93 research outputs found
A 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.Comment: 7 pages, 5 figure
Full Counting Statistics of a Non-adiabatic Electron Pump
Non-adiabatic charge pumping through a single-level quantum dot with
periodically modulated parameters is studied theoretically. By means of a
quantum-master-equation approach the full counting statistics of the system is
obtained. We find a trinomial-probability distribution of the charge transfer,
which adequately describes the reversal of the pumping current by sweeping the
driving frequency. Further, we derive equations of motion for current and
noise, and solve those numerically for two different driving schemes. Both show
interesting features which can be fully analyzed due to the simple and generic
model studied.Comment: 7 pages, 4 figure
Strain-tuning of vacancy-induced magnetism in graphene nanoribbons
Vacancies in graphene lead to the appearance of localized electronic states
with non-vanishing spin moments. Using a mean-field Hubbard model and an
effective double-quantum dot description we investigate the influence of strain
on localization and magnetic properties of the vacancy-induced states in
semiconducting armchair nanoribbons. We find that the exchange splitting of a
single vacancy and the singlet-triplet splitting for two vacancies can be
widely tuned by applying uniaxial strain, which is crucial for spintronic
applications
Emergence of Bloch oscillations in one-dimensional systems
Electrons in periodic potentials exhibit oscillatory motion in presence of an
electric field. Such oscillations are known as Bloch oscillations. In this
article we theoretically investigate the emergence of Bloch oscillations for
systems where the electric field is confined to a finite region, like in
typical electronic devices. We use a one-dimensional tight-binding model within
the single-band approximation to numerically study the dynamics of electrons
after a sudden switching-on of the electric field. We find a transition from a
regime with direct current to Bloch oscillations when increasing the system
size or decreasing the field strength. We propose a pump-probe scheme to
observe the oscillations by measuring the accumulated charge as a function of
the pulse-length
Pseudomodes and the corresponding transformation of the temperature-dependent bath correlation function
In open system approaches with non-Markovian environments, the process of
inserting an individual mode (denoted as "pseudomode") into the bath or
extracting it from the bath is widely employed. This procedure, however, is
typically performed on basis of the spectral density (SD) and does not
incorporate temperature. Here, we show how the - temperature-dependent - bath
correlation function (BCF) transforms in such a process. We present analytic
formulae for the transformed BCF and numerically study the differences between
factorizing initial state and global thermal (correlated) initial state of mode
and bath, respectively. We find that in the regime of strong coupling of the
mode to both system and bath, the differences in the BCFs give rise to
pronounced differences in the dynamics of the system.Comment: 12 pages, 4 figure
Nonlinear phononics using atomically thin membranes
Phononic crystals and acoustic meta-materials are used to tailor phonon and
sound propagation properties by facilitating 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 meta-materials 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
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.Comment: 23 pages, 8 figures; Minor revisions; Accepted for publication in NJ
Multi-scale approach for strain-engineering of phosphorene
A multi-scale approach for the theoretical description of deformed
phosphorene is presented. This approach combines a valence-force model to
relate macroscopic strain to microscopic displacements of atoms and a
tight-binding model with distance-dependent hopping parameters to obtain
electronic properties. The resulting self-consistent electromechanical model is
suitable for large-scale modeling of phosphorene devices. We demonstrate this
for the case of an inhomogeneously deformed phosphorene drum, which may be used
as an exciton funnel
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