Matthias Droth

Acoustic phonons and spin relaxation in graphene nanoribbons

Phonons are responsible for limiting both the electron mobility and the spin relaxation time in solids and provide a mechanism for thermal transport. In view of a possible transistor function as well as spintronics applications in graphene nanoribbons, we present a theoretical study of acoustic phonons in these nanostructures. Using a two-dimensional continuum model which takes into account the monatomic thickness of graphene, we derive Hermitian wave equations and infer phonon creation and annihilation operators. We elaborate on two types of boundary configuration, which we believe can be realized in experiment: (i) fixed and (ii) free boundaries. The former leads to a gapped phonon dispersion relation, which is beneficial for high electron mobilites and long spin lifetimes. The latter exhibits an ungapped dispersion and a finite sound velocity of out-of-plane modes at the center of the Brillouin zone. In the limit of negligible boundary effects, bulk-like behavior is restored. We also discuss the deformation potential, which in some cases gives the dominant contribution to the spin relaxation rate T_1^{-1}.

Piezoelectricity in planar boron nitride via a geometric phase

Due to their low surface mass density, two-dimensional materials with a strong piezoelectric response are interesting for nanoelectromechanical systems with high force sensitivity. Unlike graphene, the two sublattices in a monolayer of hexagonal boron nitride (hBN) are occupied by different elements, which breaks inversion symmetry and allows for piezoelectricity. This has been confirmed with density functional theory calculations of the piezoelectric constant of hBN. Here, we formulate an entirely analytical derivation of the electronic contribution to the piezoelectric response in this system based on the concepts of strain-induced pseudomagnetic vector potential and the modern theory of polarization that relates the polar moment to the Berry curvature. Our findings agree with the symmetry restrictions expected for the hBN lattice and reproduce well the magnitude of the piezoelectric effect previously obtained ab initio.

Electron spin relaxation in graphene nanoribbon quantum dots

Graphene is promising as a host material for electron spin qubits because of its predicted potential for long coherence times. In armchair graphene nanoribbons (aGNRs) a small bandgap is opened, allowing for electrically gated quantum dots, and furthermore the valley degeneracy is lifted. The spin lifetime T_1 is limited by spin relaxation, where the Zeeman energy is absorbed by lattice vibrations, mediated by spin-orbit and electron-phonon coupling. We have calculated T_1 by treating all couplings analytically and find that T_1 can be in the range of seconds for several reasons: (i) low phonon density of states away from Van Hove singularities; (ii) destructive interference between two relaxation mechanisms; (iii) Van Vleck cancellation at low magnetic fields; (iv) vanishing coupling to out-of-plane modes in lowest order due to the electronic structure of aGNRs. Owing to the vanishing nuclear spin of 12C, T_1 may be a good measure for overall coherence. These results and recent advances in the controlled production of graphene nanoribbons make this system interesting for spintronics applications.

Spintronics with graphene quantum dots

Thanks to its intrinsic ability to preserve spin coherence, graphene is a prime material for spintronics. In this review article, we summarize recent achievements related to spintronics in graphene quantum dots and motivate this field from a spintronics and a materials science point of view. We focus on theory but also discuss recent experiments. The main sources of spin decoherence are interactions with lattice excitations and the hyperfine interaction with present nuclear spins. We explain effective spin-phonon coupling in detail and present a generic power law for the spin relaxation time T1 as a function of the magnetic field. For specific cases, we discuss spin relaxation in detail. The Heisenberg exchange interaction is paramount for coherent spin qubit operation and addressed in the context of magnetism in graphene nanoflakes. Nuclear spins in the host and surrounding material can be considered by several means and the influence of C nuclei has been studied in detail. Impressive advances in general spintronics and the fabrication of graphene devices are likely to spark significant advances in spintronics with graphene quantum dots in the near future.

Electron-electron attraction in an engineered electromechanical system

Two electrons in a quantum dot repel each other: their interaction can be characterized by a positive interaction energy. From the theory of superconductivity, we also know that mechanical vibrations of the crystal lattice can make the electron-electron interaction attractive. Analogously, if a quantum dot interacts with a mechanical degree of freedom, the effective interaction energy can be negative; that is, the electron-electron interaction might be attractive. In this work, we propose and theoretically study an engineered electromechanical system that exhibits electron-electron attraction: a quantum dot suspended on a nonlinear mechanical resonator, tuned by a bottom and a top gate electrode. We focus on the example of a dot embedded in a suspended graphene ribbon, for which we identify conditions for electron-electron attraction. Our results suggest the possibility of electronic transport via tunneling of packets of multiple electrons in such devices, similar to that in superconducting nanostructures, but without the use of any superconducting elements.