Plasmons in double quantum wells in a parallel magnetic field

Collective intraband charge-density excitations in the quasi-two-dimensional electron system of double GaAs/AlGaAs quantum wells in an external parallel magnetic field B_∥ are studied by inelastic light scattering. It has been found that the energy of the excitations under study (acoustic and optical plasmons) exhibits anisotropy depending on the mutual orientation of B_∥ and the excitation quasi-momentum k. It is shown theoretically that, in a strong parallel magnetic field, the effects associated with the finite width of the quantum wells dominate over the effects associated with interlayer tunneling and determine the anisotropy of plasmons. The experimental data are compared with a theoretical calculation.     

Optical evidence of quantum rotor orbital excitations in orthorhombic manganites

In magnetic compounds with Jahn–Teller (JT) ions (such as Mn³⁺ or Cu²⁺), the ordering of the electron or hole orbitals is associated with cooperative lattice distortions. There the role of JT effect, although widely recognized, is still elusive in the ground state properties. Here we discovered that, in these materials, there exist excitations whose energy spectrum is described in terms of the total angular momentum eigenstates and is quantized as in quantum rotors found in JT centers. We observed features originating from these excitations in the optical spectra of a model compound LaMnO₃ using ellipsometry technique. They appear clearly as narrow sidebands accompanying the electron transition between the JT split orbitals at neighboring Mn³⁺ ions, displaying anomalous temperature behavior around the Néel temperature T_N ≈ 140 K. We present these results together with new experimental data on photoluminescence found in LaMnO₃, which lend additional support to the ellipsometry implying the electronic-vibrational origin of the quantum rotor orbital excitations. We note that the discovered orbital excitations of quantum rotors may play an important role in many unusual properties observed in these materials upon doping, such as high-temperature superconductivity and colossal magnetoresistance.     

Topological superfluid <Superscript>3</Superscript>He-B in magnetic field and ising variable

The topological superfluid ³He-B provides many examples of the interplay of symmetry and topology. Here we consider the effect of magnetic field on topological properties of ³He-B. Magnetic field violates the time reversal symmetry. As a result, the topological invariant supported by this symmetry ceases to exist; and thus the gapless fermions on the surface of ³He-B are not protected any more by topology: they become fully gapped. Nevertheless, if perturbation of symmetry is small, the surface fermions remain relativistic with mass proportional to symmetry violating perturbation—magnetic field. The ³He-B symmetry gives rise to the Ising variable I = ±1, which emerges in magnetic field and which characterizes the states of the surface of ³He-B. This variable also determines the sign of the mass term of surface fermions and the topological invariant describing their effective Hamiltonian. The line on the surface, which separates the surface domains with different I, contains 1 + 1 gapless fermions, which are protected by combined action of symmetry and topology.     

Bloch electrons in a magnetic field: Topology of quantum states and transport

Quantum states and Hall conductances of electrons in n-type heterojunctions and holes in p-type heterojunctions in a field of a lateral superlattice and a perpendicular magnetic field were studied. It is shown that the energy spectrum of magnetic subbands in a periodic potential without inversion center is not symmetric about the reversal of the quasi-momentum sign. The properties of wave functions and the related topological invariants determining the Hall conductance were examined. The method of calculating the magnetic Bloch states of holes was developed on the basis of the Luttinger Hamiltonian, allowing the spin and spin-orbit interactions to be taken into account in this problem. The Hall conductance quantization law was determined for 2D holes in a periodic superlattice potential.     

Magnetic properties of HoFe3(BO3)4

The magnetic properties of an antiferromagnet with trigonal symmetry, namely, HoFe₃(BO₃)₄, have been investigated theoretically. The calculations have been performed in the molecular field approximation and in the framework of the crystal field model for the rare-earth subsystem. Extensive experimental data on the magnetic properties of HoFe₃(BO₃)₄ have been interpreted and good agreement between theory and experiment has been achieved using the obtained theoretical dependences. The spontaneous spin-reorientation transition and the spin-reorientation transition induced by a magnetic field B ‖ a from the easy-axis to easy-plane state, as well as the spin-flop transition in a magnetic field B ‖ c, have been described. It has been shown that the spontaneous spin-reorientation transition is a magnetic analog of the Jahn-Teller effect. The temperature dependences of the initial magnetic susceptibility at temperatures ranging from 2 to 300 K, the nonlinear curves of magnetization for B ‖ c and B ⊥ c in a magnetic field up to 1.2 T (which indicate the occurrence of first-order phase transitions), and their evolution with variations in the temperature have been described, as well as the temperature and field dependences of the magnetization in a magnetic field up to 9 T. The parameters of the trigonal crystal field for the rare-earth ion Ho³⁺ and the parameters of the Fe-Fe and Ho-Fe exchange interactions have been determined in the course of interpretation of the experimental data.     

Microwave study of proximity effects in superconductivity

The microwave surface resistance of a thin layer of copper in close contact with the surface of bulk lead is investigated. It is found that the basic ideas about proximity effects in superconductivity developed in recent years are capable of explaining the observed behaviour very satisfactorily. Our data give evidence of a complex excitation spectrum in the copper, with low energy excitations above a true gap and a group of high energy excitations which is usually observed in tunneling experiments. The response to a magnetic field shows that scattering at the free copper surface is diffuse. This leads at low fields, where a Meissner shielding current flows at the copper surface, to a decrease of the depairing energy by a large amount of first order in the vector potentialA instead of only a small second order amount. This also explains an initial decrease of the absorption when a weak magnetic field is applied. For fields over a large range below the critical field of lead superconductivity is effectively suppressed in copper. The data also give information on the increase of the penetration depth in lead because of the coating with copper and on the effective electron-electron interaction in copper: $$\lambda \to 2\lambda _L and (NV)_{Cu} \cong 0.05.$$      

“Soft” modes of the excitation spectrum constructed on perturbations of the Abrikosov lattice with a single flux quantum in the unit cell

We have analyzed the spectrum of gapless excitations emerging upon the perturbation of the Abrikosov lattice with a single flux quantum in the unit cell. Superconductors with Ginzburg–Landau parameter κ close to unity are of special interest. We have determined the spectrum of gapless excitations close to zeroth shear modes for an arbitrary angle ? between the unit cell vectors. Analysis of the excitation spectra of triangular and square lattices with a single flux quantum in the unit cell has shown that solutions with a number of flux quanta greater than one exist at least in the range of parameters κ close to unity (κ > 1) and give smaller values of the free energy as compared to its values for a triangular lattice with a single flux quantum. For small values of momentum k (in the k ² approximation), the excitation spectrum of the “transverse” mode in the triangular lattice is independent of the direction of the momentum lying in the plane perpendicular to the magnetic field. For the square lattice (? = π/2), the transverse mode is anisotropic in the k ² approximation also.     

Effective Field Theory Description of the Higher Dimensional Quantum Hall Liquid

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern–Simons theory over the total configuration space CP₃, or as a SU(2) Chern–Simons theory over S⁴. The new quantum Hall liquid supports various types of topological excitations, including the 0-brane (particles), the 2-brane (membranes), and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.     

Static properties of the one-dimensional planar ferromagnet in an external field

The thermodynamic functions and the correlation length of the classical one-dimensionalX Y model in an external field are calculated by the numerical integration of the transfer matrix equation in both ferro- and antiferromagnetic cases. We show that for a finite but weak magnetic field the low temperature structure of the ferromagnetic partition function consists of a spin-wave part and a factor corresponding to the interaction of topological excitations. The contributions of the soliton like topological objects to the static properties are calculated through a systematic perturbative method. Finally we discuss in detail the regions of validity of different analytical approaches by comparing them with our exact numerical solution.     

Low energy magnetic fluctuations in an ordered invar alloy of Fe3Pt

The low energy magnetic response has been studied for a perfectly ordered Fe₃Pt alloy with high resolution triple axis spectrometers. In addition to the magnon excitations which exhibit no softening effect down to q = 0.03 A⁻¹, the central mode starts to develop below q = 0.03 A⁻¹. The intensity of this mode is significantly reduced in a magnetic field of 5 kOe.     

Symmetrical broken and nonlinear response of Weyl semimetal TaAs influenced by the topological surface states and Weyl nodes

A Weyl semimetal (WSM) features Weyl fermions in its bulk and topological surface states on surfaces, and is novel material hosting Weyl fermions, a kind of fundamental particles. The WSM was regarded as a three‐dimensional version of “graphene” under the illusion. In order to explore its promising photoelectric properties and applications in photonics and photoelectronics, here, we study the anisotropic linear and nonlinear optical responses of a WSM TaAs, which are determined by the relationship and balance between its topological surface states and Weyl nodes. We demonstrate that topological surface states which break the bulk symmetry are responsible for the anisotropy of the mobility, and the anisotropic nonlinear response shows saturable characteristic with extremely large saturable intensity. We also find that the mobility is anisotropic with the magnitude of 10⁴ cm²V⁻¹s⁻¹ at room temperature and can be accelerated by the optical field. By analyzing the symmetry, the nonlinear response is mainly contributed by the fermions close to the Weyl nodes, and is related to the Pauli's blocking of fermions, electron‐electron interaction. This work experimentally discovers the anisotropic ultrahigh mobility of WSMs in the optical field and may start the field for the applications of WSMs in photonics and photoelectronics.

     

Low-energy excitations of Yb As in a magnetic field

We discuss the effects of an applied magnetic field on the low-energy excitations in the low temperature phase of Yb₄As₃. We show also why the magnetic interaction of the Yb³⁺ ions is nearly of an isotropic Heisenberg spin-1/2 type. A small anisotropy due to an intrachain dipolar interaction leads to the opening of a gap when a magnetic field is applied. The model agrees with available experimental data. Simple experiments are suggested in order to further test the present theory. Received 3 February 1999     

Features of low-temperature thermal expansion of n-type Bi<Subscript>2</Subscript>Se<Subscript>3</Subscript> single crystals in magnetic field

Tensometric study of n-type Bi₂Se₃ single crystals in dc magnetic fields to 6 T in a temperature range of 7–23 K detected a weak negative thermal expansion (NTE) in the basal plane. The NTE increases with the field strength and depends on its orientation with respect to the trigonal c axis. In a magnetic field of 6 T, parallel to the c axis, the linear NTE coefficient reaches ?7 · 10^?7 K^?1, and a minimum sample length is reached at a temperature of 13 K, where a Hall carrier concentration maximum is also detected. The found magnetoelastic anomaly can be associated with the topological insulator state.     

Anticommutativity equation in topological quantum mechanics

We consider topological quantum mechanics as an example of topological field theory and show that its special properties lead to numerous interesting relations for topological correlators in this theory. We prove that the generating function ? for these correlators satisfies the anticommutativity equation (D?F)². We show that the commutativity equation [dB, dB]=0 can be considered as a special case of the anticommutativity equation.     

Magnetic Bloch states and Hall conductivity of a two-dimensional electron gas in a periodic potential without inversion center

Quantum states of 2D electrons are studied in a periodic potential without inversion center in the presence of a magnetic field. It is shown that the energy spectrum in magnetic subbands is not symmetric about the center of magnetic Brillouin zone E(k)≠E(?k). Singularities (phase branching points) of the electron wave function, which determine the quantization law of Hall conductivity σ_xy, are studied in the k space. It is found that a sharp change takes place in the number of points in the magnetic Brillouin zone and in the corresponding values of topological invariants determining the Hall conductivity of filled subbands. It is noted that the longitudinal conductivity of a lattice without inversion center placed in a magnetic field is not invariant with respect to a change in sign of the electric field, and a photovoltaic effect must arise in an ac electromagnetic field.     

Impurity and exciton effects on the nonlinear optical properties of a disc-like quantum dot under a magnetic field

A detailed investigation of the nonlinear optical properties of the (D⁺, X) complex in a disc-like quantum dot (QD) with the parabolic confinement, under applied magnetic field, has been carried by using the perturbation method and the compact density-matrix approach. The linear and nonlinear optical absorption coefficients between the ground (L = 0) and the first excited state (L = 1) have been examined based on the computed energies and wave functions. The competition between the confinement and correlation effects on the one hand, and the magnetic field effects on the other hand, is also discussed. The results show that the confinement strength of QDs and the intensity of the illumination have drastic effects on the nonlinear optical properties. In addition, we note that the absorption coefficients of an exciton in QDs depend strongly on the impurity but weakly on the magnetic field. Furthermore, the light and heavy hole excitons should be taken into account when we study the optical properties of an exciton in a disc-like QD.     

Multi-orbital physics in lithium-molybdenum purple-bronze: going beyond paradigm

We investigate the role of inter-orbital fluctuations in the low energy physics of a quasi-1D material – lithium molybdenum purple bronze (LMO). It is an exceptional material that may provide us a long sought realization of a Tomonaga-Luttinger liquid (TLL) physics, but its behaviour at temperatures of the order of T ^? ≈ 30 K remains puzzling despite numerous efforts. Here we make a conjecture that the physics around T ^? is dominated by multi-orbital excitations. Their properties can be captured using an excitonic picture. Using this relatively simple model we compute fermionic Green’s function in the presence of excitons. We find that the spectral function is broadened with a Gaussian and its temperature dependence acquires an extra T ¹ factor. Both effects are in perfect agreement with experimental findings. We also compute the resistivity for temperatures above and below critical temperature T ₀. We explain an upturn of the resistivity at 28 K and interpret the suppression of this extra component of resistivity when a magnetic field is applied along the conducting axis. Furthermore, in the framework of our model, we qualitatively discuss and consistently explain other experimentally detected peculiarities of purple bronze: the breaking of Wiedmann-Franz law and the magnetochromatic behaviour. Our model consistently explains all these.     

The possibility of the “giant” isotope effect for ultrasound absorption in crystals

The Zeeman effect, magnetization M(H), and differential magnetic susceptibility dM/dH of ErVO₄ crystals in a pulsed magnetic field have been experimentally and theoretically studied. In magnetic fields H ∥ [001] and H ∥ [100], the energy levels of Er³⁺ ions exhibit mutual approach and crossing (the crossover effect), which results in the peaks in dM/dH and the jumps in M(H) curves at low temperatures. The anomalies in the magnetic properties related to the crossover in ErVO₄ for H ∥ [001] are highly sensitive to the electronic structure of Er³⁺ ion, which allows this effect to be used for refining the crystal field parameters. The influence of the temperature, field misorientation from the symmetry axis, parameters of pair interactions, and other factors on the magnitude and character of magnetic anomalies in ErVO₄ crystals is considered.