Zero-energy states in graphene quantum dots and rings

We present exact analytical zero-energy solutions for a class of smooth decaying potentials, showing that the full confinement of charge carriers in electrostatic potentials in graphene quantum dots and rings is indeed possible without recourse to magnetic fields. These exact solutions allow us to draw conclusions on the general requirements for the potential to support fully confined states, including a critical value of the potential strength and spatial extent.Comment: 8 pages, 3 figures, references added, typos corrected, discussion section expande

Ionization degree of the electron-hole plasma in semiconductor quantum wells

The degree of ionization of a nondegenerate two-dimensional electron-hole plasma is calculated using the modified law of mass action, which takes into account all bound and unbound states in a screened Coulomb potential. Application of the variable phase method to this potential allows us to treat scattering and bound states on the same footing. Inclusion of the scattering states leads to a strong deviation from the standard law of mass action. A qualitative difference between mid- and wide-gap semiconductors is demonstrated. For wide-gap semiconductors at room temperature, when the bare exciton binding energy is of the order of T, the equilibrium consists of an almost equal mixture of correlated electron-hole pairs and uncorrelated free carriers.Comment: 22 pages, 6 figure

Levinson's theorem and scattering phase shift contributions to the partition function of interacting gases in two dimensions

We consider scattering state contributions to the partition function of a two-dimensional (2D) plasma in addition to the bound-state sum. A partition function continuity requirement is used to provide a statistical mechanical heuristic proof of Levinson's theorem in two dimensions. We show that a proper account of scattering eliminates singularities in thermodynamic properties of the nonideal 2D gas caused by the emergence of additional bound states as the strength of an attractive potential is increased. The bound-state contribution to the partition function of the 2D gas, with a weak short-range attraction between its particles, is found to vanish logarithmically as the binding energy decreases. A consistent treatment of bound and scattering states in a screened Coulomb potential allowed us to calculate the quantum-mechanical second virial coefficient of the dilute 2D electron-hole plasma and to establish the difference between the nearly ideal electron-hole gas in GaAs and the strongly correlated exciton/free-carrier plasma in wide-gap semiconductors such as ZnSe or GaN.Comment: 10 pages, 3 figures; new version corrects some minor typo

Two-phonon scattering of magnetorotons in fractional quantum Hall liquids

We study the phonon-assisted process of dissociation of a magnetoroton, in a fractional quantum Hall liquid, into an unbound pair of quasiparticles. Whilst the dissociation is forbidden to first order in the electron-phonon interaction, it can occur as a two-phonon process. Depending on the value of final separation between the quasiparticles, the dissociation is either a single event involving absorption of one phonon and emission of another phonon of similar energy, or a two-phonon diffusion of a quasiexciton in momentum space. The dependence of the magnetoroton dissociation time on the filling factor of the incompressible liquid is found.Comment: 4 pages, no figure

Nanohelices as superlattices: Bloch oscillations and electric dipole transitions

Subjecting a nanohelix to a transverse electric field gives rise to superlattice behavior with tunable electronic properties. We theoretically investigate such a system and find Bloch oscillations and negative differential conductance when a longitudinal electric field (along the nanohelix axis) is also applied. Furthermore, we study dipole transitions across the transverse-electric-field-induced energy gap, which can be tuned to the eulogized terahertz frequency range by experimentally attainable external fields. We also reveal a photogalvanic effect by shining circularly polarized light onto our helical quantum wire.We acknowledge financial support from the CNRS and from the ANR under Grant No. ANR-14-CE26-0005 Q-MetaMat, as well as the EU H2020 RISE project CoExAN (Grant No. H2020-644076), EU FP7 ITN NOTEDEV (Grant No. FP7-607521), and the FP7 IRSES projects CANTOR (Grant No. FP7-612285), QOCaN (Grant No. FP7-316432), and InterNoM (Grant No. FP7-612624)

Addendum: “The two-dimensional hydrogen atom revisited” [J. Math. Phys. 43, 4681 (2002)]

Copyright © 2003 American Institute of Physic

Theory of anyon excitons: Relation to excitons of nu=1/3 and nu=2/3 incompressible liquids

Elementary excitations of incompressible quantum liquids (IQL's) are anyons, i.e., quasiparticles carrying fractional charges and obeying fractional statistics. To find out how the properties of these quasiparticles manifest themselves in the optical spectra, we have developed the anyon exciton model (AEM) and compared the results with the finite-size data for excitons of nu=1/3 and nu=2/3 IQL's. The model considers an exciton as a neutral composite consisting of three quasielectrons and a single hole. The AEM works well when the separation between electron and hole confinement planes, h, is larger than the magnetic length l. In the framework of the AEM an exciton possesses momentum k and two internal quantum numbers, one of which can be chosen as the angular momentum, L, of the k=0 state. Existence of the internal degrees of freedom results in the multiple branch energy spectrum, crater-like electron density shape and 120 degrees density correlations for k=0 excitons, and the splitting of the electron shell into bunches for non-zero k excitons. For h larger than 2l the bottom states obey the superselection rule L=3m (m are integers starting from 2), all of them are hard core states. For h nearly 2l there is one-to-one correspondence between the low-energy spectra found for the AEM and the many- electron exciton spectra of the nu=2/3 IQL, whereas some states are absent from the many-electron spectra of the nu=1/3 IQL. We argue that this striking difference in the spectra originates from the different populational statistics of the quasielectrons of charge conjugate IQL's and show that the proper account of the statistical requirements eliminates excessive states from the spectrum. Apparently, this phenomenon is the first manifestation of the exclusion statistics in the anyon bound states.Comment: 26 pages with 9 figures, typos correcte

Spin-orbit terms in multi-subband electron systems: A bridge between bulk and two-dimensional Hamiltonians

We analyze the spin-orbit terms in multi-subband quasi-two-dimensional electron systems, and how they descend from the bulk Hamiltonian of the conduction band. Measurements of spin-orbit terms in one subband alone are shown to give incomplete information on the spin-orbit Hamiltonian of the system. They should be complemented by measurements of inter-subband spin-orbit matrix elements. Tuning electron energy levels with a quantizing magnetic field is proposed as an experimental approach to this problem.Comment: Typos noticed in the published version have been corrected and several references added. Published in the special issue of Semiconductors in memory of V.I. Pere

Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.Comment: Revtex file 14 pages, submitted to Phys. Rev.

Electron-phonon scattering at the intersection of two Landau levels

We predict a double-resonant feature in the magnetic field dependence of the phonon-mediated longitudinal conductivity $\sigma_{xx}$ of a two-subband quasi-two-dimensional electron system in a quantizing magnetic field. The two sharp peaks in $\sigma_{xx}$ appear when the energy separation between two Landau levels belonging to different size-quantization subbands is favorable for acoustic-phonon transitions. One-phonon and two-phonon mechanisms of electron conductivity are calculated and mutually compared. The phonon-mediated interaction between the intersecting Landau levels is considered and no avoided crossing is found at thermal equilibrium.Comment: 13 pages, 8 figure