Optical selection rules of graphene nanoribbons

Optical selection rules for one-dimensional graphene nanoribbons are analytically studied and clarified based on the tight-binding model. A theoretical explanation, through analyzing the velocity matrix elements and the features of wavefunctions, can account for the selection rules, which depend on the edge structure of nanoribbon, namely armchair or zigzag edges. The selection rule of armchair nanoribbons is \Delta J=0, and the optical transitions occur from the conduction to valence subbands of the same index. Such a selection rule originates in the relationships between two sublattices and between conduction and valence subbands. On the other hand, zigzag nanoribbons exhibit the selection rule |\Delta J|=odd, which results from the alternatively changing symmetry property as the subband index increases. An efficiently theoretical prediction on transition energies is obtained with the application of selection rules. Furthermore, the energies of band edge states become experimentally attainable via optical measurements

Wide-band current preamplifier for conductance measurements with large input capacitance

A wide-band current preamplifier based on a composite operational amplifier is proposed. It has been shown that the bandwidth of the preamplifier can be significantly increased by enhancing the effective open-loop gain of the composite preamplifier. The described preamplifier with current gain 10$^7$ V/A showed the bandwidth of about 100 kHz with 1 nF input shunt capacitance. The current noise of the amplifier was measured to be about 46 fA/$\sqrt{\rm Hz}$ at 1 kHz, close to the design noise minimum. The voltage noise was found to be about 2.9 nV/$\sqrt{\rm Hz}$ at 1 kHz, which is in a good agreement with the value expected for the operational amplifier used in the input stage. By analysing the total noise produced by the preamplifier we found the optimal frequency range suitable for the fast lock-in measurements to be from 1 kHz to 2 kHz. To get the same signal-to-noise ratio, the reported preamplifier requires roughly 10% of the integration time used in measurements made with a conventional preamplifier.Comment: 5 pages, 4 figure

Non-equilibrium frequency-dependent noise through a quantum dot: A real time functional renormalization group approach

We construct a real time current-conserving functional renormalization group (RG) scheme on the Keldysh contour to study frequency-dependent transport and noise through a quantum dot in the local moment regime. We find that the current vertex develops a non-trivial non-local structure in time, governed by a new set of RG equations. Solving these RG equations, we compute the complete frequency and temperature-dependence of the noise spectrum. For voltages large compared to the Kondo temperature, $eV \gg k_BT_K$, two sharp anti-resonances are found in the noise spectrum at frequencies $\hbar \omega = \pm e V$, and correspondingly, two peaks in the ac conductance through the dot.Comment: 4 pages, 4 figure

On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends

The self-consistent field (SCF) theory of dense polymer liquids assumes that short-range correlations are almost independent of how monomers are connected into polymers. Some limits of this idea are explored in the context of a perturbation theory for mixtures of structurally identical polymer species, A and B, in which the AB pair interaction differs slightly from the AA and BB interaction, and the difference is controlled by a parameter alpha Expanding the free energy to O(\alpha) yields an excess free energy of the form alpha $z(N)\phi_{A}\phi_{B}$, in both lattice and continuum models, where z(N) is a measure of the number of inter-molecular near neighbors of each monomer in a one-component liquid. This quantity decreases slightly with increasing N because the self-concentration of monomers from the same chain is slightly higher for longer chains, creating a deeper correlation hole for longer chains. We analyze the resulting $N$-dependence, and predict that $z(N) = z^{\infty}[1 + \beta \bar{N}^{-1/2}]$, where $\bar{N}$ is an invariant degree of polymerization, and $\beta=(6/\pi)^{3/2}$. This and other predictions are confirmed by comparison to simulations. We also propose a way to estimate the effective interaction parameter appropriate for comparisons of simulation data to SCF theory and to coarse-grained theories of corrections to SCF theory, which is based on an extrapolation of coefficients in this perturbation theory to the limit $N \to \infty$. We show that a renormalized one-loop theory contains a quantitatively correct description of the $N$-dependence of local structure studied here.Comment: submitted to J. Chem. Phy

Kondo effect in coupled quantum dots with RKKY interaction: Finite temperature and magnetic field effects

We study transport through two quantum dots coupled by an RKKY interaction as a function of temperature and magnetic field. By applying the Numerical Renormalization Group (NRG) method we obtain the transmission and the linear conductance. At zero temperature and magnetic field, we observe a quantum phase transition between the Kondo screened state and a local spin singlet as the RKKY interaction is tuned. Above the critical RKKY coupling the Kondo peak is split. However, we find that both finite temperature and magnetic field restore the Kondo resonance. Our results agree well with recent transport experiments on gold grain quantum dots in the presence of magnetic impurities.Comment: 4 pages, 5 figure

Acoustically evoked potentials in two cephalopods inferred using the auditory brainstem response (ABR) approach

It is still a matter of debate whether cephalopods can detect sound frequencies above 400 Hz. So far there is no proof for the detection of underwater sound above 400 Hz via a physiological approach. The controversy of whether cephalopods have a sound detection ability above 400 Hz was tested using the auditory brainstem response (ABR) approach, which has been successfully applied in fish, crustaceans, amphibians, reptiles and birds. Using ABR we found that auditory evoked potentials can be obtained in the frequency range 400 to 1500 Hz (Sepiotheutis lessoniana) and 400 to 1000 Hz (Octopus vulgaris), respectively. The thresholds of S. lessoniana were generally lower than those of O. vulgaris

Two-stage Kondo effect in side-coupled quantum dots: Renormalized perturbative scaling theory and Numerical Renormalization Group analysis

We study numerically and analytically the dynamical (AC) conductance through a two-dot system, where only one of the dots is coupled to the leads but it is also side-coupled to the other dot through an antiferromagnetic exchange (RKKY) interaction. In this case the RKKY interaction gives rise to a ``two-stage Kondo effect'' where the two spins are screened by two consecutive Kondo effects. We formulate a renormalized scaling theory that captures remarkably well the cross-over from the strongly conductive correlated regime to the low temperature low conductance state. Our analytical formulas agree well with our numerical renormalization group results. The frequency dependent current noise spectrum is also discussed.Comment: 6 pages, 7 figure

Time evolution towards q-Gaussian stationary states through unified Ito-Stratonovich stochastic equation

We consider a class of single-particle one-dimensional stochastic equations which include external field, additive and multiplicative noises. We use a parameter $\theta \in [0,1]$ which enables the unification of the traditional It\^o and Stratonovich approaches, now recovered respectively as the $\theta=0$ and $\theta=1/2$ particular cases to derive the associated Fokker-Planck equation (FPE). These FPE is a {\it linear} one, and its stationary state is given by a $q$-Gaussian distribution with $q = \frac{\tau + 2M (2 - \theta)}{\tau + 2M (1 - \theta)}<3$, where $\tau \ge 0$ characterizes the strength of the confining external field, and $M \ge 0$ is the (normalized) amplitude of the multiplicative noise. We also calculate the standard kurtosis $\kappa_1$ and the $q$-generalized kurtosis $\kappa_q$ (i.e., the standard kurtosis but using the escort distribution instead of the direct one). Through these two quantities we numerically follow the time evolution of the distributions. Finally, we exhibit how these quantities can be used as convenient calibrations for determining the index $q$ from numerical data obtained through experiments, observations or numerical computations.Comment: 9 pages, 2 figure

Quantum pump driven fermionic Mach-Zehnder interferometer

We have investigated the characteristics of the currents in a pump-driven fermionic Mach-Zehnder interferometer. The system is implemented in a conductor in the quantum Hall regime, with the two interferometer arms enclosing an Aharonov-Bohm flux $\Phi$. Two quantum point contacts with transparency modulated periodically in time drive the current and act as beam-splitters. The current has a flux dependent part $I^{(\Phi)}$ as well as a flux independent part $I^{(0)}$. Both current parts show oscillations as a function of frequency on the two scales determined by the lengths of the interferometer arms. In the non-adiabatic, high frequency regime $I^{(\Phi)}$ oscillates with a constant amplitude while the amplitude of the oscillations of $I^{(0)}$ increases linearly with frequency. The flux independent part $I^{(0)}$ is insensitive to temperature while the flux dependent part $I^{(\Phi)}$ is exponentially suppressed with increasing temperature. We also find that for low amplitude, adiabatic pumping rectification effects are absent for semitransparent beam-splitters. Inelastic dephasing is introduced by coupling one of the interferometer arms to a voltage probe. For a long charge relaxation time of the voltage probe, giving a constant probe potential, $I^{(\Phi)}$ and the part of $I^{(0)}$ flowing in the arm connected to the probe are suppressed with increased coupling to the probe. For a short relaxation time, with the potential of the probe adjusting instantaneously to give zero time dependent current at the probe, only $I^{(\Phi)}$ is suppressed by the coupling to the probe.Comment: 10 pages, 4 figure

Competing topological and Kondo insulator phases on a honeycomb lattice

We investigate the competition between the spin-orbit interaction of itinerant electrons and their Kondo coupling with local moments densely distributed on the honeycomb lattice. We find that the model at half-filling displays a quantum phase transition between topological and Kondo insulators at a nonzero Kondo coupling. In the Kondo-screened case, tuning the electron concentration can lead to a new topological insulator phase. The results suggest that the heavy-fermion phase diagram contains a new regime with a competition among topological, Kondo-coherent and magnetic states, and that the regime may be especially relevant to Kondo lattice systems with $5d$-conduction electrons. Finally, we discuss the implications of our results in the context of the recent experiments on SmB$_6$ implicating the surface states of a topological insulator, as well as the existing experiments on the phase transitions in SmB$_6$ under pressure and in CeNiSn under chemical pressure.Comment: (v3) Published version including the main text (5 pages + 4 figures) and a supplementary material discussing the effects of quantum fluctuations of the slave bosons and antiferromagnetic ordering of the local moments on the transitions among the Kondo, magnetic and topological state