Predicting the critical temperature $T_c$ of new superconductors is a notoriously difficult task, even for electron-phonon paired superconductors, for which the theory is relatively well understood. Early attempts to obtain a simple $T_c$ formula consistent with strong-coupling theory, by McMillan and by Allen and Dynes, led to closed-form approximate relations between $T_c$ and various measures of the phonon spectrum and the electron-phonon interaction appearing in Eliashberg theory. Here we propose that these approaches can be improved with the use of machine-learning algorithms. As an initial test, we train a model for identifying low-dimensional descriptors using the $T_c<10$ K dataset by Allen and Dynes, and show that a simple analytical expression thus obtained improves upon the Allen-Dynes fit. Furthermore, the prediction for the recently discovered high-$T_c$ material ${\mathrm{H}}_3\mathrm{S}$ at high pressure is quite reasonable. Interestingly, $T_c$'s for more recently discovered superconducting systems with a more two-dimensional electron-phonon coupling, which do not follow Allen and Dynes's expression, also do not follow our analytic expression. Thus, this machine-learning approach appears to be a powerful method for highlighting the need for a new descriptor beyond those used by Allen and Dynes to describe their set of isotropic electron-phonon coupled superconductors. We argue that this machine-learning method, and its implied need for a descriptor characterizing Fermi-surface properties, represents a promising approach to superconductor materials discovery which may eventually replace the serendipitous discovery paradigm begun by Kamerlingh Onnes.

The low-energy lattice dynamics of the quasiperiodic spin-ladder cuprate ${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ are investigated using terahertz frequency synchrotron radiation. A high density of low-lying optical excitations is present in the 1–3 THz energy range, while at least two highly absorbing excitations stemming from long-wavelength acoustic oscillations of the incommensurate chain and ladder sublattices, are observed at subterahertz frequencies. The effects of Ca substitution on the subterahertz quasiacoustic sliding mode gaps is investigated using coherent synchrotron radiation. Analysis of the results suggest increasing substitution of Sr for Ca is accompanied by a transfer of spectral weight between sliding modes associated with different chain-ladder dynamics. The observation is consistent with a transfer of hole charges from the chains to the ladders and modification of the sublattice dimensions following Ca substitution. The results are discussed in context to the significance of low-lying vibrational dynamics and electron-phonon coupling in the superconducting state of certain quasiperiodic systems.

By means of angle-resolved photoemission spectroscopy (ARPES) measurements and density functional theory (DFT) calculations, the electronic band structure of the topological insulator ${\mathrm{PbBi}}_4{\mathrm{Te}}_4{\mathrm{Se}}_3$ for both five-layer and seven-layer surface terminations is investigated. The measured and calculated band structure features are in good agreement and indicate two well-resolved topological surface states with distinct spatial localizations within bulk band gap of about 0.3 eV.

We extend the periodic table of phases of free fermions in the tenfold way symmetry classes to a classification of free fermionic phases protected by an arbitrary on-site unitary symmetry $\widehat{G}$ in an arbitrary dimension. The classification is described as a function of the real representation theory of $\widehat{G}$ and the data of the original periodic table. We also systematically study in low dimensions the relationship between the free invariants and the invariants of short-range entangled interacting phases of fermions. Namely we determine whether a given symmetry protected phase of free fermions is destabilized by sufficiently strong interactions or it remains stable even in the presence of interactions. We also determine which interacting fermionic phases cannot be realized by free fermions. Examples of both destabilized free phases and intrinsically interacting phases are common in all dimensions.

The toroidal dipole is a fundamental electromagnetic excitation independent from the well-known electric and magnetic dipoles, which enables strong resonances in nanostructure systems due to the reduction of radiative loss. In this paper, we demonstrate multiple toroidal dipole resonances in a series of silicon nanohole structures with symmetry breaking in the near-infrared range. Detailed multipole decompositions and field distributions are performed to discuss the excitation of these resonances. The following experimental verifications support the theoretical predictions. Such a two-dimensional nanohole platform could be more technically available compared to other complicated nanostructures. Our results may provide remarkable potentials in facilitating the light-matter interaction at the nanoscale, such as light emission, subtle sensing, and so on.

Photoinduced force microscopy (PiFM) measures changes in the force between an atomically sharp tip and the sample under the influence of applied radiation. Several mechanisms contribute to the overall force, including forces introduced due to thermal heating of the sample and the tip. In this paper, we study the effect of laser heating of the retracted tip under illumination conditions relevant to PiFM and how it affects the mechanical resonance properties of the cantilever. Using a gold-coated silicon cantilever with its tip irradiated by a tightly focused 532-nm laser beam, we find that the tip temperature increases linearly at 7.5 K/mW of average laser power, irrespective of whether the laser is pulsed or continuous wave. The temperature rise gives rise to a decrease of the cantilever's spring constant and an increase of the damping coefficient. We demonstrate that for retracted tips, these thermally induced changes to the mechanical resonance only moderately impact the measured photoinduced force, as the measured scattering force is at least an order of magnitude stronger than the effective force introduced by laser heating under experimentally relevant conditions.

We describe a method and its implementation for calculating electronic structure and electron transport without approximating the structure using periodic supercells. This effectively removes spurious periodic images and interference effects. Our method is based on already established methods readily available in the nonequilibrium Green's function formalism and allows for nonequilibrium transport. We present examples of a nitrogen defect in graphene, finite voltage bias transport in a point contact to graphene, and a graphene-nanoribbon junction. This method is less costly, in terms of CPU hours, than the supercell approximation.

We theoretically investigate the temperature-gradient-dependent or unidirectional Seebeck effect (USE) in a magnetic/nonmagnetic topological insulator (TI) heterostructure with in-plane magnetization in terms of the semiclassical electron dynamics and Fermi golden rule. The USE has a quantum origin arising from the magnon asymmetric scattering of surface Dirac electrons on TI. We discuss the USE in the heterostructures, ${\mathrm{Cr}}_x{\left({\mathrm{Bi}}_{1-y}{\mathrm{Sb}}_y\right)}_{2-x}{\mathrm{Te}}_3/{\left({\mathrm{Bi}}_{1-y}{\mathrm{Sb}}_y\right)}_2{\mathrm{Te}}_3$. The USE exhibits $cos\varphi$ dependence (measured from $y$ direction) on the orientation of magnetization. It is found that the sign of USE stays unchanged when the system is transferred from $p$ doping to $n$ doping. The USE shows on inverse-linearly temperature dependent at high temperature.

Monolayer and multilayer graphene are promising materials for applications such as electronic devices, sensors, energy generation and storage, and medicine. In order to perform large-scale atomistic simulations of the mechanical and thermal behavior of graphene-based devices, accurate interatomic potentials are required. Here, we present an interatomic potential for multilayer graphene structures referred to as “$\mathrm{hNN}\text{−}{\mathrm{Gr}}_x$.” This hybrid potential employs a neural network to describe short-range interactions and a theoretically motivated analytical term to model long-range dispersion. The potential is trained against a large dataset of monolayer graphene, bilayer graphene, and graphite configurations obtained from ab initio total-energy calculations based on density functional theory (DFT). The potential provides accurate energy and forces for both intralayer and interlayer interactions, correctly reproducing DFT results for structural, energetic, and elastic properties such as the equilibrium layer spacing, interlayer binding energy, elastic moduli, and phonon dispersions to which it was not fit. The potential is used to study the effect of vacancies on thermal conductivity in monolayer graphene and interlayer friction in bilayer graphene. The potential is available through the openkim interatomic potential repository at https://openkim.org.

Cubic Pr-based compounds with ${\mathrm{\Gamma }}_3$ non-Kramers doublet ground states can realize a novel heavy Fermi liquid with spinorial hybridization (“hastatic” order) that breaks time-reversal symmetry. Several Pr-“1-2-20” materials exhibit a suggestive heavy Fermi liquid stabilized in intermediate magnetic fields; these provide key insight into the quadrupolar Kondo lattice. We develop a simple yet realistic microscopic model of ferrohastatic order and elaborate its experimental signatures and behavior in field, where it is a good candidate to explain the observed heavy Fermi liquids at intermediate fields in $\mathrm{Pr}{(\mathrm{Ir},\mathrm{Rh})}_2{\mathrm{Zn}}_{20}$. In addition, we develop the Landau theory of ferrohastatic order, which allows us to understand its behavior close to the transition and explore thermodynamic signatures from magnetic susceptibility to thermal expansion.

Group IB metal halides ($\mathrm{Cu}X$ and $\mathrm{Ag}X, X=$ Cl, Br, and I) are widely used in optoelectronic devices and photochemical catalysis due to their appropriate optical and electronic properties. First-principles calculations have confronted difficulties in accurately predicting their electronic band structures. Here, we study $\mathrm{Cu}X$ and $\mathrm{Ag}X$ with many-body perturbation theory in the $GW$ approximation, implemented in the full-potential linearized augmented plane waves (FP-LAPW) framework. Comparing the quasiparticle band structures calculated with the default LAPW basis and the one extended by high-energy local orbitals (HLOs), denoted as $\mathrm{LAPW}+\mathrm{HLOs}$, we find that it is crucial to include HLOs to achieve sufficient numerical accuracy in $GW$ calculations of these materials. Using $\mathrm{LAPW}+\mathrm{HLOs}$ in semilocal density functional approximation based $G{W}_0$ calculations leads to good agreement between theory and experiment for both band gaps and the splitting between metal (Cu or Ag) $d$ and $X-p$ states. This work emphasizes the importance of numerical accuracy in the description of unoccupied states for quasiparticle band structure of materials with the $d^{10}$ electronic configuration.

Tunable symmetry breaking plays a crucial role for the manipulation of topological phases of quantum matter. Here, through combined high-pressure magnetotransport measurements, Raman spectroscopy, and x-ray diffraction, we demonstrate a pressure-induced topological phase transition in nodal-line semimetal ZrSiS. Symmetry analysis and first-principles calculations suggest that this pressure-induced topological phase transition may be attributed to weak lattice distortions by nonhydrostatic compression, which breaks some crystal symmetries, such as the mirror and inversion symmetries. This finding provides some experimental evidence for crystal symmetry protection for the topological semimetal state, which is at the heart of topological relativistic fermion physics.

We study the bulk and boundary properties of fragile topological insulators (TIs) protected by inversion symmetry, mostly focusing on the class A of the Altland-Zirnbauer classification. First, we propose an efficient method for diagnosing fragile band topology by using the symmetry data in momentum space. Using this method, we show that among all the possible parity configurations of inversion-symmetric insulators, at least $17\%$ of them have fragile topology in two dimensions while fragile TIs are less than $3\%$ in three dimensions. Second, we study the bulk-boundary correspondence of fragile TIs protected by inversion symmetry. In particular, we generalize the notion of $d$-dimensional ($d\mathrm{D}$) $k\mathrm{th}\text{−}\mathrm{order}$ TIs, which is normally defined for $0<k\le d$, to the cases with $k>d$, and show that they all have fragile topology. In terms of the Dirac Hamiltonian, a $d\mathrm{D}k\mathrm{th}\text{−}\mathrm{order}$ TI has $(k-1)$ boundary mass terms. We show that a minimal fragile TI with the filling anomaly can be considered as the $d\mathrm{D}(d+1)\mathrm{th}\text{−}\mathrm{order}$ TI, and all the other $d\mathrm{D}k\mathrm{th}$-order TIs with $k>(d+1)$ can be constructed by stacking $d\mathrm{D}(d+1)\mathrm{th}\text{−}\mathrm{order}$ TIs. Although $d\mathrm{D}(d+1)\mathrm{th}\text{−}\mathrm{order}$ TIs have no in-gap states, the boundary mass terms carry an odd winding number along the boundary, which induces localized charges on the boundary at the positions where the boundary mass terms change abruptly. In the cases with $k>(d+1)$, we show that the net parity of the system with boundaries can distinguish topological insulators and trivial insulators. Also, by studying the Wilson loop and nested Wilson loop spectra, we show that all the spectral windings of the Wilson loop and nested Wilson loop should be unwound to resolve the Wannier obstruction of fragile TIs. By counting the minimal number of bands required to unwind the spectral winding of the Wilson loop and nested Wilson loop, we determine the minimal number of bands to resolve the Wannier obstruction, which is consistent with the prediction from our diagnosis method of fragile topology. Finally, we show that a $(d+1)\mathrm{D}(k-1)\mathrm{th}\text{−}\mathrm{order}$ TI can be obtained by an adiabatic pumping of $d\mathrm{D}k\mathrm{th}\text{−}\mathrm{order}$ TI, which generalizes the previous study of the $2\mathrm{D}\mathrm{third}\text{−}\mathrm{order}$ TI.

We study the photon thermal Hall effect and the persistent heat current in radiative heat transfer. We show that the photon thermal Hall effect is not a uniquely nonreciprocal effect; it can arise in some reciprocal systems with broken-mirror symmetry. This is in contrast with the persistent heat current, which is a uniquely nonreciprocal effect that cannot exist in any reciprocal system. Nevertheless, for a specific class of systems with $C_4$ rotational symmetry, we note that the photon thermal Hall effect is uniquely nonreciprocal, and moreover there is a direct connection between the persistent heat current and the photon thermal Hall effect. In the near-equilibrium regime, the magnitude of the photon thermal Hall effect is proportional to the temperature derivative of the persistent heat current in such systems. Therefore, the persistent heat current as predicted for the equilibrium situation can be probed by the photon thermal Hall effect away from equilibrium.

We have investigated the interplay between band inversion and size quantization in spherically shaped nanoparticles made from topological-insulator (TI) materials. A general theoretical framework is developed based on a versatile continuum-model description of the TI bulk band structure and the assumption of a hard-wall mass confinement. Analytical results are obtained for the wave functions of single-electron energy eigenstates and the matrix elements for optical transitions between them. As expected from spherical symmetry, quantized levels in TI nanoparticles can be labeled by quantum numbers $j$ and $m=-j,-j+1,\dots ,j$ for total angular momentum and its projection on an arbitrary axis. The fact that TIs are narrow-gap materials, where the charge-carrier dynamics is described by a type of two-flavor Dirac model, requires $j$ to assume half-integer values and also causes a doubling of energy-level degeneracy where two different classes of states are distinguished by being parity eigenstates with eigenvalues ${(-1)}^{j\mp 1/2}$. The existence of energy eigenstates having the same $j$ but opposite parity enables optical transitions where $j$ is conserved, in addition to those adhering to the familiar selection rule where $j$ changes by $\pm 1$. All optical transitions satisfy the usual selection rule $\mathrm{\Delta }m=0,\pm 1$. We treat intra- and interband optical transitions on the same footing and establish ways for observing unusual quantum-size effects in TI nanoparticles, including oscillatory dependencies of the band gap and of transition amplitudes on the nanoparticle radius. Our theory also provides a unified perspective on multiband models for charge carriers in semiconductors and Dirac fermions from elementary-particle physics.

Contrary to empirical observations, lowest-order $\mathit{k}·\widehat{\mathit{p}}$ theory predicts that monolayer black phosphorus (“phosphorene”) is completely immune to zigzag-polarized optical excitation at the band-gap energy. Using symmetry arguments, we derive a $2\times 2$ Hamiltonian under the $\mathit{k}·\widehat{\mathit{p}}$ formalism including higher-order corrections, which is used to show that the experimentally measured band-gap transition with zigzag polarization is dominated by the third-order $\mathit{k}·\widehat{\mathit{p}}$ perturbation in the interband optical matrix element, whereas the effects of the spin-orbit interaction are negligible in this material, consistent with a trivial orbital diamagnetic contribution to the $g$-factors.