Explore the vast range of titles available.

We have recently shown that the critical Anderson electron in D=3 dimensions effectively occupies a spatial region of the infrared (IR) scaling dimension dIR≈8/3. Here, we inquire about the dimensional substructure involved. We partition space into regions of equal quantum occurrence probabilities, such that the points comprising a region are of similar relevance, and calculate the IR scaling dimension d of each. This allows us to infer the probability density p(d) for dimension d to be accessed by the electron. We find that p(d) has a strong peak at d very close to two. In fact, our data suggest that p(d) is non-zero on the interval [dmin,dmax]≈[4/3,8/3] and may develop a discrete part (δ-function) at d=2 in the infinite-volume limit. The latter invokes the possibility that a combination of quantum mechanics and pure disorder can lead to the emergence of integer (topological) dimensions. Although dIR is based on effective counting, of which p(d) has no a priori knowledge, dIR≥dmax is an exact feature of the ensuing formalism. A possible connection of our results to the recent findings of dIR≈2 in Dirac near-zero modes of thermal quantum chromodynamics is emphasized.

We consider Anderson transitions in two-dimensional (2D) spinful electron gases subject to random scalar potentials with time-reversal-symmetric spin-mixing tunneling (SMT) and spin-preserving tunneling (SPT) at potential saddle points (PSPs). A symplectic quantum network model (QNM), named as SMT-QNM, is constructed in which SMT and SPT have the same status and contribute independent tunneling channels rather than sharing a total-probability-fixed one. 2D continuous Dirac Hamiltonian is then extracted out from this discrete network model as the generator of certain unitary transformation. With the help of high-accuracy numerics based on transfer matrix technique, finite-size analysis on two-terminal conductance and normalized localization length provides a phase diagram drawn in the SMT-SPT plane. As a manifestation of symplectic ensembles, a normal-metal (NM) phase emerges between the quantum spin Hall (QSH) and normal-insulator (NI) phases when SMT appears. We systematically analyze the quantum phases on the boundary and in the interior of the phase space. Particularly, the phase diagram is closely related to that of disordered three-dimensional weak topological insulators by appropriate parameter mapping. At last, if time-reversal symmetry in electron trajectories between PSPs is destroyed, the system falls into unitary class with no more NM phase. A direct SMT-driven transition from QSH to NI phases exists and can be explained by spin-flip backscattering between the degenerate doublets at the same sample edge.

Macroscopic manifestations of quantum mechanics are among the most spectacular effects of physics. In most of them, novel collective properties emerge from the quantum mechanical behaviour of their microscopic constituents. Others, like superconductivity, extend a property typical of the atomic scale to macroscopic length scale. Similarly, features of quantum transport in Hubbard systems which are only observed at nanometric distances in natural and artificial atoms embedded in quantum devices, could be in principle extended to macroscopic distances in microelectronic devices. By employing an atomic chain consists of an array of 20 atoms implanted along the channel of a silicon transistor with length of 1 μm, we extend to such unprecedented distance both the single electron quantum transport via sequential tunneling and to room temperature the features of the Hubbard bands. Their observation provides a new example of scaling of quantum mechanical properties, previously observed only at the nanoscale, up to lengths typical of microelectronics, by opening new perspectives towards passage of quantum states and band engineering in silicon devices.

In this study, we calculate the dc resistivity of the half-filled disordered Hubbard model near the Mott and Anderson metal–insulator transitions. We employ the standard Kubo formula with typical medium dynamical mean field theory to perform our calculations. Our investigation explores the effects of random potential, on-site Coulomb interaction, and temperature on the dc resistivity within the model. In addition, we highlight and discuss the distinct resistivity behaviors observed near the Mott and Anderson transitions.

We investigate bulk and boundary multifractality at the metal-quantum spin Hall (QSH) insulator transition driven by disorder in two-dimensions. Recently, we have shown that boundary multifractality at this transition is different from that of the symplectic class by using the network model with random spin-orbit interactions. To give the another evidence for this result, we investigate multifractality at the metal-QSH insulator transition by using a different model, namely, the network model with a constant spin-orbit interaction. It is found that bulk multifractality at the metal-QSH insulator transition is that of the symplectic class while boundary multifractality is different, confirming identical with the previous result.

We consider Anderson localization in the half-filled Anderson–Hubbard model in the presence of either random on-site interactions or spatially alternating interactions in the lattice. By using dynamical mean field theory with the equation of motion method as an impurity solver, we calculate the arithmetically and geometrically averaged local density of states and derive the equations determining the critical value for the phase transition between metallic, Anderson and Mott insulating phases. The nonmagnetic ground state phase diagrams are constructed numerically. We figure out that the presence of Coulomb disorder drives the system toward the Anderson localized phase that can occur even in the absence of Anderson structural disorder. For the spatially alternating interactions, we find that the metallic region is reduced and the Anderson insulator one is enlarged with increasing interaction modulation. Our obtained results are relevant to current research in ultracold atoms in disordered optical lattices where metal–insulator transition can be observed experimentally by using ultracold atom techniques.

Whether a metallic ground state exists in a two-dimensional system beyond Anderson localization remains an unresolved question. We studied how quantum phase coherence evolves across superconductor–metal–insulator transitions through magnetoconductance quantum oscillations in nanopatterned high-temperature superconducting films. We tuned the degree of phase coherence by varying the etching time of our films. Between the superconducting and insulating regimes, we detected a robust intervening anomalous metallic state characterized by saturating resistance and oscillation amplitude at low temperatures. Our measurements suggest that the anomalous metallic state is bosonic and that the saturation of phase coherence plays a prominent role in its formation.