Recently, several authors have investigated topological phenomena in periodically driven systems of noninteracting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band structures of static Hamiltonians. Intriguingly, these works have revealed phenomena that cannot be characterized by analogy to the topological classification framework for static systems. In particular, in driven systems in two dimensions (2D), robust chiral edge states can appear even though the Chern numbers of all the bulk Floquet bands are zero. Here, we elucidate the crucial distinctions between static and driven 2D systems, and construct a new topological invariant that yields the correct edge-state structure in the driven case. We provide formulations in both the time and frequency domains, which afford additional insight into the origins of the “anomalous” spectra that arise in driven systems. Possibilities for realizing these phenomena in solid-state and cold-atomic systems are discussed.

Parity is a fundamental quantum number used to classify a state of matter. Materials rarely possess ground states with odd parity. We show that the superconducting state in iron-based superconductors is classified as an odd-parity $s$-wave spin-singlet pairing state in a single trilayer $\mathrm{FeAs}/\mathrm{Se}$, the building block of the materials. In a low-energy effective model constructed on the Fe square bipartite lattice, the superconducting order parameter in this state is a combination of an $s$-wave normal pairing between two sublattices and an $s$-wave $\eta$ pairing within the sublattices. The state has a fingerprint with a real-space sign inversion between the top and bottom $\mathrm{As}/\mathrm{Se}$ layers. The results suggest that iron-based superconductors are a new quantum state of matter, and the measurement of the odd parity can help to establish high-temperature superconducting mechanisms.

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.

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.

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.

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.

We discuss physical properties of “integer” topological phases of bosons in $D=3+1$ dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not possess topological order; they are bosonic analogs of free-fermion topological insulators and superconductors. While a formal cohomology-based classification of such states was recently discovered, their physical properties remain mysterious. Here, we develop a field-theoretic description of several of these states and show that they possess unusual surface states, which, if gapped, must either break the underlying symmetry or develop topological order. In the latter case, symmetries are implemented in a way that is forbidden in a strictly two-dimensional theory. While these phases are the usual fate of the surface states, exotic gapless states can also be realized. For example, tuning parameters can naturally lead to a deconfined quantum critical point or, in other situations, to a fully symmetric vortex metal phase. We discuss cases where the topological phases are characterized by a quantized magnetoelectric response $\theta$, which, somewhat surprisingly, is an odd multiple of $2\pi$. Two different surface theories are shown to capture these phenomena: The first is a nonlinear sigma model with a topological term. The second invokes vortices on the surface that transform under a projective representation of the symmetry group. We identify a bulk-field theory consistent with these properties, which is a multicomponent background-field theory supplemented, crucially, with a topological term. We also provide bulk sigma-model field theories of these phases and discuss a possible topological phase characterized by the thermal analog of the magnetoelectric effect.

As an exemplary Kondo insulator, ${\mathrm{SmB}}_6$ has been studied for several decades. However, direct evidence for the development of the Kondo coherent state and for the evolution of the electronic structure in the material has not been obtained due to the compound’s rather complicated electronic and thermal transport behavior. Recently, these open questions have attracted increasing attention as the emergence of a time-reversal-invariant topological surface state in the Kondo insulator has been suggested. Here, we use point-contact spectroscopy to reveal the temperature dependence of the electronic states in ${\mathrm{SmB}}_6$. We demonstrate that ${\mathrm{SmB}}_6$ is a model Kondo insulator: Below 100 K, the conductance spectra reflect the Kondo hybridization of Sm ions, but, below about $30\mathrm{K}$, signatures of inter-ion correlation effects clearly emerge. Moreover, we find evidence that the low-temperature insulating state of this exemplary Kondo-lattice compound harbors conduction states on the surface, in support of predictions of nontrivial topology in Kondo insulators.

We report an investigation with angle-resolved photoemission spectroscopy of the Fermi surface and electronic band structure of ${\mathrm{BaCo}}_2{\mathrm{As}}_2$. Although its quasinesting-free Fermi surface differs drastically from that of its Fe-pnictide cousins, we show that the ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ system can be used as an approximation to the bare unoccupied band structure of the related ${\mathrm{BaFe}}_{2-x}{\mathrm{Co}}_x{\mathrm{As}}_2$ and ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ compounds. However, our experimental results, in agreement with dynamical-mean-field-theory calculations, indicate that electronic correlations are much less important in ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ than in the ferropnictides. Our findings suggest that this effect is due to the increased filling of the electronic $3d$ shell in the presence of significant Hund’s exchange coupling.

Thin membranes exhibit complex responses to external forces or geometrical constraints. A familiar example is the wrinkling, exhibited by human skin, plant leaves, and fabrics, that results from the relative ease of bending versus stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest known membrane, deposited on a silica substrate decorated with silica nanoparticles. At small nanoparticle density, monolayer graphene adheres to the substrate, detached only in small regions around the nanoparticles. With increasing nanoparticle density, we observe the formation of wrinkles which connect nanoparticles. Above a critical nanoparticle density, the wrinkles form a percolating network through the sample. As the graphene membrane is made thicker, global delamination from the substrate is observed. The observations can be well understood within a continuum-elastic model and have important implications for strain-engineering the electronic properties of graphene.

The appearance of massless Dirac fermions in graphene requires two equivalent carbon sublattices of trigonal shape. While the generation of an effective mass and a band gap at the Dirac point remains an unresolved problem for freestanding extended graphene, it is well established by breaking translational symmetry by confinement and by breaking sublattice symmetry by interaction with a substrate. One of the strongest sublattice-symmetry-breaking interactions with predicted and measured band gaps ranging from 400 meV to more than 3 eV has been attributed to the interfaces of graphene with Ni and Co, which are also promising spin-filter interfaces. Here, we apply angle-resolved photoemission to epitaxial graphene on Ni(111) and Co(0001) to show the presence of intact Dirac cones 2.8 eV below the Fermi level. Our results challenge the common belief that the breaking of sublattice symmetry by a substrate and the opening of the band gap at the Dirac energy are in a straightforward relation. A simple effective model of a biased bilayer structure composed of graphene and a sublattice-symmetry-broken layer, corroborated by density-functional-theory calculations, demonstrates the general validity of our conclusions.

Heating a solid sphere at its surface induces mechanical stresses inside the sphere. If a finite amount of heat is supplied, the stresses gradually disappear as temperature becomes homogeneous throughout the sphere. We show that before this happens, there is a temporary lowering of pressure and density in the interior of the sphere, inducing a transient lowering of the temperature here. For ordinary solids this effect is small because $c_p\cong c_V$. For fluent liquids the effect is negligible because their dynamic shear modulus vanishes. For a liquid at its glass transition, however, the effect is generally considerably larger than in solids. This paper presents analytical solutions of the relevant coupled thermoviscoelastic equations. In general, there is a difference between the isobaric specific heat $c_p$ measured at constant isotropic pressure and the longitudinal specific heat $c_l$ pertaining to mechanical boundary conditions that confine the associated expansion to be longitudinal. In the exact treatment of heat propagation, the heat-diffusion constant contains $c_l$ rather than $c_p$. We show that the key parameter controlling the magnitude of the “cooling-by-heating“ effect is the relative difference between these two specific heats. For a typical glass-forming liquid, when the temperature at the surface is increased by 1 K, a lowering of the temperature at the sphere center of the order of 5 mK is expected if the experiment is performed at the glass transition. The cooling-by-heating effect is confirmed by measurements on a glucose sphere at the glass transition.

The main characteristic of Mott insulators, as compared to band insulators, is to host low-energy spin fluctuations. In addition, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in the majority of Mott insulators, spins and orbitals develop long-range order, the possibility for the ground state to be a quantum liquid opens new perspectives. In this paper, we provide clear evidence that the spin-orbital $\mathrm{SU}(4)$ symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breaking—lattice or $\mathrm{SU}(\mathrm{N})$—is supported by a combination of semiclassical and numerical approaches: flavor-wave theory, tensor network algorithm, and exact diagonalizations. In addition, all properties revealed by these methods are very accurately accounted for by a projected variational wave function based on the $\pi$-flux state of fermions on the honeycomb lattice at $1/4$ filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the honeycomb lattice is an algebraic quantum spin-orbital liquid. This model provides an interesting starting point to understanding the recently discovered spin-orbital-liquid behavior of ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$. The present results also suggest the choice of optical lattices with honeycomb geometry in the search for quantum liquids in ultracold four-color fermionic atoms.

Interest in femtosecond demagnetization dynamics was sparked by Bigot’s experiment in 1996, which unveiled the elementary mechanisms that relate the electrons’ temperature to their spin order. Simultaneously, the application of fast demagnetization experiments has been demonstrated to provide key insight into technologically important systems such as high-spin-polarization metals, and consequently there is broad interest in further understanding the physics of these phenomena. To gain new and relevant insights, we performed ultrafast optical pump-probe experiments to characterize the demagnetization processes of highly spin-polarized magnetic thin films on a femtosecond time scale. Full spin polarization is obtained in half-metallic ferro- or ferrimagnets, where only one spin channel is populated at the Fermi level, whereas the other one exhibits a gap. In these materials, the spin-scattering processes is controlled via the electronic structure, and thus their ultrafast demagnetization is solely related to the spin polarization via a Fermi golden-rule model. Accordingly, a long demagnetization time correlates with a high spin polarization due to the suppression of the spin-flip scattering at around the Fermi level. Here we show that isoelectronic Heusler compounds (${\mathrm{Co}}_2\mathrm{MnSi}$, ${\mathrm{Co}}_2\mathrm{MnGe}$, and ${\mathrm{Co}}_2\mathrm{FeAl}$) exhibit a degree of spin polarization between 59% and 86%. We explain this behavior by considering the robustness of the gap against structural disorder. Moreover, we observe that CoFe-based pseudogap materials, such as partially ordered Co-Fe-Ge and Co-Fe-B alloys, can reach similar values of the spin polarization. By using the unique features of these metals we vary the number of possible spin-flip channels, which allows us to pinpoint and control the half-metals’ electronic structure and its influence on the elementary mechanisms of ultrafast demagnetization.

We study the non-Abelian statistics characterizing systems where counterpropagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of $\nu =1/m$, while electrons of the opposite spin occupy a similar state with $\nu =-1/m$. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-Abelian anyon of quantum dimension $\sqrt{2m}$. We calculate the unitary transformations that are associated with the braiding of these anyons, and we show that they are able to realize a richer set of non-Abelian representations of the braid group than the set realized by non-Abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.

We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length $\xi$. We show that, for the divergence-free portion of the superfluid velocity field, the kinetic-energy spectrum over wave number $k$ may be decomposed into an ultraviolet regime ($k\gg {\xi }^{-1}$) having a universal $k^{-3}$ scaling arising from the vortex core structure, and an infrared regime ($k\ll {\xi }^{-1}$) with a spectrum that arises purely from the configuration of the vortices. The Novikov power-law distribution of intervortex distances with exponent $-1/3$ for vortices of the same sign of circulation leads to an infrared kinetic-energy spectrum with a Kolmogorov $k^{-5/3}$ power law, which is consistent with the existence of an inertial range. The presence of these $k^{-3}$ and $k^{-5/3}$ power laws, together with the constraint of continuity at the smallest configurational scale $k\approx {\xi }^{-1}$, allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous, compressible, two-dimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kinetic-energy distribution, once we introduce the concept of a clustered fraction consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding two-dimensional quantum turbulence and interpreting similarities and differences with classical two-dimensional turbulence, and suggests new methods to characterize vortex turbulence in two-dimensional quantum fluids via vortex position and circulation measurements.