Bulk Limit Research Articles

Strong enhancement of bulk superconductivity by engineered nanogranularity

It is now well established, both theoretically and experimentally, that very small changes in the size of isolated nanograins lead to substantial nonmonotonic variations, and sometimes enhancement, of the mean-field spectroscopic gap of conventional superconductors. A natural question to ask, of broad relevance for the theory and applications of superconductivity, is whether these size effects can also enhance the critical temperature of a bulk granular material composed of such nanograins. Here we answer this question affirmatively. We combine mean-field, semiclassical, and percolation techniques to show that engineered nanoscale granularity in conventional superconductors can enhance the critical temperature by up to a few times compared to the nongranular bulk limit. This prediction is valid for three-dimensional and also quasi-two-dimensional samples, provided the thickness is much larger than the grain size. Our model takes into account an experimentally realistic distribution of grain sizes in the array, charging effects, tunnelling by quasiparticles, and limitations related to the proliferation of thermal fluctuations for sufficiently small grains.

First-principles real-space study of electronic and optical excitations in rutileTiO2nanocrystals

We model rutile titanium dioxide nanocrystals (NCs) up to $\ensuremath{\sim}1.5$ nm in size to study the effects of quantum confinement on their electronic and optical properties. Ionization potentials (IPs) and electron affinities (EAs) are obtained via the perturbative $GW$ approximation (${G}_{0}{W}_{0}$) and $\ensuremath{\Delta}\mathrm{SCF}$ method for NCs up to 24 and 64 ${\mathrm{TiO}}_{2}$ formula units, respectively. These demanding $GW$ computations are made feasible by using a real-space framework that exploits quantum confinement to reduce the number of empty states needed in $GW$ summations. Time-dependent density functional theory (TDDFT) is used to predict the optical properties of NCs up to 64 ${\mathrm{TiO}}_{2}$ units. For a NC containing only 2 ${\mathrm{TiO}}_{2}$ units, the offsets of the IP and the EA from the corresponding bulk limits are of similar magnitude. However, as NC size increases, the EA is found to converge more slowly to the bulk limit than the IP. The EA values computed at the ${G}_{0}{W}_{0}$ and $\ensuremath{\Delta}\mathrm{SCF}$ levels of theory are found to agree fairly well with each other, while the IPs computed with $\ensuremath{\Delta}\mathrm{SCF}$ are consistently smaller than those computed with ${G}_{0}{W}_{0}$ by a roughly constant amount. TDDFT optical gaps exhibit weaker size dependence than $GW$ quasiparticle gaps, and result in exciton binding energies on the order of eV. Altering the dimensions of a fixed-size NC can change electronic and optical excitations up to several tenths of an eV. The largest NCs modeled are still quantum confined and do not yet have quasiparticle levels or optical gaps at bulk values. Nevertheless, we find that classical Mie-Gans theory can quite accurately reproduce the line shape of TDDFT absorption spectra, even for (anisotropic) ${\mathrm{TiO}}_{2}$ NCs of subnanometer size.

Electron mobilities approaching bulk limits in "surface-free" GaAs nanowires.

Achieving bulk-like charge carrier mobilities in semiconductor nanowires is a major challenge facing the development of nanowire-based electronic devices. Here we demonstrate that engineering the GaAs nanowire surface by overcoating with optimized AlGaAs shells is an effective means of obtaining exceptionally high carrier mobilities and lifetimes. We performed measurements of GaAs/AlGaAs core-shell nanowires using optical pump-terahertz probe spectroscopy: a noncontact and accurate probe of carrier transport on ultrafast time scales. The carrier lifetimes and mobilities both improved significantly with increasing AlGaAs shell thickness. Remarkably, optimized GaAs/AlGaAs core-shell nanowires exhibited electron mobilities up to 3000 cm(2) V(-1) s(-1), reaching over 65% of the electron mobility typical of high quality undoped bulk GaAs at equivalent photoexcited carrier densities. This points to the high interface quality and the very low levels of ionized impurities and lattice defects in these nanowires. The improvements in mobility were concomitant with drastic improvements in photoconductivity lifetime, reaching 1.6 ns. Comparison of photoconductivity and photoluminescence dynamics indicates that midgap GaAs surface states, and consequently surface band-bending and depletion, are effectively eliminated in these high quality heterostructures.

The thermodynamics of proton hydration and the electrochemical surface potential of water.

The free energy change for transferring a single ion across the water liquid/vapor interface includes an electrochemical surface potential contribution. Since this potential is not directly accessible to thermodynamic measurement, several extra-thermodynamic approaches have been employed to infer its sign and magnitude, with a resulting wide spread of values. Here, we examine further the thermodynamics of proton hydration and the electrochemical surface potential of water along three directions: (1) a basic relation of interfacial electrostatics and experimental results on ion distributions near a water/organic interface are employed to infer a solvent contribution to the electrochemical surface potential, (2) a re-analysis is performed of the existing bulk and cluster ion hydration data, and (3) extensive computational modeling is conducted to examine the size dependence of hydration enthalpy differences for the NaF ion pair between the small cluster and the converged bulk limits. The computational studies include classical polarizable models and high-level quantum chemical methods. The new theoretical analysis of existing experimental data and the combined classical/quantum modeling lead to results consistent with our previously derived proton hydration quantities.

Hybrid Density Functionals for Clusters of Late Transition Metals: Assessing Energetic and Structural Properties.

We present the first application of hybrid density functional theory (DFT) methods to larger transition-metal clusters. To assess such functionals for this class of systems, we compare the performance of three modern hybrid DFT methods (PBE0, TPSSh, M06) and their semilocal counterparts (PBE, TPSS, M06L) regarding average bond distances and binding energies per atom for a series of octahedral model clusters Mn (M = Ni, Pd, Pt; n = 13, 38, 55, 79, 116). With application to large particles in mind, we extrapolated the results to their respective bulk limits and compared them to experimental values. In some cases, average nearest-neighbor distances are notably overestimated by the PBE0 and M06 hybrid functionals. Results on energies allow a grouping of the tested functionals into sets of similar behavior for the three metals studied. Among the methods examined, the TPSSh hybrid density functional shows the best overall performance.

Strain-induced metal-insulator transition in ultrathin films ofSrRuO3

The ultrathin film limit has been shown to be a rich playground for unusual low dimensional physics. Taking the example of SrRuO$_3$ which is ferromagnetic and metallic at the bulk limit, one finds that it becomes antiferromagnetic and insulating at the three monolayers limit when grown on SrTiO$_3$. The origin of the insulating state is traced to strongly orbital dependent exchange splittings. A modest compressive strain of 1% of the SrTiO$_3$ substrate is then found to drive the system into a highly confined two-dimensional 100% spin polarized metallic state. This metal-insulator transition driven by a modest strain could be useful in two state device applications.

Number theory, periodic orbits, and superconductivity in nanocubes

We study superconductivity in isolated superconducting nano-cubes and nano-squares of size $L$ in the limit of negligible disorder, $\delta/\Delta_0 \ll 1$ and $k_F L \gg 1$ for which mean-field theory and semiclassical techniques are applicable, with $k_F$ the Fermi wave vector, $\delta$ the mean level spacing and $\Delta_0$ the bulk gap. By using periodic orbit theory and number theory we find explicit analytical expressions for the size dependence of the superconducting order parameter. Our formalism takes into account contributions from both the spectral density and the interaction matrix elements in a basis of one-body eigenstates. The leading size dependence of the energy gap in three dimensions seems to be universal as it agrees with the result for chaotic grains. In the region of parameters corresponding to conventional metallic superconductors, and for sizes $L \gtrsim 10$nm, the contribution to the superconducting gap from the matrix elements is substantial ($\sim 20\%$). Deviations from the bulk limit are still clearly observed even for comparatively large grains $L \sim 50$nm. These analytical results are in excellent agreement with the numerical solution of the mean-field gap equation.

Predicting energies of small clusters from the inhomogeneous unitary Fermi gas

We investigate the inhomogeneous unitary Fermi gas and use the long-wavelength properties to predict the energies of small clusters of unitary fermions trapped in harmonic potentials. The large pairing gap and scale invariance place severe restrictions on the form of the density functional. We determine the relevant universal constants needed to constrain the functional from calculations of the bulk in oscillating external potentials. Comparing with exact Quantum Monte Carlo calculations, we find that the same functional correctly predicts the lack of shell closures for small clusters of fermions trapped in harmonic wells as well as their absolute energies. A rapid convergence to the bulk limit in three dimensions, where the surface to volume ratio is quite large, is demonstrated. The resulting functional can be tested experimentally, and is a key ingredient in predicting possible polarized superfluid phases and the properties of the unitary Fermi gas in optical lattices.

Diamondoids approach to electronic, structural, and vibrational properties of GeSi superlattice nanocrystals: a first-principles study

Germanium silicide diamondoids are used to determine electronic, structural, and vibrational properties of GeSi superlattice nanocrystals and bulk as their building block limit. Density functional theory at the generalized gradient approximation level of Perdew, Burke, and Ernzerhof (PBE) with 6-31G(d) basis including polarization functions is used to investigate the electronic structure of these diamondoids. The investigated molecules and diamondoids range from GeSiH6 to Ge63Si63H92. The variation of the energy gap is shown from nearly 7 eV toward bulk value which is slightly higher than the average of Si and Ge energy gaps. Variations of bond lengths, tetrahedral, and dihedral angles as the number of atoms increases are shown taking into account the effect of shape fluctuations. Localized and delocalized electronic charge distribution and bonds for these molecules are discussed. Vibrational radial breathing mode (RBM) converges from its initial molecular value at 332 cm−1 to its bulk limit at 0 cm−1 (blue shift). Longitudinal optical-highest reduced mass mode (HRMM) converges from its initial molecular value 332 cm−1 to experimental bulk limit at 420.7 cm−1 (red shift). Hydrogen vibrational modes are nearly constant in their frequencies as the size of diamondoids increases in contrast with lower frequency Ge–Si vibrational modes. GeSi diamondoids can be identified from surface hydrogen vibrational modes fingerprint, while the size of these diamondoids can be identified from Ge–Si vibrational modes.

Simulated solvation of organic ions: protonated methylamines in water nanodroplets. Convergence toward bulk properties and the absolute proton solvation enthalpy.

We applied an alternative, purely theoretical route to estimate thermodynamical properties of organic ions in bulk solution. The method performs a large ensemble of simulations of ions solvated in water nanodroplets of different sizes, using a polarizable molecular dynamics approach. We consider protonated ammonia and methylamines, and K(+) for comparison, solvated in droplets of 50-1000 water molecules. The parameters of the model are assigned from high level quantum computations of small clusters. All the bulk phase results extrapolated from droplet simulations match, and confirm independently, the relative and absolute experiment-based ion solvation energies. Without using experiment-based parameters or assumptions, the results confirm independently the solvation enthalpy of the proton, as -270.3 ± 1.1 kcal mol(-1). The calculated relative solvation enthalpies of these ions are constant from small water clusters, where only the ionic headgroups are solvated, up to bulk solution. This agrees with experimental thermochemistry, that the relative solvation energies of alkylammonium ions by only four H2O molecules reproduce the relative bulk solvation energies, although the small clusters lack major bulk solvation factors. The droplet results also show a slow convergence of ion solvation properties toward their bulk limit, and predict that the stepwise solvation enthalpies of ion/water droplets are very close to those of pure neutral water droplets already after 50 water molecules. Both the ionic and neutral clusters approach the bulk condensation energy very gradually up to 10,000 water molecules, consistent with the macroscopic liquid drop model for pure water droplets. Compared to standard computational methods based on infinite periodic systems, our protocol represents a new purely theoretical approach to investigate the solvation properties of ions. It is applicable to the solvation of organic ions, which are pivotal in environmental, industrial, and biophysical chemistry but have been little investigated theoretically up to the present.

Observation of quantum-tunnelling-modulated spin texture in ultrathin topological insulator Bi2Se3 films.

Understanding the spin-texture behaviour of boundary modes in ultrathin topological insulator films is critically essential for the design and fabrication of functional nanodevices. Here, by using spin-resolved photoemission spectroscopy with p-polarized light in topological insulator Bi2Se3 thin films, we report tunnelling-dependent evolution of spin configuration in topological insulator thin films across the metal-to-insulator transition. We report a systematic binding energy- and wavevector-dependent spin polarization for the topological surface electrons in the ultrathin gapped-Dirac-cone limit. The polarization decreases significantly with enhanced tunnelling realized systematically in thin insulating films, whereas magnitude of the polarization saturates to the bulk limit faster at larger wavevectors in thicker metallic films. We present a theoretical model that captures this delicate relationship between quantum tunnelling and Fermi surface spin polarization. Our high-resolution spin-based spectroscopic results suggest that the polarization current can be tuned to zero in thin insulating films forming the basis for a future spin-switch nanodevice.

Spectroscopy of Nitrophenolates in Vacuo: Effect of Spacer, Configuration, and Microsolvation on the Charge-Transfer Excitation Energy

In a charge-transfer (CT) transition, electron density moves from one end of the molecule (donor) to the other end (acceptor). This type of transition is of paramount importance in nature, for example, in photosynthesis, and it governs the excitation of several protein biochromophores and luminophores such as the oxyluciferin anion that accounts for light emission from fireflies. Both transition energy and oscillator strength are linked to the coupling between the donor and acceptor groups: The weaker the coupling, the smaller the excitation energy. But a weak coupling necessarily also causes a low oscillator strength possibly preventing direct excitation (basically zero probability in the noncoupling case). The coupling is determined by the actual spacer between the two groups, and whether the spacer acts as an insulator or a conductor. However, it can be difficult or even impossible to distinguish the effect of the spacer from that of local solvent molecules that often cause large solvent shifts due to different ground-state and excited-state stabilization. This calls for gas-phase spectroscopy experiments where absorption by the isolated molecule is identified to unequivocally establish the intrinsic molecular properties with no perturbations from a microenvironment. From such insight, the effect of a protein microenvironment on the CT excited state can be deduced. In this Account, we review our results over the last 5 years from mass spectroscopy experiments using specially designed apparatus on several charged donor-acceptor ions that are based on the nitrophenolate moiety and π-extended derivatives, which are textbook examples of donor-acceptor chromophores. The phenolate oxygen is the donor, and the nitro group is the acceptor. The choice of this system is also based on the fact that phenolate is a common structural motif of biochromophores and luminophores, for example, it is a constituent of the oxyluciferin anion. A presentation of the setups used for gas-phase ion spectroscopy in Aarhus is given, and we address issues of whether double bonds or triple bonds best convey electronic coupling between the phenolate oxygen and the nitro group, the significance of separating the donor and acceptor spatially, the influence of cross-conjugation versus linear conjugation, and along this line ortho versus meta versus para configuration, and not least the effect of a single solvent molecule (water, methanol, or acetonitrile). From systematic studies, a clear picture has emerged that has been supported by high-level calculations of electronically excited states. Our work shows that CC2 coupled-cluster calculations of vertical excitation energies are within 0.2 eV of experimental band maxima, and importantly, that the theoretical method is excellent in predicting the relative order of excitation energies of a series of nitrophenolates. Finally, we discuss future challenges such as following the change in absorption as a function of the number of solvent molecules and when gradually approaching the bulk limit.

Melting of “non-magic” argon clusters and extrapolation to the bulk limit

The melting of argon clusters ArN is investigated by applying a parallel-tempering Monte Carlo algorithm for all cluster sizes in the range from 55 to 309 atoms. Extrapolation to the bulk gives a melting temperature of 85.9 K in good agreement with the previous value of 88.9 K using only Mackay icosahedral clusters for the extrapolation [E. Pahl, F. Calvo, L. Koči, and P. Schwerdtfeger, "Accurate melting temperatures for neon and argon from ab initio Monte Carlo simulations," Angew. Chem., Int. Ed. 47, 8207 (2008)]. Our results for argon demonstrate that for the extrapolation to the bulk one does not have to restrict to magic number cluster sizes in order to obtain good estimates for the bulk melting temperature. However, the extrapolation to the bulk remains a problem, especially for the systematic selection of suitable cluster sizes.

Shape resonances and shell effects in thin-film multiband superconductors

We study analytically the evolution of superconductivity in clean quasi-two-dimensional multiband supercon- ductors as the film thickness enters the nanoscale region by mean-field and semiclassical techniques. Tunneling into the substrate and finite lateral size effects, which are important in experiments, are also considered in our model. As a result, it is possible to investigate the interplay between quantum coherence effects, such as shape resonances and shell effects, with the potential to enhance superconductivity, and the multiband structure and the coupling to the substrate that tend to suppress it. The case of magnesium diboride, which is the conventional superconductor with the highest critical temperature, is discussed in detail. Once the effect of the substrate is considered, we still observe quantum size effects such as the oscillation of the critical temperature with the thickness but without a significant enhancement of superconductivity. In thin films with a sufficiently longer superconducting coherence length, it is, however, possible to increase the critical temperature above the bulk limit by tuning the film thickness or lateral size.

Monte Carlo simulations of phonon transport in nanoporous silicon and germanium

Heat conduction of nanoporous silicon and germanium thin films is studied thanks to a statistical approach. Resolution of phonon Boltzmann transport equation is performed with a Monte Carlo technique in order to assess thermal conductivity. Sensitivity of this latter property with respect to parameters such as phonon mean free path and characteristics of the pores (distribution, size, porosity) is discussed and compared to predictions from analytical models. Results point out that thermal properties might be tailored through the design of the porosity and more specifically by the adjustment of the phonon-pore mean free path. Finally, an effective medium technique is used to extend our work to multilayered crystalline-nanoporous structures. Results show that ought to pore scattering, a diffusive Fourier regime can be recovered even when the film thickness is below the bulk limit.

Elementary Polarizability of Sc/Fullerene/Graphene Aggregates and Di/Graphene–Cation Interactions

Elementary Polarizability of Sc/Fullerene/Graphene Aggregates and Di/Graphene–Cation Interactions Interacting induced-dipoles polarization in code POLAR allows molecular polarizability, which is tested with Scn/Cn [fullerene/ graphene (GR)]/Scn@Cm clusters. Polarizability sees clusters of unlike sizes, parting isomers. Bulk limit is estimated from Clausius– Mossotti relation. Clusters are more polarizable than the bulk. Theory yielded this for small Sin/Gen/GanAsm; however, experiment, reversely for larger Sin/GanAsm/GenTem. Smaller clusters need not act like middle: surface dangling bonds cause small-clusters polarizability that resembles metallic. Code AMYR models GR(2)– Mz+. A 24-atom plane models GR. Mz+ is placed on GR top (T)/ bridge (B)/hollow (H). GR–Mz+ stability decays: H>E>T. From H to T, stability drops 75%, 16%, 14%, 35%, 19% and 31% for Li+/Na+/ K+/M+ mean/Ca2+/average. In GR2–Mz+ from H to B to T, stability decays 4%/1%. Drops are smaller than GR–Mz+. Dispersion differs less than GR–Mz+. GR is more aware than GR2 to Mz+, M+/2+ swap and site.

Orbital magnetism of graphene nanostructures

We study the orbital magnetism of graphene ribbons and graphene flakes with various shapes and edge configurations. The property is significantly different depending on the relative magnitude of the thermal broadening energy kBT to the characteristic level spacing ɛ0 due to the quantum confinement. In the low-temperature regime where kBT⪯¡ɛ0, the susceptibility as a function of Fermi energy rapidly changes between diamagnetism and paramagnetism in accordance with the discrete spectral structure due to the quantum confinement. In the high-temperature regime kBT⪢ɛ0, the oscillatory structures due to the finite-size effect are all gone leaving a single diamagnetic peak in the bulk limit, regardless of atomic configuration of the graphene nanostructures. The diamagnetic current circulates entirely over the graphene nanostructures in the low-temperature regime, reflecting the absence of characteristic length scale in the massless Dirac system. As temperature increases, the current gradually becomes to circulate only near the edge, with the characteristic depth of λedge=ℏv/2πkBT.

Real-Time Observation of Interlayer Vibrations in Bilayer and Few-Layer Graphene

We report real-time observation of the interlayer shearing mode, corresponding to the lateral oscillation of graphene planes, for bi- and few-layer graphene. Using a femtosecond pump-probe technique, we have followed coherent oscillations of this vibrational mode directly in the time domain. The shearing-mode frequency, as expected for an interlayer mode, exhibits a strong and systematic dependence on the number of layers, varying from 1.32 THz for the bulk limit to 0.85 THz for bilayer graphene. We explored the role of interactions with the external environment on this vibrational mode by comparing the response observed for graphene layers supported by different substrates and suspended in free space. No significant frequency shifts were observed.

Orbital-Ordering-Induced Ferroelectricity inSrCrO3

Using density functional theory calculations, ultrathin films of SrVO3(d1) and SrCrO3(d2) on SrTiO3 substrates have been studied as possible multiferroics. Although both are metallic in the bulk limit, they are found to be insulating as a result of orbital ordering driven by lattice distortions at the ultrathin limit. While the distortions in SrVO3 have a first-order Jahn-Teller origin, those in SrCrO3 are ferroelectric in nature. This route to ferroelectricity results in polarizations comparable with conventional ferroelectrics.

Quantum energy density: Improved efficiency for quantum Monte Carlo calculations

We establish a physically meaningful representation of a quantum energy density for use in Quantum Monte Carlo calculations. The energy density operator, defined in terms of Hamiltonian components and density operators, returns the correct Hamiltonian when integrated over a volume containing a cluster of particles. This property is demonstrated for a helium-neon "gas," showing that atomic energies obtained from the energy density correspond to eigenvalues of isolated systems. The formation energies of defects or interfaces are typically calculated as total energy differences. Using a model of delta-doped silicon (where dopant atoms form a thin plane) we show how interfacial energies can be calculated more efficiently with the energy density, since the region of interest is small. We also demonstrate how the energy density correctly transitions to the bulk limit away from the interface where the correct energy is obtainable from a separate total energy calculation.