Spin-density-wave instability in graphene doped near the van Hove singularity

We study the instability of the metallic state towards the formation of a new ground state in graphene doped near the van Hove singularity. The system is described by the Hubbard model and a field theoretical approach is used to calculate the charge and spin susceptibility. We find that for repulsive interactions, within the random phase approximation, there is a competition between ferromagnetism and spin-density wave (SDW). It turns out that a SDW with a triangular geometry is more favorable when the Hubbard parameter is above the critical value U_c(T), which depends on the temperature T, even if there are small variations in the doping. Our results can be verified by ARPES or neutron scattering experiments in highly doped graphene.Comment: 5 pages, 5 figures, 1 tabl

Transport properties of a quantum wire: the role of extended time-dependent impurities

We study the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several extended time-dependent impurities (barriers). Employing the B\" uttiker-Landauer approach, we first consider the scattering of noninteracting electrons ($g=1$) by a rectangular-like barrier and find an exact solution for the backscattering current, as well as a perturbative solution for a weak static potential with an arbitrary shape. We then include electron-electron interactions and use the Keldysh formalism combined with the bosonization technique to study oscillating extended barriers. We show that the backscattering current off time-dependent impurities can be expressed in terms of the current for the corresponding static barrier. Then we determine the backscattering current for a static extended potential, which, in the limit of noninteracting electrons ($g=1$), coincides with the result obtained using the B\" uttiker-Landauer formalism. In particular, we find that the conductance can be increased beyond its quantized value in the whole range of repulsive interactions $0<g<1$ already in the case of a single oscillating extended impurity, in contrast %contrary to the case of a point-like impurity, where this phenomenon occurs only for $0<g<1/2$.Comment: 9 pages, 5 figure

Coupled quantum wires

We study a set of crossed 1D systems, which are coupled with each other via tunnelling at the crossings. We begin with the simplest case with no electron-electron interactions and find that besides the expected level splitting, bound states can emerge. Next, we include an external potential and electron-electron interactions, which are treated within the Hartree approximation. Then, we write down a formal general solution to the problem, giving additional details for the case of a symmetric external potential. Concentrating on the case of a single crossing, we were able to explain recent experinents on crossed metallic and semiconducting nanotubes [J. W. Janssen, S. G. Lemay, L. P. Kouwenhoven, and C. Dekker, Phys. Rev. B 65, 115423 (2002)], which showed the presence of localized states in the region of crossing.Comment: 11 pages, 10 figure

Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field

We consider the combined effects of large spin-orbit couplings and a perpendicular magnetic field in a 2D honeycomb fermionic lattice. This system provides an elegant setup to generate versatile spin textures propagating along the edge of a sample. The spin-orbit coupling is shown to induce topological phase transitions between a helical quantum spin Hall phase and a chiral spin-imbalanced quantum Hall state. Besides, we find that the spin orientation of a single topological edge state can be tuned by a Rashba spin-orbit coupling, opening an interesting route towards quantum spin manipulation. We discuss the possible realization of our results using cold atoms trapped in optical lattices, where large synthetic magnetic fields and spin-orbit couplings can be engineered and finely tuned. In particular, this system would lead to the observation of a time-reversal-symmetry-broken quantum spin Hall phase.Comment: 8 pages, 3 figures, Accepted in Europhys. Lett. (Dec 2011

Pumping current of a Luttinger liquid with finite length

We study transport properties in a Tomonaga-Luttinger liquid in the presence of two time-dependent point like weak impurities, taking into account finite-length effects. By employing analytical methods and performing a perturbation theory, we compute the backscattering pumping current (I_bs) in different regimes which can be established in relation to the oscillatory frequency of the impurities and to the frequency related to the length and the renormalized velocity (by the electron-electron interactions) of the charge density modes. We investigate the role played by the spatial position of the impurity potentials. We also show how the previous infinite length results for I_bs are modified by the finite size of the system.Comment: 9 pages, 7 figure

Median-point approximation and its application for the study of fermionic systems

We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a novel extension of Laplace's method (saddle-point approximation) for evaluating the corresponding partition function. There, we introduce dual free bosonic fields, with a propagator corresponding to an effective (renormalized) interaction with Maki-Thompson and Aslamazov-Larkin type corrections and beyond, and demonstrate that the superconducting pairing originates as an instability of the effective interaction. We derive the corresponding Bethe-Salpeter equation (instability criterion) and show that the interaction enters the equation only in its effective form to all orders, including the exchange part of the self-energy. An important implication of this result is that the effective interaction always remains finite, even at phase-transition points, directly contradicting the often used assumption of linear relationship between the interaction and susceptibility, established within the random-phase approximation. By analyzing the Bethe-Salpeter equation in the context of unconventional superconductivity, we find that the presence of a flat band close the Fermi level, found in materials such as twisted bilayer graphene, has a twofold favorable impact persisting beyond the weak-coupling approximation: a reduced kinetic energy cost of the gap formation and an increased anisotropy of the effective interaction, favoring a momentum dependent order parameter

Electric double-layer capacitance between an ionic liquid and few-layer graphene

Ionic-liquid gates have a high carrier density due to their atomically thin electric double layer (EDL) and extremely large geometrical capacitance C-g. However, a high carrier density in graphene has not been achieved even with ionic-liquid gates because the EDL capacitance C-EDL between the ionic liquid and graphene involves the series connection of C-g and the quantum capacitance C-q, which is proportional to the density of states. We investigated the variables that determine C-EDL at the molecular level by varying the number of graphene layers n and thereby optimising C-q. The C-EDL value is governed by C-q at n, 4, and by C-g at n > 4. This transition with n indicates a composite nature for C-EDL. Our finding clarifies a universal principle that determines capacitance on a microscopic scale, and provides nanotechnological perspectives on charge accumulation and energy storage using an ultimately thin capacitor

Chiral superconductivity from repulsive interactions in doped graphene

Author Manuscript 17 Sep 2011Chiral superconductivity, which breaks time-reversal symmetry, can exhibit a wealth of fascinating properties that are highly sought after for nanoscience applications. We identify doped graphene monolayer as a system where chiral superconductivity can be realized. In this material, a unique situation arises at a doping where the Fermi surface is nested and the density of states is singular. In this regime, d-wave superconductivity can emerge from repulsive electron–electron interactions. Using a renormalization group method, we argue that superconductivity dominates over all competing orders for generic weak repulsive interactions. Superconductivity develops simultaneously in two degenerate d-wave pairing channels. We argue that the resulting superconducting state is of chiral type, with the phase of the superconducting order parameter winding by 4π around the Fermi surface. Realization of this state in doped graphene will prove that superconductivity can emerge from electron–electron repulsion, and will open the door to applications of chiral superconductivity