1/\tau_{\rm th}^{\rm ee}$ in the important case of doped, clean
single layers of graphene, which exhibit record-high thermal conductivities. We
show that at low temperature $1/\tau_{\rm th}^{\rm ee}$ is $8/5$ of the
quasiparticle decay rate. We also show that the many-body renormalization of
the thermal Drude weight coincides with that of the Fermi velocity.