Hole Liquids Research Articles

Preparation and application method of CNTs dispersion solution for direct electroplating on circuit board holes

Abstract The utilization of carbon black dispersion solutions for the black hole method is common in the electronics industry due to their cost-effectiveness and stable performance. However, the slow electroplating speed caused by carbon black’s poor conductivity can impact industrial processes and time. This paper introduces a water-based dispersion solution of carbon nanotubes (CNTs) for the direct copper electroplating process on circuit board holes and its application method. The dispersion solution comprises “shortened” CNTs with a small aspect ratio, a dispersant, a pH adjuster, and other optimization agents. This black hole liquid functions as a conductive fluid with “shortened” CNTs as the conductive medium, exhibiting high dispersibility, strong through-hole capability, low resistance, and excellent adhesion. Its performance surpasses that of black hole liquids using single-carbon black as the conductive medium. The key advantage lies in avoiding the entanglement associated with conventional long aspect ratio CNTs, thereby enhancing the conductivity of the water-based dispersion solution. This facilitates the formation of a uniform conductive film through the electrostatic self-adsorption method, which is suitable for preparing a conductive film on circuit board hole walls before copper electroplating.

Comment on “Bulk and surface plasmons: Wave-mechanical and second-quantized theories”

The effective Lagrangian for plasmons in an electron liquid is given and is further generalized to a mixture of electron and hole liquids, which we take to model the carriers in a semiconductor. The coupling between plasmon and external electromagnetic field is also discussed. These results show the main conclusions in the paper by Jung and Keller [Phys. Rev. A 103, 063501 (2021)] are uncorrect.

Conductivity bound of the strongly interacting and disordered graphene from gauge/gravity duality

The carriers in graphene tuned close to the Dirac point envisage signatures of the strongly interacting fluid and are subject to hydrodynamic description. The important question is whether strong disorder induces the metal-insulator transition in this two-dimensional material. The bound on the conductivity tensor found earlier within the single current description, implies that the system does not feature metal-insulator transition. The linear spectrum of the graphene imposes the phase-space constraints and calls for the two-current description of interacting electron and hole liquids. Based on the gauge/gravity correspondence, using the linear response of the black brane with broken translation symmetry in Einstein-Maxwell gravity with the auxiliary U(1)-gauge field, responsible for the second current, we have calculated the lower bound of the DC-conductivity in holographic model of graphene. The calculations show that the bound on the conductivity depends on the coupling between both U(1) fields and for a physically justified range of parameters it departs only weakly from the value found for a model with the single U(1) field.

Near Band‐Edge Optical Excitation Leading to Catastrophic Ionization and Electron–Hole Liquid in Room‐Temperature Monolayer MoS2

Atomically thin materials exhibit exotic electronic and optical properties. Strong many‐body interactions from the reduced dielectric environment lead to electronic phases that drastically change conductivity and optical response. For example, these many‐body interactions can give rise to the formation of collective states such as Mott metal–insulator transitions, electron–hole liquids and plasmas, and excitonic condensates, which typically occur at cryogenic temperatures and high excitation densities. Herein, it is demonstrated that in monolayer MoS2 at room temperature, a low‐density (1010 cm−2) excitonic gas is formed with continuous wave (CW) below‐gap optical excitation. A slight increase in the excitation fluence triggers a nanosecond phase transition into a dense electron–hole liquid state with three orders of magnitude higher carrier density. This investigation suggests that while the material is in equilibrium with the CW excitation at the threshold fluence, thermomechanical expansion combined with continuous renormalization of the band gap leads to a sudden increase of optical absorption, which initiates runaway exciton ionization and the formation of a high density electron–hole plasma. Such abrupt changes in the excitation density and carrier population can be the basis of unprecedented applications based on 2D materials.

Electron–hole liquids form at room temperature

Electron–hole liquids form at room temperature

Electron–hole liquid in semiconductors and low-dimensional structures

The condensation of excitons into an electron–hole liquid (EHL) and the main EHL properties in bulk semiconductors and low-dimensional structures are considered. The EHL properties in bulk materials are discussed primarily in qualitative terms based on the experimental results obtained for germanium and silicon. Some of the experiments in which the main EHL thermodynamic parameters (density and binding energy) have been obtained are described and the basic factors that determine these parameters are considered. Topics covered include the effect of external perturbations (uniaxial strain and magnetic field) on EHL stability; phase diagrams for a nonequilibrium exciton-gas–EHL system; information on the size and concentration of electron–hole drops (EHDs) under various experimental conditions; the kinetics of exciton condensation and of recombination in the exciton-gas–EHD system; dynamic EHD properties and the motion of EHDs under the action of external forces; the properties of giant EHDs that form in potential wells produced by applying an inhomogeneous strain to the crystal; and effects associated with the drag of EHDs by nonequilibrium phonons (phonon wind), including the dynamics and formation of an anisotropic spatial structure of the EHD cloud. In discussing EHLs in low-dimensional structures, a number of studies are reviewed on the observation and experimental investigation of phenomena such as spatially indirect (dipolar) electron–hole and exciton (dielectric) liquids in GaAs/AlGaAs structures with double quantum wells (QWs), EHDs containing only a few electron–hole pairs (dropletons), EHLs in type-I silicon QWs, and spatially direct and dipolar EHLs in type-II silicon–germanium heterostructures.

Electron–hole liquid in low-dimensional silicon–germanium heterostructures

A brief review is given of the studies in which quasi-two-dimensional spatially-direct and dipolar electron–hole liquids in Si/SiGe/Si type-II heterostructures with a low Ge content in the SiGe layer were discovered and investigated.

Introduction to Strongly Correlated Electrons in New Materials

The discovery of new natural and artificial materials has revolutionized condensed matter physics and our views on the role of correlations between electrons. Novel properties such as high-temperature superconductivity and colossal magnetoresistance discovered in these materials have overturned our conventional representations of condensed matter physics and pushed us to reconsider many well-established concepts. For example, we must treat the Coulomb interaction between electrons far beyond perturbation theory; we must recall long-forgotten ideas of electronic phase separation introduced originally by Nagaev in the 1960s; we must reconsider the role of electron--phonon and electron--magnon interactions, orbital degrees of freedom, the Rashba effect and many other aspects of condensed matter physics that are becoming increasingly important. In many novel materials, such as the two-dimensional electron gas, the energy associated with the Coulomb interaction is typically of the order of (or even larger than) the kinetic energy of electrons or the Fermi energy. Therefore perturbation theory and associated renormalization group methods are not applicable to these situations and we may expect to find a novel state of matter associated with correlation effects. It is worth mentioning the known examples of these states proposed recently, such as marginal Fermi liquids, novel metal--insulator phase transitions in the two-dimensional electron gas associated with new metallic and insulating states, structured liquids, microscopic electronic phase separations, stripes, strings, polarons and others. The discussion of these states is now on the frontier of modern condensed matter physics and is partially covered in this special issue. The demand to treat the Coulomb interaction properly has stimulated a development of many-body theory, which considers correlations as fully as possible. Strong correlations may play an important role in the dynamics of the electronic system. In a two-dimensional electron gas subjected to a transverse magnetic field, correlations associated with the Coulomb interaction transform normal electrons into composite fermions consisting of electrons with integer magnetic fluxes attached to them. The quasiparticle excitations, such as holes, arising in these systems may have fractional statistics (the so-called anyons). Thus, a strong Coulomb interaction in novel materials may change the face of electrons, transforming their statistical properties. Such a phenomenon has already been established in quasi-one-dimensional materials, where an arbitrarily weak interaction transforms the Fermi liquid state associated with fermions into a bosonic Luttinger liquid. Will this effect happen in other types of novel materials? Future studies will answer this question. Many-body correlations may change the nature of the Coulomb interaction between electrons, leading to screening and over-screening effects. In the latter case the Coulomb repulsion between electrons will be transformed into a mutual attraction at certain distances. At some critical electron density, when the average distance between electrons is within this attractive region, this over-screening effect will obviously lead to the formation of electronic clusters and eventually to the formation of a clustered liquid or stripes. A similar effect may also arise through lattice distortions or electron--phonon interaction. In many new materials there exists an insulating antiferromagnetic state, which is transformed under doping, eventually leading to a metallic state. The evolution of the antiferromagnetic state under doping has been a central issue in scientific discussions for decades. How the metal--insulator transition arises and the nature of the eventual metallic state are still not clear, although many interesting ideas are competing. The motion of a single doped hole leaves a trace behind, a piece of a single domain wall. Such pieces of domain walls arising from the motion of holes may be self-organized into a network of channels or a network of string and stripes. Such a network serves as a roadmap for hole motion and may be responsible for anomalies in physical properties of novel materials. The Department of Physics at Loughborough University held an international workshop on Strongly Correlated Electrons in New Materials (SCENM02) which took place in conjunction with the annual meeting of the Condensed Matter Theory Group of the Institute of Physics on 14--17 December 2002. There were about 40 invited speakers and many poster presenters from a total of 12 countries, covering many aspects of the physics of colossal magnetoresistance manganites, high-temperature superconductors, two-dimensional electron gases displaying metal--insulator transition, electron--hole liquids, hydrogen at high pressures, semiconductor superlattices, magnetic multilayers and other novel materials. The abstract book is available on the physics department website at http://www.lboro.ac.uk/departments/ph/events/Abstracts.pdf. In this special issue we have collected papers covering these and many other important aspects of correlated electrons in new materials presented at the international workshop. We hope that this issue will stimulate further development in the physics of correlated electrons and lead to many new phenomena still waiting to be discovered.

Superconducting transition temperatures and coherence length in non-s-wave pairing materials correlated with spin-fluctuation mediated interaction

Following earlier work on electron or hole liquids flowing through assemblies with magnetic fluctuations, we have recently exposed a marked correlation of the superconducting temperature Tc, for non s-wave pairing materials, with coherence length xi and effective mass m*. The very recent study of Abanov et al. [Europhys. Lett. 54, 488 (2001)] and the prior investigation of Monthoux and Lonzarich [Phys. Rev. B 59, 14598 (1999)] have each focussed on the concept of a spin-fluctuation temperature T_sf, which again is intimately related to Tc. For the d-wave pairing via antiferromagnetic spin fluctuations in the cuprates, these studies are brought into close contact with our own work, and the result is that k_B T_sf ~ hbar^2 / m* xi^2. This demonstrates that xi is also determined by such antiferromagnetic spin-fluctuation mediated pair interaction. The coherence length in units of the lattice spacing is then essentially given in the cuprates as the square root of the ratio of two characteristic energies, namely: the kinetic energy of localization of a charge carrier of mass m* in a specified magnetic correlation length to the hopping energy. The quasi-2D ruthenate Sr_2RuO_4, with Tc ~ 1.3 K, has p-wave spin-triplet pairing and so is also briefly discussed here.

Electron (Hole) Liquids Flowing Through Both Heavy Fermion and Cuprate Materials in Superconducting and Normal States

In earlier work, we have considered electron (hole) liquids flowing through assemblies with antiferromagnetic fluctuations in the normal state of high-Tc cuprates. The present review has as its focus to compare and contrast these high-Tc cuprates with heavy Fermion superconductors. Both classes of materials will be considered in superconducting as well as in normal phases. In the former phase, a further focal point will be the symmetry of the pairing. In underdoped cuprates with d-wave symmetry, evidence continues to mount for preformed (2e) Bosons in the normal state, especially from neutron scattering experiments. This is in marked contrast to the heavy Fermion material UBe13, where very recent differential conductivity measurements on a UBe13-Au junction appear to exclude the formation of such precursor Bosons.

Is the Asymptotic Scenario of Precursor r space Bosons Consistent with Observation for Electron (hole) Liquids in Underdoped High-T cCuprates?

The motivation for this study is the review by Timusk and Statt [Rep. Prog. Phys. 62, 61 (1999)] on the pseudogap in high-temperature superconductors. Here, we confront the experimental data they present, plus that of Norman et al. [Nature 392, 157 (1998)] on the Fermi surface in underdoped high-Tc materials with the theoretical asymptotic scenario of precursor r space Boson formation. This reveals no inconsistencies with available observations concerning electron (hole) liquids flowing through such underdoped cuprates with their antiferromagnetic spin fluctuations.

Exciton and charge density wave formation in spatially separated electron–hole liquids

We present a microscopic many-body calculation investigating the competition between the charge density wave and exciton formation in coupled electron–hole layer systems at finite temperature. We find that as the layer separation is decreased there is a divergence at a finite wave vector in the static susceptibility, indicating an instability in the liquid to a coupled charge density wave. We also see evidence in the pair correlation function g( r ) for the liquid phase of a divergence occurring at small r when the layer separation is reduced sufficiently, which would indicate the onset of a bound state instability. However, the charge density wave instability occurs in the liquid before g( r ) can actually diverge. The unified picture which starts to emerge from our results is of a charge density wave instability occurring in the liquid phase at a layer separation larger than the exciton radius. This leaves open the possibility of a second transition from the charge density wave state to the excitonic phase.

Relation Between Electrical Resistivity and Nuclear Relaxation Rate in Metallic States for both Fermi– and Non–Fermi–Liquid Phases

Abstract Fermi–liquid theory in two dimensions, for electron or hole liquids flowing through antiferromagnetic assemblies, yields RT 1 α T, where R is the electrical resistivity and T 1 −1 the nuclear relaxation rate. This relation holds over an appropriate temperature range for Cu spins in underdoped high Tc cuprates. Here a non–Fermi–liquid phase of a strongly disordered metallic spin glass is pointed out to exhibit a relation RT 1 ∝ Tn , again over a restricted temperature range, where the exponent n has the meanfield value of 5/4.

Static and dynamic properties of coupled electron-electron and electron-hole layers.

We have investigated coupled layers of electron and hole liquids in semiconductor heterostructures in zero magnetic field for densities ${\mathit{r}}_{\mathit{s}}$\ensuremath{\lesssim}20 using the Singwi-Tosi-Land-Sj\"olander self-consistent formalism generalized for layers of unequal density. We calculate susceptibilities, local fields, pair correlation functions, and the dispersion of the collective modes for a range of layer spacings. We include cases where the densities in the two layers are not equal. We find generally that static correlations acting between layers do not have a large effect on the correlations within the layers. For coupled electron-hole layers we find that as the spacing between the layers decreases there is a divergence in the static susceptibility of the liquid that signals an instability towards a charge-density-wave ground state. When the layer spacing approaches the effective Bohr radius the electron-hole correlation function starts to diverge at small interparticle separations. This effect is a precursor to the onset of excitonic bound states but this is preempted by the charge-density-wave instability. The acoustic plasmon exhibits a crossover in behavior from a coupled mode to a mode that is confined to a single layer. Correlations sometimes push the acoustic plasmon dispersion curve completely into the single-particle excitation spectrum. For layers with different densities the Landau damping within the single-particle excitation region is sometimes so weak that the acoustic plasmon can exist inside the region as a sharp resonance. We find for the electron-hole case that proximity to the charge-density-wave instability has an unusual effect on the dispersion of the optical plasmon mode. \textcopyright{} 1996 The American Physical Society.

Transport Properties of Electron or Hole Liquids in Normal State of HighTcCopper Oxides

Abstract In earlier work on strongly correlated liquid metals, taken along the liquid-vapour coexistence curve towards the critical point, a relation between a transport property, electrical resistivity, and a thermodynamic quantity, magnetic susceptibility, has been demonstrated. This same type of correlation is pressed here for electron or hole liquids flowing through antiferromagnetic assemblies in the normal state of some high Tc copper oxide materials. Elimination of magnetic susceptibility in a Fermi liquid framework then leads to the prediction that electrical resistivity is intimately linked with nuclear spin-lattice relaxation time and empirical data is employed to test this relation. Finally, experiments on Hall constant and thermopower are also briefly referred to.

Electron or Hole Liquids Flowing Through Antiferromagnetic Assemblies: Relevance to High Tc Materials

Abstract The effects of electron or hole liquids flowing through antiferromagnetic assemblies were discussed in early work by de Gennes. After a brief survey of his main conclusions, attention will be focused on the way such mobile carriers influence the magnetic properties of high Tc cuprates. The effective interaction J between localized Cu spins becomes a function of carrier concentration, p say, while the effective ionic magnetic moment becomes also dependent on p. Other recent work in which both itinerant and bound dopants have been studied are related to de Gennes findings. Finally, some comments are made on Fermi surface and transport properties in relation to certain theoretical models.