We investigate the appearance of quantum chaos in a single many-body wave function by analyzing the statistical properties of the eigenvalues of its reduced density matrix ${\widehat{\rho }}_A$ of a spatial subsystem $A$. We find that (i): the spectrum of the density matrix is described by so-called Wishart random matrix theory, which (ii): exhibits besides level repulsion, spectral rigidity, and universal spectral correlations between eigenvalues separated by distances ranging from one up to many mean level spacings, which we investigate. We use these universal spectral characteristics of the reduced density matrix as a definition of chaos in the wave function. A simple and precise characterization of such universal correlations in a spectrum is a segment of strictly linear growth at sufficiently long times, recently called the “ramp,” of the spectral form factor which is the Fourier transform of the correlation function between a pair of eigenvalues. It turns out that Wishart and standard random matrix theory have the same universal “ramp.” Specifically, here numerical results for the spectral form factor of the density matrix of generic nonintegrable many-body systems, such as one-dimensional quantum Ising and Floquet spin models, are found to exhibit a universal “ramp” identical to that appearing for a “random pure state” (“Page state,” or “Haar state”). The density matrix of the latter is precisely the Wishart random matrix, the reduced density matrix of a completely random wave function. In addition, we study the development of chaos in the wave function by letting an initial direct product state evolve under the unitary time evolution. We find that the universal spectral correlations as manifested by the “ramp” set in as soon as the entanglement entropy begins to grow, and first develop for the eigenvalues at the top of the spectrum of the density matrix ${\widehat{\rho }}_A$, subsequently spreading over the entire spectrum at later times. Finally, we study a prethermalized regime described by a generalized Gibbs ensemble, which develops in a rapidly driven Floquet model at intermediate times. We find that the prethermalized regime exhibits no chaos, as evidenced by the absence of a “ramp” in the spectral form factor of the density matrix, while the universal spectral correlations start to develop when the prethermalized regime finally relaxes at late times to the fully thermalized (infinite temperature) chaotic regime.

Cuprate superconductors have a universal tendency to form charge density-wave (CDW) order which competes with superconductivity and is strongest at a doping $p\simeq 0.12$. Here we show that in the archetypal cuprate ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ (YBCO) pressure suppresses charge order but does not affect the pseudogap phase. This is based on transport measurements under pressure, which reveal that the onset of the pseudogap at $T^{*}$ is independent of pressure, while the negative Hall effect, a clear signature of CDW order in YBCO, is suppressed by pressure. We also find that pressure and magnetic field shift the superconducting transition temperature $T_{\mathrm{c}}$ of YBCO in the same way as a function of doping—but in opposite directions—and most effectively at $p\simeq 0.12$. This shows that the competition between superconductivity and CDW order can be tuned in two ways, either by suppressing superconductivity with field or suppressing CDW order by pressure. Based on existing high-pressure data and our own work, we observe that when CDW order is fully suppressed at high pressure, the so-called “1/8 anomaly” in the superconducting dome vanishes, revealing a smooth $T_{\mathrm{c}}$ dome which now peaks at $p\simeq 0.13$. We propose that this $T_{\mathrm{c}}$ dome is shaped by the competing effects of the pseudogap phase below its critical point $p^{★}\sim 0.19$ and spin order at low doping.

We present a study of the resonant inelastic scattering response of ${\mathrm{YbInCu}}_4$ excited at the tender Yb $M_5$ x-ray edge. In the high-temperature, paramagnetic phase, we observe a multiplet structure which can be understood at an ionic level. Upon cooling through the valence transition at $T_v\sim 40$ K, we observe a strong renormalization of the low-energy spectra, indicating a sensitivity to the formation of an intermediate valence phase at low temperatures. Similar spectrum renormalization has been observed in the optical conductivity, which suggests that the low-energy electronic structure possesses both mixed conduction and localized character.

The nuclear spin state of a phosphorus donor (${}^{31}\mathrm{P}$) in isotopically enriched silicon-28 is an excellent host to store quantum information in the solid state. The spin's insensitivity to electric fields yields a solid-state qubit with record coherence times but also renders coupling to other quantum systems very challenging. Here, we describe how to generate a strong electric dipole ($>100$ D) at microwave frequencies for the nuclear spin. This is achieved by applying a magnetic drive to the spin of the donor-bound electron while simultaneously controlling its charge state with electric fields. Under certain conditions, the microwave magnetic drive also renders the nuclear spin resonance frequency and electric dipole strongly insensitive to electrical noise, yielding long ($>1$ ms) dephasing times and robust gate operations. The nuclear spin could then be strongly coupled to microwave resonators, with a vacuum Rabi splitting of the order of 1 MHz, or to other nuclear spins, nearly half a micrometer apart, via strong electric dipole-dipole interaction. This work brings the ${}^{31}\mathrm{P}$ nuclear qubit into the realm of hybrid quantum systems and opens up new avenues in quantum information processing.

We use large-scale DFT calculations to investigate with unprecedented detail the so-called spin-orbit (SO) proximity effect in graphene adsorbed on the Pt(111) and Ni(111)/Au semi-infinite surfaces, previously studied via spin and angle resolved photoemission (SP-ARPES) experiments. The key finding is that, due to the hybridization with the metal's bands, the Dirac cones manifest an unexpectedly rich spin texture including out-of-plane and even radial in-plane spin components at (anti)crossings where local gap openings and deviations from linearity take place. Both the continuum character of the metallic bands and the back folding associated to the moiré patterns enhance the spin texture and induce sizable splittings which, nevertheless, only become giant ($\sim 100$ meV) at anticrossing regions; that is, where electronic transport is suppressed. At the quasilinear regions the splitted bands typically disperse with different broadenings and tend to cross with their magnetization continuously changing in order to match that at the edges of the upper and lower gaps. As a result, both the splittings and spin direction become strongly $k$ dependent. The SO manifests in an analogous way for the spin-polarized G/Au/Ni(111) system, although here the magnetic exchange interactions dominate inducing small splittings ($\sim 10$ meV) in the $\pi$ bands while the SO mainly introduces a small Rashba splitting in the Dirac cones as their magnetization acquires a helical component. While revealing such complex spin texture seems challenging from the experimental side, our results provide an important reference for future SP-ARPES measurements of similar graphene based systems extensively investigated for applications in spintronics.

Silicene, the silicon equivalent of graphene, is most commonly grown on Ag(111) substrates where it undergoes reconstruction due to the strong interaction between the Si and Ag atoms. We demonstrate through first-principles density functional theory for eight reconstructions that the Raman spectrum is unique for each configuration. We argue that the reconstructions can, in fact, be identified by their Raman spectra and suggest key features within the spectra as points of reference to be used for identification.

An insulator-metal transition (IMT) is a fascinating yet hotly debated phenomenon in condensed-matter physics. Here we report on the evolution of electronic structure across IMT as in $\mathrm{E}{\mathrm{u}}_{1-x}\mathrm{B}{\mathrm{a}}_x\mathrm{Ti}{\mathrm{O}}_3$ as a function of $x$ ($x=0$ for ETO and $x=0.5$ for EBTO) and temperature comprehensively using high-resolution spectroscopic ellipsometry, soft x-ray absorption spectroscopy at Ti $L$ and O $K$ edges, and transport measurements. We observe different types of spectral weight transfers (SWTs), which are responsible for tuning optical band gaps, accompanied by dramatic changes in electrical conductivity. At room temperature, when $x$ increases, SWT occurs due to the high energy of O $2p$ to low-energy bands. Such a SWT increases Eu-O-Ti hybridization and enhances Drude response, which increases electrical conductivity in EBTO. Interestingly, upon cooling, SWT arises from low-energy to high-energy bands and opens up a gap of a low-energy oxygen band, which then suppresses electrical conductivity in EBTO. We argue that the unscreened electron-electron interaction in oxygen yields a metal-to-charge-transfer insulator-like transition. Our result reveals comprehensively the importance of oxygen screening effects and hybridizations in the IMT, and it provides insight into $\mathrm{E}{\mathrm{u}}_{1-x}\mathrm{B}{\mathrm{a}}_x\mathrm{Ti}{\mathrm{O}}_3$.

We numerically investigate the low-lying entanglement spectrum of the ground state of random one-dimensional spin chains obtained after partition of the chain into two equal halves. We consider two paradigmatic models: the spin-1/2 random transverse-field Ising model, solved exactly, and the spin-1 random Heisenberg model, simulated using the density matrix renormalization group. In both cases we analyze the mean Schmidt gap, defined as the difference between the two largest eigenvalues of the reduced density matrix of one of the two partitions, averaged over many disorder realizations. We find that the Schmidt gap detects the critical point very well and scales with universal critical exponents.

Two-dimensional (2D) lattices composed exclusively of pentagons represent an exceptional structure of materials correlated to the famous pentagonal tiling problem in mathematics, but their π conjugation and the related electronic properties have never been reported. Here, we propose a tight-binding (TB) model for a 2D Cairo pentagonal lattice and demonstrate that p-d π conjugation in the unique framework leads to intriguing properties, such as an intrinsic direct band gap, ultrahigh carrier mobility, and even slant Dirac cones. On the basis of first-principles calculations, we predict a candidate material, 2D penta-$\mathrm{Ni}{\mathrm{P}}_2$ monolayer, derivated from bulk $\mathrm{Ni}{\mathrm{P}}_2$ crystal, to realize the predictions of the TB model. It has ultrahigh carrier mobility ($\sim {10}^5-{10}^6\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$) comparable to that of graphene and an intrinsic direct band gap of 0.818 eV, properties which have long been desired for high-speed electronic devices. The stability and possible synthetic routes of penta-$\mathrm{Ni}{\mathrm{P}}_2$ monolayer are also discussed.

Spin-orbit (SO) interactions in two dimensional systems split the Fermi surface and allow for the spatial separation of spin states via transverse magnetic focusing (TMF). In this paper, we consider the case of combined Rashba and Zeeman interactions, which leads to a Fermi surface without cylindrical symmetry. While the classical trajectories are effectively unchanged, we predict an additional contribution to the phase, linear in the applied in-plane magnetic field. We show that this term is unique to TMF and vanishes for magnetic (Shubnikov de Haas) oscillations. Finally we propose some experimental signatures of this phase.

High-order harmonic generation (HHG) from hexagonal boron nitride is simulated by solving extended multiband semiconductor Bloch equations under strong laser fields. By changing the angle of the laser polarization with respect to the crystal orientation, we find that harmonic spectra present a double-plateau structure and HHG is dominantly emitted along Γ-M direction in the first plateau, but special anisotropic distribution is observed in the secondary plateau. In-depth analyses reveal that two plateaus originate from different pair of conduction band and valence band, and the shapes of band dispersion and transition dipole moment determine anisotropic harmonic emission in $h$-BN crystal. Furthermore, we show that band energies of high-lying unoccupied bands and low-lying occupied ones can be directly extracted from laser polarization dependent high harmonic spectra. This paves a way to image the two-dimensional band information of solid materials by using laser-induced HHG.

Many efforts have been devoted to studying the robustness of topologically protected edge states in acoustics; however, the robustness of conventional edge states is rarely reported. In this work we theoretically study interface acoustic states appearing in finite arrays of resonators on a thin plate with topologically protected and conventional designs. Topologically protected interface states are first analyzed by employing the concept of breaking inversion symmetry within the unit cell of a honeycomb lattice for cylindrical and spherical resonators; we further demonstrate the robustness of the wave propagation along a zigzag path containing sharp corners and defects. In parallel, a conventional interface state is also designed and compared to the same situations. We found that the conventional interface state suffers backscattering in the zigzag path while it can show a more confined wave transport in some cases. The presence of a defect along the propagation path scatters the conventional interface wave and in particular can prohibit full propagation in the presence of a localized state at the defect. Then, we show that the immunity of the topologically protected design needs the interface to be surrounded by at least two hexagons of the phononic crystals on both sides, especially at the sharp corners in the zigzag path, while the conventional design only needs one hexagon of bulk media with the advantage of compact wave transport. Position and height disorders are further introduced to the interface pillars for both designs. It is revealed that in both designs, the transmission decreases quasilinearly with position disorder while it exhibits an abrupt drop with height disorder showing a transition threshold. With high disorder perturbation, waves can hardly enter the interface for the topologically protected design, while waves are trapped at the interface for the conventional design. A certain robustness against disorder is exhibited for conventional edge states. This work provides insight into the interface states in micro- and nanoscale characterization and figures out the behaviors for both topologically protected and conventional interface states.

Nanostructured rare-earth-ion-doped materials are increasingly being investigated for on-chip implementations of quantum information processing protocols as well as commercial applications such as fluorescent lighting. However, achieving high-quality and optimized materials at the nanoscale is still challenging. Here we present a detailed study into the restriction of phonon processes in the transition from bulk crystals to small ($\le 40$-nm) nanocrystals by observing the relaxation dynamics between crystal-field levels of ${\mathrm{Tb}}^{3+}:{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$. We find that the population relaxation dynamics are modified as the particle size is reduced, consistent with our simulations of inhibited relaxation through a modified vibrational density of states and hence modified phonon emission. However, our experiments also indicate that nonradiative processes not driven by phonons are also present in the smaller particles, causing transitions and rapid thermalization between the levels on a time scale of $<100\mathrm{ns}$.

Superconductors can support large dissipation-free electrical currents only if vortex lines are effectively immobilized by material defects. Macroscopic critical currents depend on elemental interactions of vortices with individual pinning centers. Pinning mechanisms are nontrivial for large-size defects such as self-assembled nanoparticles. We investigate the problem of a vortex system interacting with an isolated defect using time-dependent Ginzburg-Landau simulations. In particular, we study the instability-limited depinning process and extract the dependence of the pin-breaking force on inclusion size and anisotropy for an isolated vortex line. In the case of a vortex lattice interacting with a large isolated defect, we find a series of first-order phase transitions at well-defined magnetic fields, when the number of vortex lines occupying the inclusion changes. The pin-breaking force has sharp local minima at those fields. As a consequence, in the case of isolated identical large-size defects, the field dependence of the critical current is composed of a series of peaks located in between the occupation-number transition points.

We studied GHz hypersound in heterostructures of ${\mathrm{SrRuO}}_3$ (SRO) and ${\mathrm{SrTiO}}_3$ (STO) by using femtosecond pulses with fluence as low as several tens of $\mu \mathrm{J}/\mathrm{c}{\mathrm{m}}^2$. We found that the efficiency of generating hypersound in SRO, through thermal expansion, is linear up to optical fluence of a few $\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. We further investigated the propagation of acoustic pulses in the STO substrate. The acoustic properties of STO dramatically changed around the temperature of structural transition (105 K) because the generated hypersound was coupled to the softening mode. Nevertheless, our experimental results revealed that the quadratic frequency dependence of acoustic attenuation in STO, predicted by the mode-coupling theory, breaks down at tens of GHz. Finally, the refractive index of STO was experimentally obtained between 365 and 400 nm, for which there was disagreement in previous results.

We theoretically investigate the temperature-dependent static susceptibility and long-range magnetic coupling of three-dimensional (3D) chiral gapless electron-hole systems (semimetals) with arbitrary band dispersion [i.e., $\varepsilon \left(k\right)\sim k^N$, where $k$ is the wave vector and $N$ is a positive integer]. We study the magnetic properties of these systems in the presence of dilute random magnetic impurities. Assuming carrier-mediated Ruderman-Kittel-Kasuya-Yosida indirect exchange interaction, we find that the magnetic ordering of intrinsic 3D chiral semimetals in the presence of dilute magnetic impurities is ferromagnetic for all values of $N$. Using finite-temperature self-consistent field approximation, we calculate the ferromagnetic transition temperature ($T_{\mathrm{c}}$). We find that $T_{\mathrm{c}}$ increases with increasing $N$ due to the enhanced density of states, and the calculated $T_{\mathrm{c}}$ is experimentally accessible, assuming reasonable coupling between the magnetic impurities and itinerant carriers.

The zero-field-cooled exchange bias (ZEB) effect is a remarkable phenomenon recently reported for some reentrant spin glass-like compounds. In this work, the time evolution of magnetization is thoroughly investigated for two ZEB materials in order to figure out the role played by the spin glass-like phase on such effect. ${\mathrm{La}}_{1.5}{\mathrm{Sr}}_{0.5}{\mathrm{CoMnO}}_6$ and ${\mathrm{La}}_{1.5}{\mathrm{Ca}}_{0.5}{\mathrm{CoMnO}}_6$ were chosen as representative samples of ZEB systems, since the former compound presents the largest ZEB reported so far, while the second has a much smaller effect, despite being structurally/chemically similar. Comprehensive magnetic measurements were carried on both samples, and the results are discussed in terms of the amount and time evolution of the spin glass-like phase under the influence of a varying field. We also propose a phenomenological model, based on the pinning of spin glass-like moments and on the dynamics of their magnetic relaxation, to explain the asymmetry observed in the hysteresis loops. The good agreement between the simulated and experimental results confirms our hypothesis that the spin glass-like phase is key to the ZEB effect.

We study Mn substitution for Ti in ${\mathrm{BaTiO}}_3$ with and without compensating oxygen vacancies using density functional theory (DFT) in combination with dynamical mean-field theory (DMFT). We find strong charge and spin fluctuations. Without compensating oxygen vacancies, the ground state is found to be a quantum superposition of two distinct atomic valences, $3d^4$ and $3d^5$. Introducing a compensating oxygen vacancy at a neighboring site reduces both charge and spin fluctuations due to the reduction of electron hopping from Mn to its ligands. As a consequence, valence fluctuations are reduced, and the valence is closely fixed to the high spin $3d^5$ state. Here we show that inclusion of charge and spin fluctuations is necessary to obtain an accurate ground state of transition metal-doped ferroelectrics.

By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the $s$-wave superconducting order parameter and the pairing correlations for the negative-$U$ Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs are much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of $\left|U\right|/t$ and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behavior of the superconducting phase by means of a suitably chosen Jastrow factor including long-range density-density correlations.

In recent years, realizing new topological phases of matter has been a hot topic in the fields of physics and materials science. Topological semimetals and metals can conventionally be classified into two types: type-I and type-II, according to the tilting degree of the fermion cone. Here we report an unexplored topological metal phase with the critical-type nodal line between type-I and type-II nodal lines. The critical-type nodal line shows a unique nontrivial band crossing, which is composed of a flat band and a dispersive band and leads to an unexplored fermionic state. We propose intermetallic CaPd can be an existing topological metal for the fermionic state, characterized with critical-type nodal line in the bulk and drumhead band structure on the surface. Our work not only promotes the concept of a critical-type nodal line, but also provides the material realization to study its exotic properties in future experiments.