Felix von Oppen

Helical Liquids and Majorana Bound States in Quantum Wires

We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical electron liquid in single-channel quantum wires, with spin and velocity perfectly correlated. We argue that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional s-wave superconductor. This occurs when the external magnetic field, the superconducting gap, or, most simply, the chemical potential vary along the wire. These Majorana states do not require the presence of a vortex in the system. Experimental consequences of the helical liquid and the Majorana states are also discussed.

Franck-condon blockade and giant fano factors in transport through single molecules

We show that Franck-Condon physics leads to a significant current suppression at low bias voltages (termed Franck-Condon blockade) in transport through single molecules with strong coupling between electronic and vibrational degrees of freedom. Transport in this regime is characterized by remarkably large Fano factors (10(2)-10(3) for realistic parameters), which arise due to avalanchelike transport of electrons. Avalanches occur in a self-similar manner over a wide range of time scales, leading to power-law dependences of the current noise on frequency and vibrational relaxation rate.

Franck–Condon blockade in suspended carbon nanotube quantum dots

Understanding the influence of vibrational motion of the atoms on electronic transitions in molecules constitutes a cornerstone of quantum physics, as epitomized by the Franck–Condon principle1, 2 of spectroscopy. Recent advances in building molecular-electronics devices3 and nanoelectromechanical systems4 open a new arena for studying the interaction between mechanical and electronic degrees of freedom in transport at the single-molecule level. The tunnelling of electrons through molecules or suspended quantum dots5, 6 has been shown to excite vibrational modes, or vibrons6, 7, 8, 9. Beyond this effect, theory predicts that strong electron–vibron coupling strongly suppresses the current flow at low biases, a collective behaviour known as Franck–Condon blockade10, 11. Here, we show measurements on quantum dots formed in suspended single-wall carbon nanotubes revealing a remarkably large electron–vibron coupling that, owing to the high quality and unprecedented tunability of our samples, allow a quantitative analysis of vibron-mediated electronic transport in the regime of strong electron–vibron coupling. This enables us to unambiguously demonstrate the Franck–Condon blockade in a suspended nanostructure. The large observed electron–vibron coupling could ultimately be a key ingredient for the detection of quantized mechanical motion12, 13. It also emphasizes the unique potential for nanoelectromechanical device applications based on suspended graphene sheets and carbon nanotubes.

Flexural Phonons in Free-Standing Graphene

Rotation and reflection symmetries impose that out-of-plane (flexural) phonons of freestanding graphene membranes have a quadratic dispersion at long wavelength and can be excited by charge carriers in pairs only. As a result, we find that flexural phonons dominate the phonon contribution to the resistivity rho below a crossover temperature T(x) where we obtain an anomalous temperature dependence rho proportional, variantT(5/2)lnT. The logarithmic factor arises from renormalizations of the flexural-phonon dispersion due to coupling between bending and stretching degrees of freedom of the membrane.

Thermopower of single-molecule devices

We investigate the thermopower of single molecules weakly coupled to metallic leads. We model the molecule in terms of the relevant electronic orbitals coupled to phonons corresponding to both internal vibrations and to oscillations of the molecule as a whole. The thermopower is computed by means of rate equations including both sequential-tunneling and cotunneling processes. Under certain conditions, the thermopower allows one to access the electronic and phononic excitation spectrum of the molecule in a linear-response measurement. In particular, we find that the phonon features are more pronounced for weak lead-molecule coupling. This way of measuring the excitation spectrum is less invasive than the more conventional currentvoltage characteristic, which, by contrast, probes the system far from equilibrium.

Theory of the Franck-Condon blockade regime

Strong coupling of electronic and vibrational degrees of freedom entails a low-bias suppression of the current through single-molecule devices, termed the Franck-Condon blockade. In the limit of slow vibrational relaxation, transport in the Franck-Condon-blockade regime proceeds via avalanches of large numbers of electrons, which are interrupted by long waiting times without electron transfer. The avalanches consist of smaller avalanches, leading to a self-similar hierarchy which terminates once the number of transferred electrons per avalanche becomes of the order of unity. Experimental signatures of self-similar avalanche transport are strongly enhanced current (shot) noise, as expressed by giant Fano factors, and a power-law noise spectrum. We develop a theory of the Franck-Condon-blockade regime with particular emphasis on the effects of electron cotunneling through highly excited vibrational states. As opposed to the exponential suppression of sequential tunneling rates for low-lying vibrational states, cotunneling rates suffer only a power-law suppression. This leads to a regime where cotunneling dominates the current for any gate voltage. Including cotunneling within a rate-equation approach to transport, we find that both the Franck-Condon blockade and self-similar avalanche transport remain intact in this regime. We predict that cotunneling leads to absorption-induced vibrational sidebands in the Coulomb-blockaded regime as well as intrinsic telegraph noise near the charge degeneracy point.

Topological superconducting phase in helical Shiba chains

Recently, it has been suggested that topological superconductivity and Majorana end states can be realized in a chain of magnetic impurities on the surface of an s-wave superconductor when the magnetic moments form a spin helix as a result of the RKKY interaction mediated by the superconducting substrate. Here, we investigate this scenario theoretically by developing a tight-binding Bogoliubov-de Gennes description starting from the Shiba bound states induced by the individual magnetic impurities. While the resulting model Hamiltonian has similarities with the Kitaev model for one-dimensional spinless p-wave superconductors, there are also important differences, most notably the long-range nature of hopping and pairing as well as the complex hopping amplitudes. We use both analytical and numerical approaches to explore the consequences of these differences for the phase diagram and the localization properties of the Majorana end states when the Shiba chain is in a topological superconducting phase.

Temperature-dependent resistivity of suspended graphene

In this paper we investigate the electron-phonon contribution to the resistivity of suspended single-layer graphene. In-plane as well as flexural phonons are addressed in different temperature regimes. We focus on the intrinsic electron-phonon coupling due to the interaction of electrons with elastic deformations in the graphene membrane. The competition between screened deformation potential vs fictitious gauge-field coupling is discussed together with the role of tension in the suspended flake. In the absence of tension, flexural phonons dominate the phonon contribution to the resistivity at any temperature T with a T 5/2 and T 2 dependence at low and high temperatures, respectively. Sample-specific tension suppresses the contribution due to flexural phonons, yielding a linear temperature dependence due to in-plane modes. We compare our results with recent experiments.

Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires

It has been proposed that localized zero-energy Majorana states can be realized in a two-dimensional network of quasi-one-dimensional semiconductor wires that are proximity coupled to a bulk superconductor. The wires should have strong spin-orbit coupling with appropriate symmetry, and their electrons should be partially polarized by a strong Zeeman field. Then, if the Fermi level is in an appropriate range, the wire can be in a topological superconducting phase, with Majorana states that occur at wire ends and at Y junctions, where three topological superconductor segments may be joined. Here we generalize these ideas to consider a three-dimensional network. The positions of Majorana states can be manipulated, and their non-Abelian properties made visible, by using external gates to selectively deplete portions of the network or by physically connecting and redividing wire segments. Majorana states can also be manipulated by reorientations of the Zeeman field on a wire segment, by physically rotating the wire about almost any axis, or by evolution of the phase of the order parameter in the proximity-coupled superconductor. We show how to keep track of sign changes in the zero-energy Hilbert space during adiabatic manipulations by monitoring the evolution of each Majorana state separately, rather than keeping track of the braiding of all possible pairs. This has conceptual advantages in the case of a three-dimensional network, and may be computationally useful even in two dimensions, if large numbers of Majorana sites are involved.

Current-induced forces in mesoscopic systems: A scattering-matrix approach.

Summary Nanoelectromechanical systems are characterized by an intimate connection between electronic and mechanical degrees of freedom. Due to the nanoscopic scale, current flowing through the system noticeably impacts upons the vibrational dynamics of the device, complementing the effect of the vibrational modes on the electronic dynamics. We employ the scattering-matrix approach to quantum transport in order to develop a unified theory of nanoelectromechanical systems out of equilibrium. For a slow mechanical mode the current can be obtained from the Landauer–Büttiker formula in the strictly adiabatic limit. The leading correction to the adiabatic limit reduces to Brouwer’s formula for the current of a quantum pump in the absence of a bias voltage. The principal results of the present paper are the scattering-matrix expressions for the current-induced forces acting on the mechanical degrees of freedom. These forces control the Langevin dynamics of the mechanical modes. Specifically, we derive expressions for the (typically nonconservative) mean force, for the (possibly negative) damping force, an effective “Lorentz” force that exists even for time-reversal-invariant systems, and the fluctuating Langevin force originating from Nyquist and shot noise of the current flow. We apply our general formalism to several simple models that illustrate the peculiar nature of the current-induced forces. Specifically, we find that in out-of-equilibrium situations the current-induced forces can destabilize the mechanical vibrations and cause limit-cycle dynamics.