Eros Mariani

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.

Dirac-like plasmons in honeycomb lattices of metallic nanoparticles.

We consider a two-dimensional honeycomb lattice of metallic nanoparticles, each supporting a localized surface plasmon, and study the quantum properties of the collective plasmons resulting from the near-field dipolar interaction between the nanoparticles. We analytically investigate the dispersion, the effective Hamiltonian, and the eigenstates of the collective plasmons for an arbitrary orientation of the individual dipole moments. When the polarization points close to the normal to the plane, the spectrum presents Dirac cones, similar to those present in the electronic band structure of graphene. We derive the effective Dirac Hamiltonian for the collective plasmons and show that the corresponding spinor eigenstates represent Dirac-like massless bosonic excitations that present similar effects to electrons in graphene, such as a nontrivial Berry phase and the absence of backscattering off smooth inhomogeneities. We further discuss how one can manipulate the Dirac points in the Brillouin zone and open a gap in the collective plasmon dispersion by modifying the polarization of the localized surface plasmons, paving the way for a fully tunable plasmonic analogue of graphene.

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.

Synthetic electric fields and phonon damping in carbon nanotubes and graphene

Within the Dirac theory of the electronic properties of graphene, smoothly varying lattice strain affects the Dirac carriers through a synthetic gauge field. For static lattice strain, the gauge field induces a synthetic magnetic field which is known to suppress weak localization corrections by a dynamical breaking of time-reversal symmetry. When the lattice strain is time dependent, as in connection with phononic excitations, the gauge field becomes time dependent and the synthetic vector potential is also associated with an electric field. In this paper, we show that this synthetic electric field has observable consequences. We find that the Joule heating associated with the currents driven by the synthetic electric field dominates the intrinsic damping, caused by the electron-phonon interaction, of many acoustic phonon modes of graphene and metallic carbon nanotubes when including the effects of disorder and Coulomb interactions. Several important consequences follow from the observation that by time-reversal symmetry, the synthetic electric field associated with the vector potential has opposite signs for the two valleys. First, this implies that the synthetic electric field drives charge-neutral valley currents and is therefore unaffected by screening. This frequently makes the effects of the synthetic vector potential more relevant than a competing effect of the scalar deformation potential which has a much larger bare coupling constant. Second, valley currents decay by electron-electron scattering (valley Coulomb drag) which causes interesting temperature dependence of the damping rates. While our theory pertains first and foremost to metallic systems such as doped graphene and metallic carbon nanotubes, the underlying mechanisms should also be relevant for semiconducting carbon nanotubes when they are doped.

Asymmetric Franck-Condon factors in suspended carbon nanotube quantum dots

Electronic states and vibrons in carbon nanotube quantum dots have in general different location and size. As a consequence, the conventional Anderson-Holstein model, coupling vibrons to the dot total charge only, may no longer be appropriated in general. Here we explicitly address the role of the spatial fluctuations of the electronic density, yielding space-dependent Franck-Condon factors. We discuss the consequent marked effects on transport which are compatible with recent measurements. This picture can be relevant for tunneling experiments in generic nano-electromechanical systems.

Zero-bias anomaly in the tunneling density of states of graphene

In the vicinity of the Fermi energy, the band structure of graphene is well described by a Dirac equation. Impurities will generally induce both a scalar potential as well as a (fictitious) gauge field acting on the Dirac fermions. We show that the angular dependence of the zero-bias anomaly in the spatially resolved tunneling density of states around a particular impurity allows one to distinguish between these two contributions. Our predictions can be tested in scanning-tunneling-microscopy measurements on graphene.

Fictitious gauge fields in bilayer graphene

We discuss the effect of elastic deformations on the electronic properties of bilayer graphene membranes. Distortions of the lattice translate into fictitious gauge fields in the electronic Dirac Hamiltonian which are explicitly derived here for arbitrary elastic deformations. We include gauge fields associated to intra- as well as inter-layer hopping terms and discuss their effects in different contexts. As a first application, we use the gauge fields in order to study the recently predicted strain-induced Lifshitz transition for the Fermi surface at low energy. As a second application, we discuss the electron-phonon coupling induced by the fictitious gauge fields and analyse its contribution to the electrical resistivity of suspended bilayer membranes. Of special interest is the appearance of a linear coupling for flexural modes, in stark contrast to the case of monolayer graphene. This new coupling channel is shown to dominate the temperature-dependent resistivity in suspended samples with low tension.

Discontinuous Euler instability in nanoelectromechanical systems

We investigate nanoelectromechanical systems near mechanical instabilities. We show that, quite generally, the interaction between the electronic and the vibronic degrees of freedom can be accounted for essentially exactly when the instability is continuous. We apply our general framework to the Euler buckling instability and find that the interaction between electronic and vibronic degrees of freedom qualitatively affects the mechanical instability, turning it into a discontinuous one in close analogy with tricritical points in the Landau theory of phase transitions.

Tight-Binding Approach to Strain and Curvature in Monolayer Transition-Metal Dichalcogenides

We thank V. Zolyomi for sharing density functional theory data with us and A. Kormanyos for fruitful discussions. AJP and GB acknowledge funding from DFG under the program SFB 767 and the EU through Marie Curie ITN S3NANO. EM acknowledges the financial support of the Royal Society (International Exchange Grant No. IE140367) and of the Leverhulme Trust (Research Project Grant RPG-2015-101).