Microscopic scale of quantum phase transitions: from doped semiconductors to spin chains, cold gases and moir\'e superlattices

In the vicinity of continuous quantum phase transitions (QPTs), quantum systems become scale-invariant and can be grouped into universality classes characterized by sets of critical exponents. We have found that despite scale-invariance and universality, the experimental data still contain information related to the microscopic processes and scales governing QPTs. We conjecture that near QPTs, various physical quantities follow the generic exponential dependence predicted by the scaling theory of localization; this dependence includes as a parameter a microscopic seeding scale of the renormalization group, $L_0$. We also conjecture that for interacting systems, the temperature cuts the renormalization group flow at the length travelled by a system-specific elementary excitation over the life-time set by the Planckian time, $\tau_P$=$\hbar/k_BT$. We have adapted this approach for QPTs in several systems and showed that $L_0$ extracted from experiment is comparable to physically-expected minimal length scales, namely (i) the mean free path for metal-insulator transition in doped semiconductors, (ii) the distance between spins in Heisenberg and Ising chains, (iii) the period of an optical lattice for cold atom boson gases, and (iv) the period of a moir\'e superlattice for the Mott QPT in dichalcogenide bilayers. In the first companion paper, we show that in superconducting films and nanowires, as well as in the high temperature superconductor La$_{1.92}$Sr$_{0.08}$CuO$_4$, $L_0$ is comparable to superconducting coherence length. In the second companion paper, we show that in quantum Hall systems, $L_0$ is comparable to the magnetic length. The developed theoretical approach quantitatively explains and unifies a large body of experimental data and can be expanded to other complex systemsComment: 12 pages, 6 figure

Quantum phase transitions in quantum Hall and other topological systems: role of the Planckian time

Transformations between the plateau states of the quantum Hall effect (QHE) are an archetypical example of quantum phase transitions (QPTs) between phases with non-trivial topological order. These transitions appear to be well-described by the single-particle network theories. The long-standing problem with this approach is that it does not account for Coulomb interactions. In this paper, we show that experimental data in the quantum critical regime for both integer and fractional QHEs can be quantitatively explained by the recently developed phenomenological model of QPTs in interacting systems. This model assumes that all effects of interactions are contained in the life-time of fluctuations as set by the Planckian time $\tau_P=\hbar/k_BT$. The dephasing length is taken as the distance traveled by a non-interacting particle along the bulk edge state over this time. We show that the model also provides quantitative description of QPTs between the ground states of anomalous QHE and axion and Chern insulators. These analyzed systems are connected in that the QPTs occur via quantum percolation. Combining the presented results with the results of two companion papers, we conclude that the Planckian time is the encompassing characteristic of QPTs in interacting systems, independent of dimensionality and microscopic physics.Comment: 6 pages, 3 figure

Adaptive observers for nonlinearly parameterized systems subjected to parametric constraints

We consider the problem of adaptive observer design in the settings when the system is allowed to be nonlinear in the parameters, and furthermore they are to satisfy additional feasibility constraints. A solution to the problem is proposed that is based on the idea of universal observers and non-uniform small-gain theorem. The procedure is illustrated with an example.Comment: 19th IFAC World Congress on Automatic Control, 10869-10874, South Africa, Cape Town, 24th-29th August, 201

Peculiarities of Electron-Beam Formation of Hydrophobic and Superhydrophobic Coatings Based on Hydrocarbons of Various Molecular Weights and PTFE

The paper studies the possibility of superhydrophobic coatings formations at exposure of powder mixture of polytetrafluorethylene and hydrocarbons having various molecular weights to low-energy electron beam in vacuum. It is shown that paraffin and PTFE based thin composite coatings may be characterized by superhydrophobic properties. The superhydrophobic properties are attained due to low surface energy of the fluorine-containing component and structured surface due to peculiarities of composite layer formation. The chemical processes observed in electron beam exposed area determine the molecular structure, morphology and the contact angle of thin organic coatings deposited. It is shown that high-molecular-weight hydrocarbon compounds should not be recommended for vacuum electron-beam deposition of superhydrophobic thin coatings because of deep changes in the molecular structure exposed to electron beam. These processes are responsible for high degree of unsaturation of the thin layer formed and for occurrence of oxygen-containing polar groups. The influence of substrate temperature on molecular structure, morphology and hydrophobic properties of thin coatings deposited is investigated. Potentially such coatings may be applied for deposition on the surface of metal capillaries used in biotechnological analyzers

Superconducting properties of polycrystalline Nb nanowires templated by carbon nanotubes

Journal ArticleContinuous Nb wires, 7-15 nm in diameter, have been fabricated by sputter-coating single fluorinated carbon nanotubes. Transmission electron microscopy revealed that the wires are polycrystalline, having grain sizes of about 5 nm. The critical current of wires thicker than ~12 nm is very high (107 A/cm2) and comparable to the expected depairing current. The resistance versus temperature curves measured down to 0.3 K are well described by the Langer-Ambegaokar-McCumber-Halperin theory of thermally activated phase slips. Quantum phase slips are suppressed

Microscopic scale of pair-breaking quantum phase transitions in superconducting films, nanowires and La1.92_{1.92}Sr0.08_{0.08}CuO4_{4}

The superconducting ground state in a large number of two-dimensional (2d) systems can be created and destroyed through quantum phase transitions (QPTs) driven by non-thermal parameters such as the carrier density or magnetic field. The microscopic mechanism of QPTs has not been established in any 2d superconductor, in part due to an emergent scale-invariance near the critical point, which conceals the specific processes driving the transitions. In this work, we find that the pair-breaking mechanism causing the suppression of the Cooper pair density gives a unifyingly consistent description of magnetic-field-driven QPTs in amorphous MoGe, Pb and TaN films, as well as in quasi-2d high-temperature superconductor La$_{1.92}$Sr$_{0.08}$CuO$_{4}$. This discovery was facilitated by the development of a novel theoretical approach, one which goes beyond the standard determination of critical exponents and allows for the extraction of a microscopic seeding length scale of the transitions. Remarkably, for the materials studied, and also for MoGe nanowires, this scale matches the superconducting coherence length. Further, this approach has been successfully applied to many other complex, non-superconducting systems.Comment: 9 pages, 5 figure

Magnetic-field enhancement of superconductivity in ultranarrow wires

Journal ArticleWe study the effect of an applied magnetic field on sub-10-nm wide MoGe and Nb superconducting wires. We find that magnetic fields can enhance the critical supercurrent at low temperatures, and do so more strongly for narrower wires. We conjecture that magnetic moments are present, but their pair-breaking effect, active at lower magnetic fields, is suppressed by higher fields. The corresponding microscopic theory, which we have developed, quantitatively explains all experimental observations, and suggests that magnetic moments have formed on the wire surfaces