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Register a new userDynamical polarizability, screening, and plasmons in one, two, and three dimensional massive Dirac systems
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We study the density-density response function of a collection of charged massive Dirac particles and present analytical expressions for the dynamical polarization function in one, two and three dimensions. The polarization function is then used to find the dispersion of the plasmon modes, and electrostatic screening of Coulomb interactions within the random phase approximation. We find that for massive Dirac systems, the oscillating screened potential decays as $r^{-1}$, $r^{-2}$ and $r^{-3}$ in one, two, and three dimensions respectively. However for massless Dirac systems there is no electrostatic screening or Friedel oscillation in one dimension, and the oscillating screened potential decays as $r^{-3}$ and $r^{-4}$, in two and three dimensions respectively. Our analytical results for the polarization function will be useful for exploring the physics of massive and massless Dirac materials in different experimental systems with varying dimensionality.
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Analytic solutions of the quantum relativistic two-body problem are obtained for an interaction potential modeled as a one-dimensional smooth square well. Both stationary and moving pairs are considered and the limit of the {delta}-function interaction is studied in depth. Our result can be utilized for understanding excitonic states in narrow-gap carbon nanotubes. We also show the existence of bound states within the gap for a pair of particles of the same charge.
Electrons on the liquid helium surface form an extremely clean two dimensional system where different plasmon-excitations can coexist. Under a magnetic field time reversal symmetry is broken and all the bulk magneto-plasmons become gaped at frequencies below cyclotron resonance while chiral one dimensional edge magneto-plasmons appear at the system perimeter. We theoretically show that the presence of a homogeneous density gradient in the electron gas leads to the formation of a delocalized magneto-plasmon mode in the same frequency range as the lowest frequency edge-magnetoplasmon mode. We experimentally confirm its existence by measuring the corresponding resonance peak in frequency dependence of the admittance of the electron gas. This allows to realize a prototype system to investigate the coupling between a chiral one-dimensional mode and a single delocalized bulk mode. Such a model system can be important for the understanding of transport properties of topological materials where states of different dimensionality can coexist.
The use of a nearby metallic ground-plane to limit the range of the Coulomb interactions between carriers is a useful approach in studying the physics of two-dimensional (2D) systems. This approach has been used to study Wigner crystallization of electrons on the surface of liquid helium, and most recently, the insulating and metallic states of semiconductor-based two-dimensional systems. In this paper, we perform calculations of the screening effect of one 2D system on another and show that a 2D system is at least as effective as a metal in screening Coulomb interactions. We also show that the recent observation of the reduced effect of the ground-plane when the 2D system is in the metallic regime is due to intralayer screening.
Dynamical screening function of the two-dimensional electron gas in wide HgTe quantum well (QW) has been numerically modelled in this work. Calculations were provided in the Random Phase Approximation (RPA) framework and were based on Lindhard equation. Our simulations directly incorporated non-parabolicity of bulk 2D carriers spectrum, which was obtained by full 8-band k.p method. In the literature exists data that transport properties of HgTe QWs are explained by graphene-like screening. We provide the comparison of the screening function for the Schrodinger fermions in the inverted bands HgTe QW with the appropriate screening function for graphene monolayer with the Dirac fermions. In addition, the dependencies of HgTe-specific screening function on temperature, scattering wave-vector and frequency are studied with the purpose to study the transport properties under high-frequency radiation the QWs structures to be used as THz detectors. Plasmon frequencies of 2DEG in HgTe quantum well under study were calculated in the long-wavelength limit for T=77K.
We investigate the effect of the mass anisotropy on Friedel Oscillations, Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, screening properties, and Boltzmann transport in two dimensional (2D) metallic and doped semiconductor systems. We calculate the static polarizability and the dielectric function within the random phase approximation with the mass anisotropy fully taken into account without making any effective isotropic approximation in the theory. We find that carrier screening exhibits an isotropic behavior for small momenta despite the anisotropy of the system, and becomes strongly anisotropic above a certain threshold momentum. Such an anisotropy of screening leads to anisotropic Friedel oscillations, and an anisotropic RKKY interaction characterized by a periodicity dependent on the direction between the localized magnetic moments. We also explore the disorder limited dc transport properties in the presence of mass anisotropy based on the Boltzmann transport theory. Interestingly, we find that the anisotropy ratio of the short range disorder limited resistivity along the heavy- and light-mass directions is always the same as the mass anisotropy ratio whereas for the long range disorder limited resistivity the anisotropy ratio is the same as the mass ratio only in the low density limit, and saturates to the square root of the mass ratio in the high density limit. Our theoretical work should apply to many existing and to-be-discovered anisotropic 2D systems.
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