Hysteresis effect due to the exchange Coulomb interaction in short-period superlattices in tilted magnetic fields

We calculate the ground-state of a two-dimensional electron gas in a short-period lateral potential in magnetic field, with the Coulomb electron-electron interaction included in the Hartree-Fock approximation. For a sufficiently short period the dominant Coulomb effects are determined by the exchange interaction. We find numerical solutions of the self-consistent equations that have hysteresis properties when the magnetic field is tilted and increased, such that the perpendicular component is always constant. This behavior is a result of the interplay of the exchange interaction with the energy dispersion and the spin splitting. We suggest that hysteresis effects of this type could be observable in magneto-transport and magnetization experiments on quantum-wire and quantum-dot superlattices.Comment: 3 pages, 3 figures, Revtex, to appear in Phys. Rev.

Aetiological process of idiopathic scoliosis: from a normal growing spine into a complex 3D spinal deformity

In more than a century of dedicated research into its aetio-pathogenesis, many attempts have been made to understand the exact cause of idiopathic scoliosis. In the literature, the number of causal theories is overwhelming and the aetiology of adolescent idiopathic scoliosis (AIS) is regarded as ‘multi-factorial’. This overview focusses on recent studies that describe the changes from a normal spinal anatomy into the complex three-dimensional deformation and support the hypothesis that several paediatric deformities are a consequence of the unique way the human spine is biomechanically loaded. This has nothing to do with bipedalism, but with the way gravity and muscle tone translate to the unique sagittal shape of the spine, with its pelvic and lumbar lordosis, and the possibility to simultaneously extend the hips and knees. This leads to three rather than two forces acting continuously on the spine axial, anterior and posterior shear. An excess of anterior shear can result in spondylolisthesis and an excess of axial loading can cause osteochondrotic lesions. Unique for human are posterior shear forces, an excess of these result in decreased rotational stiffness of the involved vertebral segments. Certain sagittal spinal profiles, especially in girls around the pubertal growth spurt, predispose for development of a rotational deformity, as is idiopathic scoliosis. Once the growing spine decompensates into an idiopathic scoliosis, it will follow the right-sided rotational pattern that is already present in the non-scoliotic adolescent spine. The rotational deformation ultimately leads to rotatory lordosis around the apices of the curvatures and has major impact on lung function and quality of life

Surgical management of early-onset scoliosis: indications and currently available techniques

Early-onset scoliosis (EOS) is a heterogeneous group of spinal deformities affecting children under the age of 10 years of which the aetiology, natural history and treatment options vary considerably. In progressive EOS, treatment is based on exhausting conservative measures (casting or bracing) to halt curve progression while allowing for continuous growth of the spine and chest development. Early spinal fusion leads to loss of longitudinal spinal growth and restriction of cardiopulmonary function. In rapidly progressive curves that have failed conservative treatment a range of ‘growth-friendly’ surgical techniques have been developed to control curve deterioration. The indications and characteristics of distraction-based or compression-based methods, growth guidance and promising new techniques are discussed according to aetiology of EOS. Definitive spinal fusion remains reserved for patients ideally towards the end of their spinal growth and for short-segment treatment in congenital scoliosis

Magnetization in short-period mesoscopic electron systems

We calculate the magnetization of the two-dimensional electron gas in a short-period lateral superlattice, with the Coulomb interaction included in Hartree and Hartree-Fock approximations. We compare the results for a finite, mesoscopic system modulated by a periodic potential, with the results for the infinite periodic system. In addition to the expected strong exchange effects, the size of the system, the type and the strength of the lateral modulation leave their fingerprints on the magnetization.Comment: RevTeX4, 10 pages with 14 included postscript figures To be published in PRB. Replaced to repair figure

Metal-insulator transitions in cyclotron resonance of periodic nanostructures due to avoided band crossings

A recently found metal-insulator transition in a model for cyclotron resonance in a two-dimensional periodic potential is investigated by means of spectral properties of the time evolution operator. The previously found dynamical signatures of the transition are explained in terms of avoided band crossings due to the change of the external electric field. The occurrence of a cross-like transport is predicted and numerically confirmed

Duality Relation among Periodic Potential Problems in the Lowest Landau Level

Using a momentum representation of a magnetic von Neumann lattice, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic short-range potential problems in the lowest Landau level.We find that the energy spectra satisfy a duality relation between a period of the potential and a magnetic length. The energy spectra consist of the Hofstadter-type bands and flat bands. We also study the connection between a periodic short-range potential problem and a tight-binding model.Comment: 6 pages, 3 figures, final version to appear in PR

Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?

We find that a 2D periodic potential with different modulation amplitudes in x- and y-direction and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization in the direction of weaker modulation. In the experimentally accessible regime we relate this new quantum transport phenomenon to avoided band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea

Hall conductance of Bloch electrons in a magnetic field

We study the energy spectrum and the quantized Hall conductance of electrons in a two-dimensional periodic potential with perpendicular magnetic field WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak Landau band coupling significant changes in the Hall conductance compared to the one-band approximation of Hofstadter's butterfly are found. The principal deviations are the rearrangement of subbands and unexpected subband contributions to the Hall conductance.Comment: to appear in PRB; Revtex, 9 pages, 5 postscript figures; figures with better resolution may be obtained from http://www.chaos.gwdg.d

Azbel-Hofstadter model on triangular lattice revisited

In the present paper, the mean of Lyapunov exponents for the Azbel-Hofstadter model on the triangular lattice is calculated. It is recently proposed that [Phys. Rev. Lett. {\bf 85}, 4920 (2000)], for the case of the square lattice, this quantity can be related to the logarithm of the partition function of the two dimensional Ising model and has a connection to the asymptotic bandwidth. We find that the correspondence of this quantity to the logarithm of the partition function of the two dimensional Ising model is not complete for the triangular lattice. Moreover, the detailed connection between this quantity and the asymptotic bandwidth is not valid. Thus the conclusions for the mean of Lyapunov exponents suggested previously depend on the lattice geometry.Comment: RevTeX, 4 page, no figur