Manuel J. Schmidt

Interaction-induced magnetism at the ends of carbon nanotubes is studied theoretically, with a special focus on magnetic anisotropies. Spin-orbit coupling, generally weak in ordinary graphene, is strongly enhanced in nanotubes. In combination with Coulomb interactions, this enhanced spin-orbit coupling gives rise to a super-spin at the ends of carbon nanotubes with an XY anisotropy on the order of 10 mK. Furthermore, it is shown that this anisotropy can be enhanced by more than one order of magnitude via a partial suppression of the super-spin.

We derive an effective low-energy theory for metallic (armchair and non-armchair) single-wall nanotubes in the presence of an electric field perpendicular to the nanotube axis, and in the presence of magnetic fields, taking into account spin-orbit interactions and screening effects on the basis of a microscopic tight binding model. The interplay between electric field and spin-orbit interaction allows us to tune armchair nanotubes into a helical conductor in both Dirac valleys. Metallic non-armchair nanotubes are gapped by the surface curvature, yet helical conduction modes can be restored in one of the valleys by a magnetic field along the nanotube axis. Furthermore, we discuss electric dipole spin resonance in carbon nanotubes, and find that the Rabi frequency shows a pronounced dependence on the momentum along the nanotube.

The tunable magnetism at graphene edges with lengths of up to 48 unit cells is analyzed by an exact diagonalization technique. For this we use a generalized interacting one-dimensional model which can be tuned continuously from a limit describing graphene zigzag edge states with a ferromagnetic phase, to a limit equivalent to a Hubbard chain, which does not allow ferromagnetism. This analysis sheds light onto the question why the edge states have a ferromagnetic ground state, while a usual one-dimensional metal does not. Essentially we find that there are two important features of edge states: (a) umklapp processes are completely forbidden for edge states; this allows a spin-polarized ground state. (b) the strong momentum dependence of the effective interaction vertex for edge states gives rise to a regime of partial spin-polarization and a second order phase transition between a standard paramagnetic Luttinger liquid and ferromagnetic Luttinger liquid.

Helical modes, conducting opposite spins in opposite directions, are shown to exist in metallic armchair nanotubes in an all-electric setup. This is a consequence of the interplay between spin-orbit interaction and strong electric fields. The helical regime can also be obtained in chiral metallic nanotubes by applying an additional magnetic field. In particular, it is possible to obtain helical modes at one of the two Dirac points only, while the other one remains gapped. Starting from a tight-binding model we derive the effective low-energy Hamiltonian and the resulting spectrum.

We study the magnetic properties of graphene edges and graphene/graphane interfaces under the influence of electrostatic gates. For this, an effective low-energy theory for the edge states, which is derived from the Hubbard model of the honeycomb lattice, is used. We first study the edge state model in a mean-field approximation for the Hubbard Hamiltonian and show that it reproduces the results of the extended 2D lattice theory. Quantum fluctuations around the mean-field theory of the effective one-dimensional model are treated by means of the bosonization technique in order to check the stability of the mean-field solution. We find that edge magnetism at graphene/graphane interfaces can be switched on and off by means of electrostatic gates. We describe a quantum phase transition between an ordinary and a ferromagnetic Luttinger liquid - a realization of itinerant one-dimensional ferromagnetism. This mechanism may provide means to experimentally discriminate between edge magnetism or disorder as the reason for a transport gap in very clean graphene nanoribbons.

We study the electronic properties of interfaces between graphene and graphane, a hydrogenated version of graphene. It is shown that these interfaces are useful for creating an effective edge for the π-electrons of graphene. If the interface is oriented along a zigzag direction, edge states are found. We consider two different interface types, corresponding to usual zigzag and bearded graphene edges. It is shown that, because of a broken symmetry, the spin-orbit interaction is strongly amplified by the graphene/graphane interface and that the edge states are particularly susceptible to this amplification. As an application, we propose a device which is capable of converting spin polarizations to valley polarizations and vice versa. Exploiting the amplification of the spin-orbit interaction, this conversion may be performed at temperatures near one Kelvin. We show that these edge states give rise to quantum spin and/or valley Hall effects.

We investigate an effective low-energy theory of HgTe quantum wells near their mass inversion thickness in a perpendicular magnetic field. By comparison of the effective band structure with a more elaborated and well-established model, the parameter regime and the validity of the effective model are scrutinized. Optical transitions in HgTe quantum wells are analyzed. We find selection rules which we functionalize to optically manipulate edge-state transport. Qualitatively, our findings equally apply to optical edge current manipulation in graphene.

A scaling theory of replica symmetry breaking (RSB) in the SK-model is presented in the framework of critical phenomena for the scaling regime of small inverse RSB-orders, small temperatures, small magnetic fields, and near opposite pseudo-dynamic limits. We employ the pseudo-dynamical picture (PRL98, 127201 (2007)) with two critical points, where separated temperature- and magnetic field-scaling is obtained. An unconventional scaling hypothesis for the free energy is given, modeling this separated scaling in accordance with detailed numerical self-consistent solutions for up to 200 orders of RSB. A divergent correlation-length describes the RSB-criticality as a long-range correlation effect occurring on the pseudo-lattice of RSB-orders. Rational-valued exponents are concluded with high precision from high-order RSB scaling and by using a new fixed point extrapolation method. Power laws, scaling relations, and scaling functions are analyzed.

We describe a novel method which allows the treatment of high orders of replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly, without a need for approximations or scaling assumptions. It yields the low temperature order function q(a,T) in the full range $0\leq a <\infty$ and is complete in the sense that all observables can be calculated from it. The behavior of some observables and the finite RSB theory itself is analyzed as one approaches continuous RSB. The validity and applicability of the traditional continuous formulation is then scrutinized and a new continuous RSB formulation is proposed.

This article reviews recent years' progress in the low temperature analysis of standard models of spin glass order such as the Sherrington-Kirkpatrick (SK) model. Applications to CdTe/CdMnTe layered systems and explanation of glassy antiferromagnetic order at lowest temperatures stimulated us to study in detail the beautifully complex physical effects of replica symmetry breaking (RSB).We discuss analytical ideas based on highly precise numerical data which lead to the construction of relatively simple effective field theories for the SK model and help to understand the mysterious features of its exact solution. The goal is to find construction principles for the theory of interplay between frustrated magnetic order and various relevant physical degrees of freedom. The emphasis in this article is on the role of Parisi's RSB, which surprisingly creates critical phenomena in the low temperature limit despite the absence of a standard phase transition.

A numerical technique is developed to solve the Luttinger-Kohn equation for impurity states directly in k-space and is applied to calculate bound hole wave functions in a ferromagnetic (Ga,Mn)As host. The rich properties of the band structure of an arbitrarily strained, ferromagnetic zinc-blende semiconductor yields various features which have direct impact on the detailed shape of a valence band hole bound to an active impurity. The role of strain is discussed on the basis of explicit calculations of bound hole states.

Numerical results up to 42nd order of replica symmetry breaking (RSB) are used to predict the singular structure of the SK spin glass at T=0. We confirm predominant single parameter scaling and derive corrections for the T=0 order function q(a), related to a Langevin equation with pseudotime 1/a. a=0 and a=\infty are shown to be two critical points for \infty-RSB, associated with two discrete spectra of Parisi block size ratios, attached to a continuous spectrum. Finite-RSB-size scaling, associated exponents, and T=0-energy are obtained with unprecedented accuracy.

We obtain control of magnetic anisotropy in epitaxial (Ga,Mn)As by anisotropic strain relaxation in patterned structures. The strain in the structures is characterized using sophisticated X-ray techniques. The magnetic anisotropy before patterning of the layer, which shows biaxial easy axes along [100] and [010], is replaced by a hard axis in the direction of large elastic strain relaxation and a uniaxial easy axis in the direction where pseudomorphic conditions are retained. This strong anisotropy can not be explained by shape anisotropy and is attributed solely to lattice strain relaxation. Upon increasing the uniaxial strain anisotropy in the (Ga,Mn)As stripes, we also observe an increase in magnetic anisotropy.

We observe the occurrence of an Efros-Shklovskii gap in (Ga,Mn)As based tunnel junctions. The occurrence of the gap is controlled by the extent of the hole wave-function on the Mn acceptor atoms. Using k.p-type calculations we show that this extent depends crucially on the direction of the magnetization in the (Ga,Mn)As (which has two almost equivalent easy axes). This implies one can reversibly tune the system into the insulating or metallic state by changing the magnetization.