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

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

Deficiency of the scaling collapse as an indicator of a superconductor-insulator quantum phase transition

Finite-size scaling analysis is a well-accepted method for identification and characterization of quantum phase transitions (QPTs) in superconducting, magnetic and insulating systems. We formally apply this analysis in the form suitable for QPTs in 2-dimensional superconducting films to magnetic-field driven superconductor-metal transition in 1-dimensional MoGe nanowires. Despite being obviously inapplicable to nanowires, the 2d scaling equation leads to a high-quality scaling collapse of the nanowire resistance in the temperature and resistance ranges comparable or better to what is accepted in the analysis of the films. Our results suggest that the appearance and the quality of the scaling collapse by itself is not a reliable indicator of a QPT. We have also observed a sign-change of the zero-bias anomaly (ZBA) in the non-linear resistance, occurring exactly at the critical field of the accidental QPT. This behavior is often taken as an additional confirmation of the transition. We argue that in nanowires, the non-linearity is caused by electron heating and has no relation to the critical fluctuations. Our observation suggests that similar to the scaling collapse, the sign-change of ZBA can be a misleading indicator of QPT.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

Effect of morphology on the superconductor-insulator transition in one-dimensional nanowires

Journal ArticleWe study the effect of morphology on the low-temperature behavior of superconducting nanowires which vary in length from 86 nm to 188 nm. A well-defined superconductor-insulator transition is observed only in the family of homogeneous wires, in which case the transition occurs when the normal resistance is close to h/4e2. Inhomogeneous wires, on the other hand, exhibit a mixed behavior, such that signatures of the superconducting and insulating regimes can be observed in the same sample. The resistance versus temperature curves of inhomogeneous wires show multiple steps, each corresponding to a weak link constriction (WLC) present in the wire. Similarly, each WLC generates a differential resistance peak when the bias current reaches the critical current of the WLC. Due to the presence of WLC's an inhomogeneous wire splits into a sequence of weakly interacting segments where each segment can act as a superconductor or as an insulator. Thus the entire wire then shows a mixed behavior

Dichotomy in short superconducting nanowires: thermal phase slippage vs. Coulomb blockade

ManuscriptQuasi-one-dimensional superconductors or nanowires exhibit a transition into a nonsuperconducting regime, as their diameter shrinks. We present measurements on ultrashort nanowires (∼40-190 nm long) in the vicinity of this quantum transition. Properties of all wires in the superconducting phase, even those close to the transition, can be explained in terms of thermally activated phase slips. The behavior of nanowires in the nonsuperconducting phase agrees with the theories of the Coulomb blockade of coherent transport through mesoscopic normal metal conductors. Thus it is concluded that the quantum transition occurs between two phases: a "true superconducting phase" and an "insulating phase". No intermediate, "metallic" phase was found

Observation of shot noise in phosphorescent organic light-emitting diodes

pre-printWe employed a cross correlation method to study current noise in phosphorescent organic light-emitting diodes. The noise spectra revealed two frequency-dependent components. The first component displays 1/ f 1.3 dependence and correlates with the light emission of the devices. The second component is dominant in low-bias regime and varies as 1/ f 2.8. It is attributed to inhomogeneities of the barrier height at metal/organic interface. The extended bandwidth of the method allowed us to resolve frequency-independent term in the noise power, which was dominated by the shot noise. At bias voltages from 2.4 to 2.5 V, the Fano factor characterizing shot noise is close to one, confirming that the electron transport in this regime is limited by the carrier injection across metal/organic interface. At higher biases, in the regime where the transport is bulk-limited, the Fano factors drops to 0.5. Possible physical reasons for such behavior are discussed

Enhancing superconductivity: magnetic impurities and their quenching by magnetic fields

ManuscriptMagnetic fields and magnetic impurities are each known to suppress superconductivity. However, as the field quenches (i.e. polarizes) the impurities, rich consequences, including field-enhanced superconductivity, can emerge when both effects are present. For the case of superconducting wires and thin films, this field-spin interplay is investigated via the Eilenberger-Usadel scheme. Non-monotonic dependence of the critical current on the field (and therefore field-enhanced superconductivity) is found to be possible, even in parameter regimes in which the critical temperature decreases monotonically with increasing field. The present work complements that of Kharitonov and Feigel'man, which predicts non-monotonic behavior of the critical temperature