arXiv subjects

Eugene B. Kolomeisky

Publications and source records attributed to Eugene B. Kolomeisky.

At least 37 records · Page 2Linked to original sources

arXiv2018

Kelvin-Mach wake in a two-dimensional Fermi sea

The dispersion law for plasma oscillations in a two-dimensional electron gas in the hydrodynamic approximation interpolates between $Ω\propto \sqrt{q}$ and $Ω\propto q$ dependences as the wave vector $q$ increases. As a result, downstream of a charged impurity in the presence of a uniform supersonic electric current flow, a wake pattern of induced charge density and potential is formed whose geometry is controlled by the Mach number $M$. For $1 \sqrt{2}$. These wakes also trail an external charge traveling supersonically a fixed distance away from the electron gas.

cond-mat.mes-hall↗

arXiv2017

Screening and plasma oscillations in an electron gas in the hydrodynamic approximation

A hydrodynamic theory of screening in a generic electron gas of arbitrary dimensionality is given that encompasses all previously studied cases and clarifies the predictions of the many-body approach. We find that long-wavelength plasma oscillations are classical phenomena with quantum-mechanical effects playing no explicit role. The character of the oscillations is solely dictated by the dimensionality of the electron system and its equation of state in the neutral limit. Materials whose excitations are described by the Dirac dispersion law -- such as doped graphene or a Weyl semimetal -- are no exception to this rule.

cond-mat.mes-hall↗

arXiv2017

Casimir interaction of arbitrarily shaped conductors

We review a systematic practical implementation of the multiple scattering formalism due to Balian and Duplantier [R. Balian and B. Duplantier, Ann. Phys. (NY) \textbf{104}, 300 (1977); \textbf{112}, 165 (1978)] for the calculation of the Casimir interaction between arbitrarily shaped smooth conductors. The leading two-point scattering term of the expansion has a simple compact form, amenable to exact or accurate numerical evaluation. It is a general expression which improves upon the proximity force and pairwise summation approximations. We show that for many geometries it captures the bulk of the interaction effect. The inclusion of terms beyond the two-point approximation provides an accuracy check and explains screening. As an illustration of the power and versatility of the method we re-evaluate sphere-sphere and sphere-plane interactions and compared the results with previous findings that employed different methods. We also compute for the first time interaction of a hyperboloid (mimicking an atomic force microscope tip) and a plane. We also analyze the anomalous situations involving long cylindrical conductors where the two-point scattering approximation fails qualitatively. In such cases analytic summation of the entire scattering series is carried out and a topological argument is put forward as an explanation of the result. We give the extension of this theory to the case of finite temperatures where the two-point scattering approximation result has a simple compact form, also amenable to exact or accurate numerical evaluation.

cond-mat.mes-hall↗

arXiv2017

Relaxation of charge in monolayer graphene: fast non-linear diffusion vs Coulomb effects

Pristine monolayer graphene exhibits very poor screening because the density of states vanishes at the Dirac point. As a result, charge relaxation is controlled by the effects of zero-point motion (rather than by the Coulomb interaction) over a wide range of parameters. Combined with the fact that graphene possesses finite intrinsic conductivity, this leads to a regime of relaxation described by a non-linear diffusion equation with a diffusion coefficient that diverges at zero charge density. Some consequences of this fast diffusion are self-similar superdiffusive regimes of relaxation, the development of a charge depleted region at the interface between electron- and hole-rich regions, and finite extinction times for periodic charge profiles.

cond-mat.mes-hall↗

arXiv2016

Anomalous screening in two-dimensional materials with an extremum ring in the dispersion law

A variety of two-dimensional materials possess a band structure with an energy extremal ridge along a ring in momentum space. Examples are biased bilayer graphene, and surfaces and interfaces with a Rashba spin-orbit interaction where at low doping the carriers fill an annulus. This topological feature causes an anomalous screening behavior, which we study using the Thomas-Fermi theory. Specifically, reducing the doping is predicted to enhance the linear screening response, while at zero doping the size of the screening cloud surrounding a Coulomb impurity is found to increase as the cube root of the impurity charge.

cond-mat.mes-hall↗

arXiv2016

Space charge and screening in bilayer graphene

Undoped bilayer graphene is a two-dimensional semimetal with a low-energy excitation spectrum that is parabolic in the momentum. As a result, the screening of an arbitrary external charge $Ze$ is accompanied by a reconstruction of the ground state: valence band electrons (for $Z>0$) are promoted to form a space charge around the charge while the holes leave the physical picture. The outcome is flat neutral object resembling the regular atom except that for $Z \gg 1$ it is described by a strictly linear Thomas-Fermi theory. This theory also predicts that the bilayer's static dielectric constant is the same as that of a two-dimensional electron gas in the long-wavelength limit.

cond-mat.mes-hall↗

arXiv2015

Optimal number of terms in QED series and its consequence in condensed matter implementations of QED

In 1952 Dyson put forward a simple and powerful argument indicating that the perturbative expansions of QED are asymptotic. His argument can be related to Chandrasekhar's limit on the mass of a star for stability against gravitational collapse. Combining these two arguments we estimate the optimal number of terms of the QED series to be $3.1(137)^{3/2}\approx5000$. For condensed matter manifestations of QED in narrow band-gap semiconductors and Weyl semimetals the optimal number of terms is around $80$ while in graphene the utility of the perturbation theory is severely limited.

cond-mat.mes-hall↗

arXiv2014

Aharonov-Bohm effect in clean strong topological insulator wires

Surface electrons of strong topological insulator wires acquire a Berry phase difference of $π$ on orbiting the wire. This can be detected in response of clean wires (whose Fermi level is tuned to the Dirac point) to the presence of the Aharonov-Bohm flux. Specifically, at half-odd integer applied flux (in units of $hc/e$), long wires undergo semimetal-semiconductor transitions characterized by logarithmically divergent susceptibility. Associated with these are oscillations of magnetization (persistent current) that vanish both at integer and half-odd integer flux. Additionally wires of arbitrary aspect ratio exhibit conductance maxima at half-odd integer applied flux and minima at integer flux. For long wires the maxima are sharp with their height approaching $e^{2}/h$. Short wires are characterized by a universal conductivity $e^{2}/πh$ attained in the disc limit.

cond-mat.mes-hall↗

arXiv2014

Casimir energy of smooth compact surfaces

We discuss the formalism of Balian and Duplantier for the calculation of the Casimir energy for an arbitrary smooth compact surface, and use it to give some examples: a finite cylinder with hemispherical caps, the torus, ellipsoid of revolution, a "cube" with rounded corners and edges, and a "drum" made of disks and part of a torus. We propose a model function which approximately captures the shape dependence of the Casimir energy.

cond-mat.stat-mech↗

arXiv2014

Casimir energy of a cylindrical shell of elliptical cross section

We calculate the increase in the number of modes (the Kac number) per unit length and the change in the zero-point energy (the Casimir energy) of the electromagnetic field resulting from the introduction of a thin perfectly conducting cylindrical shell of elliptical cross-section. Along the way we give a novel route to the calculation of these physical quantities. The Casimir energy is found to be attractive with the circular case corresponding to the energy maximum and the large eccentricity limit being the divergent energy minimum. As a result, with only Casimir stresses present, a fixed area shell is unstable with respect to collapse onto itself. This instability is argued to persist at arbitrary temperature.

cond-mat.stat-mech↗

arXiv2013

Fermion space charge in narrow-band gap semiconductors, Weyl semimetals and around highly charged nuclei

The field of charged impurities in narrow-band gap semiconductors and Weyl semimetals can create electron-hole pairs when the total charge $Ze$ of the impurity exceeds a value $Z_{c}e$. The particles of one charge escape to infinity, leaving a screening space charge. The result is that the observable dimensionless impurity charge $Q_{\infty}$ is less than $Z$ but greater than $Z_{c}$. There is a corresponding effect for nuclei with $Z >Z_{c} \approx 170$, however in the condensed matter setting we find $Z_{c} \simeq 10$. Thomas-Fermi theory indicates that $Q_{\infty} = 0$ for the Weyl semimetal, but we argue that this is a defect of the theory. For the case of a highly-charged recombination center in a narrow band-gap semiconductor (or of a supercharged nucleus), the observable charge takes on a nearly universal value. In Weyl semimetals the observable charge takes on the universal value $Q_{\infty} = Z_{c}$ set by the reciprocal of material's fine structure constant.

cond-mat.mes-hall↗

arXiv2013

Optimal number of terms in QED series

hep-th↗

arXiv2013

Weyl problem and Casimir effects in spherical shell geometry

We compute the generic mode sum that quantifies the effect on the spectrum of a harmonic field when a spherical shell is inserted into vacuum. This encompasses a variety of problems including the Weyl spectral problem and the Casimir effect of quantum electrodynamics. This allows us to resolve several long-standing controversies regarding the question of universality of the Casimir self-energy; the resolution comes naturally through the connection to the Weyl problem. Specifically we demonstrate that in the case of a scalar field obeying Dirichlet or Neumann boundary conditions on the shell surface the Casimir self-energy is cutoff-dependent while in the case of the electromagnetic field perturbed by a conductive shell the Casimir self-energy is universal. We additionally show that an analog non-relativistic Casimir effect due to zero-point magnons takes place when a non-magnetic spherical shell is inserted inside a bulk ferromagnet.

cond-mat.stat-mech↗

arXiv2012

Fermion condensation around a Coulomb impurity in a Weyl semimetal and in a narrow band gap semiconductor as manifestations of the Landau zero-charge problem

A Coulomb impurity placed in an undoped Weyl semimetal spontaneously surrounds itself with a cloud of condensed Weyl fermions. We find that the ground-state of this system exhibits an experimentally accessible Landau zero-charge effect: the fermion condensate completely screens out the impurity charge. In a narrow band gap semiconducor this effect manifests itself in the near universality of observable charge of a highly-charged recombination center.

cond-mat.mes-hall↗

arXiv2012

Fermion condensation around a Coulomb impurity in a Weyl semimetal as a manifestation of the Landau zero-charge problem

A Coulomb impurity placed in an undoped Weyl semimetal spontaneously surrounds itself with a cloud of condensed Weyl fermions. We study this system within the Thomas-Fermi approximation. We find that the ground-state of the system is electrically neutral and exhibits an experimentally accessible Landau zero-charge effect: the impurity charge is screened out at any finite distance in the limit of vanishing impurity size. Specifically, we show how in this limit the Thomas-Fermi equation for the electrostatic potential transforms into the Gell-Mann-Low equation for the charge.

cond-mat.mes-hall↗

arXiv2012

Brownian motion of the electron and the Lamb shift at finite temperature

By enhancing electron position fluctuations, equilibrium electromagnetic radiation modifies the potential for an electron in a Hydrogen atom. This can have significant effects for weakly bound states and especially at finite temperature. This implies a 2% correction to Bethe's value for 2S-2P Lamb shift for weak fluctuations, but the effect is an order of magnitude larger for strong fluctuations where it provides direct measure of the proton diameter.

physics.atom-ph↗

arXiv2012

Interplay of Aharonov-Bohm, chirality, and aspect ratio effects in the axial conductance of a nanotube

A magnetic flux applied along the axis of a nanotube can counteract the effect of the tube chirality and dramatically affect its conductance, leading to a way to determine the chirality of a nanotube. The effect of the applied flux is strongest in the long tube limit where the conductance is (i) either a sequence of sharp $4e^{2}/h$ height peaks located at integer (in units of the flux quantum) values of the flux (for an armchair tube) or (ii) a periodic sequence of pairs of $2e^{2}/h$ height peaks for a chiral tube, with the spacing determined by the chirality. In the short tube limit the conductance takes on the value that gives the universal conductivity of an undoped graphene sheet, with a small amplitude modulation periodic in the flux.

cond-mat.mes-hall↗

arXiv2010

Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.

cond-mat.mes-hall↗