Excitation Gap Research Articles

Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states

Numerical studies by W\'ojs, Yi and Quinn have suggested that an unconventional fractional quantum Hall effect is plausible at filling factors $\nu=$ 1/3 and 1/5, provided the interparticle interaction has an unusual form for which the energy of two fermions in the relative angular momentum three channel dominates. The interaction between composite fermions in the second $\Lambda$ level (composite fermion analog of the electronic Landau level) satisfies this property, and recent studies have supported unconventional fractional quantum Hall effect of composite fermions at $\nu^*=$ 4/3 and 5/3, which manifests as fractional quantum Hall effect of electrons at $\nu=$ 4/11, 4/13, 5/13, and 5/17. I investigate in this article the nature of the fractional quantum Hall states at $\nu=$ 4/5, 5/7, 6/17, and 6/7, which correspond to composite fermions at $\nu^*=$ 4/3, 5/3 and 6/5, and find that all these fractional quantum Hall states are conventional. The underlying reason is that the interaction between composite fermions depends substantially on both the number and the direction of the vortices attached to the electrons. I also study in detail the states with different spin polarizations at 6/17 and 6/7 and predict the critical Zeeman energies for the spin phase transitions between them. I calculate the excitation gaps at 4/5, 5/7, 6/7, and 6/17 and compare them against recent experiments.

Photoemission of Energetic Hot Electrons Produced via Up-Conversion in Doped Quantum Dots.

The benefits of the hot electrons from semiconductor nanostructures in photocatalysis or photovoltaics result from their higher energy compared to that of the band-edge electrons facilitating the electron-transfer process. The production of high-energy hot electrons usually requires short-wavelength UV or intense multiphoton visible excitation. Here, we show that highly energetic hot electrons capable of above-threshold ionization are produced via exciton-to-hot-carrier up-conversion in Mn-doped quantum dots under weak band gap excitation (∼10 W/cm2) achievable with the concentrated solar radiation. The energy of hot electrons is as high as ∼0.4 eV above the vacuum level, much greater than those observed in other semiconductor or plasmonic metal nanostructures, which are capable of performing energetically and kinetically more-challenging electron transfer. Furthermore, the prospect of generating solvated electron is unique for the energetic hot electrons from up-conversion, which can open a new door for long-range electron transfer beyond short-range interfacial electron transfer.

Inelastic Neutron Scattering Investigations of an Anisotropic Hybridization Gap in the Kondo Insulators: CeT<sub>2</sub>Al<sub>10</sub> (T=Fe, Ru and Os)

The recent discovery of topological Kondo insulating behaviour in strongly correlated electron systems has generated considerable interest in Kondo insulators both experimentally and theoretically. The Kondo semiconductors CeT2Al10 (T=Fe, Ru and Os) possessing a c-f hybridization gap have received considerable attention recently because of the unexpected high magnetic ordering temperature of CeRu2Al10 (TN=27 K) and CeOs2Al10 (TN=28.5 K) and the Kondo insulating behaviour observed in the valence fluctuating compound CeFe2Al10 with a paramagnetic ground state down to 50 mK. We are investigating this family of compounds, both in polycrystalline and single crystal form, using inelastic neutron scattering to understand the role of anisotropic c-f hybridization on the spin gap formation as well as on their magnetic properties. We have observed a clear sign of a spin gap in all three compounds from our polycrystalline study as well as the existence of a spin gap above the magnetic ordering temperature in T=Ru and Os. Our inelastic neutron scattering studies on single crystals of CeRu2Al10 and CeOs2Al10 revealed dispersive gapped spin wave excitations below TN. Analysis of the spin wave spectrum reveals the presence of strong anisotropic exchange, along the c-axis (or z-axis) stronger than in the ab-plane. These anisotropic exchange interactions force the magnetic moment to align along the c-axis, competing with the single ion crystal field anisotropy, which prefers moments along the a-axis. In the paramagnetic state (below 50 K) of the Kondo insulator CeFe2Al10, we have also observed dispersive gapped magnetic excitations which transform into quasi-elastic scattering on heating to 100 K. We will discuss the origin of the anisotropic hybridization gap in CeFe2Al10 based on theoretical models of heavy-fermion semiconductors.

Quasi-two-dimensional Bose-Einstein condensation of spin triplets in the dimerized quantum magnetBa2CuSi2O6Cl2

We synthesized single crystals of composition Ba$_2$CuSi$_2$O$_6$Cl$_2$ and investigated its quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet BaCuSi$_2$O$_6$ also known as Han purple. Ba$_2$CuSi$_2$O$_6$Cl$_2$ has a singlet ground state with an excitation gap of ${\Delta}/k_{\rm B}\,{=}\,20.8$ K. The magnetization curves for two different field directions almost perfectly coincide when normalized by the $g$-factor except for a small jump anomaly for a magnetic field perpendicular to the $c$ axis. The magnetization curve with a nonlinear slope above the critical field is in excellent agreement with exact-diagonalization calculations based on a 2D coupled spin-dimer model. Individual exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate a 2D exchange network and weak frustration between interdimer exchange interactions, supported by weak spin-lattice coupling implied from our magnetostriction data. The magnetic-field-induced spin ordering in Ba$_2$CuSi$_2$O$_6$Cl$_2$ is described as the quasi-2D Bose-Einstein condensation of triplets.

Effects of gap size and excitation frequency on the vibrational behavior and wear rate of fuel rods

Grid-to-rod fretting (GTRF) wear is a major cause of fuel leaks. Understanding its mechanism is crucial for improving the reliability of nuclear reactors. In this paper we present a three-dimensional, finite-element based approach, which reveals how the wear rate depends on the size of the gap between the grid and the fuel rod, and on the frequency of the excitation force. We show that these two factors affect the dynamic vibration of the rod, which leads to three different regimes: harmonic, period-doubling and chaotic. The wear rate in the harmonic regime is significantly larger than that in the other two regimes, and reaches a maximum when the excitation frequency is close to the resonant frequency of the system, which is dependent on the gap size. We introduce the concept of a critical gap size that gives the maximum wear rate, and we identify the properties and values of this critical gap size. A wear map is developed as a result of a large number of parametric studies. This map shows quantitatively the wear rate as a function of the gap size and excitation frequency, and will be a valuable tool for the design and optimization of the fuel assembly to reduce the risk of fuel leaks caused by GTRF.

Magnetic-field- and pressure-induced quantum phase transition inCsFeCl3proved via magnetization measurements

We have performed magnetization measurements of the gapped quantum magnet CsFeCl$_3$ at temperatures ($T$) down to 0.5\,K at ambient pressure and down to 1.8\,K at hydrostatic pressures ($P$) of up to 1.5\,GPa. The lower-field ($H$) phase boundary of the field-induced ordered phase at ambient pressure is found to follow the power-law behavior expressed by the formula $H_{\rm N}(T)$\,$-$\,$H_{\rm c}$\,$\propto$\,$T_{\rm N}^{\phi}$. The application of pressure extends the phase boundary to both a lower field and higher temperature. Above the critical pressure $P_{\rm c}$\,$\sim$\,0.9\,GPa, the transition field $H_{\rm N}$ associated with the excitation gap becomes zero, and a signature of the magnetic phase transition is found in the $T$-dependence of magnetization in a very low applied field. This suggests that CsFeCl$_3$ exhibits a pressure-induced magnetic phase transition at $P_{\rm c}$.

Spin-orbit coupling control of anisotropy, ground state and frustration in 5d(2) Sr2MgOsO6.

The influence of spin-orbit coupling (SOC) on the physical properties of the 5d2 system Sr2MgOsO6 is probed via a combination of magnetometry, specific heat measurements, elastic and inelastic neutron scattering, and density functional theory calculations. Although a significant degree of frustration is expected, we find that Sr2MgOsO6 orders in a type I antiferromagnetic structure at the remarkably high temperature of 108 K. The measurements presented allow for the first accurate quantification of the size of the magnetic moment in a 5d2 system of 0.60(2) μB –a significantly reduced moment from the expected value for such a system. Furthermore, significant anisotropy is identified via a spin excitation gap, and we confirm by first principles calculations that SOC not only provides the magnetocrystalline anisotropy, but also plays a crucial role in determining both the ground state magnetic order and the size of the local moment in this compound. Through comparison to Sr2ScOsO6, it is demonstrated that SOC-induced anisotropy has the ability to relieve frustration in 5d2 systems relative to their 5d3 counterparts, providing an explanation of the high TN found in Sr2MgOsO6.

Paramagnetically induced gapful topological superconductors

We propose a generic scenario for realizing gapful topological superconductors (TSCs) from gapless spin-singlet superconductors (SCs). Noncentrosymmetric nodal SCs in two dimension are shown to be gapful under a Zeeman field, as a result of the cooperation of inversion-symmetry breaking and time-reversal-symmetry breaking. In particular, non-s-wave SCs acquire a large excitation gap. Such paramagnetically-induced gapful SCs may be classified into TSCs in the symmetry class D specified by the Chern number. We show nontrivial Chern numbers over a wide parameter range for spin-singlet SCs. A variety of the paramagnetically-induced gapful TSCs are demonstrated, including D+p-wave TSC, extended S+p-wave TSC, p+D+f-wave TSC, and s+P-wave TSC. Natural extension toward three-dimensional Weyl SCs is also discussed.

Rutile TiO2 as an Anode Material for Water-Splitting Dye-Sensitized Photoelectrochemical Cells

Water-splitting dye-sensitized photoelectrochemical cells (WS-DSPECs) use a wide bandgap metal oxide semiconductor functionalized with a light-absorbing dye and water-oxidation catalyst to harvest light and drive water oxidation, respectively. We demonstrate here that the rutile polymorph of TiO2 (r-TiO2) is a promising anode material for WS-DSPECs. Recombination between the injected electron and oxidized sensitizer with r-TiO2 is an order of magnitude slower than with anatase TiO2 (a-TiO2), with injection yields approaching 100%. Studies with a reductive quencher demonstrate that r-TiO2 is significantly more efficient than a-TiO2, while exhibiting greater dye stability. Furthermore, comparison of direct band gap excitation photocurrent generation for bare and sensitized r-TiO2 suggests that the sensitizer functions as a light harvester and redox mediator.

Structural and optical study of CaF2 nanoparticles produced by a microwave-assisted hydrothermal method

CaF2 nanoparticles were synthesized by the microwave-assisted hydrothermal method. With the addition of the ethylenediamine (EDA) as chelating agent, the size of the particles was reduced. The CaF2 exhibit single phase identified for X-ray diffraction (XRD) and confirmed by Rietveld refinement. Scanning electron microscopy (SEM) images showed nanoparticles with non-uniform morphology and statistical analysis of collections of particles reviewed that the EDA decreases both the average particle size and average aspect ratio of the particles. The chemical composition of the surface of the particles was investigated by X-ray Photoelectron Spectroscopy (XPS) and the results indicated the presence of reasonable amounts of hydroxyl groups and oxygen ions in the samples produced with EDA. Radioluminescence (RL) measurements showed that both types of nanoparticles presented intrinsic scintillation emission formed by two main bands and that the CaF2 samples produced without EDA presented higher emission intensity. The broad RL band centered at approximately 293nm is related to self-trapped exciton (STE) emission of calcium fluoride, while the band at 428nm can be due to the presence of F centers. The STE excitation and optical band gap were measured through photoluminescent excitation spectra in the VUV range.

Coulomb interactions, Dirac sea polarization, andSU(4)symmetry breaking of the integer quantum Hall states of graphene

We investigate effects of the filled Dirac sea on the $SU(4)$ symmetry breaking in the integer quantum Hall states of graphene with long-ranged Coulomb interactions. Our model also includes Hubbard and nearest neighbour repulsive interactions with strengths $U$ and $V$ respectively. We find that the symmetry breaking of the $n=0$ Landau levels induces an $SU(4)$ polarization of the Dirac sea. This results in several phases which are absent when the effects of the Dirac sea are neglected. We compute the phase diagram in the $U$-$V$ space. We also calculate the excitation gaps in tilted magnetic fields for all the phases. We compare our model results with experiments and find a range of $U$ and $V$ that are consistent with them.

Plasmon excitations in layered high-Tccuprates

Motivated by the recent resonant inelastic x-ray scattering (RIXS) experiment for the electron-doped cuprates Nd_{2-x}Ce_{x}CuO_{4} with x around 0.15, we compute the density-density correlation function in the t-J model on a square lattice by including interlayer hopping and the long-range Coulomb interaction. We find that collective charge excitations are realized not inside the particle-hole continuum, but above the continuum as plasmons. The plasmon mode has a rather flat dispersion near the in-plane momentum q=(0,0) with a typical excitation energy of the order of the intralayer hopping t when the out-of-plane momentum qz is zero. However, when qz becomes finite, the plasmon dispersion changes drastically near q=(0,0), leading to a strong dispersive feature with an excitation gap scaled by the interlayer hopping tz. We discuss that the mode recently observed by RIXS near q=(0,0) can be associated with the plasmon mode with a finite qz.

Superconductivity and fluctuations in Ba1–pKpFe2As2 and Ba(Fe1–nCon)2As2

AbstractWe study the interplay of fluctuations and superconductivity in BaFe2As2 (Ba‐122) compounds with Ba and Fe substituted by K (p doping) and Co (n doping), respectively. To this end, we measured electronic Raman spectra as a function of polarization and temperature. We observe gap excitations and fluctuations for all doping levels studied. The response from fluctuations is much stronger for Co substitution and, according to the selection rules and the temperature dependence, originates from the exchange of two critical spin fluctuations with characteristic wave vectors and . At 22% K doping (), we find the same selection rules and spectral shape for the fluctuations but the intensity is smaller by a factor of 5. Since there exists no nematic region above the orthorhombic spin‐density‐wave (SDW) phase, the identification of the fluctuations via the temperature dependence is not possible. The gap excitations in the superconducting state indicate strongly anisotropic near‐nodal gaps for Co substitution which make the observation of collective modes difficult. The variation with doping of the spectral weights of the and gap features does not support the influence of fluctuations on Cooper pairing. Therefore, the observation of Bardasis–Schrieffer modes inside the nearly clean gaps on the K‐doped side remains the only experimental evidence for the relevance of fluctuations for pairing.

Milestones Toward Majorana-Based Quantum Computing

We introduce a scheme for preparation, manipulation, and readout of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate-control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current; (2) validation of a prototype topological qubit; and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and readout schemes as well.

Interplay of topology and interactions in quantum Hall topological insulators: U(1) symmetry, tunable Luttinger liquid, and interaction-induced phase transitions

We consider a class of {\em quantum Hall topological insulators}: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counter-propagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. HgTe-type heterostructures and graphene are among the relevant systems. We study the effect of electron interactions on the topological properties of the system. We particularly focus on the vicinity of the topological phase transition, marked by the crossing of two Landau levels, where the system is a strongly interacting quantum Hall ferromagnet. We analyse the edge properties using the formalism of the nonlinear $\sigma$-model. We establish the symmetry requirement for the topological protection in this interacting system: effective continuous U(1) symmetry with respect to uniaxial isospin rotations must be preserved. If U(1) symmetry is preserved, the topologically nontrivial phase persists; its edge is a helical Luttinger liquid with highly tunable effective interactions. We obtain explicit analytical expressions for the parameters of the Luttinger liquid. However, U(1) symmetry may be broken, either spontaneously or by U(1)-asymmetric interactions. In either case, interaction-induced transitions occur to the respective topologically trivial phases with gapped edge charge excitations.

Hard gap in a normal layer coupled to a superconductor

The ability to induce a sizable gap in the excitation spectrum of a normal layer placed in contact with a conventional superconductor has become increasingly important in recent years in the context of engineering a topological superconductor. The quasiclassical theory of the proximity effect shows that Andreev reflection at the superconductor/normal interface induces a nonzero pairing amplitude in the metal but does not endow it with a gap. Conversely, when the normal layer is atomically thin, the tunneling of Cooper pairs induces an excitation gap that can be as large as the bulk gap of the superconductor. We study how these two seemingly different views of the proximity effect evolve into one another as the thickness of the normal layer is changed. We show that a fully quantum-mechanical treatment of the problem predicts that the induced gap is always finite but falls off with the thickness of the normal layer $d$. If $d$ is less than a certain crossover scale, which is much larger than the Fermi wavelength, the induced gap is comparable to the bulk gap. As a result, a sizable excitation gap can be induced in normal layers that are much thicker than the Fermi wavelength.

First-order topological phase transition of the Haldane-Hubbard model

We study the interplay of topological band structure and conventional magnetic long-range order in spinful Haldane model with onsite repulsive interaction. Using the dynamical cluster approximation with clusters of up to 24 sites we find evidence of a first order phase transition from a Chern insulator at weak coupling to a topologically trivial antiferromagnetic insulator at strong coupling. These results call into question a previously found intermediate state with coexisting topological character and antiferromagnetic long-range order. Experimentally measurable signatures of the first order transition include hysteretic behavior of the double occupancy, single-particle excitation gap and nearest neighbor spin-spin correlations. This first order transition is contrasted with a continuous phase transition from the conventional band insulator to the antiferromagnetic insulator in the ionic Hubbard model on the honeycomb lattice.

Quantum phase transitions in a generalized compass chain with three-site interactions

We consider a class of one-dimensional compass models with XYZ$-$YZX-type of three-site exchange interaction in an external magnetic field. We present the exact solution derived by means of Jordan-Wigner transformation, and study the excitation gap, spin correlations, and establish the phase diagram. Besides the canted antiferromagnetic and polarized phases, the three-site interactions induce two distinct chiral phases, corresponding to gapless spinless-fermion systems having two or four Fermi points. We find that the $z$ component of scalar chirality operator can act as an order parameter for these chiral phases. We also find that the thermodynamic quantities including the Wilson ratio can characterize the liquid phases. Finally, a nontrivial magnetoelectric effect is explored, and we show that the polarization can be manipulated by the magnetic field in the absence of electric field.

Nonequilibrium electron dynamics in a solid with a changing nodal excitation gap

We develop a computationally inexpensive model to examine the dynamics of boson-assisted electron relaxation in solids, studying nonequilibrium dynamics in a metal, in a nodal superconductor with a stationary density of states, and in a nodal superconductor where the gap dynamically opens. In the metallic system, the electron population resembles a thermal population at all times, but the presence of even a fixed nodal gap both invalidates a purely thermal treatment and sharply curtails relaxation rates. For a gap that is allowed to open as electron relaxation proceeds, effects are even more pronounced, and gap dynamics become coupled to the dynamics of the electron population. Comparisons to experiments reveal that phase-space restrictions in the presence of a gap are likely to play a significant role in the widespread observation of coexisting femtosecond and picosecond dynamics in the cuprate high-temperature superconductors.

Frustrated Ising chains on the triangular lattice inSr3NiIrO6

Inelastic neutron scattering study on the spin-chain compound ${\mathrm{Sr}}_{3}{\mathrm{NiIrO}}_{6}$ reveals gapped quasi-1D magnetic excitations. The observed one-magnon band between 29.5 and 39 meV consists of magnon modes of the ${\mathrm{Ni}}^{2+}$ ions. The fitting of the spin wave spectrum reveals strongly coupled Ising-like chains along the $c$ axis that are weakly coupled into a frustrated triangular lattice in the $ab$ plane. The magnetic excitations survive up to 200 K well above the magnetic ordering temperature of ${T}_{N}\ensuremath{\sim}75$ K, also indicating a quasi-1D nature of the magnetic interactions in ${\mathrm{Sr}}_{3}{\mathrm{NiIrO}}_{6}$. Our microscopic model is in agreement with ab initio electronic structure calculations and explains the giant spin-flip field observed in bulk magnetization measurements.