Bose glass and Fermi glass.

It is known that two-dimensional superconducting materials undergo a quantum phase transition from a localized state to superconductivity. When the disordered samples are cooled, bosons (Cooper pairs) are generated from Fermi glass and reach superconductivity through Bose glass. However, there has been no universal expression representing the transition from Fermi glass to Bose glass. Here, we discovered an experimental renormalization group flow from Fermi glass to Bose glass in terms of simple [Formula: see text]-function analysis. To discuss the universality of this flow, we analyzed manifestly different systems, namely a Nd-based two-dimensional layered perovskite and an ultrathin Pb film. We find that all our experimental data for Fermi glass fall beautifully into the conventional self-consistent [Formula: see text]-function. Surprisingly, however, flows perpendicular to the conventional [Formula: see text]-function are observed in the weakly localized regime of both systems, where localization becomes even weaker. Consequently, we propose a universal transition from Bose glass to Fermi glass with the new two-dimensional critical sheet resistance close to [Formula: see text].

Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms.

We explore the eigenvalue statistics of a non-Hermitian version of the Su-Schrieffer-Heeger model, with imaginary on-site potentials and randomly distributed hopping terms. We find that owing to the structure of the Hamiltonian, eigenvalues can be purely real in a certain range of parameters, even in the absence of parity and time-reversal symmetry. As it turns out, in this case of purely real spectrum, the level statistics is that of the Gaussian orthogonal ensemble. This demonstrates a general feature which we clarify that a non-Hermitian Hamiltonian whose eigenvalues are purely real can be mapped to a Hermitian Hamiltonian which inherits the symmetries of the original Hamiltonian. When the spectrum contains imaginary eigenvalues, we show that the density of states (DOS) vanishes at the origin and diverges at the spectral edges on the imaginary axis. We show that the divergence of the DOS originates from the Dyson singularity in chiral-symmetric one-dimensional Hermitian systems and derive analytically the asymptotes of the DOS which is different from that in Hermitian systems.

Finite-size effects and irrelevant corrections to scaling near the integer quantum Hall transition.

We present a numerical finite-size scaling study of the localization length in long cylinders near the integer quantum Hall transition employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent y is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate |y|>/~0.4, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent 2.62±0.06 confirming recent results. Our stability analysis has broad applicability to other observables at integer quantum Hall transition, as well as other critical points where corrections to scaling are present.

Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization.

We discuss, for a two-dimensional Dirac Hamiltonian with a random scalar potential, the presence of a Z2 topological term in the nonlinear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. The Z2 topological term realizes the sign of the Pfaffian of a family of Dirac operators. We compute the corresponding global anomaly, i.e., the change in the sign of the Pfaffian by studying a spectral flow numerically. This Z2 topological effect can be relevant to graphene when the impurity potential is long ranged and, also, to the two-dimensional boundaries of a three-dimensional lattice model of Z2 topological insulators in the symplectic symmetry class.