Electron tunneling between superconductors and normal metals has been used for an efficient refrigeration of electrons in the latter. Such cooling is a nonlinear effect and usually requires a large voltage. Here we study the electron cooling in heterostructures based on superconductors with a spin-splitting field coupled to normal metals via spin-filtering barriers. The cooling power shows a linear term in the applied voltage. This improves the coefficient of performance of electron refrigeration in the normal metal by shifting its optimum cooling to lower voltage, and also allows for cooling the spin-split superconductor by reverting the sign of the voltage. We also show how tunnel coupling spin-split superconductors with regular ones allows for a highly efficient refrigeration of the latter.

High-melting-point oxides of chemical formula $AB{\mathrm{O}}_3$ with $A=\mathrm{Ca}$, Sr, Ba and $B=\mathrm{Zr}$, Hf are investigated as a function of hydrostatic pressure up to 200 GPa by combining first-principles calculations with a particle swarm optimization method. Ca- and Sr-based systems: (1) first undergo a reconstructive phase transition from a perovskite state to a novel structure that belongs to the post-post-perovskite family and (2) then experience an isostructural transition to a second, also new post-post-perovskite state at higher pressures, via the sudden formation of a specific out-of-plane $B\text{−}\mathrm{O}$ bond. In contrast, the studied Ba compounds evolve from a perovskite phase to a third novel post-post-perovskite structure via another reconstructive phase transition. The original characteristics of these three different post-post-perovskite states are emphasized. Unusual electronic properties, including significant piezochromic effects and an insulator-metal transition, are also reported and explained.

We provide a study of various quantum phase transitions occurring in the XY Heisenberg chain in a transverse magnetic field using the Meyer-Wallach (MW) measure of (global) entanglement. Such a measure, while being readily evaluated, is a multipartite measure of entanglement as opposed to more commonly used bipartite measures. Consequently, we obtain analytic expression of the measure for finite-size systems and show that it can be used to obtain critical exponents via finite-size scaling with great accuracy for the Ising universality class. We also calculate an analytic expression for the isotropic (XX) model and show that global entanglement can precisely identify the level-crossing points. The critical exponent for the isotropic transition is obtained exactly from an analytic expression for global entanglement in the thermodynamic limit. Next, the general behavior of the measure is calculated in the thermodynamic limit considering the important role of symmetries for this limit. The so-called oscillatory transition in the ferromagnetic regime can only be characterized by the thermodynamic limit where global entanglement is shown to be zero on the transition curve. Finally, the anisotropic transition is explored where it is shown that global entanglement exhibits an interesting behavior in the finite-size limit. In the thermodynamic limit, we show that global entanglement shows a cusp singularity across the Ising and anisotropic transition, while showing non-analytic behavior at the XX multicritical point. It is concluded that global entanglement, despite its relative simplicity, can be used to identify all the rich structure of the ground-state Heisenberg chain.

We present an experimental investigation of stochastic switching of a bistable Josephson junction array resonator with a resonance frequency in the GHz range. As the device is in the regime where the anharmonicity is on the order of the linewidth, the bistability appears for a pump strength of only a few photons. We measure the dynamics of the bistability by continuously observing the jumps between the two metastable states, which occur with a rate ranging from a few Hz down to a few mHz. The switching rate strongly depends on the pump strength, readout strength and the temperature, following Kramers' theory. The interplay between nonlinearity and coupling, in this little explored regime, could provide a new resource for nondemolition measurements, single photon switches, or even elements for autonomous quantum error correction.

In the Fock representation, we construct matrix product states (MPS) for one-dimensional gapped phases for ${\mathbb{Z}}_p$ parafermions. From the analysis of irreducibility of MPS, we classify all possible gapped phases of ${\mathbb{Z}}_p$ parafermions without extra symmetry other than ${\mathbb{Z}}_p$ charge symmetry, including topological phases, spontaneous symmetry breaking phases, and a trivial phase. For all phases, we find the irreducible forms of local matrices of MPS, which span different kinds of graded algebras. The topological phases are characterized by the nontrivial simple ${\mathbb{Z}}_p$ graded algebras with the characteristic graded centers, yielding the degeneracies of the full transfer matrix spectra uniquely. However, the spontaneous symmetry breaking phases correspond to the trivial semisimple ${\mathbb{Z}}_{p/n}$ graded algebras, which can be further reduced to the trivial simple ${\mathbb{Z}}_{p/n}$ graded algebras, where $n$ is the divisor of $p$. So the present results provide the complete classification of the parafermionic gapped phases and deepen our understanding of topological phases in one dimension.

We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states in an energy continuum and flat energy bands for periodically repeated local symmetries in one- and two-dimensional lattices. The framework is based on very recent theorems in graph theory which are here employed to obtain a block partitioning of the Hamiltonian induced by the symmetry of a given system under local site permutations. The diagonalization of the Hamiltonian is thereby reduced to finding the eigenspectra of smaller matrices, with eigenvectors automatically divided into compact localized and extended states. We distinguish between local symmetry operations which commute with the Hamiltonian, and those which do not commute due to an asymmetric coupling to the surrounding sites. While valuable as a computational tool for versatile discrete systems with locally symmetric structures, the approach provides in particular a unified, intuitive, and efficient route to the flexible design of compact localized states at desired energies.

The $4\pi$-periodic Josephson effect is a distinguishing feature of a topological Josephson junction. However, stringent conditions make it hard to observe in experiments. In this work, we study the transient transport properties in a topological Josephson junction numerically. We show that the $4\pi$ Josephson current can be sustained under nonequilibrium conditions. The properties of the Josephson current are analyzed for different conditions and three main regimes are identified. First, when both the superconducting wires of the Josephson junction lie in the topologically nontrivial region, a $4\pi$ Josephson current can appear upon suddenly applying a dc voltage. Second, when one superconducting wire lies in the trivial region, while the other wire lies in the nontrivial region, the Josephson current is $2\pi$ periodic but the component of the higher-order Josephson current increases. Third, when both wires lie in the trivial region, a stable $2\pi$ Josephson current is observed. Most importantly, the fractional Josephson effect is fragile in the presence of disorder. Hence experiments should be designed carefully to eliminate the effect of disorder. These results could be helpful to optimize fine-tuning of the experimental parameters to observe the $4\pi$-periodic Josephson current in a topological Josephson junction.

For passive, lossless impenetrable metasurfaces, a design technique for arbitrary beam control of receiving, guiding, and launching is presented. Arbitrary control is enabled by a custom surface wave in an orthogonal polarization such that its addition to the incident (input) and the desired scattered (output) fields is supported by a reactive surface impedance everywhere on the reflecting surface. Such a custom surface wave (SW) takes the form of an evanescent wave propagating along the surface with a spatially varying envelope. A growing SW appears when an illuminating beam is received. The SW amplitude stays constant when power is guided along the surface. The amplitude diminishes as a propagating wave (PW) is launched from the surface as a leaky wave. The resulting reactive tensor impedance profile may be realized as an array of anisotropic metallic resonators printed on a grounded dielectric substrate. Illustrative design examples of a Gaussian beam translator-reflector, a probe-fed beam launcher, and a near-field focusing lens are provided.

Twist, as a simple and unique degree of freedom, could lead to enormous novel quantum phenomena in bilayer graphene. A small rotation angle introduces low-energy van Hove singularities (VHSs) approaching the Fermi level, which result in unusual correlated states in the bilayer graphene. It is reasonable to expect that the twist could also affect the electronic properties of few-layer graphene dramatically. However, such an issue has remained experimentally elusive. Here, by using scanning tunneling microscopy/spectroscopy (STM/STS), we systematically studied a twisted trilayer graphene (TTG) with two different small twist angles between adjacent layers. Two sets of VHSs, originating from the two twist angles, were observed in the TTG, indicating that the TTG could be simply regarded as a combination of two different twisted bilayers of graphene. By using high-resolution STS, we observed a split of the VHSs and directly imaged the spatial symmetry breaking of electronic states around the VHSs. These results suggest that electron-electron interactions play an important role in affecting the electronic properties of graphene systems with low-energy VHSs.

In time-resolved pump-probe spectroscopy of carbon nanotubes, the fundamental understanding of the optical generation and detection processes of radial-breathing-mode (RBM) phonons has been inconsistent among the previous reports. In this study, the tunable-pumping/broadband-probing scheme was used to fully reveal the amplitude and phase of the phonon-modulated signals. We observed that signals detected off resonantly to excitonic transitions are delayed by $\pi /2$ radians with respect to resonantly detected signals, which demonstrates that RBM phonons are detected through dynamically modulating the linear response, not through adiabatically modulating the light absorption. Furthermore, we found that the initial phases are independent of the pump detuning across the first $\left(E_{11}\right)$ and the second $\left(E_{22}\right)$ excitonic resonances, evidencing that the RBM phonons are generated by the displacive excitation rather than stimulated Raman process.

Graphene nanoribbons with armchair edges are studied for externally enhanced but realistic parameter values: enhanced Rashba spin-orbit coupling due to proximity to a transition-metal dichalcogenide, such as ${\mathrm{WS}}_2$, and enhanced Zeeman field due to exchange coupling with a magnetic insulator, such as EuS under an applied magnetic field. The presence of $s$-wave superconductivity, induced either by proximity or by decoration with alkali-metal atoms, such as Ca or Li, leads to a topological superconducting phase with Majorana end modes. The topological phase is highly sensitive to the application of uniaxial strain with a transition to the trivial state above a critical strain well below 0.1%. This sensitivity allows for real-space manipulation of Majorana fermions by applying nonuniform strain profiles. Similar manipulation is also possible by applying an inhomogeneous Zeeman field or chemical potential.

When a quantum system is quenched from its ground state, the time evolution can lead to nonanalytic behavior in the return rate at critical times $t_c$. Such dynamical phase transitions (DPTs) can occur, in particular, for quenches between phases with different topological properties in Gaussian models. In this paper we discuss Loschmidt echos generalized to density matrices and obtain results for quenches in closed Gaussian models at finite temperatures as well as for open-system dynamics described by a Lindblad master equation. While cusps in the return rate are always smoothed out by finite temperatures we show that dissipative dynamics can be fine-tuned such that DPTs persist.

We investigate the Kondo effect of the Fermi arcs in a time-reversal-invariant Weyl semimetal with the variational method. To show the consequence brought out by the nontrivial spin texture, we calculate the spatial spin-spin correlation functions. The correlation functions exhibit high anisotropy. The diagonal correlation functions are dominated by the antiferromagnetic correlation while the off-diagonal part has a more complicated pattern. The correlation functions obey the same symmetry as the spin texture. Tuning chemical potential changes the pattern of the correlation functions and the correlation length. The correlation functions of the Weyl semimetal Fermi arcs and that from a Dirac semimetal show a discrepancy.

Density functional calculations and model tight-binding Hamiltonian studies are carried out to examine the bulk and surface electronic structure of the largely unexplored perovskite family of $A{\mathrm{BiO}}_3$, where $A$ is a group I-II element. From the study, we reveal the existence of two TI states, one in valence band (V-TI) and the other in conduction band (C-TI), as the universal feature of $A{\mathrm{BiO}}_3$. The V-TI and C-TI are, respectively, born out of bonding and antibonding states caused by Bi-$\{\mathrm{s},\mathrm{p}\}$-O-$\left\{\mathrm{p}\right\}$ coordinated covalent interactions. Further, we outline a classification scheme in this family where one class follows spin orbit coupling and the other follows the second neighbor Bi-Bi hybridization to induce s-p band inversion for the realization of C-TI states. Below a certain critical thickness of the film, which varies with $A$, TI states of top and bottom surfaces couple to destroy the Dirac type linear dispersion and consequently to open narrow surface energy gaps.

We calculate the absorptive part of the ac optical conductivity of a multi-Weyl semimetal with winding number $J$ in both the direction of the tilt ${\sigma }_{zz}\left(\mathrm{\Omega }\right)$ and perpendicular to it ${\sigma }_{xx}\left(\mathrm{\Omega }\right)$ as a function of photon energy $\mathrm{\Omega }$, tilt C, and chemical potential $\mu$ (doping). For zero tilt there is a discontinuous rise in the conductivity at twice the value of the chemical potential $\mathrm{\Omega }=2\mu$. Below $2\mu$, both ${\sigma }_{xx}\left(\mathrm{\Omega }\right)$ and ${\sigma }_{zz}\left(\mathrm{\Omega }\right)$ are zero and above $2\mu$ they merge with their value at charge neutrality and display a linear in $\mathrm{\Omega }$ dependence for $J=1$ while for $J=2, {\sigma }_{xx}\left(\mathrm{\Omega }\right)$ remains linear but ${\sigma }_{zz}\left(\mathrm{\Omega }\right)$ is instead constant. For finite tilt the sharp jump at $\mathrm{\Omega }=2\mu$ is lost and the onset of absorption starts instead from zero at a lower photon energy $\mathrm{\Omega }=2\mu /(1+C)$ after which it acquires a quasilinear rise to merge with the undoped untilted interband background at $\mathrm{\Omega }=2\mu /(1-C)$ for type I Weyl while for type II the undoped untilted background is never recovered. For noncentrosymmetric materials the energies of a pair of opposite chirality Weyl nodes become shifted by $\pm Q_0$ and this leads to two separate absorption edges corresponding to the effective chemical potential of each of the two nodes at $2(\mu +\chi Q_0)$ depending on chirality $\chi =\pm$. We provide analytic expressions for the conductivity in this case which depend only on the ratio $Q_0/\mu$ and tilt when plotted against $\mathrm{\Omega }/\mu$. The signature of finite energy shift $Q_0$ is more pronounced for ${\sigma }_{zz}$ and $J=2$ than for the other cases.

Helices of increased electron density emerging spontaneously in materials containing multiple, interacting density waves, are an example of how orbital and charge degrees of freedom may combine to form a single ordered phase. Although a macroscopic order parameter theory describing this behavior has been proposed and experimentally tested, a microscopic understanding of such simultaneous orbital and electronic order in specific materials is still lacking. Here we present the elemental chalcogens selenium and tellurium as model materials for the development of combined charge and orbital order. We formulate minimal models capturing the formation of spiral structures consisting of ordered occupied orbitals and increased charge density, both in terms of a macroscopic Landau theory and a microscopic Hamiltonian. Both reproduce the known chiral crystal structure and are consistent with its observed thermal evolution and behavior under pressure. The combination of microscopic and macroscopic frameworks allows us to distill the essential ingredients in the emergence of combined orbital and charge order, and may serve as a general guide to predicting and understanding spontaneous chirality as well as other, more general, types of combined charge and orbital order in other materials.

We investigate theoretically the influence of an external magnetic field on the spin dynamics of excitons in diluted magnetic semiconductor quantum wells. To this end, we apply a quantum kinetic theory beyond the Markov approximation which reveals that non-Markovian effects can significantly influence the exciton spin dynamics. If the magnetic field is oriented parallel to the growth direction of the well, the Markovian spin-transfer rate decreases monotonically with increasing field as predicted by Fermi's golden rule. The quantum kinetic theory follows this result qualitatively but predicts pronounced quantitative differences in the spin-transfer rate as well as in the long-time spin polarization. However, for an in-plane magnetic field, where the Markovian spin-transfer rate first drops and then increases again, quantum kinetic effects become so pronounced that the Markovian trend is completely reversed. This is made evident by a distinct maximum of the rate followed by a monotonic decrease. The deviations can be traced back to a redistribution of carriers in energy space caused by correlations between excitons and magnetic dopants. The same effect leads to a finite electron-spin polarization at long times in longitudinal as well as transverse fields which is much larger than the corresponding Markovian prediction.

We investigate the magnetic susceptibility $\chi \left(T\right)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic couplings as a function of their spatial decay exponent $\alpha$ and cutoff length $\xi$. The calculations are based on the strong disorder renormalization method which is used to obtain the temperature dependence of $\chi \left(T\right)$ and distribution functions of couplings at each renormalization step. For the case with only algebraic decay $\left(\xi =\infty \right)$ we find a crossover at ${\alpha }^{*}=1.066$ between a phase with a divergent low-temperature susceptibility $\chi (T\to 0)$ for $\alpha >{\alpha }^{*}$ to a phase with a vanishing $\chi (T\to 0)$ for $\alpha <{\alpha }^{*}$. For finite cutoff lengths $\xi$, this crossover occurs at a smaller ${\alpha }^{*}\left(\xi \right)$. Additionally, we study the localization of spin excitations for $\xi =\infty$ by evaluating the distribution function of excitation energies, and we find a delocalization transition that coincides with the opening of the pseudogap at ${\alpha }_c={\alpha }^{*}$.

Conventional wisdom suggests that the long-time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal-entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy nonthermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit nonthermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even with no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have nonthermal average doublon densities. We show that this nonthermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law dependence on system size.