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Inverted-gap GaSb/InAs quantum wells have long been predicted to show quantum spin Hall insulator (QSHI) behavior. The experimental characterization of the QSHI phase in these systems has relied on the presence of quantized edge transport near charge neutrality. However, experimental data showing the presence of edge conductance in the \emph{trivial} regime suggest that additional experimental signatures are needed to characterize the QSHI phase. Here we show that electric field- induced gap oscillations can be used as an indicator of the presence of helical edge states in system. By studying a realistic low-energy model GaSb/InAs quantum wells derived from $k \cdot p$ band theory, we show that such oscillations are bound to appear in narrow samples as the system is driven to the the the topological phase by the electric field. Our results can serve as a guide for the search of additional experimental signatures of the presence of topologically-protected helical edge states in GaSb/InAs systems., Comment: 9 pages, 9 figures

The development of computational models for the numerical simulation of chemically reacting flows operating in the turbulent regime requires the solution of partial differential equations that represent the balance of mass, linear momentum, chemical species, and energy. The chemical reactions of the model may involve detailed reaction mechanisms for the description of the physicochemical phenomena. One of the biggest challenges is the stiffness of the numerical simulation of these models and the nonlinear nature of species rate of reaction. This work presents a study of in situ adaptive tabulation (ISAT) technique, focusing on the accuracy, efficiency, and memory usage in the simulation of homogeneous stirred reactor models using simple and complex reaction mechanisms. The combustion of carbon monoxide with oxygen and methane with air mixtures are considered, using detailed reaction mechanisms with 4 and 53 species, 3 and 325 reactions, respectively. The results of these simulations indicate that the developed implementation of ISAT technique has a absolute global error smaller than 1 %. Moreover, ISAT technique provides gains, in terms of computational time, of up to 80% when compared with the direct integration of the full chemical kinetics. However, in terms of memory usage the present implementation of ISAT technique is found to be excessively demanding.

Parafermionic zero modes, $\mathbb{Z}_n$-symmetric generalizations of the well-known $\mathbb{Z}_2$ Majorana zero modes, can emerge as edge states in topologically nontrivial strongly correlated systems displaying fractionalized excitations. In this paper, we investigate how signatures of parafermionic zero modes can be detected by its effects on the properties of a quantum dot tunnel-coupled to a system hosting such states. Concretely, we consider a strongly-correlated 1D fermionic model supporting $\mathbb{Z}_4$ parafermionic zero modes coupled to an interacting quantum dot at one of its ends. By using a combination of density matrix renormalization group calculations and analytical approaches, we show that the dot's zero-energy spectral function and average occupation numbers can be used to distinguish between trivial, $\mathbb{Z}_4$ and $2\times \mathbb{Z}_2$ phases of the system. The present work opens the prospect of using quantum dots as detection tools to probe non-trivial topological phases in strongly correlated systems., Comment: 9 pages, 7 figures

The most promising mechanisms for the formation of Majorana bound states (MBSs) in condensed matter systems involve one-dimensional systems (such as semiconductor nanowires, magnetic chains, and quantum spin Hall insulator (QSHI) edges) proximitized to superconducting materials. The choice between each of these options involves trade-offs between several factors such as reproducibility of results, system tunability, and robustness of the resulting MBS. In this article, we propose that a combination of two of these systems, namely a magnetic chain deposited on a QSHI edge in contact with a superconducting surface, offers a better choice of tunability and MBS robustness compared to magnetic chain deposited on bulk. We study how the QSHI edge interacts with the magnetic chain, and see how the topological phase is affected by edge proximity. We show that MBSs near the edge can be realized with lower chemical potential and Zeeman field than the ones inside the bulk, independently of the chain's magnetic order (ferromagnetic or spiral order). Different magnetic orderings in the chain modify the overall phase diagram, even suppressing the boundless topological phase found in the bulk for chains located at the QSHI edge. Moreover, we quantify the "quality" of MBSs by calculating the Majorana Polarization (MP) for different configurations. For chains located at the edge, the MP is close to its maximum value already for short chains. For chains located away from the edge, longer chains are needed to attain the same quality as chains located at the edge. The MP also oscillates in phase with the in-gap states, which is relatively unexpected as peaks in the energy spectrum corresponds to stronger overlap of MBSs., Comment: Published version

This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless. Afterwards, approximated expressions that relate the two equations parameters for the case that the fractional order is close to an integer number are presented. Following, a numerical regression is made using power series expansion, and, also from fractional calculus, the fact that both equations cannot be equivalent is concluded. In the end, from the numerical regression data, the analytical approximated expressions that relate the two equations' parameters are refined., Comment: 10 pages, 5 figures

We study the single impurity Anderson model (SIAM) using the equations of motion method (EOM), the non-crossing approximation (NCA), the one-crossing approximation (OCA), and Wilson's numerical renormalization group (NRG). We calculate the density of states and the linear conductance focusing on their dependence on the chemical potential and on the temperature paying special attention to the Kondo and Coulomb blockade regimes for a large range of model parameters. We report that some standard approximations based on the EOM technique display a rather unexpected poor behavior in the Coulomb blockade regime even at high temperatures. Our study offers a critical comparison between the different methods as well as a detailed compilation of the shortcomings and limitations due the approximations involved in each technique, thus allowing for a cost-benefit analysis of the different solvers that considers both numerical precision and computational performance.

The prospect of using semiconductor quantum dots as an experimental tool to distinguish Majorana zero modes (MZMs) from other zero-energy excitations such as Kondo resonances has brought up the fundamental question of whether topological superconductivity and the Kondo effect can coexist in these systems. Here, we study the Kondo effect in a quantum dot coupled to a metallic contact and to a pair of MZMs. We consider a situation in which the MBS are spin polarized in opposite directions. By using numerical renormalization-group calculations and scaling analysis of the renormalization group equations, we show that the Kondo effect takes place at low temperatures, regardless the coupling to the MZMs. Interestingly, we find that the Kondo singlet essentially decouples from the MZMs such that the residual impurity entropy can show local non-Fermi liquid properties characteristic of the single Majorana excitations. This offers the possibility of tuning between Fermi-liquid and non-Fermi-liquid regimes simply by changing the quantum dot-MZM couplings., Comment: 10 pages, 4 figures

Majorana zero modes (MZMs) emerging at the edges of topological superconducting wires have been proposed as the building blocks of novel, fault-tolerant quantum computation protocols. Coherent detection and manipulation of such states in scalable devices are, therefore, essential in these applications. Recent detection proposals include semiconductor quantum dots (QDs) coupled to the end of these wires, as changes in the QD electronic spectral density due to the MZM coupling could be detected in transport experiments. Here, we propose that multi-QD systems can also be used to manipulate MZMs through precise control over the QDs' parameters. The simplest case where Majorana manipulation is possible is in a double quantum dot (DQD) geometry. By using exact analytical methods and numerical renormalization-group calculations, we show that the QDs' spectral functions can be used to characterize the presence or not of MZMs "leaking" into the DQD. More importantly, we find that these signatures respond to changes in the DQD parameters such as gate-voltages and couplings in a consistent fashion. Additionally, we show that different MZM-DQD coupling geometries ("symmetric" , "in-series" and "T-shaped" junctions) offer distinct ways in which MZMs can be switched from dot to dot. These results highlight the interesting possibilities that DQDs offer for all-electrical MZM control in scalable devices., Comment: Published version. 14 pages, 11 figures