Excitation Gap Research Articles

Origin of the U(1) field mass in superconductors

Recently, a new theory for superconductivity has been put forward, in which the persistent current generation is attributed to the emergent singularities of the electronic wave function that are created by the spin-twisting itinerant circular motion of electrons. The persistent current generated by this mechanism behaves in every respect like supercurrent in superconductors, yielding the flux quantum h/2e and the Josephson frequency 2eV/h, where h is Planck’s constant, −e is the electron charge, and V is the voltage across the Josephson junction. The mass generation of the U(1) gauge field (or the Meissner effect) in the new theory is due to the emergence of topological objects, ‘instantons’ generated by the single-valued requirement of the wave function in the presence of the emergent singularities.The current standard theory of superconductivity is based on the BCS theory, and explains the emergence of superconductivity as due to the global U(1) gauge symmetry breaking realized by the Cooper pair formation. The U(1) field mass generation is believed to be due to this global U(1) gauge symmetry breaking. However, the feasibility of this mechanism has been questioned since no known interaction can prepare the global U(1) symmetry broken state from the normal state. We argue here that the U(1) mass generation in the BCS superconductor can be attributed to the one by the instanton mentioned above if the Rashba spin-orbit interaction is added. Then, the occurrence of persistent current generation becomes due to the instanton formation, and the role of the Cooper pair formation is to stabilize the instanton by providing an energy gap for perturbative excitations. Upon forming the Cooper pair, the instanton is stabilized and persistent current generation becomes possible. Thus, the superconducting transition temperature coincides with the Cooper pair formation temperature.

Bogoliubov Fermi Surfaces in Superconductors with Broken Time-Reversal Symmetry.

It is commonly believed that, in the absence of disorder or an external magnetic field, there are three possible types of superconducting excitation gaps: The gap is nodeless, it has point nodes, or it has line nodes. Here, we show that, for an even-parity nodal superconducting state which spontaneously breaks time-reversal symmetry, the low-energy excitation spectrum generally does not belong to any of these categories; instead, it has extended Bogoliubov Fermi surfaces. These Fermi surfaces can be visualized as two-dimensional surfaces generated by "inflating" point or line nodes into spheroids or tori, respectively. These inflated nodes are topologically protected from being gapped by a Z_{2} invariant, which we give in terms of a Pfaffian. We also show that superconducting states possessing these Fermi surfaces can be energetically stable. A crucial ingredient in our theory is that more than one band is involved in the pairing; since all candidate materials for even-parity superconductivity with broken time-reversal symmetry are multiband systems, we expect these Z_{2}-protected Fermi surfaces to be ubiquitous.

Energy Gap of Neutral Excitations Implies Vanishing Charge Susceptibility.

In quantum many-body systems with a U(1) symmetry, such as particle number conservation and axial spin conservation, there are two distinct types of excitations: charge-neutral excitations and charged excitations. The energy gaps of these excitations may be independent from each other in strongly correlated systems. The static susceptibility of the U(1) charge vanishes when the charged excitations are all gapped, but its relation to the neutral excitations is not obvious. Here we show that a finite excitation gap of the neutral excitations is, in fact, sufficient to prove that the charge susceptibility vanishes (i.e., the system is incompressible). This result gives a partial explanation for why the celebrated quantization condition n(S-m_{z})∈Z at magnetization plateaus works even in spatial dimensions greater than one.

NMR study on the competing spin chain Rb2Cu2Mo3O12

Quasi-one-dimensional S = 1/2 Heisenberg system Rb2Cu2Mo3O12 described by the J1 - J2 model with the nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic exchange interactions have been investigated by 87/85Rb-NMR under extended field range up to 18 T. From the thermal-activation-type temperature dependence of l/T1, opening of the spin excitation gap was confirmed under the low field below 2 T. With increasing the field, the system becomes gapless, and the gap opens again in the high field saturation region, where the field dependence of the gap size showed the coherent excitation of the neighbouring two spins.

Zero-gap semiconductor to excitonic insulator transition in Ta2NiSe5

The excitonic insulator is a long conjectured correlated electron phase of narrow-gap semiconductors and semimetals, driven by weakly screened electron–hole interactions. Having been proposed more than 50 years ago, conclusive experimental evidence for its existence remains elusive. Ta2NiSe5 is a narrow-gap semiconductor with a small one-electron bandgap EG of <50 meV. Below TC=326 K, a putative excitonic insulator is stabilized. Here we report an optical excitation gap Eop ∼0.16 eV below TC comparable to the estimated exciton binding energy EB. Specific heat measurements show the entropy associated with the transition being consistent with a primarily electronic origin. To further explore this physics, we map the TC–EG phase diagram tuning EG via chemical and physical pressure. The dome-like behaviour around EG∼0 combined with our transport, thermodynamic and optical results are fully consistent with an excitonic insulator phase in Ta2NiSe5.

Thermal Hall conductivity of spin-triplet superconductor with time reversal symmetry breaking

The thermal Hall conductivity is investigated for the superconductor Sr2RuO4 assuming a time reversal symmetry breaking order parameter. The γ band of Sr2RuO4 has its Fermi level near the van Hove points, close to the Lifshitz transition. Within a Bogoliubov-de Gennes approach we calculate the thermal Hall conductivity for pairing symmetries including two exemplary cases, the usual chiral p-wave phase and a fx2−y2-wave phase of the structure . In the chiral p-wave phase the thermal Hall conductivity consists of a universal temperature-linear term and an exponential correction due to quasiparticle activation with a full excitation gap. Due to line-nodes in the gap we find a correction which is quadratic in temperature for fx2−y2-wave state. This difference in the corrections allows to analyze the gap structure of the superconducting phase.

Thermal Hall conductivity in the spin-triplet superconductor with broken time-reversal symmetry

Motivated by the spin-triplet superconductor Sr2RuO4, the thermal Hall conductivity is investigated for several pairing symmetries with broken time-reversal symmetry. In the chiral p-wave phase with a fully opened quasiparticle excitation gap, the temperature dependence of the thermal Hall conductivity has a temperature linear term associated with the topological property directly, and an exponential term, which shows a drastic change around the Lifshitz transition. Examining f-wave states as alternative candidates with $\bm d=\Delta_0\hat{z}(k_x^2-k_y^2)(k_x\pm ik_y)$ and $\bm d=\Delta_0\hat{z}k_xk_y(k_x\pm ik_y)$ with gapless quasiparticle excitations, we study the temperature dependence of the thermal Hall conductivity, where for the former state the thermal Hall conductivity has a quadratic dependence on temperature, originating from the linear dispersions, in addition to linear and exponential behavior. The obtained result may enable us to distinguish between the chiral p-wave and f-wave states in Sr2RuO4.

Observation of charge transfer cascades in α-Fe2O3/IrOx photoanodes by operando X-ray absorption spectroscopy.

Electrochemical devices for energy conversion and storage are central for a sustainable economy. The performance of electrodes is driven by charge transfer across different layer materials and an understanding of the mechanistics is pivotal to gain improved efficiency. Here, we directly observe the transfer of photogenerated charge carriers in a photoanode made of hematite (α-Fe2O3) and a hydrous iridium oxide (IrOx) overlayer, which plays a key role in photoelectrochemical water oxidation. Through the use of operando X-ray absorption spectroscopy (XAS), we probe the change in occupancy of the Ir 5d levels during optical band gap excitation of α-Fe2O3. At potentials where no photocurrent is observed, electrons flow from the α-Fe2O3 photoanode to the IrOx overlayer. In contrast, when the composite electrode produces a sustained photocurrent (i.e., 1.4 V vs. RHE), a significant transfer of holes from the illuminated α-Fe2O3 to the IrOx layer is clearly demonstrated. The analysis of the operando XAS spectra further suggests that oxygen evolution actually occurs both at the α-Fe2O3/electrolyte and α-Fe2O3/IrOx interfaces. These findings represent an important outcome for a better understanding of composite photoelectrodes and their use in photoelectrochemical systems, such as hydrogen generation or CO2 reduction from sunlight.

Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase

Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil "finger print" evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian $(331)$ Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a "proof-of-principle" demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral $p-$wave pairing states.

Synthesis, characterization and performance of visible light active C-TiO2 for pharmaceutical photodegradation

The present paper deals with photocatalytic degradation of carbamazepine and diclofenac by using a modified catalyst with band gap excitations in visible light. The C-doped TiO2 was synthesized using a microwave digestion method from titanium oxyacetylacetate with glucose as the carbon source. The synthesized catalyst was then characterized using Scanning Electron microscopy (SEM), X-ray Diffractometry (XRD), X-ray photoelectron spectroscopy (XPS) and UV-VIS-NIR spectrophotometer. The TiO2 present was in anatase phase and showed significant absorption in visible region. The catalyst was tested for the degradation of carbamazepine and diclofenac under visible light, where complete removal was achieved and the reaction followed first order kinetics. System parameters like catalyst and pollutant concentration, light intensity and time of reaction, were optimized using response surface methodology. In optimum conditions (catalyst concentration of 244mg/L and light intensity of 7715lx) 99% removal was achieved.

Frontispiece: Modelling a Linker Mix‐and‐Match Approach for Controlling the Optical Excitation Gaps and Band Alignment of Zeolitic Imidazolate Frameworks

Frontispiece: Modelling a Linker Mix‐and‐Match Approach for Controlling the Optical Excitation Gaps and Band Alignment of Zeolitic Imidazolate Frameworks

Characterization of recombination in P3HT:fullerene blends: Clarifying the influence of interfacial states

The influence of an interfacial dipole at the donor/acceptor interface on the generation and bulk recombination in P3HT:fullerene blends is clarified. We use P3HT:PC60BM and P3HT:ICBA blends which have a large and small interfacial dipole, respectively. We show that polarons are generated using above and below gap excitations in both blends. The polaron density generated using below gap excitation is lower in P3HT:ICBA blends which is suggested to be due to a higher lying CT state compared to P3HT:PC60BM blends. Using intensity and frequency dependent measurements, we show that the bulk recombination is surprisingly similar in both blends. The bulk recombination is dominated by bimolecular recombination at all light-intensities for the delocalized polarons, while for the localized polaron trap-assisted recombination dominates at low intensities which becomes bimolecular at high intensities. For the localized polaron we find that the characteristic energy for the trap depth to be Ech=24.4±0.7meV and Ech=21.3±0.3 for the P3HT:ICBA and P3HT:PC60BM blends, respectively. Comparing the ratio between the bimolecular recombination constant and the mobility, we find the recombination to be practically the same in the two blends. However, while the localized polaron does show a difference of a factor of two, suggesting faster bimolecular recombination and stronger trap-assisted recombination in the P3HT:ICBA blend having a small interfacial dipole, we conclude that interfacial dipoles have little or no effect on the bulk recombination of long-lived photoexcitations in these blends.

Charge Transfer Reductive in situ Doping of Mesoporous TiO2 Photoelectrodes - Impact of Electrolyte Composition and Film Morphology.

Some material properties depend not only on synthesis and processing parameters, but may furthermore significantly change during operation. This is particularly true for high surface area materials. We used a combined electrochemical and spectroscopic approach to follow the changes of the photoelectrocatalytic activity and of the electronic semiconductor properties of mesoporous TiO2 films upon charge transfer reductive doping. Shallow donors (i.e. electron/proton pairs) were introduced into the semiconductor by the application of an external potential or, alternatively, by band gap excitation at open circuit conditions. In the latter case the effective open circuit doping potential depends critically on electrolyte composition (e.g. the presence of electron or hole acceptors). Transient charge accumulation (electrons and protons) in nanoparticle electrodes results in a photocurrent enhancement which is attributed to the deactivation of recombination centers. In nanotube electrodes the formation of a space charge layer results in an additional decrease of charge recombination at positive potentials. Doping is transient in nanoparticle films, but turns out to be stable for nanotube arrays.

Geometry and Response of Lindbladians

Markovian reservoir engineering, in which time evolution of a quantum system is governed by a Lindblad master equation, is a powerful technique in studies of quantum phases of matter and quantum information. It can be used to drive a quantum system to a desired (unique) steady state, which can be an exotic phase of matter difficult to stabilize in nature. It can also be used to drive a system to a unitarily-evolving subspace, which can be used to store, protect, and process quantum information. In this paper, we derive a formula for the map corresponding to asymptotic (infinite-time) Lindbladian evolution and use it to study several important features of the unique state and subspace cases. We quantify how subspaces retain information about initial states and show how to use Lindbladians to simulate any quantum channels. We show that the quantum information in all subspaces can be successfully manipulated by small Hamiltonian perturbations, jump operator perturbations, or adiabatic deformations. We provide a Lindblad-induced notion of distance between adiabatically connected subspaces. We derive a Kubo formula governing linear response of subspaces to time-dependent Hamiltonian perturbations and determine cases in which this formula reduces to a Hamiltonian-based Kubo formula. As an application, we show that (for gapped systems) the zero-frequency Hall conductivity is unaffected by many types of Markovian dissipation. Finally, we show that the energy scale governing leakage out of the subspaces, resulting from either Hamiltonian/jump-operator perturbations or corrections to adiabatic evolution, is different from the conventional Lindbladian dissipative gap and, in certain cases, is equivalent to the excitation gap of a related Hamiltonian.

Modelling a Linker Mix‐and‐Match Approach for Controlling the Optical Excitation Gaps and Band Alignment of Zeolitic Imidazolate Frameworks

AbstractTuning the electronic structure of metal–organic frameworks is the key to extending their functionality to the photocatalytic conversion of absorbed gases. Herein we discuss how the band edge positions in zeolitic imidazolate frameworks (ZIFs) can be tuned by mixing different imidazole‐based linkers within the same structure. We present the band alignment for a number of known and hypothetical Zn‐based ZIFs with respect to the vacuum level. Structures with a single type of linker exhibit relatively wide band gaps; however, by mixing linkers of a low‐lying conduction edge with linkers of a high‐lying valence edge, we can predict materials with ideal band positions for visible‐light water splitting and CO2 reduction photocatalysis. By introducing copper in the tetrahedral position of the mixed‐linker ZIFs, it would be possible to increase both photo‐absorption and the electron–hole recombination times.

Semiclassical ground-state phase diagram andmulti-Qphase of a spin-orbit-coupled model on triangular lattice

Motivated by recent experiments on the frustrated quantum magnetic compound YbMgGaO4, we study an effective spin model on triangular lattice taking into account the effects of the spin-orbit coupling. We determine the classical ground-state phase diagram of this model, which includes a 120 degree Neel and two collinear antiferromagnetic phases. In the vicinity of the phase boundary between the Neel and collinear phases, we identify three intermediate non-collinear antiferromagnetic phases. In each of them the magnetic moments are ordered at multiple incommensurate wave vector Q values. We further study the effects of quantum fluctuations in this model via a linear spin-wave theory. We find that the spin excitation gap of the non-collinear multi-Q antiferromagnetic state is finite but can be vanishingly small, and this state is unstable to a spin liquid phase under strong quantum fluctuations in some large J_{z+-} regime.

Thermal Hall Conductivity in a Multiband Chiral p-Wave Superconductor

For the spin-triplet superconductor Sr2RuO4, multiband effects on the thermal Hall conductivity are investigated in the superconducting phase. While the gap functions of all bands (α–β and γ) are assumed to have chiral p-wave symmetry, the thermal Hall conductivity at very low temperatures is dominated by the γ band due to its topological nontrivial state and the presence of nodeless quasiparticle excitation gaps.

Modelling a Linker Mix-and-Match Approach for Controlling the Optical Excitation Gaps and Band Alignment of Zeolitic Imidazolate Frameworks.

Tuning the electronic structure of metal–organic frameworks is the key to extending their functionality to the photocatalytic conversion of absorbed gases. Herein we discuss how the band edge positions in zeolitic imidazolate frameworks (ZIFs) can be tuned by mixing different imidazole‐based linkers within the same structure. We present the band alignment for a number of known and hypothetical Zn‐based ZIFs with respect to the vacuum level. Structures with a single type of linker exhibit relatively wide band gaps; however, by mixing linkers of a low‐lying conduction edge with linkers of a high‐lying valence edge, we can predict materials with ideal band positions for visible‐light water splitting and CO2 reduction photocatalysis. By introducing copper in the tetrahedral position of the mixed‐linker ZIFs, it would be possible to increase both photo‐absorption and the electron–hole recombination times.

Treatment of Oil Wastewater and Electricity Generation by Integrating Constructed Wetland with Microbial Fuel Cell.

Conventional oil sewage treatment methods can achieve satisfactory removal efficiency, but energy consumption problems during the process of oil sewage treatment are worth attention. The integration of a constructed wetland reactor and a microbial fuel cell reactor (CW-MFC) to treat oil-contaminated wastewater, compared with a microbial fuel cell reactor (MFC) alone and a constructed wetland reactor (CW) alone, was explored in this research. Performances of the three reactors including chemical oxygen demand (COD), oil removal, and output voltage generation were continuously monitored. The COD removals of three reactors were between 73% and 75%, and oil removals were over 95.7%. Compared with MFC, the CW-MFC with a MnO2 modified cathode produced higher power density and output voltage. Maximum power densities of CW-MFC and MFC were 3868 mW/m3 (102 mW/m2) and 3044 mW/m3 (80 mW/m2), respectively. The plants in CW-MFC play a positive role for reactor cathode potential. Both plants and cathode modification can improve reactor performance of electricity generation.

Two-photon Rabi model: analytic solutions and spectral collapse

The two-photon quantum Rabi model is analyzed using the -symmetry and -algebra. We derive the G-function whose zeros give the exact eigenvalues of the Hamiltonian. The singularity structure of the G-function allows to draw conclusions about the distribution of these eigenvalues along the real axis and we derive the spectral collapse phenomenon at critical coupling , found numerically before. The spectrum at consists of a discrete and a continuous part: the ground state is always separated from the continuum by a finite excitation gap, ruling out a quantum phase transition in the usual sense. For large qubit splitting, also other low lying states split off from the continuum. However, perturbation theory predicts the vanishing of the gap to all orders, demonstrating its non-perturbative nature. We corroborate this result with a variational calculation for the ground state.