Electronic states at the ends of a narrow armchair nanoribbon give rise to a pair of non-locally entangled spins. We propose two experiments to probe these magnetic states, based on magnetometry and tunneling spectroscopy, in which correlation effect
s lead to a striking, nonlinear response to external magnetic fields. On the basis of low-energy theories that we derive here, it is remarkably simple to assess these nonlinear signatures for magnetic edge states. The effective theories are especially suitable in parameter regimes where other methods such as quantum Monte-Carlo simulations are exceedingly difficult due to exponentially small energy scales. The armchair ribbon setup discussed here provides a promisingly well-controlled (both experimentally and theoretically) environment for studying the principles behind edge magnetism in graphene-based nano-structures.
We describe a method for deriving effective low-energy theories of electronic interactions at graphene edges. Our method is applicable to general edges of honeycomb lattices (zigzag, chiral, and even disordered) as long as localized low-energy states
(edge states) are present. The central characteristic of the effective theories is a dramatically reduced number of degrees of freedom. As a consequence, the solution of the effective theory by exact diagonalization is feasible for reasonably large ribbon sizes. The quality of the involved approximations is critically assessed by comparing the correlation functions obtained from the effective theory with numerically exact quantum Monte-Carlo calculations. We discuss effective theories of two levels: a relatively complicated fermionic edge state theory and a further reduced Heisenberg spin model. The latter theory paves the way to an efficient description of the magnetic features in long and structurally disordered graphene edges beyond the mean-field approximation.
A bosonic field theory is derived for the tunable edge magnetism at graphene zigzag edges. The derivation starts from an effective fermionic theory for the interacting graphene edge states, derived previously from a two-dimensional interacting tight-
binding model for graphene. The essential feature of this effective model, which gives rise to the weak edge magnetism, is the momentum-dependent non-local electron-electron interaction. It is shown that this momentum-dependence may be treated by an extension of the bosonization technique, and leads to interactions of the bosonic fields. These interactions are reminiscent of a phi^4 field theory. Focussing onto the regime close to the quantum phase transition between the ferromagnetic and the paramagnetic Luttinger liquid, a semiclassical interpretation of the interacting bosonic theory is given. Furthermore, it is argued that the universal critical behavior at the quantum phase transition between the paramagnetic and the ferromagnetic Luttinger liquid is governed by a small number of terms in this theory, which are accessible by quantum Monte-Carlo methods.
The criteria for strong correlations on surfaces of three-dimensional topological insulators are discussed. Usually, the Coulomb repulsion at such surfaces is too weak for driving a phase transition to a strongly correlated regime. I discuss a mechan
ism and possibilities of its experimental implementation by which the strength of the Coulomb interaction can be tuned over a wide range. In the strongly interacting regime, the surface states are gapped, even though the topological classification of the bulk band structure predicts gapless surface states.
We propose and study a realistic model for the decoherence of topological qubits, based on Majorana fermions in one-dimensional topological superconductors. The source of decoherence is the fluctuating charge on a capacitively coupled gate, modeled b
y non-interacting electrons. In this context, we clarify the role of quantum fluctuations and thermal fluctuations and find that quantum fluctuations do not lead to decoherence, while thermal fluctuations do. We explicitly calculate decay times due to thermal noise and give conditions for the gap size in the topological superconductor and the gate temperature. Based on this result, we provide simple rules for gate geometries and materials optimized for reducing the negative effect of thermal charge fluctuations on the gate.
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 Co
ulomb 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 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 lat
tice, 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 interfaces between graphene and graphane. If the interface is oriented along a zigzag direction, edge states are found which exhibit a strong amplification of effects related to the spin-orbit interaction. The enhanced spin splitting of the
edge states allows a conversion between valley polarization and spin polarization 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 is 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.
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 Parisis RSB, which surprisingly creates critical phenomena in the low temperature limit despite the absence of a standard phase transition.
