Orientation dependence of the optical spectra in graphene at high frequencies

On the basis of the Kubo formula we evaluated the optical conductivity of a graphene sheet. The full behavior of frequency as well as temperature dependence of the optical conductivity is presented. We show that the anisotropy of conductivity can be significantly enhanced at high frequencies. The photon absorption depends on the field polarization direction. At the frequency comparable to the maximum separation of upper and lower bands the photon-induced conduction of electrons is strongly suppressed if the polarization of field is along the zigzag direction. The corresponding optical conductivity is several orders of magnitude weaker than that when the light is polarizing along the armchair direction. We propose that the property of orientation selection of absorption in the graphene can be used as a basis for a high-frequency partial polarizer.Comment: 5 pages, 5 figure

Charge and Spin Transport at the Quantum Hall Edge of Graphene

Landau level bending near the edge of graphene, described using 2d Dirac equation, provides a microscopic framework for understanding the quantum Hall Effect (QHE) in this material. We review properties of the QHE edge states in graphene, with emphasis on the novel phenomena that arise due to Dirac character of electronic states. A method of mapping out the dispersion of the edge states using scanning tunneling probes is proposed. The Zeeman splitting of Landau levels is shown to create a particularly interesting situation around the Dirac point, where it gives rise to counter-circulating modes with opposite spin. These chiral spin modes lead to a rich variety of spin transport phenomena, including spin Hall effect, spin filtering and injection, and electric detection of spin current. The estimated Zeeman spin gap, enhanced by exchange, of a few hundred Kelvin, makes graphene an attractive system for spintronics. Comparison to recent transport measurements near nu=0 is presented.Comment: 10 pages, 6 figures, invited pape

Many-body exchange-correlation effects in graphene

We calculate, within the leading-order dynamical-screening approximation, the electron self-energy and spectral function at zero temperature for extrinsic (or gated/doped) graphene. We also calculate hot carrier inelastic scattering due to electron-electron interactions in graphene. We obtain the inelastic quasiparticle lifetimes and associated mean free paths from the calculated self-energy. The linear dispersion and chiral property of graphene gives energy dependent lifetimes that are qualitatively different from those of parabolic-band semiconductors.Comment: Submitted on July 8, 2007 to EP2DS-17, Genova, Ital

Raman imaging and electronic properties of graphene

Graphite is a well-studied material with known electronic and optical properties. Graphene, on the other hand, which is just one layer of carbon atoms arranged in a hexagonal lattice, has been studied theoretically for quite some time but has only recently become accessible for experiments. Here we demonstrate how single- and multi-layer graphene can be unambiguously identified using Raman scattering. Furthermore, we use a scanning Raman set-up to image few-layer graphene flakes of various heights. In transport experiments we measure weak localization and conductance fluctuations in a graphene flake of about 7 monolayer thickness. We obtain a phase-coherence length of about 2 $\mu$m at a temperature of 2 K. Furthermore we investigate the conductivity through single-layer graphene flakes and the tuning of electron and hole densities via a back gate

О вычислении группы классов идеалов мнимых мультиквадратичных полей

In the paper, we extend Biasse | van Vredendaal (OBS, 2019, vol. 2) implementation and experiments of the class group computation from real to imaginary multi-quadratic elds. The implementation is optimized by introducing an explicit prime ideal lift operation and by using LLL reduction instead of HNF computation. We provide examples of class group computation of the imaginary multiquadratic elds of degree 64 and 128, that has been previously unreachable

Hyperelliptic curves, Cartier-Manin matrices and Legendre polynomials

We investigate the hyperelliptic curves of the form C1 : y2 = x2g+1 + ax9+1 + bx and C2 : y2 = x2g+2 + ax9+1 + b over the finite field Fq, q = pn, p > 2. We transform these curves to the form C1,p : y2 = x2g+1 —2px9+1 + x and C2,p : y2 = x2g+2 — 2px9+1 + 1 and prove that the coefficients of corresponding Cartier — Manin matrices are Legendre polynomials. As a consequence, the matrices are centrosymmetric and, therefore, it’s enough to compute a half of coefficients to compute the matrix. Moreover, they are equivalent to block-diagonal matrices under transformation of the form S(p)WS-1 . In the case of gcd(p,g) = 1, the matrices are monomial, and we prove that characteristic polynomial of the Frobenius endomorphism x(A) (mod p) can be found in factored form in terms of Legendre polynomials by using permutation attached to the monomial matrix. As an application of our results, we list all the possible polynomials x(A) (mod p) for the case of gcd(p,g) = 1, g e {1,. . ., 7} and the curve C1 is over Fp or Fp2

Hyperelliptic curves, Cartier - Manin matrices and Legendre polynomials

Using hyperelliptic curves in cryptography requires the computation of the Jacobian order of a curve. This is equivalent to computing the characteristic polynomial of Frobenius x(A) e Z[A|. By calculating Cartier — Manin matrix, we can recover the polynomial x(A) modulo the characteristic of the base field. This information can further be used for recovering full polynomial in combination with other methods. In this paper, we investigate the hyperelliptic curves of the form C1 : y2 = x2g+1 + + ax9+1 + bx and C2 : y2 = x2g+2 + ax9+1 + b over the finite field Fq, q = pn, p > 2. We transform these curves to the form C1,p : y2 = x2g+1 — 2px9+1 + x and C2,p : y2 = x2g+2 — 2px9+1 +1, where p = —a/(2Vb), and prove that the coefficients of the corresponding Cartier — Manin matrices for the curves in this form are Legendre polynomials. As a consequence, the matrices are centrosymmetric and therefore, for finding the matrix, it’s enough to compute a half of coefficients. Cartier — Manin matrices are determined up to a transformation of the form S(p)WS- 1. It is known that centrosymmetric matrices can be transformed to the block-diagonal form by an orthogonal transformation. We prove that this transformation can be modified to have a form S(p)WS- 1 and be defined over the base field of the curve. Therefore, Cartier — Manin matrices of curves C1,p and C2,p are equivalent to block-diagonal matrices. In the case of gcd(p,g) = 1, Miller and Lubin proved that the matrices of curves C1 and C2 are monomial. We prove that the polynomial x(A) (mod p) can be found in factored form in terms of Legendre polynomials by using permutation attached to the monomial matrix. As an application of our results, we list all possible polynomials x(A) (mod p) in the case of gcd(p,g) = 1, g is from 2 to 7 and the curve C1 is over Fp if /b e Fp and over Fp2 if / b £ Fp

Wave packet revivals in a graphene quantum dot in a perpendicular magnetic field

We study the time-evolution of localized wavepackets in graphene quantum dots under a perpendicular magnetic field, focusing on the quasiclassical and revival periodicities, for different values of the magnetic field intensities in a theoretical framework. We have considered contributions of the two inequivalent points in the Brillouin zone. The revival time has been found as an observable that shows the break valley degeneracy.Comment: 5 pages, 4 figures, corrected typo, To appear in Phys. Rev.

2D materials and van der Waals heterostructures

The physics of two-dimensional (2D) materials and heterostructures based on such crystals has been developing extremely fast. With new 2D materials, truly 2D physics has started to appear (e.g. absence of long-range order, 2D excitons, commensurate-incommensurate transition, etc). Novel heterostructure devices are also starting to appear - tunneling transistors, resonant tunneling diodes, light emitting diodes, etc. Composed from individual 2D crystals, such devices utilize the properties of those crystals to create functionalities that are not accessible to us in other heterostructures. We review the properties of novel 2D crystals and how their properties are used in new heterostructure devices