56 research outputs found
Valley relaxation in graphene due to charged impurities
Monolayer graphene is an example of materials with multi-valley electronic
structure. In such materials, the valley index is being considered as an
information carrier. Consequently, relaxation mechanisms leading to loss of
valley information are of interest. Here, we calculate the rate of valley
relaxation induced by charged impurities in graphene. A special model of
graphene is applied, where the orbitals are two-dimensional Gaussian
functions, with a spatial extension characterised by an effective Bohr radius
. We obtain the valley relaxation rate by solving the Boltzmann
equation, for the case of noninteracting electrons, as well as for the case
when the impurity potential is screened due to electron-electron interaction.
For the latter case, we take into account local-field effects and evaluate the
dielectric matrix in the random phase approximation. Our main findings: (i) The
valley relaxation rate is proportional to the electronic density of states at
the Fermi energy. (ii) Charged impurities located in the close vicinity of the
graphene plane, at distance , are much more
efficient in inducing valley relaxation than those farther away, the effect of
the latter being suppressed exponentially with increasing graphene-impurity
distance . (iii) Both in the absence and in the presence of
electron-electron interaction, the valley relaxation rate shows pronounced
dependence on the effective Bohr radius . The trends are
different in the two cases: in the absence (presence) of screening, the valley
relaxation rate decreases (increases) for increasing effective Bohr radius.
This last result highlights that a quantitative calculation of the valley
relaxation rate should incorporate electron-electron interactions as well as an
accurate knowledge of the electronic wave functions on the atomic length scale.Comment: 15 pages, 8 figure
Orbital hyperfine interaction and qubit dephasing in carbon nanotube quantum dots
Hyperfine interaction (HF) is of key importance for the functionality of
solid-state quantum information processing, as it affects qubit coherence and
enables nuclear-spin quantum memories. In this work, we complete the theory of
the basic hyperfine interaction mechanisms (Fermi contact, dipolar, orbital) in
carbon nanotube quantum dots by providing a theoretical description of the
orbital HF. We find that orbital HF induces an interaction between the nuclear
spins of the nanotube lattice and the valley degree of freedom of the electrons
confined in the quantum dot. We show that the resulting
nuclear-spin--electron-valley interaction (i) is approximately of Ising type,
(ii) is essentially local, in the sense that a radius- and
dot-length-independent atomic interaction strength can be defined, and (iii)
has an atomic interaction strength that is comparable to the combined strength
of Fermi contact and dipolar interactions. We argue that orbital HF provides a
new decoherence mechanism for single-electron valley qubits and spin-valley
qubits in a range of multi-valley materials. We explicitly evaluate the
corresponding inhomogeneous dephasing time for a nanotube-based valley
qubit.Comment: 7 pages, 3 figure
Maximal Rabi frequency of an electrically driven spin in a disordered magnetic field
We present a theoretical study of the spin dynamics of a single electron
confined in a quantum dot. Spin dynamics is induced by the interplay of
electrical driving and the presence of a spatially disordered magnetic field,
the latter being transverse to a homogeneous magnetic field. We focus on the
case of strong driving, i.e., when the oscillation amplitude of the
electron's wave packet is comparable to the quantum dot length . We show
that electrically driven spin resonance can be induced in this system by
subharmonic driving, i.e., if the excitation frequency is an integer fraction
(1/2, 1/3, etc) of the Larmor frequency. At strong driving we find that (i) the
Rabi frequencies at the subharmonic resonances are comparable to the Rabi
frequency at the fundamental resonance, and (ii) at each subharmonic resonance,
the Rabi frequency can be maximized by setting the drive strength to an
optimal, finite value. Our simple model is applied to describe electrical
control of a spin-valley qubit in a weakly disordered carbon nanotube.Comment: 5 pages, 2 figure
Hyperfine-induced valley mixing and the spin-valley blockade in carbon-based quantum dots
Hyperfine interaction (HFI) in carbon nanotube and graphene quantum dots is
due to the presence of 13C atoms. We theoretically show that in these
structures the short-range nature of the HFI gives rise to a coupling between
the valley degree of freedom of the electron and the nuclear spin, in addition
to the usual electron spin-nuclear spin coupling. We predict that this property
of the HFI affects the Pauli blockade transport in carbon-based double quantum
dots. In particular, we show that transport is blocked only if both the spin
and the valley degeneracies of the quantum dot levels are lifted, e.g., by an
appropriately oriented magnetic field. The blockade is caused by four
"supertriplet" states in the (1,1) charge configuration.Comment: 5 pages, 3 figures; v2: published versio
Rashba billiards
We study the energy levels of non-interacting electrons confined to move in
two-dimensional billiard regions and having a spin-dependent dynamics due to a
finite Rashba spin splitting. The Green's function for such Rashba billiards is
constructed analytically and used to find the area and perimeter contributions
to the density of states, as well as the smooth counting function. We show
that, in contrast to systems with spin-rotational invariance, Rashba billiards
always possess a negative energy spectrum. A semi-classical analysis is
presented to interpret the singular behavior of the density of states at
certain negative energies. Our detailed analysis of the spin structure of
Rashba billiards reveals a finite out-of-plane spin projection for electron
eigenstates.Comment: 12 pages, 6 figures, minor changes in the text, submitted to PR
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.Comment: 9 pages, 4 figure
Subharmonic transitions and Bloch-Siegert shift in electrically driven spin resonance
We theoretically study coherent subharmonic (multi-photon) transitions of a
harmonically driven spin. We consider two cases: magnetic resonance (MR) with a
misaligned, i.e., non-transversal driving field, and electrically driven spin
resonance (EDSR) of an electron confined in a one-dimensional, parabolic
quantum dot, subject to Rashba spin-orbit interaction. In the EDSR case, we
focus on the limit where the orbital level spacing of the quantum dot is the
greatest energy scale. Then, we apply time-dependent Schrieffer-Wolff
erturbation theory to derive a time-dependent effective two-level Hamiltonian,
allowing to describe both MR and EDSR using the Floquet theory of periodically
driven two-level systems. In particular, we characterise the fundamental
(single-photon) and the half-harmonic (two-photon) spin transitions. We
demonstrate the appearance of two-photon Rabi oscillations, and analytically
calculate the fundamental and half-harmonic resonance frequencies and the
corresponding Rabi frequencies. For EDSR, we find that both the fundamental and
the half-harmonic resonance frequency changes upon increasing the strength of
the driving electric field, which is an effect analogous to the Bloch-Siegert
shift known from MR. Remarkably, the drive-strength dependent correction to the
fundamental EDSR resonance frequency has an anomalous, negative sign, in
contrast to the corresponding Bloch-Siegert shift in MR which is always
positive. Our analytical results are supported by numerical simulations, as
well as by qualitative interpretations for simple limiting cases.Comment: 16 pages, 7 figure
Probing individual split Cooper-pairs using the spin qubit toolkit
A superconductor is a natural source of spin-entangled spatially separated
electron pairs. Although the first Cooper-pair splitter devices have been
realized recently, an experimental confirmation of the spin state and the
entanglement of the emitted electron pairs is lacking up to now. In this paper
a method is proposed to confirm the spin-singlet character of individual split
Cooper pairs. Two quantum dots (QDs), each of them holding one spin-prepared
electron, serve as the detector of the spin state of a single Cooper pair that
is forced to split when it tunnels out from the superconductor to the QDs. The
number of charges on the QDs, measured at the end of the procedure, carries
information on the spin state of the extracted Cooper pair. The method relies
on the experimentally established toolkit of QD-based spin qubits: resonant
spin manipulation, Pauli blockade, and charge measurement.Comment: 15 pages, 7 figure
- …