In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a discretized characteristic function and derive formulas for its cumulants and moments. In the case of a noninteracting system, our scheme leads to the gauge-invariant cumulants known from polarization theory. We study the behavior of such cumulants for several interacting models. In a one-dimensional system of spinless fermions with nearest neighbor interaction the transition at which gap closure occurs can be clearly identified from the finite size scaling exponent of the variance. When next nearest neighbor interactions are turned on a model with a richer phase diagram emerges, but the finite size scaling exponent is still an effective way to identify the localization transition.

We classify time-reversal breaking (class A) spinful topological crystalline insulators with crystallographic nonmagnetic (32 types) and magnetic (58 types) point groups. The classification includes all possible magnetic topological crystalline insulators protected by point group symmetry. Whereas the classification of topological insulators is known to be given by the $K$-theory in the momentum space, computation of the $K$-theory has been a difficult task in the presence of complicated crystallographic symmetry. Here we consider the $K$-homology in the real space for this problem, instead of the $K$-theory in the momentum space, both of which give the same topological classification. We apply the Atiyah-Hirzebruch spectral sequence (AHSS) for computation of the $K$-homology, which is a mathematical tool for generalized (co)homology. In the real-space picture, the AHSS naturally gives the classification of higher-order topological insulators at the same time. By solving the group extension problem in the AHSS on the basis of physical arguments, we completely determine possible topological phases including higher-order ones for each point group. Relationships among different higher-order topological phases are argued in terms of the AHSS in the $K$-homology. We find that in some nonmagnetic and magnetic point groups, a stack of two ${\mathbb{Z}}_2$ second-order topological insulators can be smoothly deformed into nontrivial fourth-order topological insulators, which implies nontrivial group extensions in the AHSS.

We reveal peculiarities of the trapped (dark) mode excitation in a polarization-insensitive all-dielectric metasurface, whose unit supercell is constructed by particularly arranging four cylindrical dielectric particles. Involving group-theoretical description we discuss in detail the effect of different orientations of particles within the supercell on characteristics of the trapped mode. The theoretical predictions are confirmed by numerical simulations and experimental investigations. Since the metasurface is realized from simple dielectric particles without the use of any metallic components, they are feasibly scalable to both $\mu \text{m-}$ and nanometer-size structures, and they can be employed in flat-optics platforms for realizing efficient light-matter interaction for multiple hot-spot light localization, optical sensing, and highly efficient light trapping.

We study theoretically the electron current across a monolayer graphene/hexagonal boron nitride/bilayer graphene tunneling junction in an external magnetic field perpendicular to the layers. We show that change in effective tunneling barrier width for electrons on different graphene layers of bilayer graphene, coupled with the fact that its Landau level wave functions are not equally distributed amongst the layers with a distribution that is reversed between the two valleys, lead to valley polarization of the tunneling current. We estimate that valley polarization $\sim 70\%$ can be achieved in high quality devices at $B=1$ T. Moreover, we demonstrate that strong valley polarization can be obtained both in the limit of strong-momentum-conserving tunneling and in lower quality devices where this constraint is lifted.

This paper demonstrates the anisotropic response of quantum critical fluctuations with respect to the direction of the magnetic field $B$ in Ni-doped ${\mathrm{CeCoIn}}_5$ by measuring the magnetization $M$ and specific heat $C$. The results show that $M/B$ at $B=0.1\mathrm{T}$ for both the tetragonal $c$ and $a$ directions exhibits $T^{-\eta }$ dependencies, and that $C/T$ at $B=0$ follows a $-lnT$ function, which are the characteristics of non-Fermi-liquid (NFL) behaviors. For $B\left|\right|c$, both the $M/B\propto T^{-\eta }$ and $C/T\propto -lnT$ dependencies change into nearly temperature-constant behaviors by increasing $B$, indicating a crossover from the NFL state to the Fermi-liquid state. For $B\left|\right|a$, however, the NFL behavior in $C/T$ persists up to $B=7\mathrm{T}$, whereas $M/B$ exhibits temperature-independent behavior for $B\ge 1\mathrm{T}$. These contrasting characteristics in $M/B$ and $C/T$ reflect the anisotropic nature of quantum critical fluctuations; the $c$-axis spin component significantly contributes to the quantum critical fluctuations. We compare this anisotropic behavior of the spin fluctuations to superconducting properties in pure ${\mathrm{CeCoIn}}_5$, especially to the anisotropy in the upper critical field and the Ising-like characteristics in the spin resonance excitation, and suggest a close relationship between them.

Lian et al. [Phys. Rev. B 94, 184310 (2016)] claim that they were able to show evidence of nonthermal characteristics during laser-induced ultrafast melting in silicon by using a time-dependent density functional theory package. In this Comment, we show that their simulated silicon crystal was not even molten within the performed simulation. This raises serious doubts about the validity of the scientific findings regarding the nonthermal nature of laser-induced ultrafast melting made in their paper. Furthermore, we demonstrate that their presented phonon band structure is unphysical and uncover crucial inconsistencies throughout their paper, which additionally question the credibility of their drawn conclusions.

In the Comment on our original publication [Phys. Rev. B 94, 184310 (2016)], Zier et al. claimed that no melting is observed in real-time time-dependent density functional simulations and there are several inconsistencies in our paper. In this Reply we demonstrate that the “correct” melting behavior indicated in the comment by Zier et al., which was adopted from empirical concept of thermal melting, is inappropriate and conflicts with ultrafast experiments on nonthermal laser melting. The barrier calculated from phonon spectra is a static barrier and different from the dynamic ones, causing no inconsistency. We confirm that nonthermal melting behaviors and interpretation in the original paper are credible.

The interplay between topology and interactions on the edge of a two-dimensional topological insulator with time-reversal symmetry is studied. We consider a simple noninteracting system of three helical channels with an inherent ${\mathbb{Z}}_2$ topological protection and hence a zero-temperature conductance of $G=e^2/h$. We show that when interactions are added to the model, the ground state exhibits two different phases as a function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the noninteracting topological phase is spontaneously broken. In this phase there is zero conductance ($G=0$) at zero temperature. The other phase displays enhanced topological properties, with a topologically protected zero-temperature conductance of $G=3e^2/h$ and an emergent ${\mathbb{Z}}_3$ symmetry not present in the lattice model. The neutral sector in this phase is described by a massive version of ${\mathbb{Z}}_3$ parafermions. This state is an example of a dynamically enhanced symmetry-protected topological state.

Recently, topological quantum states of non-Hermitian systems, exhibiting rich, new exotic states, have attracted great attention in condensed-matter physics. As for the demonstration, most of non-Hermitian topological phenomena previously focused on are in one- and two-dimensional systems. Here, we investigate three-dimensional non-Hermitian nodal-line semimetals in the presence of a particle gain-and-loss perturbation. It is found that this perturbation will split the original nodal ring into two exceptional rings (ERs). The topological nature of the bulk electronic structure is characterized by two different topological invariants, namely, the vorticity and the winding number defined for a one-dimensional loop in momentum space, both of which are shown to take half-integer (integer) values when an odd (even) number of ERs thread through the loop. The conventional bulk-surface correspondence in non-Hermitian nodal-line semimetals is found to break down, where the surface zero-energy flat bands are no longer bounded by projections of bulk ERs. Alternatively, a macroscopic fraction of the bulk eigenstates can be localized near the surface, thus leading to the so-called non-Hermitian skin effect.

Nodal-line metals and semimetals, as interesting topological states of matter, have been mostly studied in nonmagnetic materials. Here, based on first-principles calculations and symmetry analysis, we predict that fully spin polarized Weyl loops can be realized in the half-metal state of the three-dimensional material ${\mathrm{Li}}_3{\left({\mathrm{FeO}}_3\right)}_2$. We show that this material has a ferromagnetic ground state, and it is a half-metal with only a single spin channel present near the Fermi level. The spin-up bands form two separate Weyl loops close to the Fermi level, which arise from band inversions and are protected by the glide mirror symmetry. One loop is type I, whereas the other loop is the hybrid type. Corresponding to these two loops in the bulk, on the (100) surface, there exist two fully spin polarized drumheads of surface states within the surface projections of the loops. The effects of the electron correlation and the spin-orbit coupling, as well as the possible hourglass Weyl chains in the nonmagnetic state, are discussed. The realization of fully spin polarized Weyl-loop fermions in the bulk and drumhead fermions on the surface for a half-metal may generate promising applications in spintronics.

Since the discovery of graphene, considerable research efforts have focused on understanding the properties of other two-dimensional materials. Herein, based on ab initio many-body calculations, we report the optical properties of monolayer ${\mathrm{SnO}}_2$. First, we apply the first-principles density functional theory, self-consistent quasiparticle Green's function, and screened Coulomb method to determine the quasiparticle electronic structure. Second, we solve the Bethe-Salpeter equation to obtain the absorption spectra. The quasiparticle band structure reveals an indirect quasiparticle band gap. The absorption spectra show that the direct optical excitation is characterized by an optical band gap of $\sim 5.36$ eV, which is dominated by strongly bound excitons.

The development of microwave photon detectors is paving the way for a wide range of quantum technologies and fundamental discoveries involving single photons. Here, we investigate the photon emission from a microwave cavity and find that distribution of photon waiting times contains information about few-photon processes, which cannot easily be extracted from standard correlation measurements. The factorial cumulants of the photon counting statistics are positive at all times, which may be intimately linked with the bosonic quantum nature of the photons. We obtain a simple expression for the rare fluctuations of the photon current, which is helpful in understanding earlier results on heat-transport statistics and measurements of work distributions. Under nonequilibrium conditions, where a small temperature gradient drives a heat current through the cavity, we formulate a fluctuation-dissipation relation for the heat noise spectra. Our work suggests a number of experiments for the near future and it offers theoretical questions for further investigation.

We develop a robust, nonperturbative approach to study the band structure of artificial graphene. Artificial graphene, as considered here, is generated by imposing a superlattice structure on top of a two-dimensional hole gas in a semiconductor heterostructure, where the hole gas naturally possesses large spin-orbit coupling. Via tuning of the system parameters we demonstrate how best to exploit the spin-orbit coupling to generate time reversal symmetry protected topological insulator phases. Our major conclusion relates to a second set of topological Dirac bands in the band structure (with spin Chern number $C=3$), which were not reliably obtainable in previous perturbative approaches to artificial graphene. Importantly, the second Dirac bands host more desirable features than the previously studied first set of Dirac bands (with $C=1$). Moreover, we find that upon tuning of the system parameters, we can drive the system to the highly desirable regime of the topological flat band. We discuss the possibilities this opens up for exotic, strongly correlated phases.

We study out-of-time ordered correlations $C(x,t)$ and entanglement growth in the random-field XX model with open boundary conditions using the exact Jordan-Wigner transformation to a fermionic Hamiltonian. For any nonzero strength of the random field, this model describes an Anderson insulator. Two scenarios are considered: a global quench with the initial state corresponding to a product state of the Néel form, and the behavior in a typical thermal state at $\beta =1$. As a result of the presence of disorder, the information spreading as described by the out-of-time correlations stops beyond a typical length scale ${\xi }_{\text{OTOC}}$. For $\left|x\right|<{\xi }_{\text{OTOC}}$, information spreading occurs at the maximal velocity $v_{\max }=J$ and we confirm predictions for the early-time behavior of $C(x,t)\sim t^{2\left|x\right|}$. For the case of the quench starting from the Néel product state, we also study the growth of the bipartite entanglement, focusing on the late- and infinite-time behavior. The approach to a bounded entanglement is observed to be slow for the disorder strengths we study.

We show that the low-temperature specific heat $\left(C_p\right)$ of the incommensurate chain-ladder system ${\left\{{\mathrm{CuO}}_2\right\}}_{\alpha }\left\{{\mathrm{Sr}}_2{\mathrm{Cu}}_2{\mathrm{O}}_3\right\}={\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ (for $\alpha =10/7)$ shows a rather large excess contribution of nonmagnetic origin. Diluted Al doping at the Cu site or annealing the crystal in an ${\mathrm{O}}_2$ atmosphere suppresses this feature considerably. Using THz time-domain spectroscopy, we relate the occurrence of excess specific heat to the presence of very low-energy $\left(\sim 1\mathrm{meV}\right)$ gapped phonon modes that originate from the sliding motion of oppositely charged $\left\{{\mathrm{CuO}}_2\right\}$ chain and $\left\{{\mathrm{Sr}}_2{\mathrm{Cu}}_2{\mathrm{O}}_3\right\}$ ladder sheets past each other.

The interplay of slight changes of the rare-earth composition and antiferromagnetic ordering of Cr in a series of high purity solid solutions of orthochromites with composition ${\mathrm{Ce}}_{1-x}\mathrm{Eu}{}_x{\mathrm{CrO}}_3\left(1\leqq x\leqq 0\right)$ was investigated by neutron and x-ray powder diffraction, magnetization, and heat capacity measurements. A careful study of the crystal structure by x-ray powder diffraction data across the whole range of $x$ enables us to correlate the magnetic properties of the Cr magnetic subsystem with the size of the lattice and minute changes of the bond and torsion angles within and between the ${\mathrm{CrO}}_6$ octahedra. We find that the sizes and the shapes of the ${\mathrm{CrO}}_6$ octahedra remain essentially unchanged as the size of the rare-earth cations and the cell volumes are gradually reduced by Eu substitution, whereas decreasing Cr-O-Cr bond angles and increasing inclination of neighboring octahedra compensate for the decreasing lattice size. Adverse to external hydrostatic pressure that reduces the cell volume but raises the ordering temperature, lowering the cell volume by replacing Ce by Eu decreases the Néel temperature linearly with the Eu concentration from 260 K for ${\mathrm{CeCrO}}_3$ to 178 K for ${\mathrm{EuCrO}}_3$.