Том 105, № 7 (2017)

3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green’s functions parametrized by a 16-element matrix e_α^μ in an expansion around the Weyl point. The matrix e_α^μ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric g_μν governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types of Weyl fermions, depending on the signs of the components g⁰⁰ and g₀₀ of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an overtilted Weyl cone for g⁰⁰ > 0 and, respectively, g₀₀ > 0 or g₀₀ < 0, we find additional “type-III” and “type-IV” Weyl fermions with instabilities (complex frequencies) for g⁰⁰ < 0 and g₀₀ > 0 or g₀₀ < 0, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where g⁰⁰ changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves.

It is found that the integration of Ge/Si heterostructures containing layers of Ge quantum dots with twodimensional regular lattices of subwave holes in a gold film on the surface of a semiconductor leads to the multiple (to 20 times) enhancement of the hole photocurrent in narrow wavelength regions of the mid-infrared range. The results are explained by the light wave excitation of the surface plasmon–polaritons at the metal–semiconductor interface effectively interacting with intraband transitions of holes in quantum dots.

The anisotropic magnetoelectric properties of an ytterbium aluminum borate YbAl (BO single crystal having noncentrosymmetric crystal structure (space group R32) are studied, including the orientational, field, and temperature dependences of the polarization in magnetic fields up to 5 T in the temperature range of 2–300 K. It has been shown experimentally for the first time that the symmetry of the observed magnetoelectric effects exactly corresponds to the trigonal structure of the crystal and is characterized by two quadratic magnetoelectric constants. The polarization in the basal plane P_{a, b} is a quadratic function of the field at low fields and reaches 250–300 μC/m² in a field of 5 T at a temperature of 2 K, almost an order of magnitude exceeding the previously reported values. A theoretical model based on the spin Hamiltonian of the ground Kramers doublet of Yb³⁺ ions in the crystal field is proposed including magnetoelectric interactions allowed by the symmetry. This model makes it possible to quantitatively describe all observed magnetic and magnetoelectric properties of YbAl₃(BO₃)₄.

A phase diagram of a magnetic material with the spin S = 2 is obtained including all allowed spin invariants for the isotropic exchange interaction at an arbitrary relation between exchange constants. New phases with two-sublattice structure and biaxial symmetry at a site are found.

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose–Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a few circulation quanta at each point, has been considered in a hydrodynamic approximation. A special class of density profiles has been chosen, so that it proves possible to calculate analytically the velocity field produced by point vortices. The equations of motion have been given in a noncanonical Hamiltonian form. The theory has been generalized to the case where the condensate forms a curved quasi-two-dimensional shell in the three-dimensional space.

The physical origin of the ambiguity related to the dependence of the polarization on the choice of the unit cell in a crystal is established in the framework of classical electrodynamics. It is shown that the electric polarization of a crystal is determined not only by the charge distribution in the unit cell (dipole moment density) but also by the microscopic mechanism of symmetry breaking in the polar phase. An approach to the calculation of the polarization invariant with respect to the choice of the unit cell is suggested. It is demonstrated that the dependence of the polarization on the mechanism of formation of the polar phase exists in the “modern topological theory” of polarization too.