Bernd Braunecker

Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase.

We study a one-dimensional interacting electronic liquid coupled to a 1D array of classical magnetic moments and to a superconductor. We show that at low energy and temperature the magnetic moments and the electrons become strongly entangled and that a magnetic spiral structure emerges. For strong enough coupling between the electrons and magnetic moments, the 1D electronic liquid is driven into a topological superconducting phase supporting Majorana fermions without any fine-tuning of external parameters. Our analysis applies at low enough temperature to a quantum wire in proximity to a superconductor when the hyperfine interaction between electrons and nuclear spins is taken into account, or to a chain of magnetic adatoms adsorbed on a superconducting surface.

Majorana edge states in interacting one-dimensional systems.

We show that one-dimensional electron systems in the proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime in which the Majorana edge states persist. We present strategies of how this regime can be reached.

Majorana single-charge transistor

We study transport through a Coulomb blockaded topologically nontrivial superconducting wire (with Majorana end states) contacted by metallic leads. An exact formula for the current through this interacting Majorana single-charge transistor is derived in terms of wire spectral functions. A comprehensive picture follows from three different approaches. We find Coulomb oscillations with universal halving of the finite-temperature peak conductance under strong blockade conditions, where the valley conductance mainly comes from elastic cotunneling. The nonlinear conductance exhibits finite-voltage sidebands due to anomalous tunneling involving Cooper pair splitting.

Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction

Interacting one-dimensional conductors with Rashba spin-orbit coupling are shown to exhibit a spin-selective Peierls-type transition into a mixed spin-charge-density-wave state. The transition leads to a gap for one-half of the conducting modes, which is strongly enhanced by electron-electron interactions. The other half of the modes remains in a strongly renormalized gapless state and conducts opposite spins in opposite directions, thus providing a perfect spin filter. The transition is driven by magnetic field and by spin-orbit interactions. As an example we show for semiconducting quantum wires and carbon nanotubes that the gap induced by weak magnetic fields or intrinsic spin-orbit interactions can get renormalized by 1 order of magnitude up to 10\char21{}30 K.

Entanglement Detection from Conductance Measurements in Carbon Nanotube Cooper Pair Splitters

Spin-orbit interaction provides a spin filtering effect in carbon nanotube based Cooper pair splitters that allows us to determine spin correlators directly from current measurements. The spin filtering axes are tunable by a global external magnetic field. By a bending of the nanotube, the filtering axes on both sides of the Cooper pair splitter become sufficiently different that a test of entanglement of the injected Cooper pairs through a Bell-like inequality can be implemented. This implementation does not require noise measurements, supports imperfect splitting efficiency and disorder, and does not demand a full knowledge of the spin-orbit strength. Using a microscopic calculation we demonstrate that entanglement detection by violation of the Bell-like inequality is within the reach of current experimental setups.

Carbon nanotubes in electric and magnetic fields

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.

Nuclear magnetism and electronic order in 13C nanotubes.

Single wall carbon nanotubes grown entirely from 13C form an ideal system to study the effect of electron interaction on nuclear magnetism in one dimension. If the electrons are in the metallic, Luttinger liquid regime, we show that even a very weak hyperfine coupling to the 13C nuclear spins has a striking effect: The system is driven into an ordered phase, which combines electron and nuclear degrees of freedom, and which persists up into the millikelvin range. In this phase the conductance is reduced by a universal factor of 2, allowing for detection by standard transport experiments.

Nuclear magnetism and electron order in interacting one-dimensional conductors

The interaction between localized magnetic moments and the electrons of a one-dimensional conductor can lead to an ordered phase in which the magnetic moments and the electrons are tightly bound to each other. We show here that this occurs when a lattice of nuclear spins is embedded in a Luttinger liquid. Experimentally available examples of such a system are single wall carbon nanotubes grown entirely from C-13 and GaAs-based quantum wires. In these systems the hyperfine interaction between the nuclear spin and the conduction electron spin is very weak; yet it triggers a strong feedback reaction that results in an ordered phase consisting of a nuclear helimagnet that is inseparably bound to an electronic density wave combining charge and spin degrees of freedom. This effect can be interpreted as a strong renormalization of the nuclear Overhauser field and is a unique signature of Luttinger liquid physics. Through the feedback the order persists up into the millikelvin range. A particular signature is the reduction in the electric conductance by the universal factor of 2.

Magnetic ordering of nuclear spins in an interacting two-dimensional electron gas

We investigate the magnetic behavior of nuclear spins embedded in a two-dimensional (2D) interacting electron gas using a Kondo lattice model description. We derive an effective magnetic Hamiltonian for the nuclear spins, which is of the Rudermann-Kittel-Kasuya-Yosida type and where the interactions between the nuclear spins are strongly modified by the electron-electron interactions. We show that the nuclear magnetic ordering at finite temperature relies on the (anomalous) behavior of the 2D static electron spin susceptibility and thus provides a connection between low-dimensional magnetism and nonanalyticities in interacting 2D electron systems. Using various perturbative and nonperturbative approximation schemes in order to establish the general shape of the electron spin susceptibility as a function of its wave vector, we show that the nuclear spins locally order ferromagnetically and that this ordering can become global in certain regimes of interest. We demonstrate that the associated Curie temperature for the nuclear system increases with the electron-electron interactions up to the millikelvin range.

Helical modes in carbon nanotubes generated by strong electric fields.

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.