Function Of Chemical Potential Research Articles

Parafermion braiding in fractional quantum Hall edge states with a finite chemical potential

Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $\mathbb{Z}_{2n}$ parafermions which have been predicted to emerge as bound states in fractional quantum Hall systems at filling factor $\nu = 1/n$ ($n$ odd). Using a combination of bosonization and refermionization, we calculate the energy splitting as a function of distance and chemical potential for a pair of parafermions separated by a gapped region. Braiding of parafermions in quantum Hall edge states can be implemented by repeated fusion and nucleation of parafermion pairs. We simulate the conventional braiding protocol of parafermions numerically, taking into account the finite separation and finite chemical potential. We show that a nonzero chemical potential poses challenges for the adiabaticity of the braiding process because it leads to accidental crossings in the spectrum. To remedy this, we propose an improved braiding protocol which avoids those degeneracies.

Field theory approach to the quantum transport in Weyl semimetals

We analyze the structure of the surface states and Fermi arcs of Weyl semimetals as a function of the boundary conditions parameterizing the Hamiltonian self-adjoint extensions of a minimal model with two Weyl points. These boundary conditions determine both the pseudospin polarization of the system on the surface and the shape of the associated Fermi arcs. We analytically derive the expectation values of the density profile of the surface current, we evaluate the anomalous Hall conductivity as a function of temperature and chemical potential and we discuss the surface current correlation functions and their contribution to the thermal noise. Based on a lattice variant of the model, we numerically study the surface states at zero temperature and we show that their polarization and, consequently, their transport properties, can be varied by suitable Zeeman terms localized on the surface. We also provide an estimate of the bulk conductance of the system based on the Landauer-B\"uttiker approach. Finally, we analyze the surface anomalous thermal Hall conductivity and we show that the boundary properties lead to a correction of the expected universal thermal Hall conductivity, thus violating the Wiedemann-Franz law.

The BPS limit of rotating AdS black hole thermodynamics

We consider rotating, electrically charged, supersymmetric AdS black holes in four, five, six and seven dimensions, and provide a derivation of the respective extremization principles stating that the Bekenstein-Hawking entropy is the Legendre transform of a homogeneous function of chemical potentials, subject to a complex constraint. Extending a recently proposed BPS limit, we start from finite temperature and reach extremality following a supersymmetric trajectory in the space of complexified solutions. We show that the entropy function is the supergravity on-shell action in this limit. Chemical potentials satisfying the extremization equations also emerge from the complexified solution.

Fluctuations in cool quark matter and the phase diagram of quantum chromodynamics

We consider the phase diagram of hadronic matter as a function of temperature, T , and baryon chemical potential, mu. Currently the dominant paradigm is a line of first order transitions which ends at a critical endpoint. In this work we suggest that spatially inhomogenous phases are a generic feature of the hadronic phase diagram at nonzero mu and low T . Familiar examples are pion and kaon condensates. At higher densities, we argue that these condensates connect onto chiral spirals in a quarkyonic regime. Both of these phases exhibit the spontaneous breaking of a global U(1) symmetry and quasi-long range order, analogous to smectic liquid crystals. We argue that there is a continuous line of first order transitions which separate spatially inhomogenous from homogenous phases, where the latter can be either a hadronic phase or a quark-gluon plasma. While mean field theory predicts that there is a Lifshitz point along this line of first order transitions, in three spatial dimensions strong infrared fluctuations wash out any Lifshitz point. Using known results from inhomogenous polymers, we suggest that instead there is a Lifshitz regime. Non-perturbative effects are large in this regime, where the momentum dependent terms for the propagators of pions and associated modes are dominated not by terms quadratic in momenta, but quartic. Fluctuations in a Lifshitz regime may be directly relevant to the collisions of heavy ions at (relatively) low energies, sqrt(s)/A : 1 to 20 GeV.

Higher cumulants of baryon number in critical QCD

We study the higher moments of the baryon number in the immediate neighbourhood of the QCD critical endpoint within the framework of Ising-QCD thermodynamics of a finite-size critical system (N. G. Antoniou et al., Phys. Rev. D 97, 034015, 2018). We show that the kurtosis, as a function of the freeze-out baryon chemical potential, becoming negative attains a sharp minimum very close to the critical point. We argue that the sharpness of this minimum is due to the narrowness of the critical region in the chemical potential direction. Our analysis reveals that the broad minimum of the kurtosis (with a positive kurtosis value) observed in Au+Au central collisions at STAR (in RHIC-BES I) in the colliding energy region 17 GeV <s<39 GeV is apparently only a precursor of the critical point and not a signature of its location.

Ion-vacancy coupled charge transfer model for ion transport in concentrated solutions

We present a conceptual framework for understanding and formulating ion transport in concentrated solutions, which pictures the ion transport as an ion-vacancy coupled charge transfer reaction. A key element in this picture is that the transport of an ion from an occupied to unoccupied site involves a transition state which exerts double volume exclusion. An ab initio random walk model is proposed to describe this process. Subsequent coarse-graining results in a continuum formula as a function of chemical potentials of the constituents, which are further derived from a lattice-gas model. The subtlety here is that what has been taken to be the chemical potential of the ion in the past is actually that of the ion-vacancy couple. By aid of this new concept, the driving force of ion transport is essentially the chemical affinity of the ion-vacancy coupled charge transfer reaction, which is a useful concept to unify transport and reaction, two fundamental processes in electrochemistry. This phenomenological model is parameterized for a specific material by the aid of first-principles calculations. Moreover, its extension to multiple-component systems is discussed.

Complete analysis of phase diversity of the simplest adsorption model of a binary gas mixture for all sets of undirected interactions between nearest neighbors

In this paper, a complete analysis of the phase diagrams of the model of adsorption of a binary gas mixture on a square lattice in the ground state for all sets of near undirected interactions between particles was performed. Using the principle of minimum of a large thermodynamic potential in a stable phase, the partition of the model parameter space (the energies of lateral interactions) into regions differing by the type of the phase diagram was constructed. Also, for some regions, partial and total coverages as functions of chemical potentials of the gases were calculated through transfer-matrix method and presented. The work is an extension of the work (Fefelov in Phys Chem Chem Phys 20(15): 10359–10368, 2018).

PH and Redox Induced Color Changes in Protein Crystals Suffused with Dyes

Protein crystals, otherwise usually colorless, can be stained a variety of hues by saturating them with dyes, by diffusion from the mother liquor or co-crystallization. The colors assumed by dyes are a function of chemical factors, particularly pH and redox potential. Protein crystals saturated with a pH sensitive dye, initially at one pH, can be exposed to the mother liquor at a second pH and the crystal will change color over time as H3O+ ions diffuse through the crystal. This allows diffusion rates of H3O+ through the crystal to be measured. Diffusion fronts are often clearly delineated. Similar experiments can be carried out with redox sensitive dyes by adding reductants, such as ascorbic acid or dithionite, or oxidants such as H2O2, to the crystal’s mother liquor. Presented here are a number of experiments using pH or redox sensitive dye-saturated protein crystals, and some experiments using double dye, sequential redox–pH changes.

Density functional theory calculations and thermodynamic analysis of bridgmanite surface structure.

Bridgmanite, a high temperature and pressure form of MgSiO3, is believed to be Earth's most abundant mineral and responsible for the observed seismic anisotropy in the mantle. Little is known about surfaces of bridgmanite but knowledge of the most stable surface terminations is important for understanding various geochemical processes as well as likely slip planes. A density functional theory based thermodynamic approach is used here to establish the range of stability of bridgmanite as well as possible termination structures of the (001), (010), (100) and (011) surfaces as a function of the chemical potential of oxygen and magnesium. The vibrational contribution to the Gibbs free energy is found to be essential for obtaining a stability region of bridgmanite in the phase diagram. The most stable surface termination of bridgmanite varies between three different atomic structures depending on the chemical potential of oxygen and magnesium. The results presented provide a basis for further theoretical studies of the chemical processes on bridgmanite surfaces in the Earth's mantle and slip plane analysis.

Electronic structure and thermoelectric properties of Ta-based half-Heusler compounds with 18 valence electrons

Recently, the half-Heusler compounds with 18 valence electrons have been considered as promising candidate for thermoelectric applications due to their interesting properties. In this work, the structural, electronic and thermoelectric properties of Ta-based half-Heusler TaXY (X = Ru, Rh; X = Sb, Bi, Sn and Pb) have been investigated using the full-potential linearized augmented plane-wave (FP-LAPW) method within the density functional theory (DFT) and the classical Boltzmann transport theory. Generalized gradient approximation as parameterized by Wu-Cohen (GGA-WC) and Tran-Blaha modified Becke-Johnson exchange potential (mBJ) are employed for taking on account the exchange-correlation electron potential. All four studied materials are semiconductor with indirect band gap 0.815 eV for TaRuSb, 0.906 eV for TaRuBi, 1.109 eV for TaRhSn and 1.138 eV for TaRhPb. Additionally, the spin-orbit coupling (SOC) decreases slightly the band gap of these materials. Thermoelectric properties, such as, Seebeck coefficient, electrical conductivity, power factor, total thermal conductivity and figure of merit are calculated in function of chemical potential. Obtained results show that TaXY compounds have good thermoelectric performance with high figure of merit value 0.99.

Evidence for a correlated phase of skyrmions observed in real space

We conduct photoluminescence microscopy that is sensitive to both electron and nuclear spin polarization to investigate the changes that occur in the magnetic ordering in the vicinity of the first integer quantum Hall state in a GaAs 2D electron system (2DES). We observe a discontinuity in the electron spin polarization and nuclear spin longitudinal relaxation time which heralds a spontaneous transition to a phase of magnetic skyrmions. We image in real space the spin phase domains that coexist at this transition, and observe hysteresis in their formation as a function of the 2DES's chemical potential. Based on measurements in a tilted magnetic field orientation, we found that the transition is protected by an energy gap containing the Zeeman energy, and conclude that the skyrmions here have formed as an ensemble.

Higher order fluctuations and correlations of conserved charges from lattice QCD

We calculate several diagonal and non-diagonal fluctuations of conserved charges in a system of 2+1+1 quark flavors with physical masses, on a lattice with size 483 × 12. Higher order fluctuations at μB = 0 are obtained as derivatives of the lower order ones, simulated at imaginary chemical potential. From these correlations and fluctuations we construct ratios of net-baryon number cumulants as functions of temperature and chemical potential, which satisfy the experimental conditions of strangeness neutrality and proton/baryon ratio. Our results qualitatively explain the behavior of the measured cumulant ratios by the STAR collaboration.

Optical properties of superconductor-graphene-superconductor junction

In this work, the optical features of the monolayer graphene surrounded by two high and low Tc superconductors or in other words a superconductor-graphene-superconductor (SGS) junction is analyzed in the visible region as a function of photon energy, chemical potential, temperature, and incident angle. Regarding that, a theoretical formalism was presented to consider the effect of optical conductivity of graphene layer on the interface of two superconductor media. The results show different behaviors for the introduced SGS junction in the visible region for both s and p polarizations. The calculated results may help the development of graphene- and superconductor-based optical devices.

Magnetic induction dependence of Hall resistance in Fractional Quantum Hall Effect

Quantum Hall effects (QHE) are observed in two-dimensional electron systems realised in semiconductors and graphene. In QHE the Hall resistance exhibits plateaus as a function of magnetic induction. In the fractional quantum Hall effects (FQHE) the values of the Hall resistance on plateaus are h/e2 divided by rational fractions, where −e is the electron charge and h is the Planck constant. The magnetic induction dependence of the Hall resistance is the strongest experimental evidence for FQHE. Nevertheless a quantitative theory of the magnetic induction and temperature dependence of the Hall resistance is still missing. Here we constructed a model for the Hall resistance as a function of magnetic induction, chemical potential and temperature. We assume phenomenological perturbation terms in the single-electron energy spectrum. The perturbation terms successively split a Landau level into sublevels, whose reduced degeneracies cause the fractional quantization of Hall resistance. The model yields all 75 odd-denominator fractional plateaus that have been experimentally found. The calculated magnetic induction dependence of the Hall resistance is consistent with experiments. This theory shows that the Fermi liquid theory is valid for FQHE.

Magnetic field induced Weyl semimetal from Wannier-function-based tight-binding model

Weyl semimetals (WSMs) have Weyl nodes where conduction and valence bands meet in the absence of inversion or time-reversal symmetry (TRS), or both. Interesting phenomena are expected in WSMs such as the chiral magnetic effect, anomalous Hall conductivity or Nernst effect, and unique quantum oscillations. The TRS-broken WSM phase can be driven from a topological Dirac semimetal (DSM) by magnetic field or magnetic dopants, considering that DSMs have degenerate Weyl nodes stabilized by rotational symmetry, i.e. Dirac nodes. Here we develop a Wannier-function-based tight-binding (WF-TB) model to investigate the formation of Weyl nodes and nodal rings induced by B field in the topological DSM Na$_3$Bi. The field is applied along the rotational axis. Remarkably, our study based on the WF-TB model shows that upon B field each Dirac node is split into four separate Weyl nodes along the rotational axis near the Fermi level; two nodes with single chiral charge (single Weyl nodes) and two with double chiral charge (double Weyl nodes). This result is in contrast to the common belief that each Dirac node splits into two Weyl nodes. In the effective models, the existence of double Weyl nodes ensures nonzero cubic terms in momentum. We further examine the evolution of Fermi arcs at a side surface as a function of chemical potential. The number of Fermi arcs is consistent with the corresponding Fermi surface Chern numbers, corroborating our finding of the double Weyl nodes. Furthermore, our study reveals the existence of nodal rings in the mirror plane below the Fermi level upon B field. These nodal rings persist with spin-orbit coupling, in contrast to typical nodal ring semimetals. Our WF-TB model can be used to compute interesting features arising from Berry curvature such as anomalous Hall and thermal conductivities, and our findings can be applied to other topological DSMs like Cd$_3$As$_2$.

Impact of chemical potential on the reflectance of graphene in the infrared and microwave domains

The reflectance of graphene is investigated in the framework of the Dirac model with account of its realistic properties, such as nonzero chemical potential and band gap, at any temperature. For this purpose, the exact reflection coefficients of the electromagnetic waves on a graphene sheet expressed via the polarization tensor and ultimately via the electrical conductivity of graphene have been used. The reflectance of graphene is computed as a function of frequency and chemical potential at different temperatures and values of the band-gap parameter. The minimum values of the reflectance are found which are reached in the infrared domain at the points of vanishing imaginary part of the conductivity of graphene. For a gapped graphene, the maximum reflectance equal to unity is reached at the points where the imaginary part of conductivity diverges. The computational results demonstrate an interesting interplay between the band gap and chemical potential in their combined effect on the reflectance. Specifically, there are wide frequency intervals where the reflectance of graphene increases with increasing chemical potential and decreasing band gap. The numerical computations are found to be in good agreement with the analytic asymptotic expressions in the regions of their applicability. Several technological areas, where the obtained results could be used, are listed.

Enhanced specular Andreev reflection in bilayer graphene

Andreev reflection in graphene is special since it can be of two types- retro or specular. Specular Andreev reflection (SAR) dominates when the position of the Fermi energy in graphene is comparable to or smaller than the superconducting gap. Bilayer graphene (BLG) is an ideal candidate to observe the crossover from retro to specular since the Fermi energy broadening near the Dirac point is much weaker compared to monolayer graphene. Recently, the observation of signatures of SAR in BLG have been reported experimentally by looking at the enhancement of conductance at finite bias near the Dirac point. However, the signatures were not very pronounced possibly due to the participation of normal quasi-particles at bias energies close to the superconducting gap. Here, we propose a scheme to observe the features of enhanced SAR even at zero bias at a normal metal (NM)-superconductor (SC) junction on BLG. Our scheme involves applying a Zeeman field to the NM side of the NM-SC junction on BLG (making the NM ferromagnetic), which energetically separates the Dirac points for up-spin and down-spin. We calculate the conductance as a function of chemical potential and bias within the superconducting gap and show that well-defined regions of specular- and retro-type Andreev reflection exist. We compare the results with and without superconductivity. We also investigate the possibility of the formation of a p-n junction at the interface between the NM and SC due to a work function mismatch.

Time-dependent Ginzburg-Landau approach to the dynamics of inhomogeneous chiral condensates in a nonlocal Nambu–Jona-Lasinio model

We study the dynamics of inhomogeneous scalar and pseudoscalar chiral order parameters within the framework of the time-dependent Ginzburg-Landau equations. We utilize a nonlocal chiral quark model to obtain the phase diagram of the model as function of temperature and baryon chemical potential and study the formation of metastable spatial domains of matter where the order parameters acquire a spatial modulation in the course their dynamical evolution. We found that, before reaching the expected equilibrium homogeneous state, both scalar and pseudoscalar chiral condensates go through long-lived metastable inhomogeneous structures. For different initial configurations of the order parameters, the lifetimes of the inhomogeneous structures are compared to timescales in a relativistic heavy-ion collision.

Understanding photocatalytic overall water splitting on CoO nanoparticles: Effects of facets, surface stoichiometry, and the CoO/water interface

Unlike CoO micropowder, which is unable to split water, CoO nanoparticles have been observed to photocatalytically split water into H2 and O2 at room temperature without an externally applied potential or co-catalyst. The photocatalytic activity of CoO nanoparticles has been suggested to stem from an upwards shift in the band edges relative to bulk CoO such that the conduction and valence band edges span the water redox potentials. However, the origin of this shift in the band edges is unknown. In this study, we use first-principles density functional theory (DFT) calculations to explore the thermodynamically stable surface configurations of CoO as a function of oxygen chemical potential. We show that the band edge positions are sensitive to surface chemistry which is determined by surface orientation, adsorbates, and stoichiometry, and thus growth conditions and operating environment. In particular, we predict that CoO nanoparticles have fully hydroxylated CoO(1 1 1) facets, with band edges spanning the water redox potentials, while larger CoO particles (such as CoO micropowders) have a full monolayer of hydrogen on the CoO(1 1 1) facets, with a band alignment that favors water oxidation but not water reduction. Furthermore, we demonstrate that explicit inclusion of liquid water is crucial for accurately predicting the band edge positions, and thus photocatalytic behavior, of CoO in an aqueous solution. Our work explains why photocatalytic overall water splitting has only been observed on CoO nanoparticles, and provides new insights into the relationships between environmental conditions, surface structure, and band alignment, which may lead to new approaches for optimizing activity in CoO and other oxide photocatalysts.

Suppression of Hydrogen Evolution Reaction in Electrochemical N2 Reduction Using Single-Atom Catalysts: A Computational Guideline

We studied electrochemical nitrogen reduction reactions (NRR) to ammonia on single atom catalysts (SACs) anchored on defective graphene derivatives by density functional calculations. We find significantly improved NRR selectivity on SACs compared to that on the existing bulk metal surface due to the great suppression of the hydrogen evolution reaction (HER) on SACs with the help of the ensemble effect. In addition, several SACs, including Ti@N4 (0.69 eV) and V@N4 (0.87 eV), are shown to exhibit lower free energy for NRR than that of the Ru(0001) stepped surface (0.98 eV) due to a strong back-bonding between the hybridized d-orbital metal atom in SAC and π* orbital in *N2. Formation energies as a function of nitrogen chemical potential suggest that Ti@N4 and V@N4 are also synthesizable under experimental conditions.