Chemical Potential Oscillations Research Articles

NLO evaluation on opto-electronic application and chemical potential oscillation analysis of 2-Chloro-4-nitro-N-methylaniline crystal using crystallographic, spectroscopic and theoretical tools

The new organic composite crystal was grown from 2-Chloro-4-nitro-N-methylaniline compound using Bridgman method and the grown crystal was characterized morphologically, optically, opto-electronically using suitable analytical tools. All the theoretical data were obtained for interpreting physical, chemical and optical characteristics of chemical species- crystal by performing different types of calculations. The crystal dimensions were measured as 0.19 × 0.68 × 0.38 mm3 and the Birefringence (Δn) Kλ/t was calculated to be 1.02. The nonlinear coefficient and nonlinear optical (NLO) efficiency were calculated as 0.8381 at 6.81pm/V. The FT-Raman and FT-IR vibrational data were evaluated to find the scattering bond lengths and bond angles and the homogeneity and heterogeneity of the bond profile was checked for estimating dielectric susceptibility. The chemical shift results for core as well as allied carbons are assessed and the delocalization of chemical potential on different atomic nodal regions was keenly studied. The dielectric property inducement over the molecule and crystal structure was monitored and the direct band gap for amplifying the optical energy was noted and the band gap tuning was discussed. The physico-chemical parameters were evaluated and the support of such parameters was tested. The geometrical parameters were evaluated and the optimized bond lengths and bond angles were checked for customizing trans free structure for constructing prearranged crystal. The UV-Visible absorption and transmission spectral data was evaluated to find the CT complex of the compound. The vibrational circular dichroism (VCD) spectral sequence was thoroughly checked for identifying the important dipole and polarized bonds for fixing enantiomer characteristics.

Effect of Arsenic Depletion on the Silicon Doping of Vapor–Liquid–Solid GaAs Nanowires

It is well known that chemical potential driving the vapor–liquid–solid growth of nanowires oscillates in synchronization with the monolayer growth. In III–V nanowires, this occurs due to depletion of group V atoms in a catalyst droplet. The amphoteric behavior of silicon doping, which often changes from n‐type in planar GaAs layers to p‐type in nanowires, is attributed to low arsenic concentrations. Herein, we present an analytical model which quantifies the doping oscillations over the monolayer formation cycle, and its impact on the electron‐to‐hole ratio for the silicon doping of GaAs nanowires. It is shown that arsenic depletion can easily double the amphoteric effect and strongly favor the tendency for p‐type doping. On a more general ground, the nanowire doping process appears highly sensitive to the chemical potential oscillations related to a restricted amount of material in a nanoscale catalyst.

Linear chemical potential leading to a closed form of the magnetization of a 2DEG in a perpendicular magnetic field

A two-dimensional electron gas (2DEG) under a perpendicular magnetic field is considered. For a given Landau level, the chemical potential can be approximated to have a linear dependence on the magnetic field. This approximation is valid except when complete filling is reached (integer filling factor). The chemical potential oscillation yields a recursion relation for every Landau level. This gives way to an exact form of the magnetization. The derivations herein hold at low temperature.

Refinement of Nucleation Theory for Vapor–Liquid–Solid Nanowires

Features of nucleation of two-dimensional islands in vapor–liquid–solid nanowires determine the nanowire growth rates, morphologies, and crystal phases and thus are central for controlling the physical properties of such structures. Herein, we present a development of nucleation theory that accurately accounts for the droplet depletion effect on the island formation energy. We show that the latter modifies itself to a curve with a maximum at a critical size and a minimum at a stationary size, which determines the size to which the island can actually grow without a refill from vapor. This effect is general and should occur in any nucleation from an isolated nanoparticle. For III–V nanowires, the depletion is extremely sensitive to the concentration of the group V atoms in the droplet and is more pronounced for smaller nanowire radii and lower concentrations. Whenever the stationary size is smaller than that of the facet, the droplet depletion decreases the amplitude of the chemical potential oscillations....

Chemical potential asymmetry and quantum oscillations in insulators

We present a theory of quantum oscillations in insulators that are particle-hole symmetric and nontopological but with arbitrary band dispersion, at both zero and nonzero temperature. At temperatures $T$ less than or comparable to the gap, the dependence of oscillations on $T$ is markedly different from that in metals and depends crucially on the position of the chemical potential $\ensuremath{\mu}$ in the gap. If $\ensuremath{\mu}$ is in the middle of the gap, oscillations do not change with $T$; however, if $\ensuremath{\mu}$ is asymmetrically positioned in the gap, surprisingly, oscillations go to zero at a critical value of the inverse field determined by $T$ and $\ensuremath{\mu}$ and then change their phase by $\ensuremath{\pi}$ and grow again. Additionally, the temperature dependence is different for quantities derived from the grand canonical potential, such as magnetization and susceptibility, and those derived from the density of states, such as resistivity. However, the nontrivial features arising from asymmetric $\ensuremath{\mu}$ are present in both.

Modulation of mechanical resonance by chemical potential oscillation in graphene

The classical picture of the force on a capacitor assumes a large density of electronic states, such that the electrochemical potential of charges added to the capacitor is given by the external electrostatic potential and the capacitance is determined purely by geometry. Here we consider capacitively driven motion of a nano-mechanical resonator with a low density of states, in which these assumptions can break down. We find three leading-order corrections to the classical picture: the first of is a modulation in the static force due to variation in the internal chemical potential, the second and third are change in static force and dynamic spring constant due to the rate of change of chemical potential, expressed as the quantum (density of states) capacitance. As a demonstration, we study a capacitively driven graphene mechanical resonators, where the chemical potential is modulated independently of the gate voltage using an applied magnetic field to manipulate the energy of electrons residing in discrete Landau levels. In these devices, we observe large periodic frequency shifts consistent with the three corrections to the classical picture. In devices with extremely low strain and disorder, the first correction term dominates and the resonant frequency closely follows the chemical potential. The theoretical model fits the data with only one adjustable parameter representing disorder-broadening of the Landau levels. The underlying electromechanical coupling mechanism is not limited the particular choice of material, geometry, or mechanism for variation in chemical potential, and can thus be extended to other low-dimensional systems.

Non-linear Coulomb blockade microscopy of a correlated one-dimensional quantum dot

We evaluate the chemical potential of a one-dimensional quantum dot coupled to an atomic force microscope tip. The dot is described within the Luttinger liquid framework, and the conductance peak positions as a function of the tip location are calculated in the linear and non-linear transport regimes for an arbitrary number of particles. The differences between the chemical potential oscillations induced by the Friedel and Wigner terms are carefully analysed in the whole range of interaction strengths. It is shown that Friedel oscillations, unlike the Wigner ones, are sensitive probes for detecting excited spin states and collective spin density waves involved in the transport.

Chemical potential oscillations from nodal Fermi surface pocket in the underdoped high-temperature superconductor YBa2Cu3O6+x

The electronic structure of the normal state of the underdoped cuprates has thus far remained mysterious, with neither the momentum space location nor the charge carrier type of constituent small Fermi surface pockets being resolved. Whereas quantum oscillations have been interpreted in terms of a nodal-antinodal Fermi surface including electrons at the antinodes, photoemission indicates a solely nodal density-of-states at the Fermi level. Here we examine both these possibilities using extended quantum oscillation measurements. Second harmonic quantum oscillations in underdoped YBa₂Cu₃O(₆+x) are shown to arise chiefly from oscillations in the chemical potential. We show from the relationship between the phase and amplitude of the second harmonic with that of the fundamental quantum oscillations that there exists a single carrier Fermi surface pocket, likely located at the nodal region of the Brillouin zone, with the observed multiple frequencies arising from warping, bilayer splitting and magnetic breakdown.

Shubnikov-de Haas oscillations spectrum of the strongly correlated quasi-2D organic metal (ET)8[Hg4Cl12(C6H5Br)2] under pressure

Pressure dependence of the Shubnikov-de Haas (SdH) oscillations spectra of the quasi-two dimensional organic metal (ET)8[ Hg4Cl12(C6H5Br)2] have been studied up to 1.1 GPa in pulsed magnetic fields of up to 54 T. According to band structure calculations, its Fermi surface can be regarded as a network of compensated orbits. The SdH spectra exhibit many Fourier components typical of such a network, most of them being forbidden in the framework of the semiclassical model. Their amplitude remains large in all the pressure range studied which likely rules out chemical potential oscillation as a dominant contribution to their origin, in agreement with recent calculations relevant to compensated Fermi liquids. In addition to a strong decrease of the magnetic breakdown field and effective masses, the latter being likely due to a reduction of the strength of electron correlations, a sizeable increase of the scattering rate is observed as the applied pressure increases. This latter point, which is at variance with data of most charge transfer salts is discussed in connection with pressure-induced features of the temperature dependence of the zero-field interlayer resistance.

Damping of field-induced chemical potential oscillations in ideal two-band compensated metals

The field and temperature dependence of the de Haas--van Alphen oscillation spectrum is studied for an ideal two-dimensional compensated metal. It is shown that the chemical potential oscillations, which are involved in the frequency combinations observed in the case of uncompensated orbits, are strongly damped and can even be suppressed when the effective masses of the electron- and hole-type orbits are the same. When a magnetic breakdown between bands occurs, this damping is even more pronounced and the Lifshits--Kosevich formalism accounts for the data within a wide field range.

Shubnikov–de Haas effect in multiband quasi-two-dimensional metals

We analyze the behavior of the longitudinal conductivity zz in a field perpendicular to the highly conducting plane of a quasi-two-dimensional multiband metal in the case of a closed system where chemical potential oscillations may be observed compared with the case of an open system for various forms of scattering. In all but one case, we find that there are mixing frequencies present. However, they exhibit different qualitative behaviors, as befits their different origins, and in the case of interband scattering in an open system, may in fact be absent in the de Haas–van Alphen oscillations of that system.

Combination quantum oscillations in canonical single-band Fermi liquids

Chemical potential oscillations mix individual-band frequencies of the de Haas--van Alphen and Shubnikov--de Haas magnetooscillations in canonical low-dimensional multiband Fermi liquids. We predict a similar mixing in canonical single-band Fermi liquids, which Fermi surfaces have two or more extremal cross sections. Combination harmonics are analyzed using a single-band almost two-dimensional energy spectrum. We outline some experimental conditions allowing for resolution of combination harmonics.

Magnetic quantum oscillations of electrons on a two-dimensional lattice: Numerical simulations and the magnetic breakdown approach

We report on analytical and numerical studies of the magnetic quantum oscillations---the de Haas--van Alphen (dHvA) effect---in a model of spinless electrons on a two-dimensional (2D) square lattice in a magnetic field $B$ known as the Azbel-Hofstadter (AH) problem. The numerical simulations of the dHvA oscillations are based on the magnetic band structure, which is obtained by numerical diagonalization of the one-electron model Hamiltonian on a square lattice in the magnetic field. At zero magnetic field and for a filling of 0.55 electrons per unit cell, the shape of the Fermi surface (FS) is close to a chessboard in which white and black cells are related to holes and electrons, respectively. The numerical simulations of the dHvA oscillations for this FS clearly display the magnetic breakdown (MB) features in the Fourier spectrum: the combinational and forbidden frequencies, which cannot be explained within the standard Lifshitz-Kosevich theory. Because of the idealized conditions of our numerical simulation (zero temperature, ideal crystal lattice) the only reason for deviation of the dHvA oscillations from the sawtooth magnetization of a 2D electron gas is the fractal magnetic band structure of the AH problem. We have also developed a semiclassical analytical approach to the dHvA oscillations taking account of the MB at the corners of the hole and electron orbits of the FS, the probability of which $0\ensuremath{\le}W(B)=\mathrm{exp}(\ensuremath{-}{B}_{\mathrm{MB}}∕B)\ensuremath{\le}1$ depends on $B$ and the MB field ${B}_{\mathrm{MB}}$. We have shown that the dHvA oscillations in this case are completely determined by the quantization of the closed hole and electron orbits and by special MB factors for these orbits ${I}^{e(h)}(p)$ ($p=1,2,3,\dots{}$, is the harmonic index). The factors ${I}^{e(h)}(p)$ not only strongly modulate the amplitudes of harmonics in the magnetization but act also through the changes in the chemical potential (CP) oscillations. The latter are very important: they control the shape of the magnetization (which can be close either to a direct or an inverted sawtoothlike profile) and add forbidden peaks in the Fourier spectrum. In the case of a fixed CP the forbidden peaks vanish and the magnetization profile is close to the direct sawtooth. As a function of the MB probability $W(B)$, the MB factors ${I}^{e(h)}(p)$ are polynomials of degree $p$ with the following fixed values at the ends: 1 at $W(B)=0$ and 0 at $W(B)=1$. Our analytic expression for the magnetization as a function of magnetic field $B$ agrees pretty well with our numerical simulations using only one fitting parameter---the MB field ${B}_{\mathrm{MB}}$. Small deviations are due to the fractal fine structure of the magnetic bands.

Frequency combinations in the magnetoresistance oscillations spectrum of a linear chain of coupled orbits with a high scattering rate

The oscillatory magnetoresistance spectrum of the organic metal (BEDO)$_5$Ni(CN)$_4\cdot$3C$_2$H$_4$(OH)$_2$ has been studied up to 50 T, in the temperature range from 1.5 K to 4.2 K. In high magnetic field, its Fermi surface corresponds to a linear chain of quasi-two-dimensional orbits coupled by magnetic breakdown (MB). The scattering rate consistently deduced from the data relevant to the basic $\alpha$ and the MB-induced $\beta$ orbits is very large which points to a significant reduction of the chemical potential oscillation. Despite of this feature, the oscillations spectrum exhibits many frequency combinations. Their effective masses and (or) Dingle temperature are not in agreement with either the predictions of the quantum interference model or the semiclassical model of Falicov and Stachowiak.

Analytical treatment of the de Haas–van Alphen frequency combination due to chemical potential oscillations in an idealized two-band Fermi liquid

The de Haas--van Alphen oscillation spectrum is studied for an idealized two-dimensional Fermi liquid with two parabolic bands in the case of canonical (fixed number of quasiparticles) and grand canonical (fixed chemical potential) ensembles. As already reported in the literature, oscillations of the chemical potential in magnetic field yield frequency combinations that are forbidden in the framework of the semiclassical theory. Exact analytical calculation of the Fourier components is derived at zero temperature, and an asymptotic expansion is given for the high-temperature and low-magnetic-field range. Good agreement is obtained between analytical formulas and numerical computations.

De Haas–van Alphen and chemical potential oscillations in the magnetic-breakdown quasi-two-dimensional organic conductorκ−(BEDT−TTF)2Cu(NCS)2

We present an analytical theory for the de Haas--van Alphen (dHvA) oscillations in layered organic conductors such as $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}\mathrm{Cu}{(\mathrm{NCS})}_{2}$ which takes into account the magnetic breakdown and the chemical potential oscillations. For this purpose we have generalized our theory for the chemical potential oscillations in layered conductors [V.M. Gvozdikov, A.G.M. Jansen, D.I. Pesin, I.D. Vagner, and P. Wyder, Phys. Rev. B 68, 155107 (2003)] to the case of an arbitrary electron dispersion within the layers. Such an approach gives a better agreement with an experimental data for $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}\mathrm{Cu}{(\mathrm{NCS})}_{2}$ salt than that taking account of the magnetic breakdown (MB) only [V.M. Gvozdikov, Yu.V. Pershin, E. Steep, A.G.M. Jansen, and P. Wyder, Phys. Rev. B 65, 165102 (2002)]. The magnetization oscillation patterns and the peaks in the fast Fourier transforms (FFT's) are studied in different combinations of the stochastic and coherent MB regimes with and without the chemical potential oscillations. It is shown that that the chemical potential oscillations in the coherent and stochastic MB regimes do not affect the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ peaks, but change the amplitudes of the higher harmonics and satellites around the $\ensuremath{\beta}$ peak. In the FFT spectrum of $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}\mathrm{Cu}{(\mathrm{NCS})}_{2}$ two satellites are resolved: $\ensuremath{\beta}\ensuremath{-}\ensuremath{\alpha}$ (the so called ``forbidden'' peak) and $\ensuremath{\beta}+\ensuremath{\alpha}$. In the stochastic MB regime all satellites are depressed. In the coherent MB regime with fixed chemical potential they are higher and have equal amplitudes. Only in the coherent MB regime with oscillating chemical potential the ``forbidden'' peak $\ensuremath{\beta}\ensuremath{-}\ensuremath{\alpha}$ becomes larger than the satellite $\ensuremath{\beta}+\ensuremath{\alpha}$ and the calculated FFT spectrum conforms with the FFT spectrum of the dHvA signal of $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}\mathrm{Cu}{(\mathrm{NCS})}_{2}$.

Reply to “Comment on ‘Origin of combination frequencies in quantum magnetic oscillations of two-dimensional multiband metals’ ”

In their comment on the paper (Phys. Rev. B 65, 153403 (2002); cond-mat/0110154), Alexandrov and Bratkovsky (cond-mat/0207173) argue that they correctly took into account the chemical potential oscillations in their analytical theory of combination frequencies in multiband low-dimensional metals by expanding the free energy in powers of the chemical potential oscillations. In this reply, we show that this claim contradicts their original paper (Phys. Rev. B 63, 033105 (2001)). We demonstrate that the condition given for the expansion is mathematically incorrect. The correct condition allows to understand the limits of validity of the analytical theory.

Giant quantum oscillations of the longitudinal magnetoresistance in quasi-two-dimensional metals

We have investigated in frame of the quantum transport theory the magnetic quantum oscillations of the longitudinal magnetoresistance ρ zz in quasi-two-dimensional (2D) metals for a magnetic field perpendicular to the layers. Giant Shubnikov–de Haas oscillations are found when the cyclotron energy ℏ ω c is much larger than the interlayer transfer integral t (the 2D limit). In large magnetic fields and at low temperatures, the minima of the magnetoconductivity σ zz = ρ zz −1 exhibit a thermally activated behavior in presence of negligibly small chemical potential oscillations, as observed in the organic layered conductor β″−(BEDT−TTF) 2SF 5CH 2CF 2SO 3. The questions concerning the absence of strong chemical potential oscillations in such compound and the impurity self-energy are discussed.

Quantum magnetic oscillations of the chemical potential in superlattices and layered conductors

A theory is presented for the chemical potential oscillations in superlattices in a quantizing magnetic field applied perpendicular to the layers which takes into account the electronic miniband structure attached to each Landau level. This miniband structure in the occupation below the Fermi energy reduces the amplitude of the chemical potential oscillations through a specific integral factor which depends on the density of states related to the electronic motion across the layers.

Interconnected magnetoquantum de Haas–van Alphen oscillations in a two-dimensional metal: Wave form and Fourier harmonics

The theory of magnetoquantum oscillations in a two-dimensional (2D) metal with overlapping 2D and 1D energy bands, admitting multiple sets of closed and open orbits and a multisheet Fermi surface, is elaborated on. A system of coupled nonlinear equations for the chemical potential and magnetization oscillations is obtained in a level and harmonic representation. In the framework of a parametrical solution the resulting wave form of oscillation patterns, due to various fundamental frequencies interconnected through chemical potential oscillations, is calculated at any temperature and strength of reservoirs of magnetically unperturbed background states. Analytical expressions for renormalized Fourier harmonics of fundamental and combination frequencies (satellites of the higher frequency and its harmonics) are obtained dependent on the strength of the reservoir. The criterion of validity of these expressions as solutions of nonlinear equations is discussed. The symmetrization effect of the oscillation wave form is found in a multiband electron system without a reservoir of background states. It can be enhanced by the presence of a reservoir. The symmetrization effect is reflected via the nonstandard behavior of second harmonics: nonmonotonic temperature--magnetic-field dependence and disappearance at certain temperatures and magnetic fields (second harmonics zeros). Effects of this kind can also be revealed in heterostructures with external reservoirs of background states.