GaSb band-structure models for electron density determinations from Raman measurements.

We investigate the use of Raman spectroscopy to measure carrier concentrations in n-type GaSb epilayers to aid in the development of this technique for the nondestructive characterization of transport properties in doped semiconductors. The carrier concentration is quantified by modeling the measured coupled optical phonon-free carrier plasmon mode spectra. We employ the Lindhard-Mermin optical susceptibility model with contributions from carriers in the two lowest GaSb conduction-band minima, the Γ and L minima. Furthermore, we evaluate three conduction-band models: (1) both minima parabolic and isotropic, (2) the Γ minimum non-parabolic and isotropic and the L minima parabolic and isotropic, and (3) the Γ minimum non-parabolic and isotropic and the L minima parabolic and ellipsoidal. For a given epilayer, the carrier concentration determined from the spectral simulations was consistently higher for the ellipsoidal L minima model than the other two models. To evaluate the conduction-band models, we calculated the L to Γ electron mobility ratio necessary for the electron concentrations from the Raman spectral measurements to reproduce those from the Hall effect measurements. We found that the model with the ellipsoidal L minima agreed best with reported carrier-dependent mobility-ratio values. Hence, employing isotropic L minima in GaSb conduction-band models, a common assumption when describing the GaSb conduction band, likely results in an underestimation of carrier concentration at room temperature and higher doping levels. This observation could have implications for Raman spectral modeling and any investigation involving the GaSb conduction band, e.g., modeling electrical measurements or calculating electron mobility.

Strong Coupling in Infrared Plasmonic Cavities.

Controlling molecular spectroscopy and even chemical behavior in a cavity environment is a subject of intense experimental and theoretical interest. In Fabry-Pérot cavities, strong (radiation-matter) coupling phenomena without an intense radiation field often rely on the number of chromophore molecules collectively interacting with a cavity mode. For plasmonic cavities, the cavity field-matter coupling can be strong enough to manifest strong coupling involving even a single molecule. To this end, infrared plasmonic cavities can be particularly useful in understanding vibrational strong coupling. Here we present a procedure for estimating the radiation-matter coupling and, equivalently, the mode volume as well as the mode lifetime and quality factor for plasmonic cavities of arbitrary shapes and use it to estimate these quantities for infrared cavities of two particularly relevant geometries comprising several n-doped semiconductors. Our calculations demonstrate very high field confinement and low mode volumes of these cavities despite having relatively low quality factors, which is often the case for plasmonic cavities.

Coupling, lifetimes, and "strong coupling" maps for single molecules at plasmonic interfaces.

The interaction between excited states of a molecule and excited states of a metal nanostructure (e.g., plasmons) leads to hybrid states with modified optical properties. When plasmon resonance is swept through molecular transition frequency, an avoided crossing may be observed, which is often regarded as a signature of strong coupling between plasmons and molecules. Such strong coupling is expected to be realized when 2|⟨U⟩|/â„Γ > 1, where ⟨U⟩ and Γ are the molecule-plasmon coupling and the spectral width of the optical transition, respectively. Because both ⟨U⟩ and Γ strongly increase with decreasing distance between a molecule and a plasmonic structure, it is not obvious that this condition can be satisfied for any molecule-metal surface distance. In this work, we investigate the behavior of ⟨U⟩ and Γ for several geometries. Surprisingly, we find that if the only contributions to Γ are lifetime broadenings associated with the radiative and nonradiative relaxation of a single molecular vibronic transition, including effects on molecular radiative and nonradiative lifetimes induced by the metal, the criterion 2|⟨U⟩|/â„Γ > 1 is easily satisfied by many configurations irrespective of the metal-molecule distance. This implies that the Rabi splitting can be observed in such structures if other sources of broadening are suppressed. Additionally, when the molecule-metal surface distance is varied keeping all other molecular and metal parameters constant, this behavior is mitigated due to the spectral shift associated with the same molecule-plasmon interaction, making the observation of Rabi splitting more challenging.

Quantum thermodynamics of periodically driven polaritonic systems.

We investigate the energy distribution and quantum thermodynamics in periodically-driven polaritonic systems in the stationary state at room temperature. Specifically, we consider an exciton strongly coupled to a harmonic oscillator and quantify the energy reorganization between these two systems and their interaction as a function of coupling strength, driving force, and detuning. After deriving the quantum master equation for the polariton density matrix with weak environment interactions, we obtain the dissipative time propagator and the long-time evolution of an equilibrium initial state. This approach provides direct access to the stationary state and overcomes the difficulties found in the numerical evolution of weakly damped quantum systems near resonance, also providing maps on the polariton lineshape. Then, we compute the thermodynamic performance during harmonic modulation and demonstrate that maximum efficiency occurs at resonance. We also provide an expression for the irreversible heat rate and numerically demonstrate that this agrees with the thermodynamic laws.

Metal adsorbate interactions and the convergence of density functional calculations.

The adsorption of metal atoms on nanostructures, such as graphene and nanotubes, plays an important role in catalysis, electronic doping, and tuning material properties. Quantum chemical calculations permit the investigation of this process to discover desirable interactions and obtain mechanistic insights into adsorbate behavior, of which the binding strength is a central quantity. Binding strengths, however, vary widely in the literature, even when using almost identical computational methods. To address this issue, we investigate the adsorption of a variety of metals onto graphene, carbon nanotubes, and boron nitride nanotubes. As is well-known, calculations on periodic structures require a sufficiently large system size to remove interactions between periodic images. Our results indicate that there are both direct and indirect mechanisms for this interaction, where the latter can require even larger system sizes than typically employed. The magnitude and distance of the effect depends on the electronic state of the substrate and the open- or closed-shell nature of the adsorbate. For instance, insulating substrates (e.g., boron nitride nanotubes) show essentially no dependence on system size, whereas metallic or semi-metallic systems can have a substantial effect due to the delocalized nature of the electronic states interacting with the adsorbate. We derive a scaling relation for the length dependence with a representative tight-binding model. These results demonstrate how to extrapolate the binding energies to the isolated-impurity limit.

Optimal in situ electromechanical sensing of molecular species.

We investigate protocols for optimal molecular detection with electromechanical nanoscale sensors under ambient conditions. Our models are representative of suspended graphene nanoribbons, which due to their piezoelectric and electronic properties provide responsive and versatile sensors. In particular, we analytically account for the corrections in the electronic transmission function and signal-to-noise ratio originating in environmental perturbations, such as thermal fluctuations and solvation effects. We also investigate the role of the sampling time in the current statistics. As a result, we formulate a protocol for optimal sensing based on the modulation of the Fermi level at a fixed bias and provide approximate forms for the current, linear susceptibility, and current fluctuations. We show how the algebraic tails in the thermally broadened transmission function affect the behavior of the signal-to-noise ratio and optimal sensing. These results provide further insights into the operation of graphene deflectometers and other techniques for electromechanical sensing.

Extracting electron densities in n-type GaAs from Raman spectra: Comparisons with Hall measurements.

We demonstrate quantitatively how values of electron densities in GaAs extracted from Raman spectra of two samples depend on models used to describe electric susceptibility and band structure. We, therefore, developed a theory that is valid for any temperature, doping level, and energy ratio proportional to q 2=(ω + iγ) (where q is the magnitude of wave vector, ω is Raman frequency, and γ is plasmon damping). We use a full Mermin-Lindhard description of Raman line shape and compare n-type GaAs spectra obtained from epilayers with our simulated spectra. Our method is unique in two ways: (1) we do a sensitivity analysis by employing four different descriptions of the GaAs band structure to give electron densities as functions of Fermi energies and (2) one of the four band structure descriptions includes bandgap narrowing that treats self-consistently the many-body effects of exchange and correlation in distorted-electron densities of states and solves the charge neutrality equation for a two-band model of GaAs at 300 K. We apply these results to obtain electron densities from line shapes of Raman spectra and thereby demonstrate quantitatively how the values of electron densities extracted from Raman spectra of n-type GaAs depend of various models for susceptibility and band structure.

Generalized Voigt broadening due to thermal fluctuations of electromechanical nanosensors and molecular electronic junctions.

Graphene and other 2D materials give a platform for electromechanical sensing of biomolecules in aqueous, room temperature environments. The electronic current changes in response to mechanical deflection, indicating the presence of forces due to interactions with, e.g., molecular species. We develop illustrative models of these sensors in order to give explicit, compact expressions for the current and signal-to-noise ratio. Electromechanical structures have an electron transmission function that follows a generalized Voigt profile, with thermal fluctuations giving a Gaussian smearing analogous to thermal Doppler broadening in solution/gas-phase spectroscopic applications. The Lorentzian component of the profile comes from the contact to the electrodes. After providing an accurate approximate form of this profile, we calculate the mechanical susceptibility for a representative two-level bridge and the current fluctuations for electromechanical detection. These results give the underlying mechanics of electromechanical sensing in more complex scenarios, such as graphene deflectometry.

Simultaneous weak measurement of non-commuting observables: a generalized Arthurs-Kelly protocol.

In contrast to a projective quantum measurement, in a weak measurement the system is only weakly perturbed while only partial information on the measured observable is obtained. A simultaneous measurement of non-commuting observables cannot be projective, however the strongest possible such measurement can be defined as providing their values at the smallest uncertainty limit. Starting with the Arthurs and Kelly (AK) protocol for such measurement of position and momentum, we derive a systematic extension to a corresponding weak measurement along three steps: First, a plausible form of the weak measurement operator analogous to the Gaussian Kraus operator, often used to model a weak measurement of a single observable, is obtained by projecting a naïve extension (valid for commuting observable) onto the corresponding Gabor space. Second, we show that the so obtained set of measurement operators satisfies the normalization condition for the probability to obtain given values of the position and momentum in the weak measurement operation, namely that this set constitutes a positive operator valued measure (POVM) in the position-momentum space. Finally, we show that the so-obtained measurement operator corresponds to a generalization of the AK measurement protocol in which the initial detector wavefunctions is suitable broadened.

Pump-Probe Noise Spectroscopy of Molecular Junctions.

The slow response of electronic components in junctions limits the direct applicability of pump-probe type spectroscopy in assessing the intramolecular dynamics. Recently the possibility of getting information on a sub-picosecond time scale from dc current measurements was proposed. We revisit the idea of picosecond resolution by pump-probe spectroscopy from dc measurements and show that any intramolecular dynamics not directly related to charge transfer in the current direction is missed by current measurements. We propose a pump-probe dc shot noise spectroscopy as a suitable alternative. Numerical examples of time-dependent and average responses of junctions are presented for generic models.

Quantum thermodynamics: a nonequilibrium Green's function approach.

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.

A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators.

We consider a projection operator approach to the non-equilibrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.

Interpreting single turnover catalysis measurements with constrained mean dwell times.

Observation of a chemical transformation at the single-molecule level yields a detailed view of kinetic pathways contributing to the averaged results obtained in a bulk measurement. Studies of a fluorogenic reaction catalyzed by gold nanoparticles have revealed heterogeneous reaction dynamics for these catalysts. Measurements on single nanoparticles yield binary trajectories with stochastic transitions between a dark state in which no product molecules are adsorbed and a fluorescent state in which one product molecule is present. The mean dwell time in either state gives information corresponding to a bulk measurement. Quantifying fluctuations from mean kinetics requires identifying properties of the fluorescence trajectory that are selective in emphasizing certain dynamic processes according to their time scales. We propose the use of constrained mean dwell times, defined as the mean dwell time in a state with the constraint that the immediately preceding dwell time in the other state is, for example, less than a variable time. Calculations of constrained mean dwell times for a kinetic model with dynamic disorder demonstrate that these quantities reveal correlations among dynamic fluctuations at different active sites on a multisite catalyst. Constrained mean dwell times are determined from measurements of single nanoparticle catalysis. The results indicate that dynamical fluctuations at different active sites are correlated, and that especially rapid reaction events produce particularly slowly desorbing product molecules.