Observation of Spin and Valley Splitting of Landau Levels under Magnetic Tunneling in Graphene/Boron Nitride/Graphene Structures

Resonance magnetic tunneling in heterostructures formed by graphene single sheets separated by a hexagonal boron nitride barrier and bounded by two gates has been investigated in a strong magnetic field, which has allowed observing transitions between spin- and valley-split Landau levels with various indices belonging to different graphene sheets. An unexpected increase with the temperature in the interlayer tunneling conductance owing to transitions between the Landau levels in strong magnetic fields cannot be explained by existing theories.     

Sum-rules of the response potential in the strongly-interacting limit of DFT

The response part of the exchange-correlation potential of Kohn–Sham density functional theory plays a very important role, for example for the calculation of accurate band gaps and excitation energies. Here we analyze this part of the potential in the limit of infinite interaction in density functional theory, showing that in the one-dimensional case it satisfies a very simple sum rule.     

Predicting Atomic Decay Rates Using an Informational-Entropic Approach

We show that a newly proposed Shannon-like entropic measure of shape complexity applicable to spatially-localized or periodic mathematical functions known as configurational entropy (CE) can be used as a predictor of spontaneous decay rates for one-electron atoms. The CE is constructed from the Fourier transform of the atomic probability density. For the hydrogen atom with degenerate states labeled with the principal quantum number n, we obtain a scaling law relating the n-averaged decay rates to the respective CE. The scaling law allows us to predict the n-averaged decay rate without relying on the traditional computation of dipole matrix elements. We tested the predictive power of our approach up to n =?20, obtaining an accuracy better than 3.7% within our numerical precision, as compared to spontaneous decay tables listed in the literature.     

Einstein-Podolsky-Rosen Steering and Quantum Phase Transition in Spin Chains

We study the Einstein-Podolsky-Rosen steering and quantum phase transitions of the transverse Ising and antiferromagnetic XXZ spin-1/2 chains. By making use of steerable weight, we calculate the steerability for the bipartite subsystems of the models. It is shown that steerability vanishes abruptly and its value maintains zero in a region close to the critical point for the Ising chain. This result is quite different from the information provided by entanglement and quantum discord. While for the XXZ chain, steerability increases and reaches maximal at the critical point, indicating the occurrence of quantum phase transition.     

Green and Cost Effective Synthesis of Fluorescent Carbon Quantum Dots for Dopamine Detection

Carbon quantum dots (CQDs) due to its high fluorescent output is evolving as novel sensing material and is considered as future building blocks for nano sensing devices. Hence, in this investigation we report microwave assisted preparation and multi sensing application of CQDs. The microwave derived CQDs are characterized by Dynamic Light Scattering (DLS) experiment and Fourier Infrared spectra (FTIR) to investigate the size distribution and chemical purity respectively. Fluorescent emission spectra recorded at varying pH shows varying fluorescence emission intensities. Further, emission spectra recorded at different temperatures shows that fluorescence emission of CQDs greatly depends on temperature. Therefore, we demonstrate the pH and temperature sensing characteristics of CQDs by fluorescence quenching behaviour. In addition, the interaction and sensing behaviour of CQDs for dopamine is also presented in this work with a detection limit of 0.2 mM. The steady state and time-resolved methods have been employed in fluorescence quenching methods for sensing dopamine through CQDs at room temperature. The bimolecular quenching rate constants for different concentration have been measured. The interaction between CQDs and dopamine indicates fluorescence quenching method is an elegant process for detecting dopamine through CQDs.     

Unidirectionally Emitting Quantum Cascade Microcavity Lasers with Patterned Contacts

We investigate unidirectionally emitting quantum cascade microcavity lasers with semicircle-patterned top contacts. We employ novel patterned top contacts while fabricating notched ellipse-shaped cavity lasers. We study experimentally the microcavity-structure-based quantum cascade (QC) laser material with a long infrared wavelength of ~10 μm. Then we characterize microcavity lasers with patterned contacts and compare them with nonpatterned ones and observe a lower operating injection threshold current as a consequence of this relatively straightforward technique, with the unidirectional emission feature being kept. We obtain a maximum light output peak power of 16 mW with unidirectional emission at a far-field divergence angle of ~7° at a full width of half maximum, while the patterned device shows low threshold even in the microcavity laser with a size of 150 μm. Furthermore, we also carry out a reliability test of the QC microcavity lasers with semicircle-patterned top contacts, and the testing results show no sudden failure or severe light-output-power drop during an operating time of thousand hours.     

Chern–Simons,Wess–Zumino and other cocycles from Kashiwara–Vergne and associators

Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern–Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as \(p= \langle F, F\rangle \) where F is the curvature 2-form and \(\langle \cdot , \cdot \rangle \) is an invariant scalar product on the corresponding Lie algebra \(\mathfrak g\). The descent for p gives rise to an element \(\omega =\omega _3+\omega _2+\omega _1+\omega _0\) of mixed degree. The 3-form part \(\omega _3\) is the Chern–Simons form. The 2-form part \(\omega _2\) is known as the Wess–Zumino action in physics. The 1-form component \(\omega _1\) is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components \(\omega _1\) and \(\omega _0\). Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara–Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara–Vergne equation F is mapped to \(\omega _1=C(F)\). Furthermore, the component \(\omega _0\) is related to the associator \(\Phi \) corresponding to F. It is surprising that while F and \(\Phi \) satisfy the highly nonlinear twist and pentagon equations, the elements \(\omega _1\) and \(\omega _0\) solve the linear descent equation.     

Conformal Galilei algebras,symmetric polynomials and singular vectors

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras \({\mathfrak {cga}}_\ell (d,\mathbb {C})\) with \(d=1\) for any integer value \(\ell \in {\mathbb {N}}\). The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials.     

Modularity of logarithmic parafermion vertex algebras

The parafermionic cosets \(\mathsf {C}_{k} = {\text {Com}} ( \mathsf {H} , \mathsf {L}_{k}(\mathfrak {sl}_{2}) )\) are studied for negative admissible levels k, as are certain infinite-order simple current extensions \(\mathsf {B}_{k}\) of \(\mathsf {C}_{k}\). Under the assumption that the tensor theory considerations of Huang, Lepowsky and Zhang apply to \(\mathsf {C}_{k}\), irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-modules are obtained from those of \(\mathsf {L}_{k}(\mathfrak {sl}_{2})\). Assuming the validity of a certain Verlinde-type formula likewise gives the Grothendieck fusion rules of these irreducible modules. Notably, there are only finitely many irreducible \(\mathsf {B}_{k}\)-modules. The irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-characters are computed and the latter are shown, when supplemented by pseudotraces, to carry a finite-dimensional representation of the modular group. The natural conjecture then is that the \(\mathsf {B}_{k}\) are \(C_2\)-cofinite vertex operator algebras.