Bernd Braunecker

We show that one-dimensional electron systems in 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 how this regime can be reached.

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.

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.

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 - 30 K.

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 ¹³C 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 of the electric conductance by the universal factor 2.

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 intothe millikelvin range. In this phase the conductance is reduced by a universal factor of 2, allowing for detection by standard transport experiments.

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.

We focus on nuclear spins embedded in a two-dimensional (2D) electron gas. The nuclear spins interact with each other through the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which is carried by the electron gas. We show that a nuclear magnetic order at finite temperature relies on the anomalous behaviour of the 2D static electron spin susceptibility due to electron-electron interactions. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. We discuss the conditions for nuclear magnetism, and show that the associated Curie temperature increases with the electron-electron interactions and may reach up into the millikelvin regime. We also shortly discussed what happens when the dimensionality is further reduced to one dimension.

The hyperfine interaction between the electron spin and the nuclear spins is one of the main sources of decoherence for spin qubits when the nuclear spins are disordered. An ordering of the latter largely suppresses this source of decoherence. Here we show that such an ordering can occur through a thermodynamic phase transition in two-dimensional (2D) Kondo-lattice type systems. We specifically focus on nuclear spins embedded in a 2D electron gas. The nuclear spins interact with each other through the RKKY interaction, which is carried by the electron gas. We show that a nuclear magnetic order at finite temperature relies on the anomalous behavior of the 2D static electron spin susceptibility due to electron-electron interactions. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. We discuss the conditions for nuclear magnetism, and show that the associated Curie temperature increases with the electron-electron interactions and may reach up into the millikelvin regime. The further reduction of dimensionality to one dimension is shortly discussed.

We consider whether nuclear spins embedded in a two-dimensional (2D) interacting electron gas can sustain some ordering at finite temperatures. We start with a Kondo lattice model description and derive an effective magnetic Hamiltonian for the nuclear spins, which is of the RKKY type. The interactions between the nuclear spins are strongly modified by 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. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. Based on various perturbative and non-perturbative approximation schemes in order to establish the general shape of the electron spin susceptibility as function of its wave vector, we show that the nuclear spins locally order ferromagnetically, and that this ordering can become global in certain samples. We also argue that the associated Curie temperature for the nuclear system increases with the electron-electron interactions up to the millikelvin range.

We analyze edge currents and edge bands at the surface of a time-reversal symmetry breaking d_x²-y² + id_xy superconductor. We show that the currents have large Friedel oscillations with two interfering frequencies: √ 2 k_F from subgap states, and 2k_F from the continuum. The results are based independently on a self-consistent slave-boson mean-field theory for the t - J model on a triangular lattice, and on a T-matrix scattering theory calculation. The shape of the edge-state band, as well as the particular frequency √ 2 k_F of the Friedel oscillations, are attributes unique for the d_x²-y² + id_xy case, and may be used as a fingerprint for its identification. Extensions to different time-reversal symmetry breaking superconductors can be achieved within the same approach.

We study a quantum quench for a semiconductor quantum dot coupled to a Fermionic reservoir, induced by the sudden creation of an exciton via optical absorption. The subsequent emergence of correlations between spin degrees of freedom of dot and reservoir, culminating in the Kondo effect, can be read off from the absorption line shape and understood in terms of the three fixed points of the singleimpurity Anderson model. At low temperatures the line shape is dominated by a power-law singularity, with an exponent that depends on gate voltage and, in a universal, symmetric fashion, on magnetic field, indicative of a tunable Anderson orthogonality catastrophe.

We provide an exact finite temperature extension to the recently developed Riemann-Hilbert approach for the calculation of response functions in nonadiabatically perturbed (multichannel) Fermi gases. We give a precise definition of the finite temperature Riemann-Hilbert problem and show that it is equivalent to a zero temperature problem. Using this equivalence, we discuss the solution of the nonequilibrium Fermi-edge singularity problem at finite temperatures.

We report exact nonperturbative results for the Fermi-edge singularity in the absorption spectrum of an out-of-equilibrium tunnel junction. We consider two metals with chemical potential difference V separated by a tunneling barrier containing a defect, which exists in one of two states. When it is in its excited state, tunneling through the otherwise impermeable barrier is possible. Our nonperturbative solution of this nonequilibrium many-body problem shows that, as well as extending below the equilibrium threshold, the line shape depends on the difference in the phase of the reflection amplitudes on the two sides of the barrier. These results have a surprisingly simple interpretation in terms of known results for the equilibrium case but with (in general complex-valued) combinations of elements of the scattering matrix replacing the equilibrium phase shifts.

We rediscuss a nonequilibrium x-ray edge problem which in recent publications led to discrepancies between the results of the perturbative and of an extended Nozières-De Dominicis approach. We show that this problem results from an uncritical separation of momenta of the scattering potential, and we propose a corrected Nozières-De Dominicis solution.

We present a didactical approach to expose the so-called which-way experiment and the counterintuitive effect of a quantum eraser for one-particle quantum interferences. The fundamental concept of entanglement plays a central role and highlights the complementarity between quantum interference and knowledge of which path was followed by the quantum particle.

We discuss a measurement-based implementation of a controlled-NOT (CNOT) quantum gate. Such a gate has recently been discussed for free electron qubits. Here we extend this scheme for qubits encoded in product states of two (or more) spins 1/2 or in equivalent systems. The key to such an extension is to find a feasible qubit-parity meter. We present a general scheme for reducing this qubit-parity meter to a local spin-parity measurement performed on two spins, one from each qubit. Two possible realizations of a multiparticle CNOT gate are further discussed: electron spins in double quantum dots in the singlet-triplet encoding, and nu=5/2 Ising non-Abelian anyons using topological quantum computation braiding operations and nontopological charge measurements.

We demonstrate that spin current can be generated by an ac voltage in a one-channel quantum wire with strong repulsive electron interactions in the presence of a nonmagnetic impurity and uniform static magnetic field. In a certain range of voltages, the spin current can exhibit a power dependence on the ac voltage bias with a negative exponent. The spin current expressed in units of ℏ/2 per second can become much larger than the charge current in units of the electron charge per second. The spin current generation requires neither spin-polarized particle injection nor time-dependent magnetic fields.

Asymmetric current-voltage [I(V)] curves, known as the diode or rectification effect, in one-dimensional electronic conductors can have their origin from scattering off a single asymmetric impurity in the system. We investigate this effect in the framework of the Tomonaga-Luttinger model for electrons with spin. We show that electron interactions strongly enhance the diode effect and lead to a pronounced current rectification even if the impurity potential is weak. For strongly interacting electrons and not too small voltages, the rectification current I_r = [I(V)+I(-V)], measuring the asymmetry in the current-voltage curve, has a power-law dependence on the voltage with a negative exponent, I_r ~ V ^-|z| , leading to a bump in the current-voltage curve.