We report results of experiments with liquid ${}^3\mathrm{He}$ confined in a high-porosity anisotropic nanostructure which we call planar aerogel. This aerogel consists of nanofibers (with diameters $\sim 10$ nm) which are randomly oriented in the plane normal to the specific axis. We used two samples of planar aerogel prepared using different techniques. We have found that on cooling from the normal phase of ${}^3\mathrm{He}$ the superfluid transition in both samples occurs into an equal spin pairing superfluid phase. NMR properties of this phase qualitatively agree with the properties of the superfluid A phase in the anisotropic Larkin-Imry-Ma state. We have observed differences between results obtained in the presence and absence of solid paramagnetic ${}^3\mathrm{He}$ on the aerogel strands. We propose that these differences may be due, at least in part, to a magnetic scattering channel, which appears in the presence of solid paramagnetic ${}^3\mathrm{He}$.

Increasing Si concentrations in the ${\mathrm{EuCu}}_2{\left({\mathrm{Ge}}_{1-x}{\mathrm{Si}}_x\right)}_2$ series tunes the divalent Eu antiferromagnetic (AF) compound ${\mathrm{EuCu}}_2{\mathrm{Ge}}_2$ $(T_N=14\mathrm{K})$ to a nonmagnetic intermediate valence (IV) system ${\mathrm{EuCu}}_2{\mathrm{Si}}_2$. There is a collapse of the magnetic state and heavy quasiparticles occur at $x\sim 0.7$ corresponding to a quantum critical point (QCP). We have systematically investigated the Eu-valence and magnetic states as well as the coupling to the lattice through the QCP in ${\mathrm{EuCu}}_2{\left({\mathrm{Ge}}_{1-x}{\mathrm{Si}}_x\right)}_2$. This involved the ${}^{151}\mathrm{Eu}$ Mössbauer effect spectroscopy and angle-resolved x-ray diffraction measurements as a function of Si concentration $(0\le x\le 1)$ at variable temperatures in the range 300–4.2 K. The ${}^{151}\mathrm{Eu}$ probe indicates that the divalent Eu AF state is stable up to $x\sim 0.5$, followed by a collapse of AF ordering for $x>0.6$, which is associated with a simultaneous sharp change of the valence state towards a nonmagnetic IV state. The crossover from the AF ordered state to the nonmagnetic IV state is found at a QCP corresponding to $x\sim 0.7$, at which the nonmagnetic IV state is inhomogeneous and exhibits an enhanced $\mathrm{E}{\mathrm{u}}^{\nu +}$ mean valence $(\nu \sim 2.5)$. We believe that the emergence of such an unusual valence state is related to the observed heavy quasiparticles at low temperatures near the QCP. Magnetic order and a nonmagnetic inhomogeneous IV state coexist in a narrow region $0.6\le x<0.7$, which evolves to a homogeneous IV state above $x\sim 0.8$. The $\mathrm{ThCr}{\mathrm{Si}}_2$-type tetragonal structure is maintained throughout the series, although there is a precipitous increase in the $c/a$ ratio at 10 K when the valence fluctuations become enhanced at the critical concentration $x=0.7$. X-ray diffraction temperature scans at the critical concentration indicate conspicuous changes to steep temperature dependences of decreasing (increasing) values of $a$ $\left(c\right)$ lattice parameters and decreasing unit-cell volume at $T<100 \mathrm{K}$, as the IV ground state become preferentially populated at low temperatures. Thus there is a clear manifestation of strong coupling between the lattice and the valence fluctuation process. A corresponding detailed phase diagram is constructed and compared with that obtained from recent external pressure studies on the system.

We study topological properties of materials in the ${\mathrm{Ca}}_2\mathrm{As}$ family without spin-orbit coupling (SOC) by combining the first-principles calculation and a tight-binding model calculation. As a result of the calculation, we reveal that the ${\mathrm{Ca}}_2\mathrm{As}$ family consists of one insulator phase and three nodal line phases including an intersecting nodal ring phase, though one of the phases is not found with realistic material parameters. Additionally, we discuss what kind of nontrivial topological invariants will emerge from each nodal line phase when SOC is introduced. We also find a mapping from a nodal line semimetal without SOC to a topological crystalline insulator with SOC. This mapping can be used to specify the realized topological phase from the candidates given by the previous phase classification method.

Valley Hall effect is an appearance of the valley current in the direction transverse to the electric current. We develop the microscopic theory of the valley Hall effect in two-dimensional semiconductors where the electrons are dragged by the phonons or photons. We derive and analyze all relevant contributions to the valley current including the skew-scattering effects together with the anomalous contributions caused by the side jumps and the anomalous velocity. The partial compensation of the anomalous contributions is studied in detail. The role of two-phonon and two-impurity scattering processes is analyzed. We also compare the valley Hall effect under the drag conditions and the valley Hall effect caused by the external static electric field.

We examine the occurrence of Bose-Einstein condensation and superfluidity of dipolar excitons for a pair of quasi-two-dimensional spatially separated hexagonal $\alpha \text{−}{\mathcal{T}}_3$ layers. In the $\alpha \text{−}{\mathcal{T}}_3$ model, the $AB$-honeycomb lattice structure is supplemented with C atoms, located at the centers of the hexagonal lattice. We have solved a two-body problem for an electron and a hole for the model Hamiltonian for the $\alpha \text{−}{\mathcal{T}}_3$ double layer in a magnetic field. The exciton binding energy is changed due to the magnetic field, and magnetoexcitons are formed as excitons in a magnetic field. The energy dispersion of collective excitations, the spectrum of sound velocity, and the effective magnetic mass of magnetoexcitons are obtained in the integer quantum Hall regime for high magnetic fields. The superfluid density and the temperature of the Kosterlitz-Thouless phase transition are probed as functions of the excitonic density, the magnetic field, and the interlayer separation.

Effects of electron-electron interactions on the optical response of graphene nanoribbons are theoretically investigated in an effective-mass approximation in a comprehensive manner. In optical absorption spectra of armchair and zigzag nanoribbons without and with doping, excitons, which are bound states of electrons and holes, and plasmons manifest themselves as various prominent peaks. For light polarized parallel to nanoribbons, exciton peaks at high energies split because of interactions with dark excitons, to which optical transition is prohibited. For light polarized perpendicular to nanoribbons, in nondoped semiconducting armchair nanoribbons, moderate exciton peaks appear while in doped armchair and zigzag nanoribbons, only when the Fermi energy crosses at least two energy bands, large plasmon peaks occur because of a nature of Dirac electrons. These peaks can be assigned to specific optical transitions in energy bands. The optical absorption peaks arising from the excitons and plasmons in a wide range of categories of nanoribbons approximately correspond to those of carbon nanotubes by appropriate scaling of energy and the wave vector.

We present an alternative representation for the anisotropic Eliashberg equations of superconductivity, whose numerical solution yields an efficiency gain of several orders of magnitude with respect to the conventional representation in momentum space. Our method is a practical realization of a long-sought approach, whose essence is a linear transformation from regular k space to a set of orthonormal functions defined as the solutions of the Helmholtz equation on the Fermi surface. In this way, all the anisotropy of the problem can be described by a handful of coefficients with built-in symmetry. We perform benchmark calculations on the gap anisotropy of $\mathrm{Mg}{\mathrm{B}}_2$, and reproduce previous results at a remarkably reduced computational cost. Furthermore, we apply our methodology to efficiently determine the transition temperature of the compressed $\mathrm{Y}{\mathrm{H}}_6$ hydride, obtaining very good agreement with recent experimental measurements. The simplification introduced by our method enables the high-throughput exploration of superconducting materials without having to resort to the isotropic approximation, and opens up possibilities towards first-principles calculations of more advanced theories of superconductivity.

We outline a numerical procedure to incorporate the crystal symmetries in the Helmholtz Fermi Surface Harmonics basis set, which are the solutions of the Helmholtz equation defined on the Fermi surface. This improvement allows for an optimal representation of anisotropic quantities defined on the Fermi surface in terms of a few symmetric elements of the set. We demonstrate the general validity of our approach by identifying the fully symmetric Helmholtz Fermi Surface Harmonics subset for several representative systems with different crystal structures, namely, FCC-Cu, $\mathrm{HEX}\text{−}\mathrm{Mg}{\mathrm{B}}_2$, and $\mathrm{BCC}\text{−}{\mathrm{YH}}_6$. Furthermore, we illustrate the potential of the method applied to the electron-phonon problem, showing that the anisotropic electron-phonon mass-enhancement parameter ${\lambda }_{\mathbf{k}}$ can be represented to high accuracy by a handful of coefficients. This works as an effective filter, paving the way for a reduction of several orders of magnitude in the computation of superconductivity, impurity problems, or any other Fermi-surface-dependent property of metals from first principles.

Heterostructures containing strongly correlated electron systems provide a platform to clarify interplay of electron correlation and Rashba spin-orbit coupling in unconventional superconductors. Motivated by recent fabrication of artificially engineered heavy fermion superlattices and high-temperature cuprate superconductors, we conduct a thorough study on superconductivity in the Rashba-Hubbard model. In contrast to previous weak coupling approaches, we employ fluctuation-exchange approximation to describe quantum critical magnetic fluctuations and resulting superconductivity. As a result, robust Fermi surfaces against magnetic fluctuations, incommensurate spin fluctuations, and a strongly parity-mixed superconducting phase are demonstrated in a wide range of electron filling from type-II van Hove singularity to half filling. We also clarify impacts of type-II van Hove singularity on magnetic fluctuations and superconductivity. Whereas the $d_{x^2-y^2}$-wave pairing is always dominant, subdominant spin-triplet pairing with either $p$-wave or $f$-wave symmetry shows a comparable magnitude, especially near the type-II van Hove singularity. Our results resolve unsettled issues on strongly correlated Rashba systems and uncover candidate systems of nonreciprocal transport and topological superconductivity.

Time-reversal broken Weyl semimetals have attracted much attention recently, but certain aspects of their behavior, including the evolution of their Fermi surface topology and anomalous Hall conductivity with Fermi-level position, have remained underexplored. A promising route to obtain such materials may be to start with a nonmagnetic Dirac semimetal and break time-reversal symmetry via magnetic doping or magnetic proximity. Here we explore this scenario in the case of the Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ based on first-principles density-functional calculations and subsequent low-energy modeling of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ in the presence of a Zeeman field applied along the symmetry axis. We clarify how each fourfold degenerate Dirac node splits into four Weyl nodes, two with chirality $\pm 1$ and two higher-order nodes with chirality $\pm 2$. Using a minimal $k·p$ model Hamiltonian whose parameters are fit to the first-principles calculations, we detail the evolution of the Fermi surfaces and their Chern numbers as the Fermi energy is scanned across the region of the Weyl nodes at fixed Zeeman field. We also compute the intrinsic anomalous Hall conductivity as a function of the Fermi-level position, finding a characteristic inverted-dome structure. ${\mathrm{Cd}}_3{\mathrm{As}}_2$ is especially well suited to such a study because of its high mobility, but the qualitative behavior revealed here should be applicable to other Dirac semimetals as well.

We develop a quantum theory for topological systems incorporating dissipations, noises, and thermal effects with strong non-Markovian dynamics, while other approaches in the literature may not be applicable. We derive the exact master equation and transient quantum transport for the study of dissipative topological systems, mainly focusing on noninteracting topological insulators and topological superconductors. The resulting exact master equation is also applicable to systems initially entangled with environments. In this theory, dissipations and topological states can be related to each other through spectral densities which tie up the reservoir spectra and topological-state wave functions in the system-reservoir couplings when either the system or environment is a topological system. We also apply the theory to study quantized Majorana conductance in superconductor-semiconductor hybrid systems incorporating different dissipations, noises, and thermal effects.

We report on the observation of an unconventional structure of the quantum Hall effect (QHE) in a $p\text{−}\mathrm{type}$ $\mathrm{HgTe}/{\mathrm{Cd}}_x{\mathrm{Hg}}_{1-x}\mathrm{Te}$ double quantum well (DQW) consisting of two HgTe layers of critical thickness. The observed QHE is a reentrant function of magnetic field between two $i=2$ states (plateaus at ${\rho }_{yx}=h/i{e}^2$) separated by an intermediate $i=1$ state in the shape of a flat-top peak placed on the remarkably long $i=2$ plateau. This anomalous $i=1$ peak separates two different regimes: (i) a traditional QHE at relatively low fields corresponding to a small density of mobile holes $p_s$ and (ii) a high-field QHE with a 2-1 plateau-plateau transition corresponding to a much larger $p_s$. The high-field part is strongly sensitive to external influences such as gate voltages, in contrast to the low-field part, which is much less responsive. We explain the observed behavior by analyzing the calculated trajectories of the Fermi level $E_F\left(B\right)$ between hole-like and electron-like Landau levels (LLs). At low fields, $E_F$ is captured by the lateral maximum (LM) of the valence subband, and only holes in the center of the Brillouin zone contribute to QHE, while holes in the LM are inactive. In contrast, at fields above the reentry, $E_F$ rises significantly higher than LM, approaching the zero-mode LLs, and all holes come into play in QHE. At intermediate fields, the reentrance is caused by a combination of two factors in the specific energy spectrum of this DQW: (i) the superposition of an electron-like LL on hole-like LLs and (ii) the stabilizing influence of the LM reservoir on $E_F\left(B\right)$.

Vibration modes of hydrogen atoms on Ni(100) are studied. The number of observed energy losses as well as their full width at half maximum (FWHM) are incompatible with the classical model of localized vibrations. Number and energy of modes agree, however, well with a previously published quantum-mechanical treatment of the motion of hydrogen in the periodic surface potential of Ni(100). For the dilute surface phase of hydrogen, the FWHM is a factor of 4 larger than expected from the dispersion of the bands. The effect is attributed to rapid tunneling of vibrationally excited hydrogen into empty neighboring sites.

In the paramagnetic phase of cubic antiferromagnet ${\mathrm{SrMnO}}_{2.997}$ ($T_{\mathrm{N}}=236\mathrm{K}$), the spin susceptibility of the localized $\mathrm{Mn}\left(t_{2g}\right)$ electrons exhibits a gapped behavior with $d{\chi }_s\left(T\right)\ge 0$, suggesting the existence of a low-dimensional short-range magnetic order above $T_{\mathrm{N}}$. The low-frequency fluctuations of the spin correlations of neighboring ${\mathrm{Mn}}^{4+}$ ions were probed by measuring the spin-lattice relaxation rate $T_1^{-1}$ and the echo-decay rate $T_2^{-1}$ of ${}^{17}\mathrm{O}$ and ${}^{87}\mathrm{Sr}$ nuclei up to 420 K. ${}^{17}\mathrm{O}$ being involved in an Mn–O–Mn bond, the echo-decay rate ${}^{17}T_2^{-1}$ probes the fluctuations of the two neighboring $S\left(t_{2g}\right)$ spins at low frequency, $\omega \le {10}^3{\text{s}}^{-1}$. It is shown that there exist local changes of the double-exchange interaction, which favor FM correlated pairs of neighboring $S\left(t_{2g}\right)$ spins in the Mn–${}^{17}\mathrm{O}$–Mn bond. The unusual thermal behavior of ${}^{17}T_2^{-1}\left(T\right)$ indicates low-frequency fluctuations of the short-range magnetic order which may include the change of AF $\leftrightarrow$ FM spin alignment of neighboring magnetic ions. For ${}^{87}\mathrm{Sr}$ nuclei, which probe the spin configuration of eight neighboring Mn ions in the cubic unit cell, ${}^{87}T_2^{-1}$ has no such anomaly, implying that FM order should be excluded within the cubic unit cell. With both NMR probes, it is deduced that the only magnetic orders which may exist in the cubic unit cells are the following: AF–G [$\mathit{q}=\pi /a(1,1,1)$], AF–C [$\mathit{q}=\pi /a(1,1,0)$], and AF–A [$\mathit{q}=\pi /a(0,0,1)$] so that the slow fluctuating short-range magnetic order is built from these three AF ordered unit cells. Furthermore, we deduce from ${}^{17}T_1^{-1}$ results that the fluctuating short-range magnetic order, i.e., corresponding to large $q$, has a high thermal stability in the PM phase of ${\mathrm{SrMnO}}_{2.997}$.

We report on the low-frequency optical excitations in the multiferroic ground state of polycrystalline ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ in the frequency range 0.3–3 THz and their changes upon applying external magnetic fields up to 7 T. In the ground state below the orbital-ordering temperature $T_{\mathrm{OO}}=9$ K we observe the appearance of several new modes. By applying the external magnetic field parallel and perpendicular to the propagation direction of the THz radiation, we can identify the strongest absorptions to be of predominantly electric-dipole origin. We discuss these modes as the low-energy electronic excitations of the ${\mathrm{Fe}}^{2+}$ ions ($3d^6, S=2$) in an tetrahedral ${\mathrm{S}}^{2-}$ environment. The eigenfrequencies and relative intensities of these absorption lines are satisfactorily reproduced by our calculation assuming an effective exchange field of $12.8{\mathrm{cm}}^{-1}$ at the ${\mathrm{Fe}}^{2+}$-ions sites. The direction of the exchange field is found to be slightly tilted out of the $ab$ plane. With our approach we can also describe previously reported results from Mössbauer studies and the order of magnitude of the electric polarization induced by orbital and noncollinear spin ordering.

We formulate an efficient scheme to perform a Migdal-Eliashberg calculation considering the retardation effect from first principles. While the conventional approach requires a huge number of Matsubara frequencies, we show that the intermediate representation of the Green's function [H. Shinaoka et al., Phys. Rev. B 96, 035147 (2017)] dramatically reduces the numerical cost to solve the linearized gap equation. Without introducing any empirical parameter, we obtain a superconducting transition temperature of elemental Nb ($\sim 10$ K), which is consistent with experiment. The present result indicates that our approach has a superior performance for many superconductors for which $T_{\mathrm{c}}$ is lower than $O\left(10\right)$ K.

Motivated by strongly correlated and frustrated systems, we propose an effective model that describes the dynamics of pairs of opposite spin fermions scattering from localized bosons. Integrating out one of the degrees, either the bosons or fermions, generates temperature-dependent long-range effective interactions between the entities that we investigate using Monte Carlo techniques. The behavior of bosons is dominated by vortex-antivortex unbinding, with effective interboson interactions beyond the nearest-neighbor Josephson coupling of phases. Remarkably, in the fermion sector we observe a temperature-driven phase transition from a SC phase with a “BCS” spectral function that shows a gap minimum on the underlying Fermi surface to a conducting phase of pairs but with a “BEC” spectral function with a gap minimum at $k=0$. Tunneling and angle-resolved photoemission spectroscopy on Bose-Fermi mixtures in cold atomic systems and superconducting islands on graphene are some of the promising experimental platforms to test our predictions.

$1T-\mathrm{Ta}{\mathrm{Se}}_2$ is host to coexisting strongly correlated phases including charge density waves (CDWs) and an unusual Mott transition at low temperature. Here, we investigate coherent phonon oscillations in $1T-\mathrm{Ta}{\mathrm{Se}}_2$ using a combination of time- and angle-resolved photoemission spectroscopy (TR-ARPES) and time-resolved reflectivity (TRR). Perturbation by a femtosecond laser pulse triggers a modulation of the valence band binding energy at the $\overline{\mathrm{\Gamma }}$ point, related to the Mott gap, that is consistent with the in-plane CDW amplitude mode frequency. By contrast, TRR measurements show a modulation of the differential reflectivity comprised of multiple frequencies belonging to the distorted CDW lattice modes. Comparison of the temperature dependence of coherent and spontaneous phonons across the CDW transition shows that the amplitude mode intensity is more easily suppressed during perturbation of the CDW state by the optical excitation compared to other modes. Our results clearly identify the relationship of the in-plane CDW amplitude mode with the Mott phase in $1T-\mathrm{Ta}{\mathrm{Se}}_2$ and highlight the importance of lattice degrees of freedom.

One-dimensional grain boundaries of two-dimensional semiconducting ${MX}_2 (M=\mathrm{Mo},\mathrm{W};X=\mathrm{S},\mathrm{Se})$ transition metal dichalcogenides are typically metallic at room temperature. The metallicity has its origin in the lattice polarization, which for these lattices with $D_{3h}$ symmetry is a topological invariant, and leads to one-dimensional boundary states inside the band gap. For boundaries perpendicular to the polarization direction, these states are necessarily 1/3 occupied by electrons or holes, making them susceptible to a metal-insulator transition that triples the translation period. Using density-functional-theory calculations, we demonstrate the emergence of combined one-dimensional spin density/charge density waves of that period at the boundary, opening up a small band gap of $\sim 0.1\mathrm{eV}$. This unique electronic structure allows for soliton excitations at the boundary that carry a fractional charge of $\pm 1/3e$.