Quantum anomalous hall effect in Hg1-yMnyTe quantum wells

The quantum Hall effect is usually observed when a two-dimensional electron gas is subjected to an external magnetic field, so that their quantum states form Landau levels. In this work we predict that a new phenomenon, the quantum anomalous Hall effect, can be realized in Hg{1-y}Mn{y}Te quantum wells, without an external magnetic field and the associated Landau levels. This effect arises purely from the spin polarization of the Mn atoms, and the quantized Hall conductance is predicted for a range of quantum well thickness and the concentration of the Mn atoms. This effect enables dissipationless charge current in spintronics devices.     

Landau levels in graphene in the presence of emergent gravity

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.     

Principles of Adaptive Optics, 3rd edn., by Robert K. Tyson

A review is made of the quantum effects which are observed in the transport coefficients of semiconductors. Quantization of the free carriers in semiconductors is produced whenever an external potential acts on an otherwise uniform and perfect crystal. Typical examples are a magnetic field, an electric field or the physical boundaries of the sample. A magnetic field quantizes the electron and hole states into a ladder of equally spaced Landau levels. This gives rise to the Shubnikov–de Haas, magnetophonon and magneto-impurity effects, where the positions of the Landau levels resonate with the Fermi, phonon, or impurity energies present in the sample. A series of oscillations in the magneto-resistance of many different types of materials results. Electric fields applied to the surface of metal oxide semiconductor (MOS) devices result in a set of quantum levels for motion perpendicular to the surface. At low temperatures the charge carriers are bound to the surface and behave as if they were two-dimensional. This is shown to give rise to very dramatic oscillatory metal–insulator behaviour in high magnetic fields. Quantization is also shown to occur in very thin layers of semiconductors which act like a simple square well potential, the energy levels of which can be studied as a function of layer thickness. The carriers are confined within the layers, and also show two-dimensional behaviour.     

Quantum spin Hall effect

The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. The existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2(e/4pi). The degenerate quantum Landau levels are created by the spin-orbit coupling in conventional semiconductors in the presence of a strain gradient. This new state of matter has many profound correlated properties described by a topological field theory.     

Nernst-Ettingshausen effect in graphene

The Nernst-Ettingshausen effect corresponds to the regime of crossed magnetic and electric fields. In the current theoretical studies of this effect in graphene, the dependence of the Landau levels on the applied electric field is neglected. This dependence takes place in the case of the nonquadratic energy spectrum of the charge carriers. In this work, oscillations of the Nernst coefficient in graphene with a zero and nonzero band gap have been studied taking into account such dependence. The effect of the Coulomb interaction on these oscillations is considered.     

Mechanism of exchange switching of spin valves by an inverse current

The exchange switching of spin valves by an inverse current can be explained by the interaction of the charge carriers with the spin-injection effective magnetic field. Such an interaction gives rise to transverse spin components, which are transferred to the magnetic lattice and cause its instability and switching. The spin-injection field is produced by longitudinal spin components, but it opens up a channel for the transverse spin transfer to the lattice. The spin transfer to the lattice and the switching occur in the free layer of the spin valve.     

De Haas-van Alphen oscillations in the quasi-two-dimensional organic metal (BEDO-TTF)5[CsHg(SCN)4]2

The magnetization oscillations in the quasi-two-dimensional organic metal (BEDO-TTF)₅[CsHg(SCN)₄]₂ are thoroughly investigated over a wide range of magnetic field directions at different temperatures down to 0.4 K. The results obtained are in good agreement with the shape and sizes of the Fermi surface calculated from the x-ray diffraction data. Apart from the fundamental frequencies, the combination frequencies are found in the magnetization oscillation spectrum. It is demonstrated that these combination frequencies are governed by the motion of charge carriers along the real closed orbits inside the network of magnetic breakdown orbits formed under the action of the magnetic field. It is uniquely established that the combination frequencies previously revealed in the magnetoresistance oscillation spectrum of the same metal are associated with the quantum interference effect. The angular dependences of the oscillation amplitude exhibit minima, which are explained by the spin splitting of the Landau levels.     

Spin depolarization and a metal-insulator transition in a two-dimensional system in zero magnetic field

The conditions for spontaneous spin polarization in a two-dimensional system in a zero magnetic field are considered in the case of a partial filling of the lower quantum-well subbands when the energy of exchange interaction of charge carriers exceeds their kinetic energy. The critical density above which the two-dimensional gas of charge carriers undergoes complete spin depolarization is determined in the Hartree-Fock approximation. It is assumed that this process can be due to a transition of the two-dimensional gas to a metallic state.     

Magnetic Effect Versus Thermal Effect on Quark Matter with a Running Coupling at Finite Densities

We investigate the quark matter in a strong magnetic field in the framework of SU(2) NJL model with a magnetic-field-dependent coupling. The spin polarization, the entropy per baryon, and the energy are studied by analyzing the competition of the magnetic effect and the thermal effect. The stronger magnetic field can enhance the spin polarization, arrange quarks in a uniform spin orientation, and change the energy per baryon drastically. However,it can hardly affect the entropy per baryon, which is dominated by the temperature. As the temperature increases, more quarks will be excited from the lowest Landau level up to higher Landau levels.     

Interacting dirac fermions on a topological insulator in a magnetic field

We study the fractional quantum Hall states on the surface of a topological insulator thin film in an external magnetic field, where the Dirac fermion nature of the charge carriers have been experimentally established only recently. Our studies indicate that the fractional quantum Hall states should indeed be observable in the surface Landau levels of a topological insulator. The strength of the effect will however be different, compared to that in graphene, due to the finite thickness of the topological insulator film and due to the admixture of Landau levels of the two surfaces of the film. At a small film thickness, that mixture results in a strongly nonmonotonic dependence of the excitation gap on the film thickness. At a large enough thickness of the film, the excitation gap in the lowest two Landau levels are comparable in strength.     

Anisotropy of the electron g factor in semiconductors with cubic symmetry

The spin-orbit corrections to electronic states in bulk cubic semiconductors without the center of inversion in an ultraquantum magnetic field are investigated. It is shown that the spin-orbit interaction results in a shift of the Landau levels and the appearance of additional terms in the relationship for the electron g factor. The corrections to the g factor lead to a deviation of the macroscopic magnetization from the direction of the magnetic field, the dependence of the spin resonance frequency on the magnetic field orientation with respect to the principal crystallographic axes, and anisotropy of the spin relaxation through the D’yakonov-Perel’ mechanism.     

Strongly anisotropic electronic transport in higher Landau levels

Low-temperature, electronic transport in higher Landau levels (N>1) in a two-dimensional electron system is strongly anisotropic. At half-filling of either spin level of such Landau levels ( etc.) the magnetoresistance either collapses to form a deep minimum or is peaked in a sharp maximum, depending on the in-plane current direction. The anisotropic axis can be reoriented by applying an in-plane magnetic field of 1–2 T strength. The magnetoresistance at and (N=1) is initially isotropic but an in-plane field induces a strong anisotropy. Our observations are strong evidence for a new many-electron phase in higher Landau levels, which forms spontaneously or can be induced by an in-plane field.     

Electron on a cylinder with topological defects in a homogeneous magnetic field

In this work we study the effects of the geometry and topology of a cylinder on the energy levels of an electron moving in a homogeneous magnetic field. We consider the existence of topological defects as a screw dislocation and a disclination. When we take the region of movement as the full cylindrical surface, we find that, by increasing the strength of the screw dislocation, the dispersion on the electronic energy levels is affected and monotonically increasing. For an electron moving in an almost flat region we show that the dispersion on the Landau levels decrease monotonically as we increase the strength of the screw dislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely given by the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as we change the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitude of such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit of an infinite cylinder radius.     

The Kapitza Effect in Charge-Ordered Layered Crystals

It is shown that the Kapitza effect in charge-ordered layered crystals can be explained for the case of a parallelism of magnetic field and measuring current when the Landau quantization and its effect on the charge-carrier scattering are considered. There is a linear correlation between the magnetic field and longitudinal resistance under the assumption that the scattering of charge carriers by acoustic phonons is dominant, and the band-to-band transitions are suppressed. The relations for the Kapitza coefficient are derived for different degrees of electron gas degeneracy and different values of interaction resulting in layered charge ordering.     

Spontaneously gapped ground state in suspended bilayer graphene

Bilayer graphene bears an eightfold degeneracy due to spin, valley, and layer symmetry, allowing for a wealth of broken symmetry states induced by magnetic or electric fields, by strain, or even spontaneously by interaction. We study the electrical transport in clean current annealed suspended bilayer graphene. We find two kinds of devices. In bilayers of type B1 the eightfold zero-energy Landau level is partially lifted above a threshold field revealing an insulating ν=0 quantum-Hall state at the charge neutrality point. In bilayers of type B2 the Landau level lifting is full and a gap appears in the differential conductance even at zero magnetic field, suggesting an insulating spontaneously broken symmetry state. Unlike B1, the minimum conductance in B2 is not exponentially suppressed, but remains finite with a value G is < or approximately equall to e(2)/h even in a large magnetic field. We suggest that this phase of B2 is insulating in the bulk and bound by compressible edge states.     

Excitation of the spin density and current by coherent light pulses in quantum wells

We study the orbital and spin dynamics of charge carriers induced by non-overlapping linearly polarized light pulses in semiconductor quantum wells. It is shown that such an optical excitation with coherent pulses leads to a spin orientation of photocarriers and an electric current. The effects are caused by the interference of optical transitions driven by individual pulses. The distribution of carriers in the spin and momentum spaces depends on the crystallographic orientation of quantum wells and can be efficiently controlled by the pulse polarizations, time delay and phase shift between the pulses, as well as an external magnetic field.     

Spin-polarized transport and submillimetric microwave spectroscopy of solids

The problem of spin transport (spin transfer and localization in space by charge carriers) is considered from the standpoint of implementing this phenomenon in microelectronic devices based on novel physical principles. Experimental data are presented to confirm the possibility of creating extremely-high-frequency solid state microelectronic devices, operating in the millimetric and submillimetric wavelength range, which can be used as the main elements for spin informatics. These devices can be based on ferromagnetic semiconductor-nonmagnetic semiconductor junctions, the output parameters of which are controlled both by the transport current and by an external magnetic field.     

Evidence for Anderson localisation in Landau level tails from the analysis of two-dimensional Shubnikov—de Haas conductivity minima

The amplitudes of the Shubnikov—de Haas conductivity minima are analysed for n-type inversion layers in Si 〈100〉 MOS devices. Thermal excitation between adjacent Landau levels, conduction through extended tail states and activated conduction from localised tail states are all detected in different magnetic field and temperature ranges. The minimum metallic conductivity found for the lowest spin extremum agrees well with theory but the values for higher Landau levels are lower than expected.     

Landau-level splitting in graphene in high magnetic fields

The quantum Hall (QH) effect in two-dimensional electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors nu = 0, +/-1, +/-4 are discovered at magnetic fields B > 20 T, indicating the lifting of the fourfold degeneracy of the previously observed QH states at nu = +/-4(absolute value(n) + 1/2), where n is the Landau-level index. In particular, the presence of the nu = 0, +/-1 QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effect at nu = +/-4 is investigated in a tilted magnetic field and can be attributed to lifting of the spin degeneracy of the n = 1 Landau level.     

Equilibrium spin currents: non-Abelian gauge invariance and color diamagnetism in condensed matter

The spin-orbit (SO) interaction acts on electrons in condensed matter as an effective non-Abelian field. I show that a magnetic component of this field inevitably generates diamagnetic color currents which are just the equilibrium spin currents discussed in a condensed matter context. Since the non-Abelian magnetic field generated by SO coupling is generically nonzero, the equilibrium spin currents are universally present in any physical system, e.g., in molecules or solids with SO interaction. These universal spin currents provide an explicit realization of a non-Abelian Landau diamagnetism.