We show that the nonlinear interactions between x rays and longer wavelengths in crystals depend strongly on the band structure and related properties. Consequently, these types of interactions can be used as a powerful probe for fundamental properties of crystalline bulk materials. In contrast to previous work that highlighted that these types of nonlinear interactions can provide microscopic information on the valence electrons at the atomic scale resolution, we show that these interactions also contain information that is related to the periodic potential of the crystal. We explain how it is possible to distinguish between the two contributions. Our work indicates on the possibility for the development of novel multidimensional pump-probe metrology techniques that will provide spectroscopic information combined with structural information including ultrafast dynamics at the atomic scale.

Magnetotransport provides key experimental signatures in Weyl semimetals. The longitudinal magnetoresistance is linked to the chiral anomaly and the transversal magnetoresistance to the dominant charge relaxation mechanism. Axial magnetic fields that act with opposite sign on opposite chiralities facilitate new transport experiments that probe the low-energy Weyl nodes. As recently realized, these axial fields can be achieved by straining samples or adding inhomogeneities to them. Here, we identify a robust signature of axial magnetic fields: an anomalous scaling of the conductance in the diffusive ultraquantum regime. In particular, we demonstrate that the longitudinal conductivity in the ultraquantum regime of a disordered Weyl semimetal subjected to an axial magnetic field increases with both the field strength and sample width due to a spatial separation of charge carriers. We contrast axial magnetic with real magnetic fields to clearly distinguish the different behavior of the conductance. Our results rely on numerical tight-binding simulations and are supported by analytical arguments. We argue that the spatial separation of charge carriers can be used for directed currents in microstructured electronic devices.

The possibility of engineering experimentally viable systems that realize gauge fluxes within plaquettes of hopping has been the subject of a search for decades due to vast amounts of theoretical study. This is of particular interest for topological band insulators, where it is known that such fluxes bind protected midgap states. These modes can hybridize in extended flux lattices, giving rise to semimetallic bands that are highly tunable. We demonstrate that within artificial materials, local $\pi$-fluxes can be naturally realized. Also, the importance of the crystalline symmetry for protecting the $\pi$-flux modes is pointed out. Consequently, we provide concrete setups and conditions to access this physics and analyze similar self-organized band structures and physical properties. Our work therefore not only pinpoints simple systems exhibiting flat bands but also opens up a route to study flux lattice models and associated effective theories.

There is a counterintuitive expectation proposed by Huse et al. [Phys. Rev. B 88, 014206 (2013)] and Chandran et al. [Phys. Rev. B 89, 144201 (2014)]: Localization protects the quantum order of the ground state, even in highly excited eigenstates. In this Rapid Communication, we numerically investigate the localization protection for symmetry-protected topological (SPT) order by considering a modified XXZ spin model, related to an interacting Su-Schrieffer-Heeger (SSH) model. We systematically study how many-body localization (MBL) protects SPT for different disorder types and different forms of interactions. A certain disorder leads to the clear degeneracy of the low-lying entanglement spectrum of each excited many-body eigenstate. This fact indicates that the existence of edge modes, which is a hallmark of SPT order, is protected by the MBL in excited many-body eigenstates. In addition, we also report how the MBL-protected edge modes in excited many-body eigenstates fade away for a diagonal-type disorder.

We introduce a Floquet spinor Bose-Einstein condensate induced by a periodically driven quadratic Zeeman coupling whose frequency is larger than any other energy scales. By examining a spin-1 system available in ultracold atomic gases, we demonstrate that such an external driving field has great effect on the condensate through emergence of a unique spin-exchange interaction. We uncover that the ferromagnetic condensate has several unconventional stationary states and thus exhibits rich continuous phase transitions. On the other hand, the antiferromagnetic condensate is found to possess a nontrivial metastable region, which supports unusual elementary excitations and hysteresis phenomena.

The Jahn-Teller distortion that can remove electronic degeneracies in partially occupied states and results in systematic atomic displacements is a common underlying feature to many of the intriguing phenomena observed in $3d$ perovskites, encompassing magnetism, superconductivity, orbital ordering, and colossal magnetoresistance. Although the seminal Jahn and Teller theorem was postulated almost a century ago, the origins of this effect in perovskite materials are still debated, including propositions such as superexchange, spin-phonon coupling, sterically induced lattice distortions, and strong dynamical correlation effects. Although the end result of Jahn-Teller distortions often includes a mix of such various contributions, due to coupling of various lattice, spin, and electronic modes with the distortions (“fingerprints” or “consequences” of Jahn-Teller), it is not clear what the primary cause is, i.e., which cases are caused by a pure electronic instability associated with degeneracy removal, as implied in the Jahn-Teller theorem, and which cases originate from other causes, such as semiclassical size effects. We propose a way to distinguish the materials with an electronic instability associated with degeneracy removal being the primary cause of the Jahn-Teller distortions, from others with octahedral rotation or tilts from a steric effect playing the primary role in electron-lattice coupling. This work provides a unified and quantitative density functional theory explanation of the experimentally observed trends of octahedral deformations in $AB{X}_3$ perovskites, without recourse to the dynamically correlated vision of electron interactions codified by the Mott-Hubbard mechanism. We inquire about the origin and predictability of different types of octahedral deformation by using a Landau-esque approach, where the orbital occupation pattern of a symmetric structure is perturbed, finding whether it is prone to total energy lowering the electronic instability or not. This is done for a systematic series of $AB{X}_3$ perovskite compounds having $3d$-orbital degeneracies, using the density functional approach. We identify (i) systems prone to an electronic instability (a true Jahn-Teller effect), such as $\mathrm{KCr}{\mathrm{F}}_3, \mathrm{KCu}{\mathrm{F}}_3, \mathrm{LaV}{\mathrm{O}}_3, \mathrm{KFe}{\mathrm{F}}_3$, and $\mathrm{KCo}{\mathrm{F}}_3$, where the instability is independent of magnetic order, and forces a specific orbital arrangement that is accommodated by a $B{X}_6$ octahedral deformation with a specific symmetry. On the other hand, (ii) compounds such as $\mathrm{LaTi}{\mathrm{O}}_3$ and $\mathrm{LaMn}{\mathrm{O}}_3$ with delocalized $d$ states do not show any electronically driven instability. Here, the alternate orbital ordering, which is an energy-lowering event irrespective of the presence of electronic instabilities, simply results from the coupling of lattice modes induced by semiclassical size effects (sterically induced), such as $B{X}_6$ octahedra rotations. (iii) Although $R\mathrm{V}{\mathrm{O}}_3$ ($R=\mathrm{Lu}-\mathrm{La}$, Y) perovskites exhibit hybridizations similarly to $\mathrm{LaTi}{\mathrm{O}}_3$, their $t_{2g}^2$ electronic structure is highly unstable and preserves the Jahn-Teller effect. However, here coexisting steric deformations and Jahn-Teller distortions result in strongly entangled spin-orbital properties.

A limit-torus solution describes a traveling and oscillating solution. It is characterized by two phase variables, spatial phase and temporal phase, which indicate the position and oscillation of the solution, respectively. Here, we develop a theoretical framework for the phase reduction of limit-torus solutions to partial differential algebraic equations or partial differential equations with constraints. We derive phase sensitivity functions for the two phases; these functions quantify the spatiotemporal phase responses of the solution under weak perturbations applied at each spatial point and at each time. We consider oscillatory thermal convection in a two-dimensional incompressible Navier-Stokes flow system with lateral periodicity as a prototype.

Domain motion during ferroelectric switching has been recently suggested to follow scale-invariant avalanche dynamics. An interesting question concerns the dynamics of ferroelastic materials where the bulk material is nonpolar, while the polarity arises at domain walls only. We tackle this issue by investigating the dynamics of ferroelastic twins in $\mathrm{SrTi}{\mathrm{O}}_3$ where the movement of domains is driven mainly by the anisotropic dielectric response at low temperatures. We find that the dynamics of the twin reconfiguration under electric field proceeds by jerks, where the energy distribution is power-law distributed, indicating avalanche dynamics. Avalanche exponents are sensitive to the complexity of the twin pattern structure, reflecting glassiness when twins are interwoven and forming junctions at the intersections between domain walls. This “glassy” behavior is attributed to the pinning originated by these self-generated defects during jamming between twins.

We analyze the localization properties of two-dimensional systems based on partite lattices with a basis. Contrary to standard results, we find that a band of critical states emerges for systems in the unitary class A preserving spin symmetry when disorder is unevenly distributed over the basis atoms. The critical metal arises when the less disordered sublattice is connected and has time-reversal symmetry broken. The unexpected robustness to disorder presented here is an appealing result which can be measured in optical lattices.

In circuit QED, a Rabi model can be derived by truncating the Hilbert space of an anharmonic qubit coupled to a resonator. This truncation breaks the gauge invariance present in the full Hamiltonian. Here we derive a simple criterion for an optimal gauge such that the differences between the truncated and the full Hamiltonian are minimized. We find that it is determined by the ratio of the anharmonicity of the qubit to an averaged resonator frequency. We demonstrate that the usual choices of flux and charge gauge are not necessarily the preferred options in the case of multiple resonator modes.

The space of density matrices is embedded in a Euclidean space to deduce the dynamical equation satisfied by the state of an open quantum system. The Euclidean norm is used to obtain an explicit expression for the speed of the evolution of the state. The unitary contribution to the evolution speed is given by the modified skew information of the Hamiltonian, while the radial component of the evolution speed, connected to the rate at which the purity of the state changes, is shown to be determined by the modified skew information of the Lindblad operators. An open-system analog of the quantum navigation problem is posed, and a perturbative analysis is presented to identify the amount of change on the speed. Properties of the evolution speed are examined further through example systems, showing that the evolution speed need not be a decreasing function of time.

A recent experiment reported a large anomalous Hall effect in magic angle twisted bilayer graphene (TBG) aligned with a hexagonal boron nitride (h-BN) substrate at 3/4 filling of the conduction band. In this paper we study this system theoretically and propose explanations of this observation. We emphasize that the physics for this system is qualitatively different from the pure TBG system. The aligned h-BN breaks in-plane twofold rotation symmetry and gaps out the Dirac crossings of ordinary TBG. The resulting valence and conduction bands of each valley carry equal and opposite Chern numbers $C=\pm 1$. A useful framework is provided by a lattice extended Hubbard model for this system, which we derive. An obvious possible explanation of the anomalous Hall effect is that at $3/4$ filling the system is a spin-valley polarized ferromagnetic insulator where the electrons completely fill a Chern band. We also examine an alternate, more radical proposal of a compressible valley-polarized but spin-unpolarized composite Fermi-liquid metallic state. We argue that either state is compatible with current experiments and propose ways to distinguish between them in the future. We also briefly discuss the physics at $1/2$ filling.

We propose an interferometric scheme for the estimation of a linear combination with non-negative weights of an arbitrary number $M>1$ of unknown phase delays, distributed across an $M$-channel linear optical network, with Heisenberg-limited sensitivity. This is achieved without the need of any sources of photon-number or entangled states, photon-number-resolving detectors, or auxiliary interferometric channels. Indeed, the proposed protocol remarkably relies upon a single squeezed-state source, an antisqueezing operation at the interferometer output, and on-off photodetectors.

The catalyzing role that influential individuals play in driving large-scale social contagion has been the focus of many recent empirical and theoretical studies. Nevertheless, complementary studies suggest that the success of social contagion depends largely on having a group of highly susceptible individuals. Here we show that being influential is not due solely to having susceptible peers and that the relative importance of influential versus susceptible individuals depends on the underlying mechanism driving the contagion. Our mathematical models show that for passive social influence both influential and susceptible individuals catalyze the spread of the contagion progressively and equitably. In contrast, for active social influence, susceptible individuals facilitate rapid initial contagion, but then influential individuals are necessary for sustaining the growth of the contagion. We show that active influence characterizes certain online social networks, like retweeting behavior on Twitter, while passive influence characterizes other online social networks, like adoption of whom to follow on the Digg network.

First-principles calculations are presented for fundamental vibrational splitting energies of tritium-bearing molecular hydrogen species with the improved treatment of the nonrelativistic, relativistic, and quantum electrodynamic energy contributions resulting in a total uncertainty of $0.00011 {\mathrm{cm}}^{-1}$ for DT, or about a 100-times improvement over previous results. Precision coherent Raman spectroscopic measurements of $Q$($J=0–5$) transitions in DT were performed at an accuracy of $<0.0004 {\mathrm{cm}}^{-1}$, representing an even larger 250-fold improvement over previous experiments. Perfect agreement between experiment and theory is found, within $1\sigma$, for all six transitions studied.

We show how a superconducting circuit consisting of three identical nonlinear oscillators in series considered in terms of its electrical modes can implement a strong, native three-body interaction among qubits. Because of strong interactions, part of the qubit subspace is coupled to higher levels. The remaining qubit states can be used to implement a restricted Fredkin gate, which in turn implements a controlled-not gate or a spin transistor. Including nonsymmetric contributions from couplings to ground and external control, we alter the circuit slightly to compensate and find average fidelities for our implementation of the above gates above $99.5\%$ with operation times on the order of a nanosecond. Additionally, we show how to analytically include all orders of the cosine contributions from Josephson junctions to the Hamiltonian of a superconducting circuit.

We study the thermodynamic energy cost required for the shortcuts-to-isothermal (ScI) process that can accelerate the isothermal process at a finite time. Our experiment uses a Brownian particle dragged by the harmonic potential between two equilibrium positions with free energy difference. We confirm theoretically and experimentally that the probability distribution functions of work done during these processes are Gaussian, and the dissipated work for ScI transport is inversely proportional to the driving time, indicating that very prompt transition is impossible because of a diverging driving cost.

Adopting an agnostic approach, the quality factor $Q$ of tantala glass is drawn via in silico mechanical spectroscopy in wide ranges of temperature (10–300 K) and frequency ($500\mathrm{MHz}\le f\le 1\mathrm{THz}$). At the highest frequencies, $Q\propto f^{-3}$, consistent with Rayleigh sound scattering. For frequencies lower than terahertz, losses exhibit a weak power-law frequency dependence $Q\propto f^{-\alpha }$ with $\alpha \sim 0.1\mathrm{to}0.2$, depending on glass preparation and temperature. Arguing the validity of the power law down to 1 kHz, we show striking agreement with the losses measured in annealed amorphous films in the whole temperature range, revealing similitude between disordered structures created by different routes (quench cooling and deposition). Our results do not support the scenario of the mechanical loss due to activated relaxation of independent two-level systems.

We investigate the microscopic description of exciton-polaritons that involves electrons, holes and photons within a two-dimensional microcavity. We show that in order to recover the simplified exciton-photon model that is typically used to describe polaritons, one must correctly define the exciton-photon detuning and exciton-photon (Rabi) coupling in terms of the bare microscopic parameters. For the case of unscreened Coulomb interactions, we find that the exciton-photon detuning is strongly shifted from its bare value in a manner akin to renormalization in quantum electrodynamics. Within the renormalized theory, we exactly solve the problem of a single exciton-polariton for the first time and obtain the full spectral response of the microcavity. In particular, we find that the electron-hole wave function of the polariton can be significantly modified by the very strong Rabi couplings achieved in current experiments. Our microscopic approach furthermore allows us to obtain the effective interaction between identical polaritons for any light-matter coupling. Crucially, we show that the standard treatment of polariton-polariton interactions in the very strong coupling regime is incorrect, since it neglects the light-induced modification of the exciton size and thus greatly overestimates the effect of Pauli exclusion on the Rabi coupling, i.e., the saturation of exciton oscillator strength. Our findings thus provide the foundations for understanding and characterizing exciton-polariton systems across the whole range of polariton densities.

Oscillatory dynamics is a key tool in optical tweezer applications. It is usually implemented by mechanical interventions that cannot be optically controlled. In this paper, we show that germanium semiconductor beads behave as optically induced oscillators when subjected to a highly focused laser beam. In turn, the well-defined direction of oscillations can be manipulated by the polarization of the light beam. Such unusual motion is due to the competition between the usual optical forces and the radiometric force related to thermal effects, which pushes the beads from the focal region. We characterize the behavior of the germanium beads in detail and propose a model accounting for the related forces in good agreement with the experimental data. Such kind of system can potentially revolutionize the field of optical manipulation, contributing to the design of single molecule machines and to the application of oscillatory forces in fundamental physics, cellular manipulation, fluid dynamics, and other soft-matter systems.