An ensemble Green's function formalism, based on the von Neumann density matrix approach, to calculate one-electron excitation spectra of a many-electron system with degenerate ground states is proposed. A set of iterative equations for the ensemble Green's function and self-energy is derived and a simplest approximation corresponding to an ensemble $\mathit{GW}$ approximation is naturally obtained. The derivation is based on the Schwinger functional derivative technique and does not assume any adiabatic connection between a noninteracting and an interacting ground state.

We study the influence of local inhomogeneities on carrier recombination dynamics in single InGaN/GaN core-shell microrods (MRs) by means of time-resolved microphotoluminescence (TRPL) at 10 K. At low carrier density ($\sim {10}^{11}{\mathrm{cm}}^{-2}$), the carrier recombination in the $m$-plane quantum well is dominated by radiative processes and the recorded decay times along the MR equally amount to about 400 ps, corresponding to a bimolecular coefficient of $1.1\pm 0.2\times {10}^{-2}{\mathrm{cm}}^2{\mathrm{s}}^{-1}$. When the excited carrier density exceeds ${10}^{12}{\mathrm{cm}}^{-2}$, both the efficiency and the decay time of the PL in the quantum well drop significantly, which indicates the onset of Auger recombination. Based on a modified ABC model, we estimate a C coefficient varying from $0.5\pm 0.2$ to $2.2\pm 0.9\times {10}^{-16}{\mathrm{cm}}^4{\mathrm{s}}^{-1}$ from the lower to the upper part of the MR. This increase is accompanied by a rise of PL linewidth in the low excitation regime, indicating an increase of alloy disorder. Relaxation of the $k$-selection rule by alloy disorder is expected to play an important role in the observed increase of Auger coefficient. These results confirm that Auger recombination is sensitive to disorder and can be significantly enhanced in strongly disordered systems. We conclude that it is therefore crucial to minimize the degree of disorder in the active layer for high power LEDs based on core-shell MRs.

We study second-order topological insulators and semimetals characterized by chiral symmetry. We investigate topological phase transitions of a model for construction of the two-dimensional second-order topological insulators protected only by chiral symmetry. By the theory of the phase transitions, we propose a second-order topological semimetal and insulators with flat hinge bands in chiral-symmetric three-dimensional systems. The three-dimensional second-order topological phases can be obtained from the stacked two-dimensional second-order topological insulators with chiral symmetry. Moreover, we show that broken chiral symmetry in the three-dimensional second-order topological phase allows a second-order topological insulator with chiral hinge states. We also demonstrate the second-order topological phases by using a lattice model.

Triple sum frequency (TSF) spectroscopy measures multidimensional spectra by resonantly exciting multiple quantum coherences of vibrational and electronic states. In this work we demonstrate pump-TSF-probe spectroscopy in which a pump excites a sample and some time later three additional electric fields generate a probe field which is measured. We demonstrate pump-TSF-probe spectroscopy on polycrystalline, smooth, thin films and spiral nanostructures of both ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$. The pump-TSF-probe spectra are qualitatively similar to the more conventional transient-reflectance spectra. While transient-reflectance sensitivity suffers under low surface coverage, pump-TSF-probe sensitivity is independent of the sample coverage and nanostructure morphologies. Our results demonstrate that pump-TSF-probe is a valuable methodology for studying microscopic material systems.

Few-layer ${\mathrm{WTe}}_2$ displays fascinating phenomena, which are believed to be closely related to the topological character of its band structure. In this work we investigate quantum oscillations of thermopower in thin ${\mathrm{WTe}}_2$ films. Besides four oscillation frequencies commonly observed in bulk materials, we observe an additional oscillation frequency, which has previously been attributed to topological surface states [Nat. Commun. 8, 2150 (2017)]. Through analysis of the temperature, angular, and film thickness dependence of the frequency, we conclude that it is not due to the cyclotron resonance of the surface Fermi arcs in Weyl semimetals, but rather from the bulk bands. Emergence of these bulk bands at the Fermi level is due to a band reconstruction in thin layers. They contribute to transport and may be responsible for some properties of few-layer ${\mathrm{WTe}}_2$.

Superconducting topological crystalline insulators (TCIs) are predicted to host new topological phases protected by crystalline symmetries, but available materials are insufficiently suitable for surface studies. To induce superconductivity at the surface of a prototypical TCI SnTe, we use molecular beam epitaxy to grow a heterostructure of SnTe and a high-$T_c$ superconductor Fe(Te,Se), utilizing a “buffer” layer to bridge the large lattice mismatch between SnTe and Fe(Te,Se). Using low-temperature scanning tunneling microscopy and spectroscopy, we measure a prominent spectral gap on the surface of SnTe, and demonstrate its superconducting origin by its dependence on temperature and magnetic field. Our work provides a platform for atomic-scale investigations of emergent topological phenomena in superconducting TCIs.

We study strong electron-phonon interacting systems where the geometry of the crystalline lattice frustrates the formation of charge order. Our results show that under such condition, high-$T_c$ superconductivity can occur in a wide range of electron-phonon coupling strengths. This result is obtained by studying the Holstein model on triangular lattice using sign-problem-free quantum Monte Carlo method.

We study the effects of an in-plane Dzyaloshinskii-Moriya interaction under an external magnetic field in the highly frustrated kagome antiferromagnet. We focus on the low-temperature phase diagram, which we obtain through extensive Monte Carlo simulations. We show that, given the geometric frustration of the lattice, highly nontrivial phases emerge. At low fields, lowering the temperature from a cooperative paramagnet phase, the kagome elementary plaquettes form noncoplanar arrangements with nonzero chirality, retaining a partial degeneracy. As the field increases, there is a transition from this “locally chiral phase” to an interpenetrated spiral phase with broken ${\mathcal{Z}}_3$ symmetry. Furthermore, we identify a quasi-skyrmion phase in a large portion of the magnetic phase diagram, which we characterize with a topological order parameter, the scalar chirality by triangular sublattice. This pseudo-skyrmion phase consists of a crystal arrangement of three interpenetrated non-Bravais lattices of skyrmionlike textures, but with a non-(fully)-polarized core. The edges of these pseudo-skyrmions remain polarized with the field, as the cores are progressively canted. Results show that this pseudo-skyrmion phase is stable up to the lowest simulated temperatures and for a broad range of magnetic fields.

Optical studies of the density wave (DW) salt of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{KHg}\left(\mathrm{SCN}\right)}_4$ revealed a pseudogap due to a charge fluctuation below $T^{*}\simeq$ 200 K. Moreover, ${}^{13}\mathrm{C}$-NMR studies of the DW salt of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{RbHg}\left(\mathrm{SCN}\right)}_4$ and of the superconductivity (SC) salt of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{NH}}_4\mathrm{Hg}{\left(\mathrm{SCN}\right)}_4$ suggested that the NMR line width of the A site increased and the charge disproportionation in the A column developed below $T^{*}$. These phenomena may be due to the development of a horizontal stripe modulation of the local charge density. However, whether the horizontal stripe modulation develops or not and the relationships among $T^{*}$ anomalies, the pseudogap, and line broadening, were unclear. In this study, ${}^{13}\mathrm{C}$-NMR measurements were obtained of the metallic salt of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{TlHg}\left(\mathrm{SeCN}\right)}_4$, and its electronic structure was compared with those of the DW and SC salts. The NMR line width of the A site and ${\chi }_{\mathrm{B}}/{\chi }_{\mathrm{C}}$ in Rb(SCN) and $\mathrm{NH}{}_4$(SCN) increased and deviated from that in Tl(SeCN) below $T^{*}$, suggesting the development of the instability of horizontal stripe modulation in Rb(SCN) and $\mathrm{NH}{}_4$(SCN) and that $T^{*}$ anomalies could be due to the instability.

We investigate the trion binding energy in a three-dimensional semiconductor, with bare Coulomb interaction between charges and effective mass approximation for the electron and hole dispersion relations. This is done by making use of a previously proposed exact method for the three-body problem. The calculations cover the complete range of electron-to-hole mass ratio. We find perfect agreement with existing variational calculations. Investigating the small- and large-mass-ratio regimes, we build a three-parameter interpolating formula for the trion binding energy $E_b\left(r\right)$ in terms of the exciton binding energy, where $r$ is the electron to exciton mass ratio. This formula, $E_b\left(r\right)=0.71347-0.11527r-0.18580\sqrt{1-r}$, in atomic units, is in full agreement, within our precision, with our numerical results over the complete range of mass ratio.

The molecular arrangement and the interfacial electronic properties of cobalt phthalocyanine (CoPc) on the deactivated B-Si(111)-$\sqrt{3}\times \sqrt{3}R{30}^{\circ }$ surface are analyzed using scanning tunneling microscopy and spectroscopy as well as photoemission studies. Our data demonstrate that for low coverages of CoPc the molecules lie flat with the $p_z$ orbital of the Si surface atom forming a hybrid state with the $d_{z^2}$ orbital of the transition metal. This hybridization is observed in a broadening of the corresponding Si $2p$ core level photoemission spectra and in an additional contribution to the valence band spectra. Furthermore, this additional hybridization state is detected in the tunneling spectra. For higher CoPc coverages, the CoPc molecules are tilted with respect to the Si surface forming highly ordered organic molecular films. The spectroscopic data of the thick film demonstrates that the electronic properties resemble those of pure CoPc.

Density functional theory is used to investigate the effect of hydrostatic pressure on the structural, energetic, electronic, and vibrational properties of bulk ${\mathrm{ReS}}_2$. The phase transition from the distorted $1T$ phase to the high-pressure distorted $1T^{\prime }$ phase is rationalized based on the evaluation of their thermodynamic potentials. The electronic band gap of the $1T$ phase is shown to undergo a nearly direct to indirect transition at about 9 GPa, while the $1T^{\prime }$ phase is found to remain a robust nearly direct band-gap material under pressure. The computational analysis of the vibrational properties of both ${\mathrm{ReS}}_2$ phases reproduces existing experimental Raman spectroscopy data for $\omega$ vs $P$ trends and provides a path towards an accurate phase discrimination using infrared spectroscopy, inelastic neutron, and x-ray scattering.

Two-dimensional ferromagnetic electron gases subject to random scalar potentials and Rashba spin-orbit interactions exhibit a striking quantum criticality. As disorder strength $W$ increases, such a system undergoes two transitions. It first changes from a normal diffusive metal consisting of extended states to a marginal metal consisting of critical states at a critical disorder $W_{c,1}$. Another transition from the marginal metal to an insulator occurs at a stronger disorder $W_{c,2}$. Through highly accurate numerical procedures based on the recursive Green's function and the exact diagonalization methods, we elucidate the nature of the quantum criticality and the properties of the pertinent states. The conductance is described by an unorthodox one-parameter scaling law: Conductance of various system sizes and disorders collapse into two branches of a scaling curve corresponding to diffusive metal and insulating phases with an exponentially diverging correlation length, $\xi \propto exp[\alpha /\sqrt{|W-W_c|}]$, near transition points. Finite-size scaling analysis of the inverse participation ratio reveals that the states of the marginal metal are fractals of a universal fractal dimension $D=1.90\pm 0.02$, while those of the diffusive metal spread over the whole system with $D=2$ and states in the insulating phase are localized with $D=0$. The phase diagram for diffusive metals, marginal metals, and the Anderson insulators is plotted in the disorder-magnetic-coupling plane.

In this paper, we study periodically modulated $s=1/2$ spin chain in a linear gradient potential (LP) that is generated by an external magnetic field. In the absence of the LP, the system has topological states that exhibit a magnetization plateau for a uniform external magnetic field. These topological states have a finite integer Chern number and their stability is clarified by an equivalent spinless fermion system derived by a Jordan-Wigner transformation. We show that the LP, which is nothing but a constant electric field in the spinless fermion system, destabilizes the topological states, because it induces localization called Wannier-Stark (WS) localization. We clarify the phase diagram in the presence of the LP and on-site diagonal disorder. To this end, we carefully study edge excitations under the open boundary condition, which are a hallmark of the topological order. We find a very interesting phenomenon indicating existence of a quasiedge modes that take the place of the genuine edge modes in certain parameter regions. This is a precursor of the WS localization realized in topological states. Finally, we investigate many-body localization induced by a sufficiently strong LP or disorder. To this end, we study the energy-level statistics for whole energy levels, and we find unexpected extended-state regimes located in intermediate potential-gradient and weak on-site disorder regimes. We verify this phenomenon by calculating variance of the entanglement entropy. The present system is closely related to quantum Hall state in two dimensions, and therefore our findings can be observed not only in experiments on ultracold atomic gases but also quantum Hall physics.

Hexagonal ferrites ($h\text{−}R\mathrm{Fe}{\mathrm{O}}_3$) have attracted great attention for their high ferroelectric transition temperature, strong magnetoelectric couplings, and tunable Néel temperature ($T_N$) and electric polarization. While introducing structural distortion has been previously found to be effective to raise $T_N$ and polarization in $h\text{−}R\mathrm{Fe}{\mathrm{O}}_3$, it is generally difficult to create sizable structural distortion by common approaches including substrate-induced epitaxial strain and chemical doping. Here, we use high-pressure x-ray-diffraction measurements to show that pressure can generate large structural distortion and R-layer displacement of $h\text{−}R\mathrm{Fe}{\mathrm{O}}_3$, resulting with dramatically enhancement of polarization and $T_N$. Density-functional theory calculations reveal that the enlarged $c/a$ ratio results in an ∼70 K increase of $T_N$ along with a significant enhancement of ferroelectric polarization. Our results suggest that pressure is effective to tune structural distortions and related multiferroicity of the $h\text{−}R\mathrm{Fe}{\mathrm{O}}_3$ system, making $h\text{−}R\mathrm{Fe}{\mathrm{O}}_3$ a promising material for spintronic applications.

We use the Ginzburg-Landau theory for a chiral $p$-wave superconductor to describe the filamentary superconducting phase nucleating at temperatures higher than the bulk transition temperature near the interfaces between Ru metal and ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ in eutectic ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$-Ru. The peculiar phase diagram of magnetic field versus temperature shows very distinct properties for different directions of the magnetic field. A clear feature of the magnetic fields in the basal plane of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, perpendicular to the chiral axis ($c$ axis), is the occurrence of a second superconducting transition with a new order parameter visible as a zero-bias anomaly in tunneling spectroscopy. For the field along the $c$ axis of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, two transitions merge, indicating that the field drives the second-order parameter through the paramagnetic coupling to a chiral supercurrent. The resulting phenomenology shows that the assumption of a chiral superconducting order parameter in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ yields an image reproducing the qualitative properties observed in the experiment. This discussion is qualitatively analogous to the corresponding chiral even- and odd-parity channels.

We analyze the bulk phase transitions of the three titanium dioxide polymorphs anatase, rutile, and brookite in thermodynamical equilibrium and after ultrafast laser excitation using the generalized solid-state nudged elastic band (G-SSNEB) method. For calculating the forces and stresses needed for G-SSNEB, we use electronic-temperature dependent density functional theory calculations. Our results show that the anatase-rutile and brookite-rutile phase transitions have a considerably lower energy barrier than the anatase-brookite phase transition in the thermodynamical equilibrium and upon laser excitation. The obtained transition temperatures in thermodynamical equilibrium are consistent with experimentally observed ones. Furthermore, our calculations show that the pathways of the phase transition are not affected considerably by the applied laser pulse. Although the pathways do not change considerably we see that the rutile phase is stabilized by the laser pulse.

Manganese hydrides and superhydrides have been studied from ambient up to high pressures by the ab initio random structure searching algorithm. At ambient pressure conditions and room temperature, the subhydride ${\mathrm{Mn}}_2\mathrm{H}$ (space group $P\overline{3}m1$) is the only compound found stable among those studied, since $\epsilon$-MnH (hcp structure, space group $P{6}_3/mmc$), although stable at 0 K, is destabilized by thermal effects. With increasing pressure, MnH is stabilized, and then hydrogen-rich hydrides appear: first ${\mathrm{MnH}}_2$ around 30 GPa, then ${\mathrm{MnH}}_7$ around 40 GPa, and finally ${\mathrm{MnH}}_3$ around 90 GPa. ${\mathrm{MnH}}_8$ is likely to become stable around 150 GPa. The body-centered tetragonal structure of ${\mathrm{MnH}}_2$ (space group $I4/mmm$) is identical to that of ${\mathrm{FeH}}_2$ and ${\mathrm{CoH}}_2$. ${\mathrm{MnH}}_3$ has an original body-centered tetragonal structure, with space group $I4/m$ and 4 formula units per primitive cell. It contains a structural unit ${\mathrm{H}}_8$ with rather short H-H distances. ${\mathrm{MnH}}_7$ is extremely stable at high pressure. ${\mathrm{MnH}}_7$ and ${\mathrm{MnH}}_8$ exhibit a mixed structure, with one hydrogen being under the molecular form (1/2 ${\mathrm{H}}_2$) and the other ones under an atomic (hydrided) form. Atomic charges computed by the Bader method confirm the electron transfer from Mn to H, with Mn oxidation increasing from MnH to ${\mathrm{MnH}}_3$, and then saturating beyond. At high pressure, nuclear quantum effects tend to stabilize ${\mathrm{MnH}}_4$ and increase the stability of ${\mathrm{MnH}}_8$.

Electric-field control of spin dynamics in ferromagnetic films and heterostructures is crucial for the development of advanced spintronic devices with ultralow power consumption. Such control can be achieved via the magnetoelastic coupling between spins and strains created in a ferromagnet by the attached piezoelectric transducer. The efficiency of strain-mediated excitation and manipulation of spin phenomena is expected to increase drastically in materials with high magnetoelastic coefficients, such as cobalt ferrite. Here we report the state-of-the-art micromagnetic simulations of the spin dynamics arising in ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ films and ${\mathrm{CoFe}}_2{\mathrm{O}}_4$/Pt bilayers traversed by longitudinal elastic waves. To fully allow for the magnetoelastic coupling, we numerically solve a system of differential equations involving the Landau-Lifshitz-Gilbert equation for the magnetization and the elastodynamic equation for the mechanical displacement. The simulations show that, despite high Gilbert damping characteristic of cobalt ferrite, the injected elastic waves with frequencies around the resonance frequency of coherent magnetization precession in unstrained ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ film efficiently generate spin waves in this ferrimagnetic insulator. Furthermore, the generated spin wave, which has the wavelength of the driving acoustic wave, creates two secondary elastic waves due to the magnetoelastic feedback. In addition, it modifies the driving elastic wave, leading to the sound attenuation of magnetic origin with decay length about 70 $\mu \mathrm{m}$. In ${\mathrm{CoFe}}_2{\mathrm{O}}_4$/Pt bilayers, the magnetization precession at the interface gives rise to a spin current flowing in the Pt layer, which creates additional damping of the precession and generates a charge current via the inverse spin Hall effect. Remarkably, a circular charge flow is predicted for thick Pt layers, which leads to inhomogeneous potential distributions along their surfaces. The magnitude of the voltage between lateral sides of the Pt layer may exceed 1 nV, which can be measured experimentally.

Recently, a class of Dirac semimetals, such as ${\mathrm{Na}}_3\mathrm{Bi}$ and ${\mathrm{Cd}}_2{\mathrm{As}}_3$, is discovered to carry ${\mathbb{Z}}_2$ monopole charges. We present an experimental mechanism to realize the ${\mathbb{Z}}_2$ anomaly in regard to the ${\mathbb{Z}}_2$ topological charges and propose to probe it by magnetotransport measurements. In analogy to the chiral anomaly in Weyl semimetals, the acceleration of electrons by a spin bias along the magnetic field can create a ${\mathbb{Z}}_2$ charge imbalance between the Dirac points, the relaxation of which contributes measurable positive longitudinal spin magnetoconductivity (LSMC) to the system. The ${\mathbb{Z}}_2$ anomaly induced LSMC is a spin version of the longitudinal magnetoconductivity (LMC) due to the chiral anomaly, which possesses all characters of the chiral anomaly induced LMC. While the chiral anomaly in the topological Dirac semimetal is very sensitive to local magnetic impurities, the ${\mathbb{Z}}_2$ anomaly is found to be immune to local magnetic disorder. It is further demonstrated that the quadratic or linear field dependence of the positive LMC is not unique to the chiral anomaly. Base on this, we argue that the periodic-in-$1/B$ quantum oscillations superposed on the positive LSMC can serve as a fingerprint of the ${\mathbb{Z}}_2$ anomaly in topological Dirac semimetals.