Anomalous Enhancement of the Boltzmann Conductivity in Disordered Zigzag Graphene Nanoribbons

We study the conductivity of disordered zigzag graphene nanoribbons in the incoherent regime by using the Boltzmann equation approach. The band structure of zigzag nanoribbons contains two energy valleys, and each valley has an excess one-way channel. The crucial point is that the numbers of conducting channels for two propagating directions are imbalanced in each valley due to the presence of an excess one-way channel. It was pointed out that as a consequence of this imbalance, a perfectly conducting channel is stabilized in the coherent regime if intervalley scattering is absent. We show that even in the incoherent regime, the conductivity is anomalously enhanced if intervalley scattering is very weak. Particularly, in the limit of no intervalley scattering, the dimensionless conductance approaches to unity with increasing ribbon length as if there exists a perfectly conducting channel. We also show that anomalous valley polarization of electron density appears in the presence of an electric field.Comment: 10 pages, 3 figure

Nonuniversal Shot Noise in Disordered Quantum Wires with Channel-Number Imbalance

The number of conducting channels for one propagating direction is equal to that for the other direction in ordinary quantum wires. However, they can be imbalanced in graphene nanoribbons with zigzag edges. Employing the model system in which a degree of channel-number imbalance can be controlled, we calculate the shot-noise power at zero frequency by using the Boltzmann-Langevin approach. The shot-noise power in an ordinary diffusive conductor is one-third of the Poisson value. We show that with increasing the degree of channel-number imbalance, the universal one-third suppression breaks down and a highly nonuniversal behavior of shot noise appears.Comment: 10 pages, 3 figure

Conductance Distribution in Disordered Quantum Wires with a Perfectly Conducting Channel

We study the conductance of phase-coherent disordered quantum wires focusing on the case in which the number of conducting channels is imbalanced between two propagating directions. If the number of channels in one direction is by one greater than that in the opposite direction, one perfectly conducting channel without backscattering is stabilized regardless of wire length. Consequently, the dimensionless conductance does not vanish but converges to unity in the long-wire limit, indicating the absence of Anderson localization. To observe the influence of a perfectly conducting channel, we numerically obtain the distribution of conductance in both cases with and without a perfectly conducting channel. We show that the characteristic form of the distribution is notably modified in the presence of a perfectly conducting channel.Comment: 7 pages, 16 figure

Conductance Fluctuations in Disordered Wires with Perfectly Conducting Channels

We study conductance fluctuations in disordered quantum wires with unitary symmetry focusing on the case in which the number of conducting channels in one propagating direction is not equal to that in the opposite direction. We consider disordered wires with $N+m$ left-moving channels and $N$ right-moving channels. In this case, $m$ left-moving channels become perfectly conducting, and the dimensionless conductance $g$ for the left-moving channels behaves as $g \to m$ in the long-wire limit. We obtain the variance of $g$ in the diffusive regime by using the Dorokhov-Mello-Pereyra-Kumar equation for transmission eigenvalues. It is shown that the universality of conductance fluctuations breaks down for $m \neq 0$ unless $N$ is very large.Comment: 6 pages, 2 figure

Asymptotic behavior of the conductance in disordered wires with perfectly conducting channels

We study the conductance of disordered wires with unitary symmetry focusing on the case in which $m$ perfectly conducting channels are present due to the channel-number imbalance between two-propagating directions. Using the exact solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation for transmission eigenvalues, we obtain the average and second moment of the conductance in the long-wire regime. For comparison, we employ the three-edge Chalker-Coddington model as the simplest example of channel-number-imbalanced systems with $m = 1$, and obtain the average and second moment of the conductance by using a supersymmetry approach. We show that the result for the Chalker-Coddington model is identical to that obtained from the DMPK equation.Comment: 20 pages, 1 figur

Chalker-Coddington model described by an S-matrix with odd dimensions

The Chalker-Coddington network model is often used to describe the transport properties of quantum Hall systems. By adding an extra channel to this model, we introduce an asymmetric model with profoundly different transport properties. We present a numerical analysis of these transport properties and consider the relevance for realistic systems.Comment: 7 pages, 4 figures. To appear in the EP2DS-17 proceeding

Random-Matrix Theory of Electron Transport in Disordered Wires with Symplectic Symmetry

The conductance of disordered wires with symplectic symmetry is studied by a random-matrix approach. It has been believed that Anderson localization inevitably arises in ordinary disordered wires. A counterexample is recently found in the systems with symplectic symmetry, where one perfectly conducting channel is present even in the long-wire limit when the number of conducting channels is odd. This indicates that the odd-channel case is essentially different from the ordinary even-channel case. To study such differences, we derive the DMPK equation for transmission eigenvalues for both the even- and odd- channel cases. The behavior of dimensionless conductance is investigated on the basis of the resulting equation. In the short-wire regime, we find that the weak-antilocalization correction to the conductance in the odd-channel case is equivalent to that in the even-channel case. We also find that the variance does not depend on whether the number of channels is even or odd. In the long-wire regime, it is shown that the dimensionless conductance in the even-channel case decays exponentially as --> 0 with increasing system length, while --> 1 in the odd-channel case. We evaluate the decay length for the even- and odd-channel cases and find a clear even-odd difference. These results indicate that the perfectly conducting channel induces clear even-odd differences in the long-wire regime.Comment: 28pages, 5figures, Accepted for publication in J. Phys. Soc. Jp

Unexpected Dirac-Node Arc in the Topological Line-Node Semimetal HfSiS

We have performed angle-resolved photoemission spectroscopy on HfSiS, which has been predicted to be a topological line-node semimetal with square Si lattice. We found a quasi-two-dimensional Fermi surface hosting bulk nodal lines, alongside the surface states at the Brillouin-zone corner exhibiting a sizable Rashba splitting and band-mass renormalization due to many-body interactions. Most notably, we discovered an unexpected Dirac-like dispersion extending one-dimensionally in k space - the Dirac-node arc - near the bulk node at the zone diagonal. These novel Dirac states reside on the surface and could be related to hybridizations of bulk states, but currently we have no explanation for its origin. This discovery poses an intriguing challenge to the theoretical understanding of topological line-node semimetals.Comment: 5 pages, 4 figures (paper proper) + 2 pages, figures (supplemental material

A Diagrammatic Theory of Random Scattering Matrices for Normal-Superconducting Mesoscopic Junctions

The planar-diagrammatic technique of large-$N$ random matrices is extended to evaluate averages over the circular ensemble of unitary matrices. It is then applied to study transport through a disordered metallic ``grain'', attached through ideal leads to a normal electrode and to a superconducting electrode. The latter enforces boundary conditions which coherently couple electrons and holes at the Fermi energy through Andreev scattering. Consequently, the {\it leading order} of the conductance is altered, and thus changes much larger than $e^2/h$ are observed when, e.g., a weak magnetic field is applied. This is in agreement with existing theories. The approach developed here is intermediate between the theory of dirty superconductors (the Usadel equations) and the random-matrix approach involving transmission eigenvalues (e.g. the DMPK equation) in the following sense: even though one starts from a scattering formalism, a quantity analogous to the superconducting order-parameter within the system naturally arises. The method can be applied to a variety of mesoscopic normal-superconducting structures, but for brevity we consider here only the case of a simple disordered N-S junction.Comment: 39 pages + 9 postscript figure