Density Of States Measurements Research Articles

Impact of Narrowing Density of States in Semiconducting Polymers on Performance of Organic Field-Effect Transistors.

To improve the performance of organic field-effect transistors (OFETs) employing π-conjugated polymers, a basic understanding of the relationships between the material properties and device characteristics is crucial. Although the density of states (DOS) distribution is one of the essential material properties of semiconducting polymers, insights into how the DOS shape affects the mobility (µ), subthreshold swing (S), and contact resistance (RC ) in OFETs remain lacking. In this study, by combining sensitive DOS measurements and multilayered OFET structures, it is experimentally demonstrated that narrower DOS widths in the polymer channels lead to higher µ, smaller S, and lower RC . By contrast, variation of the DOS in the bulk layer does not affect the performance. These results demonstrate a direct relationship between the polymer properties and OFET performance and highlight the importance of controlling the DOS width in π-conjugated polymers.

Orlicz-Sobolev embeddings, extensions and Orlicz-Poincaré inequalities

We provide necessary conditions on the regularity of domains for the optimal embeddings of first order (and higher order) Orlicz–Sobolev spaces into Orlicz spaces in the sense of [5], [6] (and [9]). We show that if A(t)≤C0tp near infinity for some p≥1 and W1,A(Ω)↪LAn(Ω), then there exists a constant C such that for every x∈Ω‾ and 0<r≤1, |B(x,r)∩Ω|≥g−1(r/C)−1, where g(s)=∫s∞An−1(t)A−1(t)dtt. In particular, if IA<n, then Ω satisfies the measure density condition. Similarly, the embedding into the space of continuous functions implies a lower bound estimate which, in the case iA>n, reduces to the measure density condition. A related condition that implies the measure density condition also in the critical case, is given by means of Orlicz–Poincaré inequalities.We also establish the optimal embeddings in an Ahlfors regular metric measure space and prove that lower bound of the measure is a necessary condition for such embeddings. More generally, we derive a lower bound for the measure of B(x,r)∩Ω under the assumption that M1,A(Ω)↪LAˆ(Ω), where Aˆ is a Young function that increases more rapidly than A near infinity. Using our results concerning embeddings combined with a generalization of a result of Heinonen and Koskela, we show that Orlicz-Sobolev extension domains satisfy the measure density condition. In the case of Hajłasz-Orlicz-Sobolev spaces, it follows that the measure density condition, or the validity of certain Orlicz-Poincaré inequalities, characterizes extension domains. We also extend the results of Korobenko-Maldonado-Rios [27] and Korobenko [26] by showing that the doubling condition on the measure is a necessary condition for some Orlicz-Poincaré inequalities.

A Review of Electronic Transport in Superconducting Sr2RuO4 Junctions

We review electronic transport in superconducting junctions with Sr2RuO4. Transport measurements provide evidence for chiral domain walls and, therefore, chiral superconductivity in superconducting Sr2RuO4, but so far, the symmetry of the underlying superconducting state remains inconclusive. Further studies involving density of states measurements and spin-polarised transport in local/non-local Sr2RuO4 junctions with magnetic materials could lead to fundamental discoveries and a better understanding of the superconducting state.

Dependence of the density of states outer measure on the potential for deterministic Schrödinger operators on graphs with applications to ergodic and random models

We prove quantitative bounds on the dependence of the density of states on the potential function for discrete, deterministic Schrödinger operators on infinite graphs. While previous results were limited to random Schrödinger operators with independent, identically distributed potentials, this paper develops a deterministic framework, which is applicable to Schrödinger operators independent of the specific nature of the potential. Following ideas by Bourgain and Klein, we consider the density of states outer measure (DOSoM), which is well defined for all (deterministic) Schrödinger operators. We explicitly quantify the dependence of the DOSoM on the potential by proving a modulus of continuity in the ℓ∞-norm. The specific modulus of continuity so obtained reflects the geometry of the underlying graph at infinity. For the special case of Schrödinger operators on Zd, this implies the Lipschitz continuity of the DOSoM with respect to the potential. For Schrödinger operators on the Bethe lattice, we obtain log-Hölder dependence of the DOSoM on the potential. As an important consequence of our deterministic framework, we obtain a modulus of continuity for the density of states measure (DOSm) of ergodic Schrödinger operators in the underlying potential sampling function. Finally, we recover previous results for random Schrödinger operators on the dependence of the DOSm on the single-site probability measure by formulating this problem in the ergodic framework using the quantile function associated with the random potential.

Variable Exponent Sobolev Spaces and Regularity of Domains

We study the embeddings of variable exponent Sobolev and Hölder function spaces over Euclidean domains, providing necessary and/or sufficient conditions on the regularity of the exponent and/or the domain in various contexts. Concerning the exponent, the relevant condition is log-Hölder continuity; concerning the domain, the relevant condition is the measure density condition.

Measure density and embeddings of Hajłasz-Besov and Hajłasz-Triebel-Lizorkin spaces

In this paper, we investigate the relation between Sobolev-type embeddings of Hajłasz-Besov spaces (and also Hajłasz-Triebel-Lizorkin spaces) defined on a metric measure space (X,d,μ) and lower bound for the measure μ. We prove that if the measure μ satisfies μ(B(x,r))≥crQ for some Q>0 and for any ball B(x,r)⊂X, then the Sobolev-type embeddings hold on balls for both these spaces. On the other hand, if the Sobolev-type embeddings hold in a domain Ω⊂X, then we prove that the domain Ω satisfies the so-called measure density condition, i.e., μ(B(x,r)∩Ω)≥crQ holds for any ball B(x,r)⊂X, where X=(X,d,μ) is an Ahlfors Q-regular and geodesic metric measure space.

Interior and boundary higher integrability of very weak solutions for quasilinear parabolic equations with variable exponents

We prove boundary higher integrability for the (spatial) gradient of very weak solutions of quasilinear parabolic equations of the form ut−divA(x,t,∇u)=0onΩ×(−T,T),u=0on∂Ω×(−T,T),where the non-linear structure A(x,t,∇u) is modeled after the variable exponent p(x,t)-Laplace operator given by |∇u|p(x,t)−2∇u. To this end, we prove that the gradients satisfy a reverse Hölder inequality near the boundary by constructing a suitable test function which is Lipschitz continuous and preserves the boundary values. In the interior case, such a result was proved in Verena Bögelein and Qifan Li (2014) provided p(x,t)≥p−≥2 holds and was then extended to the singular case 2nn+2<p−≤p(x,t)≤p+≤2 in Qifan Li (2017). This restriction was necessary because the intrinsic scalings for quasilinear parabolic problems are different in the case p+≤2 andp−≥2.In this paper, we develop a new approach, using which, we are able to extend the results of Verena Bögelein and Qifan Li (2014), Qifan Li (2017) to the full range 2nn+2<p−≤p(x,t)≤p+<∞ and also obtain analogous results up to the boundary. The main novelty of this paper is that we make use of a unified intrinsic scaling using which our methods are able to handle both the singular case and degenerate case simultaneously. Our techniques improve and simplify many aspects of the method of parabolic Lipschitz truncation (even in the constant exponent case) studied extensively in existing literature. To simplify the exposition, we will only prove the higher integrability result near the boundary, provided the domain Ω satisfies a uniform measure density condition and are non perturbative in nature, hence we make no regularity assumptions for the coefficients of the nonlinear operator. Our techniques are also applicable to higher order equations as well as systems.

Dependence of the Density of States on the Probability Distribution for Discrete Random Schrödinger Operators

Abstract We prove that the density of states measure (DOSm) for random Schrödinger operators on $\mathbb{Z}^d$ is weak-$^{\ast }$ Hölder-continuous in the probability measure. The framework we develop is general enough to extend to a wide range of discrete, random operators, including the Anderson model on the Bethe lattice, as well as random Schrödinger operators on the strip. An immediate application of our main result provides quantitive continuity estimates for the disorder dependence of the DOSm and the integrated density of states (IDS) in the weak disorder regime. These results hold for a general compactly supported single-site probability measure, without any further assumptions. The few previously available results for the disorder dependence of the IDS valid for dimensions $d \geqslant 2$ assumed absolute continuity of the single-site measure and thus excluded the Bernoulli–Anderson model. As a further application of our main result, we establish quantitative continuity results for the Lyapunov exponent of random Schrödinger operators for $d=1$ in the probability measure with respect to the weak-$^{\ast }$ topology.

Uniform measure density condition and game regularity for tug-of-war games

We show that a uniform measure density condition implies game regularity for all $2<p<\infty$ in a stochastic game called 'tug-of-war with noise'. The proof utilizes suitable choices of strategies combined with estimates for the associated stopping times and density estimates for the sum of independent and identically distributed random vectors.

Exact-Dimensional Property of Density of States Measure of Sturm Hamiltonian

For frequency $\alpha$ of bounded type and coupling $\lambda>20$, we show that the density of states measure $\NN_{\alpha,\lambda}$ of the related Sturm Hamiltonian is exact upper and lower dimensional, however, in general it is not exact-dimensional.

Influence of Domain Walls in the Incommensurate Charge Density Wave State of Cu Intercalated 1T-TiSe_{2}.

We report a low-temperature scanning tunneling microscopy study of the charge density wave (CDW) order in 1T-TiSe_{2} and Cu_{0.08}TiSe_{2}. In pristine 1T-TiSe_{2} we observe a long-range coherent commensurate CDW (CCDW) order. In contrast, Cu_{0.08}TiSe_{2} displays an incommensurate CDW (ICDW) phase with localized CCDW domains separated by domain walls. Density of states measurements indicate that the domain walls host an extra population of fermions near the Fermi level which may play a role in the emergence of superconductivity in this system. Fourier transform scanning tunneling spectroscopy studies suggest that the dominant mechanism for CDW formation in the ICDW phase may be electron-phonon coupling.

Mixed spectral regimes for square Fibonacci Hamiltonians

For the square tridiagonal Fibonacci Hamiltonian, we prove existence of an open set of parameters which yield mixed interval-Cantor spectra (i.e. spectra containing an interval as well as a Cantor set), as well as mixed density of states measure (i.e. one whose absolutely continuous and singular continuous components are both nonzero). Using the methods developed in this paper, we also show existence of parameter regimes for the square continuum Fibonacci Schrodinger operator yielding mixed interval-Cantor spectra.

Measure Density and Extension of Besov and Triebel–Lizorkin Functions

We show that a domain is an extension domain for a Hajlasz–Besov or for a Hajlasz–Triebel–Lizorkin space if and only if it satisfies a measure density condition. We use a modification of the Whitney extension where integral averages are replaced by median values, which allows us to handle also the case $$0<p<1$$ . The necessity of the measure density condition is derived from embedding theorems; in the case of Hajlasz–Besov spaces we apply an optimal Lorentz-type Sobolev embedding theorem which we prove using a new interpolation result. This interpolation theorem says that Hajlasz–Besov spaces are intermediate spaces between $$L^p$$ and Hajlasz–Sobolev spaces. Our results are proved in the setting of a metric measure space, but most of them are new even in the Euclidean setting, for instance, we obtain a characterization of extension domains for classical Besov spaces $$B^s_{p,q}$$ , $$0<s<1$$ , $$0<p<\infty $$ , $$0<q\le \infty $$ , defined via the $$L^p$$ -modulus of smoothness of a function.

Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian

We prove for the square Fibonacci Hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants. This is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact-dimensional measures.

Phonon anharmonicity in silicon from 100 to 1500 K

Inelastic neutron scattering was performed on silicon powder to measure the phonon density of states (DOS) from 100 to 1500 K. The mean fractional energy shifts with temperature of the modes were $\ensuremath{\langle}\ensuremath{\Delta}{\ensuremath{\varepsilon}}_{i}/{\ensuremath{\varepsilon}}_{i}\ensuremath{\Delta}T\ensuremath{\rangle}=\ensuremath{-}0.07$, giving a mean isobaric Gr\uneisen parameter of $+6.95\ifmmode\pm\else\textpm\fi{}0.67$, which is significantly different from the isothermal parameter of +0.98. These large effects are beyond the predictions from quasiharmonic models using density functional theory or experimental data, demonstrating large effects from phonon anharmonicity. At 1500 K the anharmonicity contributes $0.15{k}_{\mathrm{B}}$/atom to the vibrational entropy, compared to $0.03{k}_{\mathrm{B}}$/atom from quasiharmonicity. Excellent agreement was found between the entropy from phonon DOS measurements and the reference NIST-JANAF thermodynamic entropy from calorimetric measurements.

Singular Density of States Measure for Subshift and Quasi-Periodic Schrödinger Operators

Simon's subshift conjecture states that for every aperiodic minimal subshift of Verblunsky coefficients, the common essential support of the associated measures has zero Lebesgue measure. We disprove this conjecture in this paper, both in the form stated and in the analogous formulation of it for discrete Schr\"odinger operators. In addition we prove a weak version of the conjecture in the Schr\"odinger setting. Namely, under some additional assumptions on the subshift, we show that the density of states measure, a natural measure associated with the operator family and whose topological support is equal to the spectrum, is singular. We also consider one-frequency quasi-periodic Schr\"odinger operators with continuous sampling functions and show that generically, the density of states measure is singular as well.

Hydrogen trapping at dislocation cores at room temperature in deformed Pd

Abstract Small-angle neutron scattering (SANS) measurements of hydrogen segregation at dislocations in heavily deformed single crystal Pd have been performed at very low solute concentration (PdH0.0016) at equilibrium with respect to hydrogen gas at 295 K. The net (the without-hydrogen measurement subtracted from with-hydrogen measurement) absolute differential macroscopic scattering cross section has been fit with a cylindrical form factor to represent the Cottrell atmosphere, yielding local trapped concentration δ ∼ 0.06 [H]/[Pd], local volumetric dilatation f ∼ 1.01, and trapping radius R ∼ 4 A of the segregated hydrogen. This measurement augments SANS results below ambient temperature [B.J. Heuser, H. Ju, Phys. Rev. B 83 (2011) 094103]. The temperature dependence of the measured radius is confirmed by a Fourier transform of hydrogen occupation at dislocations based on an elastic continuum treatment [Trinkle et al., Phys. Rev. B 83 (2011) 174116]. The measured trapping parameters are consistent with a depopulation of weak long-range dislocation strain fields at ambient temperature; hydrogen binding to stronger core dislocation sites persists at 295 K and results in the measured net scattering. The local solute concentration and trapping radius (less than two Burgers vectors in Pd), are both too small to support optic mode dispersion due to inter-hydrogen interactions. This result supports the conclusion that trapped hydrogen undergoes a hydride to solid solution phase transformation between 200 and 300 K based on hydrogen vibration density of states measurements using incoherent inelastic neutron scattering [Trinkle et al., Phys. Rev. B 83 (2011) 174116, Ju et al., Nucl. Instr. Meth. Phys. Res. A 654, (2011) 522, and Heuser et al., Phys. Rev. B 78 (2008) 214101].

Topological Transition of Dirac Points in a Microwave Experiment

By means of a microwave tight-binding analogue experiment of a graphenelike lattice, we observe a topological transition between a phase with a pointlike band gap characteristic of massless Dirac fermions and a gapped phase. By applying a controlled anisotropy on the structure, we investigate the transition directly via density of states measurements. The wave function associated with each eigenvalue is mapped and reveals new states at the Dirac point, localized on the armchair edges. We find that with increasing anisotropy, these new states are more and more localized at the edges.

Trap Energy Levels in Graphene Oxide Determined by Ballistic Electron Emission Spectroscopy

We show that the first derivative (dIB/dV) of the ballistic electron emission spectroscopy (BEES) current contains information on trap energy levels in graphene-oxide (GO). The devices were sandwiched in an Au/GO/modified-silicon (Au/GO/m-Si) stack. The extracted trap energy levels correlate well with the GO density of states measurements. Since trap states play an important role in charge transport through GO, our results provide relevant insights for graphene-related electronic engineering.

A-Si:H transport parameters from experiments based on photoconductivity

In this paper we review some of the techniques based on the photoconductivity property of hydrogenated amorphous silicon (a-Si:H) from which it is possible to extract transport parameters as well as density of states (DOS) spectroscopies. We also present a new experiment based on the steady state photocarrier grating technique. We show that combined with simple steady state photoconductivity it gives information on the DOS. The comparison of these results with those of other techniques used for DOS measurements theoretically allows determination of transport parameters in a-Si:H.