We study the excitation spectroscopy of few-electron, parallel coupled double quantum dots (QDs). By applying a finite source drain voltage to a double QD (DQD), the first excited states observed in nonequilibrium charging diagrams can be classified
into two kinds in terms of the total effective electron number in the DQD, assuming a core filling. When there are an odd (even) number of electrons, one (two)-electron antibonding (triplet) state is observed as the first excited state. On the other hand, at a larger source drain voltage we observe higher excited states, where additional single-particle excited levels are involved. Eventually, we identify the excited states with a calculation using the Hubbard model and, in particular, we elucidate the quadruplet state, which is normally forbidden by the spin blockade caused by the selection rule.
By considering analytical expressions for the self-energies of intervalley and intravalley phonons in graphene, we describe the behavior of D, 2D, and D$$ Raman bands with changes in doping ($mu$) and light excitation energy ($E_L$). Comparing the se
lf-energy with the observed $mu$ dependence of the 2D bandwidth, we estimate the wavevector $q$ of the constituent intervalley phonon at $hbar vqsimeq E_L/1.6$ ($v$ is electrons Fermi velocity) and conclude that the self-energy makes a major contribution (60%) to the dispersive behavior of the D and 2D bands. The estimation of $q$ is based on an image of shifted Dirac cones in which the resonance decay of a phonon satisfying $q > omega/v$ ($omega$ is the phonon frequency) into an electron-hole pair is suppressed when $mu < (vq-omega)/2$. We highlight the fact that the decay of an intervalley (and intravalley longitudinal optical) phonon with $q=omega/v$ is strongly suppressed by electron-phonon coupling at an arbitrary $mu$. This feature is in contrast to the divergent behavior of an intravalley transverse optical phonon, which bears a close similarity to the polarization function relevant to plasmons.
By analytically constructing the matrix elements of an electron-phonon interaction for the $D$ band in the Raman spectra of armchair graphene nanoribbons, we show that pseudospin and momentum conservation result in (i) a $D$ band consisting of two co
mponents, (ii) a $D$ band Raman intensity that is enhanced only when the polarizations of the incident and scattered light are parallel to the armchair edge, and (iii) the $D$ band softening/hardening behavior caused by the Kohn anomaly effect is correlated with that of the $G$ band. Several experiments are mentioned that are relevant to these results. It is also suggested that pseudospin is independent of the boundary condition for the phonon mode, while momentum conservation depends on it.
The universality of $k$-dependent electron-photon and electron-phonon matrix elements is discussed for graphene nanoribbons and carbon nanotubes. An electron undergoes a change in wavevector in the direction of broken translational symmetry, dependin
g on the light polarization direction. We suggest that this phenomenon originates from a microscopic feature of chirality.
Matrix elements of electron-light interactions for armchair and zigzag graphene nanoribbons are constructed analytically using a tight-binding model. The changes in wavenumber ($Delta n$) and pseudospin are the necessary elements if we are to underst
and the optical selection rule. It is shown that an incident light with a specific polarization and energy, induces an indirect transition ($Delta n=pm1$), which results in a characteristic peak in absorption spectra. Such a peak provides evidence that the electron standing wave is formed by multiple reflections at both edges of a ribbon. It is also suggested that the absorption of low-energy light is sensitive to the position of the Fermi energy, direction of light polarization, and irregularities in the edge. The effect of depolarization on the absorption peak is briefly discussed.
The rapidly rising fields of spintronics and quantum information science have led to a strong interest in developing the ability to coherently manipulate electron spins. Electron spin resonance (ESR) is a powerful technique to manipulate spins that i
s commonly achieved by applying an oscillating magnetic field. However, the technique has proven very challenging when addressing individual spins. In contrast, by mixing the spin and charge degrees of freedom in a controlled way through engineered non-uniform magnetic fields, electron spin can be manipulated electrically without the need of high-frequency magnetic fields. Here we realize electrically-driven addressable spin rotations on two individual electrons by integrating a micron-size ferromagnet to a double quantum dot device. We find that the electrical control and spin selectivity is enabled by the micro-magnets stray magnetic field which can be tailored to multi-dots architecture. Our results demonstrate the feasibility of manipulating electron spins electrically in a scalable way.
