We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analog of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft–Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a noncommutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.

We present a formalism to calculate the macroscopic magnetoelectric monopolization from first principles within the density-functional-theory framework. An expression for the monopolization in the case of insulating collinear magnetism is derived first in terms of spin-polarized Wannier functions, and then recast as a Berry phase. We propose an extension to the general, noncollinear case, which we implement computationally in the Wannier function form and use to calculate the magnetoelectric monopolization of ${\text{LiMnPO}}_4$ and ${\text{Cr}}_2{\text{O}}_3$. We find that, while the former is well approximated by a summation over the formal local spin moments, the latter shows significant deviations from this approximation. We suggest that equating the Berry phase value with a sum over local moments provides an unambiguous route to defining the size of the local magnetic moment in magnetoelectric antiferromagnets containing only one type of magnetic ion.

We have investigated structural, electrical, and magnetic properties of single crystals of modified pyrochlore fluorides ${\mathrm{Rb}}_{}{\mathrm{V}}_2{\mathrm{F}}_6$ and ${\mathrm{Cs}}_{}{\mathrm{V}}_2{\mathrm{F}}_6$, which have mixed-valent V atoms. At room temperature, they have orthorhombic structures. With increasing temperature, each of them exhibits two structural transitions, and electrical resistivity rapidly decreases accompanied with one of these structural changes. The changes of unit cell volume and electrical resistivity at these transition temperatures indicate that the structural instability and the charge ordering cause structural transitions of ${\mathrm{Rb}}_{}{\mathrm{V}}_2{\mathrm{F}}_6$ and ${\mathrm{Cs}}_{}{\mathrm{V}}_2{\mathrm{F}}_6$, respectively. At low temperatures, ${\mathrm{Cs}}_{}{\mathrm{V}}_2{\mathrm{F}}_6$ shows antiferromagnetic ordering at $5\mathrm{K}$, and ${\mathrm{Rb}}_{}{\mathrm{V}}_2{\mathrm{F}}_6$ shows two-step magnetic transitions.

We investigate the modulation of optical phonons in semiconductor crystals by a surface acoustic wave (SAW) propagating on the crystal surface. The SAW fields induce changes on the order of ${10}^{-3}$ in the time-averaged Raman peak intensity by optical phonons in Si and GaN crystals. The SAW-induced modifications in the intensity of the Raman lines are dominated by the modulation of the longitudinal optical (LO) phonon energy by the SAW strain field. We show that while the strain field of the excited Rayleigh SAWs changes the LO phonon energy, it does not mix it with the transversal optical modes. In addition to the previous contribution, which is of a local character, the experiments give evidence for a weaker and nonlocal contribution attributed to the spatial variation of the SAW strain field. The latter activates optical modes with large wave vectors and, therefore, lower energies. The experimental results, which are well described by theoretical models for the two contributions, prove that optical phonons can be manipulated by SAWs with $\mu \mathrm{m}$ wavelengths.

It is shown, using density functional theory, that a 2D electron gas induced in a monolayer of Pb or Tl adatoms on the $\mathrm{Si}\left(111\right)-1\times 1$ surface is insensitive to the structural asymmetry of the system and its spin polarization is governed by the interaction between the adlayer and the substrate. It is demonstrated that this interaction changes the in-plane inversion symmetry of the charge distribution within the monolayer and can either suppress $\text{[Pb/Si(111)]}$ or enhance $\left[\text{Tl/Si(111)}\right]$ the adatom intra-atomic spin-orbit effect on a Rashba-Bychkov-type spin splitting.

We study analytically the free induction decay and the spin echo decay originating from the localized carriers moving between the sites which host random magnetic fields. Due to disorder in the site positions and energies, the on-site residence times, $\tau$, are widely spread according to the Lévy distribution. The power-law tail $\propto {\tau }^{-1-\alpha }$ in the distribution of $\tau$ does not affect the conventional spectral narrowing for $\alpha >2$ but leads to a dramatic acceleration of the free induction decay in the domain $2>\alpha >1$. The next abrupt acceleration of the decay takes place as $\alpha$ becomes smaller than 1. In the latter domain the decay does not follow a simple-exponent law. To capture the behavior of the average spin in this domain, we solve the evolution equation for the average spin using the approach different from the conventional approach based on the Laplace transform. Unlike the free induction decay, the tail in the distribution of the residence times leads to the slow decay of the spin echo. The echo is dominated by realizations of the carrier motion for which the number of sites, visited by the carrier, is minimal.

Kelvin probe force microscopy (KPFM) is a popular tool for studying properties of semiconductors. However, the interpretation of its results is complicated by the possibility of so-called band bending and the presence of surface charges. In this work, we study two different interpretations for KPFM on semiconductors: the contact potential difference (CPD) interpretation, which interprets the measured potential as the work-function difference between the sample and the probe, and a newer, alternative interpretation proposed by Baumgart, Helm, and Schmidt (BHS). By performing model calculations, we demonstrate that these models generally lead to very different results. Hence it is important to decide which one is correct. We demonstrate that BHS predictions for the Kelvin voltage difference between the $p$ and $n$ parts of a $pn$ junction are inconsistent with a set of experimental results from the literature. In addition, the BHS interpretation predicts an independence from the probe material as well as from surface treatments, which we both find to disagree with experiment. On the other hand, we present a theoretical argument for the validity of the CPD interpretation and we show that the CPD interpretation is able to accommodate all of these experimental results. Thus we posit that the BHS interpretation is generally not suitable for the analysis of KPFM on semiconductors and that the CPD interpretation should be used instead.

Semiconducting single-wall carbon nanotubes are classified into two types by means of the orbital angular momentum of the valley state, which is useful to study their low-energy electronic properties in finite length. The classification is given by an integer $d$, which is the greatest common divisor of two integers $n$ and $m$ specifying the chirality of nanotubes, by analyzing cutting lines. For the case that $d$ is greater than or equal to four, the two lowest subbands from two valleys have different angular momenta with respect to the nanotube axis. Reflecting the decoupling of two valleys, discrete energy levels in finite-length nanotubes exhibit fourfold degeneracy and small lift of fourfold degeneracy by the spin-orbit interaction. For the case that $d$ is less than or equal to two, in which the two lowest subbands from two valleys have the same angular momentum, discrete levels exhibit a lift of fourfold degeneracy reflecting the coupling of two valleys. Especially, two valleys are strongly coupled when the chirality is close to the armchair chirality. An effective one-dimensional lattice model is derived by extracting states with relevant angular momentum, which reveals the valley coupling in the eigenstates. A bulk-edge correspondence, which is a relationship between the number of edge states and the winding number calculated in the corresponding bulk system, is analytically shown by using the argument principle, and this enables us to estimate the number of edge states from the bulk property. The number of edge states depends not only on the chirality but also on the shape of boundary.

The remarkable ability of phase change materials (PCM) to switch between amorphous and crystalline states on a nanosecond time scale could provide new opportunities for graphene engineering. We have used density functional calculations to investigate the structures and electronic properties of heterostructures of thin amorphous and crystalline films of the PCM GeTe (16 Å thick) and ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ (20 Å) between graphene layers. The interaction between graphene and PCM is very weak, charge transfer is negligible, and the structures of the chalcogenide films differ little from those of bulk phases. A crystalline GeTe (111) layer induces a band gap opening of 80 meV at the Dirac point. This effect is absent for the amorphous film, but the Fermi energy shifts down along the Dirac cone by $-60$ meV. ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ shows similar features, although inherent disorder in the crystalline rocksalt structure reduces the contrast in band structure from that in the amorphous structure. These features originate in charge polarization within the crystalline films, which show electromechanical response (piezoelectricity) upon compression, and show that the electronic properties of graphene structures can be tuned by inducing ultrafast structural transitions within the chalcogenide layers. Graphene can also be used to manipulate the structural state of the PCM layer and its electronic and optical properties.

Photoexcited scanning tunneling spectroscopy is a promising technique for the determination of carrier concentrations, surface photovoltages, and potentials of semiconductors with atomic spatial resolution. However, extraction of the desired quantities requires computation of the electrostatic potential induced by the proximity of the tip and the tunnel current. This calculation is based on an accurate solution of the Poisson as well as the continuity equations for the tip-vacuum-semiconductor system. For this purpose, the carrier current densities are modeled by classical drift and diffusion equations. However, for small tip radii and highly doped materials, the drift and diffusion transport model significantly overestimates a semiconductor's carrier concentration near the surface, making the quantification of physical properties impossible. In this paper, we apply quantum correction to the drift and diffusion model, in order to account for the so-called quantum compressibility, i.e., reduced compressibility of the carrier gas due to the Pauli principle, in the region of the tip-induced band bending. We compare carrier concentrations, potentials, and tunnel currents derived with and without quantum correction for $\mathrm{GaN}(10\overline{1}0)$ and GaAs(110) surfaces to demonstrate its necessity.

Nodal topological superconductors display zero-energy Majorana flat bands at generic edges. The flatness of these edge bands, which is protected by time-reversal and translation symmetry, gives rise to an extensive ground-state degeneracy. Therefore, even arbitrarily weak interactions lead to an instability of the flat-band edge states towards time-reversal and translation-symmetry-broken phases, which lift the ground-state degeneracy. We examine the instabilities of the flat-band edge states of $d_{xy}$-wave superconductors by performing a mean-field analysis in the Majorana basis of the edge states. The leading instabilities are Majorana mass terms, which correspond to coherent superpositions of particle-particle and particle-hole channels in the fermionic language. We find that attractive interactions induce three different mass terms. One is a coherent superposition of imaginary $s$-wave pairing and current order, and another combines a charge-density-wave and finite-momentum singlet pairing. Repulsive interactions, on the other hand, lead to ferromagnetism together with spin-triplet pairing at the edge. Our quantum Monte Carlo simulations confirm these findings and demonstrate that these instabilities occur even in the presence of strong quantum fluctuations. We discuss the implications of our results for experiments on cuprate high-temperature superconductors.

The unique atomic positions in quasicrystals lead to peculiar self-similarity and fractal-like structural morphology. Accordingly, many of the material properties are supposed to manifest exceptional characteristics. In this Rapid Communication, we explain through numerical simulations the fundamental and peculiar aspects of quasicrystals wearless friction manifested in a 30° twisted bilayer graphene system. In particular, the sliding force exhibits a fractal structure with distinct area correlations due to the natural mixture between both periodic and aperiodic lateral modulations. In addition, zero power scaling of the sliding force with respect to the contact area is demonstrated for a geometric sequence of dodecagonal elements.

We present a theoretical framework for understanding the wave functions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a symmetry of wave functions under permutation of site and energy indices. We compute the wave-function renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wave functions, as well as their global averages. The multifractality of wave functions is seen to appear at next-to-leading order in $\rho$. Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of $\rho$ well outside the domain of applicability of perturbation theory.

The existence of nematic order, which breaks the lattice rotational symmetry with nonequivalent $a$ and $b$ axes in iron-based superconductors, is a well-established experimental fact. An antiferromagnetic (AFM) transition is accompanying this order, observed in nearly all parent compounds, except bulk FeSe. The absence of the AFM order in FeSe casts doubt on the magnetic mechanism of iron-based superconductivity, since the nematic order is believed to be driven by the same interaction that is responsible for the superconducting pairing in these materials. Here we show, through systematic first-principles electronic structure calculations, that the ground state of FeSe is in fact strongly AFM correlated but without developing a magnetic long-range order. Actually, there are a series of staggered $n\text{-mer}$ AFM states with corresponding energies below that of the single stripe AFM state, which is the ground state for the parent compounds of most iron-based superconductors. Here, the staggered $n\text{-mer}$ $(n$ any integer $>1)$ means a set of $n$ adjacent parallel spins on a line along the $b$ axis with antiparallel spins between $n$-mers along both $a$ and $b$ axes. Moreover, different $n\text{-mers}$ can antiparallelly mix with each other to coexist. Among all the states, we find that the lowest energy states formed by the staggered dimer, staggered trimer, and their random antiparallel aligned spin states along the $b$ axis are quasidegenerate. The thermal average of these states does not show any magnetic long-range order, but it does possess a hidden one-dimensional AFM order along the $a$ axis, which can be detected by elastic neutron scattering measurements. Our finding gives a natural account for the absence of long-range magnetic order and suggests that the nematicity is driven predominantly by spin fluctuations even in bulk FeSe, providing a unified description on the phase diagram of iron-based superconductors.

We report, as an example, a complete analysis of nuclear spin-lattice relaxation time $\left(T_1\right)$ data for the strongly correlated antiferromagnet ${\mathrm{UPtGa}}_5$, which has a typical ${\mathrm{HoCoGa}}_5$ (115) structure. Using a high-quality single-crystal sample, the $T$ dependence of $T_1$ at ${}^{195}\mathrm{Pt}$ and at two crystallographically inequivalent ${}^{69}\mathrm{Ga}$ sites has been measured for $H\parallel a$ and $c$ axes. Using previously obtained hyperfine coupling tensors from static Knight shift results, the anisotropic spin fluctuation energy and $\vec{q}$ dependence of the dynamic susceptibility have been determined completely, forming a clear contrast to the cases of superconducting ${\mathrm{CeRhIn}}_5,{\mathrm{CeCoIn}}_5$, and ${\mathrm{CeIrIn}}_5$, which are considered to be very near to a quantum critical point. We also note that a similar hyperfine coupling scheme to that of ${\mathrm{CeRhIn}}_5$ has been found for ${\mathrm{UPtGa}}_5$.

We report the discovery of two-dimensional electron gas (2DEG) at the surface of thermoelectric material ${\mathrm{In}}_4{\mathrm{Se}}_3$ by angle-resolved photoemission spectroscopy. The observed 2DEG exhibits a nearly isotropic band dispersion with a considerably small effective mass of $m^{*}=0.16 m_0$, and its carrier density shows a significant temperature dependence, leading to unconventional metal-semiconductor transition at the surface. The observed wide-range thermal tunability of 2DEG in ${\mathrm{In}}_4{\mathrm{Se}}_3$ gives rise to additional degrees of freedom to better control the surface carriers of semiconductors.

Symmetry-protected topological phases (SPT) are short-range entangled gapped states protected by global symmetry. Nontrivial SPT phases cannot be adiabatically connected to the trivial disordered state (or atomic insulator) as long as certain global symmetry $G$ is unbroken. At low energies, most of the two-dimensional SPTs with Abelian symmetry can be described by topological quantum field theory (TQFT) of the multicomponent Chern-Simons type. However, in contrast to the fractional quantum Hall effect where TQFT can give rise to interesting bulk anyons, TQFT for SPTs only supports trivial bulk excitations. The essential question in TQFT descriptions for SPTs is to understand how the global symmetry is implemented in the partition function. In this paper, we systematically study TQFT of three-dimensional SPTs with unitary Abelian symmetry (e.g., ${\mathbb{Z}}_{N_1}\times {\mathbb{Z}}_{N_2}\times ...$). In addition to the usual multicomponent $BF$ topological term at level-1, we find that there are new topological terms with quantized coefficients (e.g., $a^1\wedge a^2\wedge d{a}^2$ and $a^1\wedge a^2\wedge a^3\wedge a^4$) in TQFT actions, where $a^1,a^2,...$ are 1-form U(1) gauge fields. These additional topological terms cannot be adiabatically turned off as long as $G$ is unbroken. By investigating symmetry transformations for the TQFT partition function, we end up with the classification of SPTs that is consistent with the well-known group cohomology approach. We also discuss how to gauge the global symmetry and possible TQFT descriptions of Dijkgraaf-Witten gauge theory.

We show that a large class of gapless states are renormalization group fixed points in the sense that they can be grown scale by scale using local unitaries. This class of examples includes some theories with a dynamical exponent different from one, but does not include conformal field theories. The key property of the states we consider is that the ground-state wave function is related to the statistical weight of a local statistical model. We give several examples of our construction in the context of Ising magnetism.

The advancement of computational tools for material property predictions enables a broad search of novel materials for various energy-related applications. However, challenges still exist in accurately predicting the mean free paths of electrons and phonons in a high-throughput frame for thermoelectric property predictions, which largely hinders the computation-driven material search for novel materials. In this work, this need is eliminated under the limit of reduced nanostructure size within a bulk material, in which these mean free paths are restricted by the nanostructure size. A criterion for $ZT$ evaluation is proposed for general nanoporous bulk materials and is demonstrated with representative oxides.