Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced where nodes attach proportionally to arbitrary fitness functions. However, in these models, attaching to a node always increases the ability of that node to gain more links in the future. We study network growth where nodes attach proportionally to the clustering coefficients, or local densities of triangles, of existing nodes. Attaching to a node typically lowers its clustering coefficient, in contrast to preferential attachment or rich-get-richer models. This simple modification naturally leads to a variety of rich phenomena, including aging, non-Poissonian bursty dynamics, and community formation. This theoretical model shows that complex network structure can be generated without artificially imposing multiple dynamical mechanisms and may reveal potentially overlooked mechanisms present in complex systems.

We describe a many-body quantum system that can be made to quantum compute by the adiabatic application of a large applied field to the system. Prior to the application of the field, quantum information is localized on one boundary of the device, and after the application of the field, this information propagates to the other side of the device, with a quantum circuit applied to the information. The applied circuit depends on the many-body Hamiltonian of the material, and the computation takes place in a degenerate ground space with symmetry-protected topological order. Such “adiabatic quantum transistors” are universal adiabatic quantum computing devices that have the added benefit of being modular. Here, we describe this model, provide arguments for why it is an efficient model of quantum computing, and examine these many-body systems in the presence of a noisy environment.

We report strong third-harmonic generation in monolayer graphene grown by chemical vapor deposition and transferred to an amorphous silica (glass) substrate; the photon energy is in three-photon resonance with the exciton-shifted van Hove singularity at the $M$ point of graphene. The polarization selection rules are derived and experimentally verified. In addition, our polarization- and azimuthal-rotation-dependent third-harmonic-generation measurements reveal in-plane isotropy as well as anisotropy between the in-plane and out-of-plane nonlinear optical responses of graphene. Since the third-harmonic signal exceeds that from bulk glass by more than 2 orders of magnitude, the signal contrast permits background-free scanning of graphene and provides insight into the structural properties of graphene.

We demonstrate a fully cryogenic microwave feedback network composed of modular superconducting devices connected by transmission lines and designed to control a mechanical oscillator that is coupled to one of the devices. The network features an electromechanical device and a tunable controller that coherently receives, processes, and feeds back continuous microwave signals that modify the dynamics and readout of the mechanical state. While previous electromechanical systems represent some compromise between efficient control and efficient readout of the mechanical state, as set by the electromagnetic decay rate, the tunable controller produces a closed-loop network that can be dynamically and continuously tuned between both extremes much faster than the mechanical response time. We demonstrate that the microwave decay rate may be modulated by at least a factor of 10 at a rate greater than ${10}^4$ times the mechanical response rate. The system is easy to build and suggests that some useful functions may arise most naturally at the network level of modular, quantum electromagnetic devices.

Electron pumps capable of delivering a current higher than 100 pA with sufficient accuracy are likely to become the direct mise en pratique of the possible new quantum definition of the ampere. We present here single-island hybrid metal-semiconductor transistor pumps that combine the simplicity and efficiency of Coulomb blockade in metals with the unsurpassed performances of silicon switches. Robust and simple pumping at 650 MHz and 0.5 K is demonstrated. The pumped current obtained over a voltage-bias range of 1.4 mV corresponds to a relative deviation of $5\times {10}^{-4}$ from the calculated value, well within the $1.5\times {10}^{-3}$ uncertainty of the measurement setup. Multicharge pumping can be performed. The simple design that is fully integrated into an industrial microelectronics process makes it an ideal candidate for national measurement institutes to realize and share a future quantum ampere.

We show that the electron-phonon coupling (EPC) in many materials can be significantly underestimated by the standard density-functional theory (DFT) in the local-density approximation (LDA) due to large nonlocal correlation effects. We present a simple yet efficient methodology to evaluate the realistic EPC, going beyond the LDA by using more advanced and accurate $GW$ and screened-hybrid-functional DFT approaches. The corrections that we propose explain the extraordinarily high superconducting temperatures that are observed in two distinct classes of compounds—the bismuthates and the transition-metal chloronitrides—thus solving a 30-year-old puzzle. Our work calls for the critical reevaluation of the EPC of certain phonon modes in many other materials, such as cuprates and iron-based superconductors. The proposed methodology can be used to design new correlation-enhanced high-temperature superconductors and other functional materials that involve electron-phonon interaction.

The relative importance of atomic defects and electron transfer in explaining conductivity at the crystalline ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface has been a topic of debate. Metallic interfaces with similar electronic properties produced by amorphous oxide overlayers on ${\mathrm{SrTiO}}_3$ [Y. Chen et al., Nano Lett. 11, 3774 (2011); S. W. Lee et al., Nano Lett. 12, 4775 (2012)] have called in question the original polarization catastrophe model [N. Nakagawa et al., Nature Mater. 5, 204 (2006)]. We resolve the issue by a comprehensive comparison of (100)-oriented ${\mathrm{SrTiO}}_3$ substrates with crystalline and amorphous overlayers of ${\mathrm{LaAlO}}_3$ of different thicknesses prepared under different oxygen pressures. For both types of overlayers, there is a critical thickness for the appearance of conductivity, but its value is always 4 unit cells (around 1.6 nm) for the oxygen-annealed crystalline case, whereas in the amorphous case, the critical thickness could be varied in the range 0.5 to 6 nm according to the deposition conditions. Subsequent ion milling of the overlayer restores the insulating state for the oxygen-annealed crystalline heterostructures but not for the amorphous ones. Oxygen post-annealing removes the oxygen vacancies, and the interfaces become insulating in the amorphous case. However, the interfaces with a crystalline overlayer remain conducting with reduced carrier density. These results demonstrate that oxygen vacancies are the dominant source of mobile carriers when the ${\mathrm{LaAlO}}_3$ overlayer is amorphous, while both oxygen vacancies and polarization catastrophe contribute to the interface conductivity in unannealed crystalline ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructures, and the polarization catastrophe alone accounts for the conductivity in oxygen-annealed crystalline ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructures. Furthermore, we find that the crystallinity of the ${\mathrm{LaAlO}}_3$ layer is crucial for the polarization catastrophe mechanism in the case of crystalline ${\mathrm{LaAlO}}_3$ overlayers.

We discuss the question of when a gapped two-dimensional electron system without any symmetry has a protected gapless edge mode. While it is well known that systems with a nonzero thermal Hall conductance, $K_H\ne 0$, support such modes, here we show that robust modes can also occur when $K_H=0$—if the system has quasiparticles with fractional statistics. We show that some types of fractional statistics are compatible with a gapped edge, while others are fundamentally incompatible. More generally, we give a criterion for when an electron system with Abelian statistics and $K_H=0$ can support a gapped edge: We show that a gapped edge is possible if and only if there exists a subset of quasiparticle types $\mathcal{M}$ such that (1) all the quasiparticles in $\mathcal{M}$ have trivial mutual statistics, and (2) every quasiparticle that is not in $\mathcal{M}$ has nontrivial mutual statistics with at least one quasiparticle in $\mathcal{M}$. We derive this criterion using three different approaches: a microscopic analysis of the edge, a general argument based on braiding statistics, and finally a conformal field theory approach that uses constraints from modular invariance. We also discuss the analogous result for two-dimensional boson systems.

Making a system state follow a prescribed trajectory despite fluctuations and errors commonly consists of monitoring an observable (temperature, blood-glucose level, etc.) and reacting on its controllers (heater power, insulin amount, etc.). In the quantum domain, there is a change of paradigm in feedback, since measurements modify the state of the system, most dramatically when the trajectory goes through superpositions of measurement eigenstates. Here, we demonstrate the stabilization of an arbitrary trajectory of a superconducting qubit by measurement-based feedback. The protocol benefits from the long coherence time ($T_2>10\mu \mathrm{s}$) of the 3D transmon qubit, the high efficiency ($82\%$) of the phase-preserving Josephson amplifier, and fast electronics that ensure less than 500 ns total delay. At discrete time intervals, the state of the qubit is measured and corrected in case an error is detected. For Rabi oscillations, where the discrete measurements occur when the qubit is supposed to be in the measurement pointer states, we demonstrate an average fidelity of $85\%$ to the targeted trajectory. For Ramsey oscillations, which do not go through pointer states, the average fidelity reaches $76\%$. Incidentally, we demonstrate a fast reset protocol that allows us to cool a 3D transmon qubit down to $0.6\%$ in the excited state.

Strained bulk HgTe is a three-dimensional topological insulator, whose surface electrons have a high mobility ($\sim 30000{\mathrm{cm}}^2/\mathrm{Vs}$), while its bulk is effectively free of mobile charge carriers. These properties enable a study of transport through its unconventional surface states without being hindered by a parallel bulk conductance. Here, we show transport experiments on HgTe-based Josephson junctions to investigate the appearance of the predicted Majorana states at the interface between a topological insulator and a superconductor. Interestingly, we observe a dissipationless supercurrent flow through the topological surface states of HgTe. The current-voltage characteristics are hysteretic at temperatures below 1 K, with critical supercurrents of several microamperes. Moreover, we observe a magnetic-field-induced Fraunhofer pattern of the critical supercurrent, indicating a dominant $2\pi$-periodic Josephson effect in the unconventional surface states. Our results show that strained bulk HgTe is a promising material system to get a better understanding of the Josephson effect in topological surface states, and to search for the manifestation of zero-energy Majorana states in transport experiments.

We propose a stochastic model for the number of different words in a given database which incorporates the dependence on the database size and historical changes. The main feature of our model is the existence of two different classes of words: (i) a finite number of core words, which have higher frequency and do not affect the probability of a new word to be used, and (ii) the remaining virtually infinite number of noncore words, which have lower frequency and, once used, reduce the probability of a new word to be used in the future. Our model relies on a careful analysis of the Google Ngram database of books published in the last centuries, and its main consequence is the generalization of Zipf’s and Heaps’ law to two-scaling regimes. We confirm that these generalizations yield the best simple description of the data among generic descriptive models and that the two free parameters depend only on the language but not on the database. From the point of view of our model, the main change on historical time scales is the composition of the specific words included in the finite list of core words, which we observe to decay exponentially in time with a rate of approximately 30 words per year for English.

Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity ($\lesssim 1\mathrm{Hz}$) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning.

A wide class of binary-state dynamics on networks—including, for example, the voter model, the Bass diffusion model, and threshold models—can be described in terms of transition rates (spin-flip probabilities) that depend on the number of nearest neighbors in each of the two possible states. High-accuracy approximations for the emergent dynamics of such models on uncorrelated, infinite networks are given by recently developed compartmental models or approximate master equations (AMEs). Pair approximations (PAs) and mean-field theories can be systematically derived from the AME. We show that PA and AME solutions can coincide under certain circumstances, and numerical simulations confirm that PA is highly accurate in these cases. For monotone dynamics (where transitions out of one nodal state are impossible, e.g., susceptible-infected disease spread or Bass diffusion), PA and the AME give identical results for the fraction of nodes in the infected (active) state for all time, provided that the rate of infection depends linearly on the number of infected neighbors. In the more general nonmonotone case, we derive a condition—that proves to be equivalent to a detailed balance condition on the dynamics—for PA and AME solutions to coincide in the limit $t\to \infty$. This equivalence permits bifurcation analysis, yielding explicit expressions for the critical (ferromagnetic or paramagnetic transition) point of such dynamics, that is closely analogous to the critical temperature of the Ising spin model. Finally, the AME for threshold models of propagation is shown to reduce to just two differential equations and to give excellent agreement with numerical simulations. As part of this work, the Octave or Matlab code for implementing and solving the differential-equation systems is made available for download.

The discovery of the quantum spin Hall (QSH) state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the quantum spin Hall state have confirmed the presence of edge states, showed ballistic edge transport in micron-sized samples, and demonstrated the spin polarization of the helical edge states. While these experiments have confirmed the broad theoretical model, the properties of the QSH edge states have not yet been investigated on a local scale. Using scanning gate microscopy to perturb the QSH edge states on a submicron scale, we identify well-localized scattering sites which likely limit the expected nondissipative transport in the helical edge channels. In the micron-sized regions between the scattering sites, the edge states appear to propagate unperturbed, as expected for an ideal QSH system, and are found to be robust against weak induced potential fluctuations.

The origin of superconductivity in bulk ${\mathrm{SrTiO}}_3$ is a mystery since the nonmonotonous variation of the critical transition with carrier concentration defies the expectations of the crudest version of the BCS theory. Here, employing the Nernst effect, an extremely sensitive probe of tiny bulk Fermi surfaces, we show that, down to concentrations as low as $5.5\times {10}^{17}{\mathrm{cm}}^{-3}$, the system has both a sharp Fermi surface and a superconducting ground state. The most dilute superconductor currently known therefore has a metallic normal state with a Fermi energy as little as 1.1 meV on top of a band gap as large as 3 eV. The occurrence of a superconducting instability in an extremely small, single-component, and barely anisotropic Fermi surface implies strong constraints for the identification of the pairing mechanism.

We have measured the electrophoretic mobility of single, optically trapped colloidal particles, while gradually depleting the co-ions and counterions in the liquid around the particle by applying a dc voltage. This is achieved in a nonpolar liquid, where charged reverse micelles act as co-ions and counterions. By increasing the dc voltage, the mobility first increases when the concentrations of co-ions and counterions near the particle start to decrease. At sufficiently high dc voltage (around 2 V), the mobility reaches a saturation value when the co-ions and counterions are fully separated. The increase in mobility is larger when the equilibrium ionic strength is higher. The dependence of the experimental data on the equilibrium ionic strength and on the applied voltage is in good agreement with the standard theory of electrophoretic retardation, assuming that the bare particle charge remains constant. This method is useful for studying the electrophoretic retardation effect and charging mechanisms for nonpolar colloids, and it sheds light on previously unexplained particle acceleration in electronic ink devices.

The oxide heterostructure ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ supports a two-dimensional electron liquid with a variety of competing phases, including magnetism, superconductivity, and weak antilocalization because of Rashba spin-orbit coupling. Further confinement of this two-dimensional electron liquid to the quasi-one-dimensional regime can provide insight into the underlying physics of this system and reveal new behavior. Here, we describe magnetotransport experiments on narrow ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ structures created by a conductive atomic force microscope lithography technique. Four-terminal local-transport measurements on Hall bar structures about 10 nm wide yield longitudinal resistances that are comparable to the resistance quantum $h/e^2$ and independent of the channel length. Large nonlocal resistances (as large as ${10}^4\Omega$) are observed in some but not all structures with separations between current and voltage that are large compared to the two-dimensional mean-free path. The nonlocal transport is strongly suppressed by the onset of superconductivity below about 200 mK. The origin of these anomalous transport signatures is not understood, but may arise from coherent transport defined by strong spin-orbit coupling and/or magnetic interactions.

The coexisting regime of spin-density wave (SDW) and superconductivity in iron pnictides represents a novel ground state. We have performed high-resolution angle-resolved photoemission measurements on ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ ($x=0.0175$) in this regime and revealed its distinctive electronic structure, which provides some microscopic understandings of its behavior. The SDW signature and the superconducting gap are observed on the same bands, illustrating the intrinsic nature of the coexistence. However, because the SDW and superconductivity are manifested in different parts of the band structure, their competition is nonexclusive. Particularly, we find that the gap distribution is anisotropic and nodeless, in contrast to the isotropic superconducting gap observed in a SDW-free ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ ($x=0.045$), which puts strong constraints on theory.

Shallow group-V donors in silicon may be thought of as hydrogenlike, and shallow acceptors are similarly described by effective-mass theory with similar energy scales, which implies that donor and acceptor excitations should be just as long-lived. Yet, spectral widths of acceptors are considerably wider. We have measured the orbital dynamics of acceptors in silicon using time-domain spectroscopy with a free-electron laser. Both the population and coherence lifetimes for acceptors in natural silicon are substantially longer—e.g. approximately 60 ps for boron—than implied by the spectral linewidths; our experiments also establish the recombination time for ionized acceptors to be, at approximately 500 ps, nearly an order of magnitude longer. We show that there are no extra sources of decoherence introduced by the host crystal, other than the population relaxation. In this sense, the crystal acts as an atom trap, and, by introducing quantum coherent control of acceptors to that previously established for donors, we open the way to optically controllable nanoscale p-n devices.