Transport properties in network models with perfectly conducting channels

We study the transport properties of disordered electron systems that contain perfectly conducting channels. Two quantum network models that belong to different universality classes, unitary and symplectic, are simulated numerically. The perfectly conducting channel in the unitary class can be realized in zigzag graphene nano-ribbons and that in the symplectic class is known to appear in metallic carbon nanotubes. The existence of a perfectly conducting channel leads to novel conductance distribution functions and a shortening of the conductance decay length.Comment: 4 pages, 6 figures, proceedings of LT2

Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class

We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the MF exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence for conformal invariance at the 2D spin-orbit MIT. The presence of boundaries modifies the MF of the whole sample even in the thermodynamic limit.Comment: 5 pages, 4 figure

Conductance distributions in disordered quantum spin-Hall systems

We study numerically the charge conductance distributions of disordered quantum spin-Hall (QSH) systems using a quantum network model. We have found that the conductance distribution at the metal-QSH insulator transition is clearly different from that at the metal-ordinary insulator transition. Thus the critical conductance distribution is sensitive not only to the boundary condition but also to the presence of edge states in the adjacent insulating phase. We have also calculated the point-contact conductance. Even when the two-terminal conductance is approximately quantized, we find large fluctuations in the point-contact conductance. Furthermore, we have found a semi-circular relation between the average of the point-contact conductance and its fluctuation.Comment: 9 pages, 17 figures, published versio

Boundary criticality and multifractality at the 2D spin quantum Hall transition

Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using the supersymmetry technique for disorder averaging. Upon mapping of the spin quantum Hall transition to the classical percolation problem with reflecting boundaries, a number of multifractal exponents governing wave function scaling near a boundary are obtained exactly. Moreover, additional exact boundary scaling exponents of the localization problem are extracted, and the problem is analyzed in other geometries.Comment: v2, 17 pages, 10 figures, published versio

Multifractality at the quantum Hall transition: Beyond the parabolic paradigm

We present an ultra-high-precision numerical study of the spectrum of multifractal exponents $\Delta_q$ characterizing anomalous scaling of wave function moments $$ at the quantum Hall transition. The result reads $\Delta_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...]$, with $b_0 = 0.1291\pm 0.0002$ and $b_1 = 0.0029\pm 0.0003$. The central finding is that the spectrum is not exactly parabolic, $b_1\ne 0$. This rules out a class of theories of Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.Comment: 4 pages, 4 figure

Disorder-Induced Multiple Transition involving Z2 Topological Insulator

Effects of disorder on two-dimensional Z2 topological insulator are studied numerically by the transfer matrix method. Based on the scaling analysis, the phase diagram is derived for a model of HgTe quantum well as a function of disorder strength and magnitude of the energy gap. In the presence of sz non-conserving spin-orbit coupling, a finite metallic region is found that partitions the two topologically distinct insulating phases. As disorder increases, a narrow-gap topologically trivial insulator undergoes a series of transitions; first to metal, second to topological insulator, third to metal, and finally back to trivial insulator. We show that this multiple transition is a consequence of two disorder effects; renormalization of the band gap, and Anderson localization. The metallic region found in the scaling analysis corresponds roughly to the region of finite density of states at the Fermi level evaluated in the self-consistent Born approximation.Comment: 5 pages, 5 figure

Point-Contact Conductance in Asymmetric Chalker-Coddington Network Model

We study the transport properties of disordered two-dimensional electron systems with a perfectly conducting channel. We introduce an asymmetric Chalker-Coddington network model and numerically investigate the point-contact conductance. We find that the behavior of the conductance in this model is completely different from that in the symmetric model. Even in the limit of a large distance between the contacts, we find a broad distribution of conductance and a non-trivial power law dependence of the averaged conductance on the system width. Our results are applicable to systems such as zigzag graphene nano-ribbons where the numbers of left-going and right-going channels are different.Comment: 6 pages, 11 figures, final versio

Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory

We study multifractal spectra of critical wave functions at the integer quantum Hall plateau transition using the Chalker-Coddington network model. Our numerical results provide important new constraints which any critical theory for the transition will have to satisfy. We find a non-parabolic multifractal spectrum and we further determine the ratio of boundary to bulk multifractal exponents. Our results rule out an exactly parabolic spectrum that has been the centerpiece in a number of proposals for critical field theories of the transition. In addition, we demonstrate analytically exact parabolicity of related boundary spectra in the 2D chiral orthogonal `Gade-Wegner' symmetry class.Comment: 4 pages, 3 figures, v2, published versio

Critical level statistics and anomalously localized states at the Anderson transition

We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution $P(s)$ for level pairs of ALS coincides with that for pairs of typical multifractal states. This implies that ALS do not affect the shape of the critical level-spacing distribution function. We also show that the insensitivity of $P(s)$ to ALS is a consequence of multifractality in tail structures of ALS.Comment: 8 pages, 5 figure