We report on the stabilization of a microresonator-based optical frequency comb (microcomb) by way of mechanical actuation. These experiments use novel ${\mathrm{CO}}_2$-laser-machined microrod resonators, which are introduced here and feature optical $Q\gtrsim 5\times {10}^8$, less than 1 minute processing time, and tunable geometry. Residual fluctuations of our 32.6 GHz microcomb line spacing reach a stability level of $5\times {10}^{-15}$ for 1 s averaging, thereby highlighting the potential of microcombs to support modern optical-frequency standards. Furthermore, measurements of the line spacing with respect to an independent frequency reference reveal stabilization of different spectral slices of the comb with a $<0.5\mathrm{\text{−}}\mathrm{mHz}$ variation among 140 comb lines spanning 4.5 THz. Together, these results demonstrate an important step in the development of microcombs, namely, that they can be fabricated and precisely controlled with simple and accessible techniques.

Progress in materials science depends on the ability to discover new materials and to obtain and understand their properties. This has recently become particularly apparent for compounds with reduced dimensionality, which often display unexpected physical and chemical properties, making them very attractive for applications in electronics, graphene being so far the most noteworthy example. Here, we report some previously unknown two-dimensional materials and their electronic structure by data mining among crystal structures listed in the International Crystallographic Structural Database, combined with density-functional-theory calculations. As a result, we propose to explore the synthesis of a large group of two-dimensional materials, with properties suggestive of applications in nanoscale devices, and anticipate further studies of electronic and magnetic phenomena in low-dimensional systems.

Nonreciprocal devices perform crucial functions in many low-noise quantum measurements, usually by exploiting magnetic effects. In the proof-of-principle device presented here, on the other hand, two on-chip coupled Josephson parametric converters (JPCs) achieve directionality by exploiting the nonreciprocal phase response of the JPC in the transmission-gain mode. The nonreciprocity of the device is controlled in situ by varying the amplitude and phase difference of two independent microwave pump tones feeding the system. At the desired working point and for a signal frequency of 8.453 GHz, the device achieves a forward power gain of 15 dB within a dynamical bandwidth of 9 MHz, a reverse gain of $-6\mathrm{dB}$, and suppression of the reflected signal by 8 dB. We also find that the amplifier adds a noise equivalent to less than 1.5 photons at the signal frequency (referred back to the input). It can process up to 3 photons at the signal frequency per inverse dynamical bandwidth. With a directional amplifier operating along the principles of this device, qubit and readout preamplifier could be integrated on the same chip.

Charge-density-wave order has been observed in cuprate superconductors whose crystal structure breaks the square symmetry of the ${\mathrm{CuO}}_2$ planes, such as orthorhombic ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ (YBCO), but not so far in cuprates that preserve that symmetry, such as tetragonal ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ (Hg1201). We have measured the Hall ($R_H$), Seebeck ($S$), and Nernst ($\nu$) coefficients of underdoped Hg1201 in magnetic fields large enough to suppress superconductivity. The high-field $R_H(T)$ and $S(T)$ are found to drop with decreasing temperature and become negative, as also observed in YBCO at comparable doping. In YBCO, the negative $R_H$ and $S$ are signatures of a small electron pocket caused by Fermi-surface reconstruction, attributed to charge-density-wave modulations observed in the same range of doping and temperature. We deduce that a similar Fermi-surface reconstruction takes place in Hg1201, evidence that density-wave order exists in this material. A striking similarity is also found in the normal-state Nernst coefficient $\nu (T)$, further supporting this interpretation. Given the model nature of Hg1201, Fermi-surface reconstruction appears to be common to all hole-doped cuprates, suggesting that density-wave order is a fundamental property of these materials.

Despite much interest in engineering new topological surface (edge) states using structural defects, such topological surface states have not been observed yet. We show that recently imaged tilt boundaries in gated multilayer graphene should support topologically protected gapless edge states. We approach the problem from two perspectives: the microscopic perspective of a tight-binding model and an ab initio calculation on a bilayer, and the symmetry-protected topological (SPT) state perspective for a general multilayer. Hence, we establish the tilt-boundary edge states as the first concrete example of the edge states of symmetry-protected $\mathbb{Z}$-type SPT, protected by no-valley mixing, electron-number conservation, and time-reversal $T$ symmetries. Further, we discuss possible phase transitions between distinct SPTs upon symmetry changes. Combined with a recently imaged tilt-boundary network, our findings may explain the long-standing puzzle of subgap conductance in gated bilayer graphene. This proposal can be tested through future transport experiments on tilt boundaries. In particular, the tilt boundaries offer an opportunity for the in situ imaging of topological edge transport.

We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly less attention than its electronic counterpart. We find rich behavior in the localization properties of the phonons as a function of the density, frequency, and spatial dimension. We use a percolation analysis to argue for a Debye spectrum at low frequencies for dimensions higher than one, and for a localization-delocalization transition (at a critical frequency) above two dimensions. We show that in contrast to the behavior in electronic systems, the transition exists for arbitrarily large disorder, albeit with an exponentially small critical frequency. The structure of the modes reflects a divergent percolation length that arises from the disorder in the springs without being explicitly present in the definition of our model. Within the percolation approach, we calculate the speed of sound of the delocalized modes (phonons), which we corroborate with numerics. We find the critical frequency of the localization transition at a given density and find good agreement of these predictions with numerical results using a recursive Green-function method that was adapted for this problem. The connection of our results to recent experiments on amorphous solids is discussed.

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.