The valley Chern and spin-valley Chern numbers are the key concepts in valleytronics. They are topological numbers in the Dirac theory but not in the tight-binding model. We analyze the bulk-edge correspondence between the two phases which have the same Chern and spin-Chern numbers but different valley Chern and spin-valley Chern numbers. Though the edge state between them is topologically trivial in the tight-binding model, it is shown to be as robust as the topological one both for zigzag and armchair edges. We construct Y-junctions made of topological edges. They satisfy the topological Kirchhoff law, where the topological charges are conserved at the junction. We may interpret a Y-junction as a scattering process of particles which have four topological numbers. It would be a milestone of future topological electronics.

We study dissipation in a small quantum system coupled to an environment held in thermodynamic equilibrium. The relaxation dynamics of a system subject to an abrupt quench in the parameters of the underlying Hamiltonian is investigated using two complementary renormalization group approaches. The methods are applied to the Ohmic spin-boson model close to the coherent-to-incoherent transition. In particular, the role of non-Markovian memory for the relaxation before and after the quench of the spin-boson coupling and the Zeeman splitting of the up and down spin is investigated.

The relation between the energy and momentum of plasmarons in bilayer graphene is investigated within the Overhauser approach, where the electron-plasmon interaction is described as a field theoretical problem. We find that the Dirac-like spectrum is shifted by $\Delta E\left(\mathbf{k}\right)\sim 100÷150\mathrm{meV}$ depending on the electron concentration $n_e$ and electron momentum. The shift increases with electron concentration as the energy of plasmons becomes larger. The dispersion of plasmarons is more pronounced than in the case of single layer graphene, which is explained by the fact that the energy dispersion of electrons is quadratic and not linear. We expect that these predictions can be verified using angle-resolved photoemission spectroscopy (ARPES).

We present a method for bridging the gap between the Dirac effective field theory and atomistic simulations in graphene based on the Husimi projection, allowing us to depict phenomena in graphene at arbitrary scales. This technique takes the atomistic wave function as an input, and produces semiclassical pictures of quasiparticles in the two Dirac valleys. We use the Husimi technique to produce maps of the scattering behavior of boundaries, giving insight into the properties of wave functions at energies both close to and far from the Dirac point. Boundary conditions play a significant role to the rise of Fano resonances, which we examine using the processed Husimi map to deepen our understanding of bond currents near resonance.

We study the free-energy landscape of a minimal model for relaxor ferroelectrics. Using a variational method which includes leading correlations beyond the mean-field approximation as well as disorder averaging at the level of a simple replica theory, we find metastable paraelectric states with a stability region that extends to zero temperature. The free energy of such states exhibits an essential singularity for weak compositional disorder pointing to their necessary occurrence. Ferroelectric states appear as local minima in the free energy at high temperatures and become stable below a coexistence temperature $T_c$. We calculate the phase diagram in the electric-field–temperature plane and find a coexistence line of the polar and nonpolar phases which ends at a critical point. First-order phase transitions are induced for fields sufficiently large to cross the region of stability of the metastable paraelectric phase. These polar and nonpolar states have distinct structure factors from those of conventional ferroelectrics. We use this theoretical framework to compare and gain physical understanding of various experimental results in typical relaxors.

An effective Hamiltonian scheme is used to reveal the properties of a multidomain structure in BiFeO${}_3$ consisting of alternating domains that are initially made of two phases, namely, $R3c$ (ferroelectric with antiphase oxygen octahedral tilting) versus $Pnma$ (antiferroelectric with in-phase and antiphase oxygen octahedral tiltings). These two types of domains dramatically modify their properties as a result of their cohabitation. The weak ferromagnetic vector and polarization rotate, and significantly change their magnitude, in the $R3c$-like region, while the $Pnma$-like region becomes polar along the direction of domain propagation. Moreover, the domain walls possess distinct polar and oxygen octahedral tilting patterns that facilitate the transition between these two regions. The studied multidomain is also predicted to exhibit other anomalous properties, such as its strain adopting several plateaus and steps when increasing the magnitude of an applied electric field.

Direct measurements of electrical resistivity and caloric equation of state have been performed for fluid tungsten in order to establish the relation between the liquid-vapor and the metal-to-nonmetal transition caused by thermal expansion. The measurements have been done with accuracy better than $\pm 10\%$ using mainly the experimental technique developed in our previous works. To estimate the systematic uncertainty of the measurements a supplementary technique has been developed which allows the thermal expansion of tungsten in the experiments to be measured directly. We demonstrate that fluid tungsten remains in a two-phase state at pressures of about one order of magnitude higher than the critical pressure of the liquid-vapor transition expected from theoretical estimates. Such behavior is very similar to that observed earlier in fluid iron [Korobenko and Rakhel, Phys. Rev. B 85, 014208 (2012)].

The quantum spin-$\frac{1}{2}$ orthogonal-dimer chain with the Heisenberg intradimer and Ising interdimer interactions in a magnetic field is considered by a rigorous approach. The model conserves the $z$ component of total spin on vertical Heisenberg bonds, and this property is used to calculate exactly the partition function using the transfer-matrix method. We have found the ground-state phase diagram of the given model in a magnetic field as well as the macroscopic degeneracy along field-induced transitions accompanied with the magnetization jumps. The model exhibits two intermediate fractional plateaux at one quarter and one half of the saturation magnetization. We have examined the effect of the exchange anisotropy in the $XXZ$ Heisenberg intradimer interaction on the ground state. It is shown that the one-quarter and one-half plateaux may disappear from the magnetization curve for the ferromagnetic Heisenberg intradimer interaction. We have also studied rigorously the effect of frustrated interactions on the thermodynamic and magnetic properties of the model and show how the macroscopic degeneracy of the ground state is reflected in the low-temperature behavior of the magnetization, entropy, and specific heat. A possibility of observing enhanced magnetocaloric effect during the adiabatic demagnetization is discussed in detail.

The magnetic responses of a spin-$1/2$ ladder doped with nonmagnetic impurities are studied combining both analytical and numerical methods. The regime where frustration induces incommensurability is taken into account. Several improvements are made on the results of the seminal work by Sigrist and Furusaki [M. Sigrist and A. Furusaki, J. Phys. Soc. Jpn. 65, 2385 (1996)] and deviations from the Brillouin magnetization curve due to interactions are also analyzed. We first discuss the magnetic profile around a single impurity and the effective interactions between impurities within the bond-operator mean-field theory. The results are compared to density-matrix renormalization group calculations. In particular, these quantities are shown to be sensitive to the transition to the incommensurate regime. We then focus on the behavior of the zero-field susceptibility through an effective Curie constant. At zero temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattices and compute exactly the distribution of ladder clusters due to chain breaking effects. Solving the effective model with exact diagonalization and quantum Monte Carlo simulations gives the temperature dependence of the Curie constant. Its high-temperature limit is understood within a random dimer model, while the low-temperature tail is compatible with a real-space renormalization group scenario. Interestingly, solving the full microscopic model does not show a plateau corresponding to the saturation of the impurities in isotropic ladders. The second magnetic response that is analyzed is the magnetic curve. Below fields of the order of the spin gap, the magnetization process is controlled by the physics of interacting impurity spins. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from a Brillouin behavior due to interactions. The effective model calculations agree rather well with density-matrix renormalization group calculations at zero temperature and with quantum Monte Carlo simulations at finite temperature. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu${}_2$PO${}_6$ compound and other spin-gapped materials are briefly mentioned.

Measurements of magnetization, specific heat, electrical resistivity, Hall effect, and magnetoresistance on single crystalline samples of LaFeAsO grown in a NaAs flux are reported. While this material is known to be a semimetal, the temperature dependence of the electrical resistivity data presented herein is reminiscent of semiconducting behavior and exhibits distinct features associated with a structural transition and spin density wave (SDW) order. Low-temperature x-ray diffraction measurements have confirmed that the structural transition in these samples occurs near 140 K, compared to a transition temperature of 156 K observed in polycrystalline samples. Magnetoresistance and Hall coefficient measurements were performed in magnetic fields up to 9 T applied perpendicular to the basal plane using a van der Pauw configuration. The charge carrier density and mobility indicate that electrons are the majority charge carriers and exhibit features indicative of the structural transition and SDW formation. Isotherms of magnetoresistivity measured as a function of magnetic field can be scaled onto a single curve.

We investigate numerically the excitation of nonlinear magnetic interactions in a ferrite material by an energetic pump pulse of terahertz (THz) radiation. The calculations are performed by solving the coupled Maxwell and Landau-Lifshitz-Gilbert differential equations. In a time-resolved THz pump/THz probe scheme, it is demonstrated that Faraday rotation of a delayed THz probe pulse can be used to map these interactions. Our study is motivated by the ability of soft x-ray free electron lasers to perform time-resolved imaging of the magnetization process at the submicrometer and subpicosecond length and time scales.

We prepare single-layer potassium-doped iron selenide (110) film by molecular-beam expitaxy. Such a single-layer film can be viewed as a two-dimensional system composed of weakly coupled two-leg iron ladders. Scanning tunneling spectroscopy reveals that superconductivity is developed in this two-leg ladder system. The superconducting gap is similar to that of the multilayer films. However, the Fermi-surface topology in this quasi-one-dimensional system is remarkably different from that of the bulk materials. Our results suggest that superconducting pairing is very short ranged or takes place rather locally in iron chalcogenides. The superconductivity is most likely driven by electron-electron correlation effect and is insensitive to the change of Fermi surfaces.

We have investigated atomistic and electronic mechanisms of hydrogen embrittlement at grain boundaries of iron in the presence and absence of vacancies by using first-principles calculations. Considering interactions between hydrogen, vacancies, and $\Sigma$3 grain boundaries in $\alpha$-Fe, we have searched for the most deleterious defect states by evaluating their influence on tensile strength under static tensile strain. The calculated results show that hydrogen and vacancies prefer to accumulate as defect complexes near grain boundaries, thereby decreasing the tensile strength of grain boundaries. Theoretical stress-strain curves show that a strength lowering at grain boundaries by the defect complexes is found to be much worse than the effect of each factor. Because of the low mobility of vacancies, this mechanism can account for the delayed brittle fractures induced by hydrogen in steel materials.

The critical magnetic behavior of the colossal magnetocapacitive spinel CdCr${}_2$S${}_4$ is revisited. Magnetization and susceptibility of single-crystalline samples measured in the temperature range 68–120 K were analyzed by the kink-point method, the modified Arrott plots, the Kouvel-Fisher method, ln $M$ versus ln $H_{\mathrm{eff}}$, and the scaling analysis. We show that the critical exponents β $=$ 0.365 and γ $=$ 1.387 of the three-dimensional (3D) Heisenberg model describe the magnetic critical behavior only in the asymptotic region. Outside the asymptotic region, the values of β are reduced and those of γ are increased. We provide experimental evidence that the critical behavior of CdCr${}_2$S${}_4$ follows that expected for an ideal 3D Heisenberg system, however, in an unusual narrow window of temperature and in low magnetic fields only.

Motivated by the magnetically driven high-temperature ferroelectric behavior of CuO and the subsequent theoretical efforts to understand this intriguing phenomenon, we study a bilinear-biquadratic Heisenberg model on a two-dimensional square lattice, which possesses some of the key features of the models proposed for CuO. We use a combination of variational calculations and classical Monte Carlo simulations to study this model at zero and finite temperatures. We show that the biquadratic coupling plays a crucial role in selecting the magnetic ground state. More importantly, a noncollinear magnetic state is found to be stable at finite temperatures. Our study demonstrates that higher-order interaction terms are of crucial importance if the stronger interactions together with the lattice geometry combine to generate a near degeneracy of magnetic states.

We analyze the effects of order-parameter fluctuations on the ground state of fully gapped charge-neutral fermionic superfluids. The Goldstone mode associated with the spontaneously broken symmetry leads to a problem of coupled singularities in $d\le 3$ dimensions. We derive a minimal set of one-loop renormalization group equations which fully captures the interplay of the singularities. The flow equations are based on a symmetry-conserving truncation of a scale-dependent effective action. We compute the low-energy behavior of longitudinal, transverse, and mixed order-parameter correlations, and their impact on the fermionic gap. We demonstrate analytically that cancellations protecting the Goldstone mode are respected by the flow, and we present a numerical solution of the flow equations for the two-dimensional attractive Hubbard model.

We have performed resistivity and inelastic neutron scattering measurements on three samples of Fe${}_{0.98-z}$Cu${}_z$Te${}_{0.5}$Se${}_{0.5}$ with $z=0$, 0.02, and 0.1. It is found that with increasing Cu doping the sample's resistivity deviates progressively from that of a metal. However, in contrast to expectations that replacing Fe with Cu would suppress the magnetic correlations, the low-energy ($\le 12$ meV) magnetic scattering is enhanced in strength, with greater spectral weight and longer dynamical spin-spin correlation lengths. Such enhancements can be a consequence of either enlarged local moments or a slowing down of the spin fluctuations. In either case, the localization of the conduction states induced by the Cu doping should play a critical role. Our results are not applicable to models that treat 3$d$ transition metal dopants simply as effective electron donors.

We present research on the superconducting properties of Nb${}_x$Re${}_{1-x}$ ($x=0.13$–0.38) obtained by measuring the electrical resistivity $\rho \left(T\right)$, magnetic susceptibility $\chi \left(T\right)$, specific heat $C_P\left(T\right)$, and London penetration depth $\Delta \lambda \left(T\right)$. It is found that the superconducting transition temperature $T_c$ decreases monotonically with an increase of $x$. The upper critical field $B_{c2}\left(T\right)$ for various $x$ can be nicely scaled by its corresponding $T_c$. The electronic specific heat $C_e\left(T\right)/T$, penetration depth $\Delta \lambda \left(T\right)$, and superfluid density ${\rho }_s\left(T\right)$ demonstrate exponential behavior at low temperatures and can be well fitted by a one-gap BCS model. The residual Sommerfeld coefficient ${\gamma }_0\left(B\right)$ in the superconducting state follows a linear field dependence. All these properties suggest an $s$-wave BCS-type of superconductivity with a very large $B_{c2}\left(0\right)$ for Nb${}_x$Re${}_{1-x}$ ($0.13\le x\le 0.38$).

We derive a formula for the electric polarization of interacting insulators, expressed in terms of the full Green's and vertex functions. We exemplify this method in the half-filled ionic Hubbard model treated within dynamical mean field theory (DMFT). The electric polarization of a correlated band insulator is determined by the interplay of ionicity and covalency, and both quantities are renormalized by the electron-electron interactions. We introduce quasiparticle approximations to the exact equation for the polarization, and compare the results of these approximations with those of the exact DMFT formulation and of static mean field theories such as the $\text{LDA}+\text{U}$. The latter overestimates the electronic contribution to the electric polarization when the quasiparticle weight of the active bands is very small.