Anomalously large conductance fluctuations in weakly disordered graphene

We have studied numerically the mesoscopic fluctuations of the conductance of a graphene strip (width W large compared to length L), in an ensemble of samples with different realizations of the random electrostatic potential landscape. For strong disorder (potential fluctuations comparable to the hopping energy), the variance of the conductance approaches the value predicted by the Altshuler-Lee-Stone theory of universal conductance fluctuations. For weaker disorder the variance is greatly enhanced if the potential is smooth on the scale of the atomic separation. There is no enhancement if the potential varies on the atomic scale, indicating that the absence of backscattering on the honeycomb lattice is at the origin of the anomalously large fluctuations.Comment: 5 pages, 8 figure

Symmetry Classes in Graphene Quantum Dots: Universal Spectral Statistics, Weak Localization, and Conductance Fluctuations

We study the symmetry classes of graphene quantum dots, both open and closed, through the conductance and energy level statistics. For abrupt termination of the lattice, these properties are well described by the standard orthogonal and unitary ensembles. However, for smooth mass confinement, special time-reversal symmetries associated with the sublattice and valley degrees of freedom are critical: they lead to block diagonal Hamiltonians and scattering matrices with blocks belonging to the unitary symmetry class even at zero magnetic field. While the effect of this structure is clearly seen in the conductance of open dots, it is suppressed in the spectral statistics of closed dots, because the intervalley scattering time is shorter than the time required to resolve a level spacing in the closed systems but longer than the escape time of the open systems.Comment: 4 pages, 4 figures, RevTex, submitted to Phys. Rev. Let

Aharonov-Bohm effect and broken valley-degeneracy in graphene rings

We analyze theoretically the electronic properties of Aharonov-Bohm rings made of graphene. We show that the combined effect of the ring confinement and applied magnetic flux offers a controllable way to lift the orbital degeneracy originating from the two valleys, even in the absence of intervalley scattering. The phenomenon has observable consequences on the persistent current circulating around the closed graphene ring, as well as on the ring conductance. We explicitly confirm this prediction analytically for a circular ring with a smooth boundary modelled by a space-dependent mass term in the Dirac equation. This model describes rings with zero or weak intervalley scattering so that the valley isospin is a good quantum number. The tunable breaking of the valley degeneracy by the flux allows for the controlled manipulation of valley isospins. We compare our analytical model to another type of ring with strong intervalley scattering. For the latter case, we study a ring of hexagonal form with lattice-terminated zigzag edges numerically. We find for the hexagonal ring that the orbital degeneracy can still be controlled via the flux, similar to the ring with the mass confinement.Comment: 7 pages, 7 figures, replaced with considerably extended new versio

Superconductivity enhanced conductance fluctuations in few layer graphene nanoribbons

We investigate the mesoscopic disorder induced rms conductance variance $\delta G$ in a few layer graphene nanoribbon (FGNR) contacted by two superconducting (S) Ti/Al contacts. By sweeping the back-gate voltage, we observe pronounced conductance fluctuations superimposed on a linear background of the two terminal conductance G. The linear gate-voltage induced response can be modeled by a set of inter-layer and intra-layer capacitances. $\delta G$ depends on temperature T and source-drain voltage $V_{sd}$. $\delta G$ increases with decreasing T and $|V_{sd}|$. When lowering $|V_{sd}|$, a pronounced cross-over at a voltage corresponding to the superconducting energy gap $\Delta$ is observed. For |V_{sd}|\ltequiv \Delta the fluctuations are markedly enhanced. Expressed in the conductance variance $G_{GS}$ of one graphene-superconducutor (G-S) interface, values of 0.58 e^2/h are obtained at the base temperature of 230 mK. The conductance variance in the sub-gap region are larger by up to a factor of 1.4-1.8 compared to the normal state. The observed strong enhancement is due to phase coherent charge transfer caused by Andreev reflection at the nanoribbon-superconductor interface.Comment: 15 pages, 5 figure

Three-Dimensional Dirac Electrons at the Fermi Energy in Cubic Inverse Perovskites: Ca_3PbO and its Family

The band structure of cubic inverse perovskites, Ca_3PbO and its family, are investigated with the first-principles method. A close observation of the band structure reveals that six equivalent Dirac electrons with a very small mass exist on the line connecting the Gamma- and X-points, and at the symmetrically equivalent points in the Brillouin zone. The discovered Dirac electrons are three-dimensional and remarkably located exactly at the Fermi energy. A tight-binding model describing the low-energy band structure is also constructed and used to discuss the origin of the Dirac electrons in this material. Materials related to Ca_3PbO are also studied, and some design principles for the Dirac electrons in this series of materials are proposed.Comment: 4.2 pages, refined versio

Valley filter and valley valve in graphene

It is known that the lowest propagating mode in a narrow ballistic ribbon of graphene may lack the twofold valley degeneracy of higher modes. Depending on the crystallographic orientation of the ribbon axis, the lowest mode mixes both valleys or lies predominantly in a single valley (chosen by the direction of propagation). We show, using a tight-binding model calculation, that a nonequilibrium valley polarization can be realized in a sheet of graphene, upon injection of current through a ballistic point contact with zigzag edges. The polarity can be inverted by local application of a gate voltage to the point contact region. Two valley filters in series may function as an electrostatically controlled ``valley valve'', representing a zero-magnetic-field counterpart to the familiar spin valve.Comment: RevTeX, 4 pages, 5 figure

Graphene based superconducting quantum point contacts

We investigate the Josephson effect in the graphene nanoribbons of length $L$ smaller than the superconducting coherence length and an arbitrary width $W$. We find that in contrast to an ordinary superconducting quantum point contact (SQPC) the critical supercurrent $I_c$ is not quantized for the nanoribbons with smooth and armchair edges. For a low concentration of the carriers $I_c$ decreases monotonically with lowering $W/L$ and tends to a constant minimum for a narrow nanoribbon with $W\lesssim L$. The minimum $I_c$ is zero for the smooth edges but $e\Delta_{0}/\hbar$ for the armchair edges. At higher concentrations of the carriers this monotonic variation acquires a series of peaks. Further analysis of the current-phase relation and the Josephson coupling strength $I_cR_N$ in terms of $W/L$ and the concentration of carriers revels significant differences with those of an ordinary SQPC. On the other hand for a zigzag nanoribbon we find that, similar to an ordinary SQPC, $I_c$ is quantized but to the half-integer values $(n+1/2)4e\Delta_{0}/\hbar$.Comment: 8 pages, 5 figure

Field-induced polarisation of Dirac valleys in bismuth

Electrons are offered a valley degree of freedom in presence of particular lattice structures. Manipulating valley degeneracy is the subject matter of an emerging field of investigation, mostly focused on charge transport in graphene. In bulk bismuth, electrons are known to present a threefold valley degeneracy and a Dirac dispersion in each valley. Here we show that because of their huge in-plane mass anisotropy, a flow of Dirac electrons along the trigonal axis is extremely sensitive to the orientation of in-plane magnetic field. Thus, a rotatable magnetic field can be used as a valley valve to tune the contribution of each valley to the total conductivity. According to our measurements, charge conductivity by carriers of a single valley can exceed four-fifth of the total conductivity in a wide range of temperature and magnetic field. At high temperature and low magnetic field, the three valleys are interchangeable and the three-fold symmetry of the underlying lattice is respected. As the temperature lowers and/or the magnetic field increases, this symmetry is spontaneously lost. The latter may be an experimental manifestation of the recently proposed valley-nematic Fermi liquid state.Comment: 14 pages + 5 pages of supplementary information; a slightly modified version will appear as an article in Nature physic

Ferromagnetism without flat bands in thin armchair nanoribbons

Describing by a Hubbard type of model a thin armchair graphene ribbon in the armchair hexagon chain limit, one shows in exact terms, that even if the system does not have flat bands at all, at low concentration a mesoscopic sample can have ferromagnetic ground state, being metallic in the same time. The mechanism is connected to a common effect of correlations and confinement.Comment: 37 pages, 12 figures, in press at Eur. Phys. Jour.