Alexander Croy

Nonlinear Damping in Graphene Resonators

Based on a continuum mechanical model for single-layer graphene, we propose and analyze a microscopic mechanism for dissipation in nanoelectromechanical graphene resonators. We find that coupling between flexural modes and in-plane phonons leads to linear and nonlinear damping of out-of-plane vibrations. By tuning external parameters such as bias and ac voltages, one can cross over from a linear-to a nonlinear-damping dominated regime. We discuss the behavior of the effective quality factor in this context. DOI: 10.1103/PhysRevB.86.235435

Propagation scheme for nonequilibrium dynamics of electron transport in nanoscale devices

A closed set of coupled equations of motion for the description of time-dependent electron transport is derived. It provides the time evolution of energy-resolved quantities constructed from nonequilibrium Greens functions. By means of an auxiliary-mode expansion a viable propagation scheme for finite temperatures is obtained, which allows to study arbitrary time dependences and structured reservoirs. Two illustrative examples are presented.

Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators

We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficients as functions of the radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings.

Fermi-Pasta-Ulam Physics with Nanomechanical Graphene Resonators: Intrinsic Relaxation and Thermalization from Flexural Mode Coupling

Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta, and Ulam. Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for Fermi-Pasta-Ulam physics. We find the thermalization rate Γ to be independent of radius and scaling as Γ∼T*/εpre2, where T* and εpre are effective resonator temperature and prestrain.

Strain–displacement relations for strain engineering in single-layer 2d materials

We investigate the electromechanical coupling in single-layer 2d materials. For non-Bravais lattices, we find important corrections to the standard macroscopic strain-microscopic atomic-displacement theory. We put forward a general and systematic approach to calculate strain-displacement relations for several classes of 2d materials. We apply our findings to graphene as a study case, by combining a tight binding and a valence force-field model to calculate electronic and mechanical properties of graphene nanoribbons under strain. The results show good agreement with the predictions of the Dirac equation coupled to continuum mechanics. For this long wave-limit effective theory, we find that the strain-displacement relations lead to a renormalization correction to the strain-induced pseudo-magnetic fields. A similar renormalization is found for the strain-induced band-gap of black phosphorous. Implications for nanomechanical properties and electromechanical coupling in 2d materials are discussed.

Partial fraction decomposition of the Fermi function

A partial fraction decomposition of the Fermi function resulting in a finite sum over simple poles is proposed. This allows for efficient calculations involving the Fermi function in various contexts of electronic structure or electron transport theories. The proposed decomposition converges in a well-defined region faster than exponential and is thus superior to the standard Matsubara expansion.

Anderson localization in 1D systems with correlated disorder

Abstract Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the localization length and the density of states and compare our numerical results with analytical predictions. Specifically, we find two distinct characteristic behaviors in the vicinity of the band center and at the unperturbed band edge, respectively. Furthermore we address the effect of the intrinsic short-range correlations.

Nonlinear phononics using atomically thin membranes

Phononic crystals and acoustic metamaterials are used to tailor phonon and sound propagation properties by utilizing artificial, periodic structures. Analogous to photonic crystals, phononic band gaps can be created, which influence wave propagation and, more generally, allow engineering of the acoustic properties of a system. Beyond that, nonlinear phenomena in periodic structures have been extensively studied in photonic crystals and atomic Bose-Einstein condensates in optical lattices. However, creating nonlinear phononic crystals or nonlinear acoustic metamaterials remains challenging and only few examples have been demonstrated. Here, we show that atomically thin and periodically pinned membranes support coupled localized modes with nonlinear dynamics. The proposed system provides a platform for investigating nonlinear phononics.

Nonadiabatic electron pumping through interacting quantum dots

We study non-adiabatic charge pumping through single-level quantum dots taking into account Coulomb interactions. We show how a truncated set of equations of motion can be propagated in time by means of an auxiliary-mode expansion. This formalism is capable of treating the timedependent electronic transport for arbitrary driving parameters. We verify that the proposed method describes very precisely the well-known limit of adiabatic pumping through quantum dots without Coulomb interactions. As an example we discuss pumping driven by short voltage pulses for various interaction strengths. Such nite pulses are particular suited to investigate transient non-adiabatic eects, which may be also important for periodic drivings, where they are much more dicult to reveal.

Multi-phonon relaxation and generation of quantum states in a nonlinear mechanical oscillator

The dissipative quantum dynamics of an anharmonic oscillator is investigated theoretically in the context of carbon-based nano-mechanical systems. In the short-time limit, it is known that macroscopic superposition states appear for such oscillators. In the long-time limit, single- and multi-phonon dissipation lead to decoherence of the non-classical states. However, at zero temperature, as a result of two-phonon losses the quantum oscillator eventually evolves into a non-classical steady state. The relaxation of this state due to thermal excitations and one-phonon losses is numerically and analytically studied. The possibility of verifying the occurrence of the non-classical state is investigated and signatures of the quantum features arising in a ring-down setup are presented. The feasibility of the verification scheme is discussed in the context of quantum nano-mechanical systems.