Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

The rise of graphene

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

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Two-dimensional gas of massless Dirac fermions in graphene

Single-layer metal dichalcogenides are two-dimensional semiconductors that present strong potential for electronic and sensing applications complementary to that of graphene.

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Electronics and optoelectronics of two-dimensional transition metal dichalcogenides.

A Comment on the Letter by G. Baskaran and S. A. Jafari, Phys. Rev. Lett. 89, 016402 (2002)

Comment on "Gapless spin-1 neutral collective mode branch for graphite".

We develop a complete analytical description of the time evolution of squeezed states of a charged particle under the Fock-Darwin (FD) Hamiltonian and a time-dependent electric field. This result generalizes a relation obtained by Infeld and Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski for states of the one-dimensional harmonic oscillator. We relate the evolution of a state-vector subjected to squeezing to that of state which is not subjected to squeezing and for which the time evolution under the simple harmonic oscillator dynamics is known (e.g., an eigenstate of the Hamiltonian). A corresponding relation is also established for the Wigner functions of the states, in view of their utility in the analysis of cold-ion experiments. In Appendix A, we compute the response functions of the FD Hamiltonian to an external electric field, using the same techniques as in the main text.

Evolution of squeezed states under the Fock-Darwin Hamiltonian

EC - European Commission(881603); Center for Nanostructured Graphene
(CNG), which is sponsored by the Danish National Research Foundation, Project No DNRF103 Additionally,
TGP is supported by the QUSCOPE Center, sponsored
by the Villum Foundation NMRP acknowledges support from the European Commission through the project
Graphene-Driven Revolutions in ICT and Beyond (Reference No 785219) and the Portuguese Foundation
for Science and Technology (FCT) in the framework of
the Strategic Financing UID/FIS/04650/2019 In addition, NMRP acknowledges COMPETE2020, PORTUGAL2020, FEDER, and the FCT through Projects
No PTDC/FIS-NAN/3668/2013, No POCI-01-0145-
FEDER-028114, No POCI-01-0145-FEDER-029265,
No PTDC/NAN-OPT/29265/2017, and No POCI-01-
0145-FEDER-02888

Anisotropic Stark shift, field-induced dissociation, and electroabsorption of excitons in phosphorene

B. Amorim acknowledges ﬁnancial support from Fundacao para a Ciencia e a Tecnologia (Portugal), through Grant No. SFRH/BD/78987/2011. R.M. Ribeiro and N.M.R. Peres acknowledge the ﬁnancial support of EC under Graphene Flagship (Contract No. CNECT-ICT-604391). N. M. R. Peres acknowledges ﬁnancial support from the FCT project EXPL-FIS-NAN1728-2013.

Multiple negative differential conductance regions and inelastic phonon assisted tunneling in graphene / h − BN / graphene structures

Within the Hartree Fock RPA analysis, we derive the spin wave spectrum for the weak ferromagnetic phase of the Hubbard model on a honeycomb lattice. Assuming a uniform magnetization, the polar (optical) and acoustic branches of the spin wave excitations are determined. The bipartite lattice geometry produces a q-dependent phase difference between the spin wave amplitudes on the two sub-lattices. We also find an instability of the uniform weakly magnetized configuration towards a weak antiferromagnetic spiraling spin structure, in the lattice plane, with wavevector Q along the ??K direction, for electron densities n>0.6. We discuss the effect of diagonal disorder on both the creation of electron bound states and the enhancement of the density of states, and the possible relevance of these effects to disorder-induced ferromagnetism, as observed in proton-irradiated graphite.

https://repositorium.sdum.uminho.pt/bitstream/1822/4694/1/0502249.pdf

Nuno M. R. Peres

Papers

Comment on "Gapless spin-1 neutral collective mode branch for graphite".

Evolution of squeezed states under the Fock-Darwin Hamiltonian

Anisotropic Stark shift, field-induced dissociation, and electroabsorption of excitons in phosphorene

Multiple negative differential conductance regions and inelastic phonon assisted tunneling in graphene / h − BN / graphene structures

Weak ferromagnetism and spiral spin structures in honeycomb Hubbard planes