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F. Reis

Publications and source records attributed to F. Reis.

6 recordsLinked to original sources
arXiv2022

Instantons and transseries of the Mathieu potential deformed by a $\mathcal{PT}$-symmetry parameter

We investigate the non-perturbative effects of a deformation of the Mathieu differential equation consistent with $\mathcal{PT}$ symmetry. First, we develop a connection between the non-Hermitian and Hermitian scenarios by a reparameterization in the complex plane, followed by a restriction of the $\mathcal{PT}$ deformation parameter. The latter is responsible for preserving the information about $\mathcal{PT}$ symmetry when we choose to work in the Hermitian scenario. We note that this factor is present in all non-perturbative results and in the transseries representation of the deformed Mathieu partition function that we have obtained. In quantum mechanics, we found that the deformation parameter of $\mathcal{PT}$ symmetry has an effect on the real instanton solution for the deformed Mathieu potential in the Hermitian scenario. As its value increases, the non-Hermiticity factor makes it smoother for the instanton to pass from one minimum to another, that is, it modifies the instanton width. The explanation for this lies in the fact that the height of the potential barrier decreases as we increase the value of the deformation parameter. We present how this effect extends to the multi-instanton level and to the bounce limit of an instanton-anti-instanton pair. As an application of the obtained results, we show that the equation of motion under a tilted version of the potential in the Hermitian scenario compares to the resistively shunted junction (RSJ) model for the Josephson junction.

hep-th↗
arXiv2022

Energy levels for $\mathcal{PT}$-symmetric deformation of the Mathieu equation

We propose a non-Hermitian deformation of the Mathieu equation that preserves $\mathcal{PT}$ symmetry and study its spectrum and the transition from $\mathcal{PT}$-unbroken to $\mathcal{PT}$-broken phases. We show that our model not only reproduces behaviors expected by the literature but also indicates the existence of a richer structure for the spectrum. We also discuss the influence of the boundary condition and the model parameters in the exceptional line that marks the $\mathcal{PT}$ breaking.

quant-ph↗
arXiv2019

Tomonaga-Luttinger liquid in the edge channels of a quantum spin Hall insulator

Topological quantum matter is characterized by non-trivial global invariants of the bulk which induce gapless electronic states at its boundaries. A case in point are two-dimensional topological insulators (2D-TI) which host one-dimensional (1D) conducting helical edge states protected by time-reversal symmetry (TRS) against single-particle backscattering (SPB). However, as two-particle scattering is not forbidden by TRS [1], the existence of electronic interactions at the edge and their notoriously strong impact on 1D states may lead to an intriguing interplay between topology and electronic correlations. In particular, it is directly relevant to the question in which parameter regime the quantum spin Hall effect (QSHE) expected for 2D-TIs becomes obscured by these correlation effects that prevail at low temperatures [2]. Here we study the problem on bismuthene on SiC(0001) which has recently been synthesized and proposed to be a candidate material for a room-temperature QSHE [3]. By utilizing the accessibility of this monolayer-substrate system on atomic length scales by scanning tunneling microscopy/spectroscopy (STM/STS) we observe metallic edge channels which display 1D electronic correlation effects. Specifically, we prove the correspondence with a Tomonaga-Luttinger liquid (TLL), and, based on the observed universal scaling of the differential tunneling conductivity (dI/dV), we derive a TLL parameter K reflecting intermediate electronic interaction strength in the edge states of bismuthene. This establishes the first spectroscopic identification of 1D electronic correlation effects in the topological edge states of a 2D-TI.

cond-mat.mes-hall↗
arXiv2017

The topological surface state of $\alpha$-Sn on InSb(001) as studied by photoemission

We report on the electronic structure of the elemental topological semimetal $\alpha$-Sn on InSb(001). High-resolution angle-resolved photoemission data allow to observe the topological surface state (TSS) that is degenerate with the bulk band structure and show that the former is unaffected by different surface reconstructions. An unintentional $p$-type doping of the as-grown films was compensated by deposition of potassium or tellurium after the growth, thereby shifting the Dirac point of the surface state below the Fermi level. We show that, while having the potential to break time-reversal symmetry, iron impurities with a coverage of up to 0.25 monolayers do not have any further impact on the surface state beyond that of K or Te. Furthermore, we have measured the spin-momentum locking of electrons from the TSS by means of spin-resolved photoemission. Our results show that the spin vector lies fully in-plane, but it also has a finite radial component. Finally, we analyze the decay of photoholes introduced in the photoemission process, and by this gain insight into the many-body interactions in the system. Surprisingly, we extract quasiparticle lifetimes comparable to other topological materials where the TSS is located within a bulk band gap. We argue that the main decay of photoholes is caused by intraband scattering, while scattering into bulk states is suppressed due to different orbital symmetries of bulk and surface states.

cond-mat.str-el↗
arXiv2016

Bismuthene on a SiC Substrate: A Candidate for a New High-Temperature Quantum Spin Hall Paradigm

Quantum spin Hall (QSH) materials promise revolutionary device applications based on dissipationless propagation of spin currents. They are two-dimensional (2D) representatives of the family of topological insulators, which exhibit conduction channels at their edges inherently protected against scattering. Initially predicted for graphene, and eventually realized in HgTe quantum wells, in the QSH systems realized so far, the decisive bottleneck preventing applications is the small bulk energy gap of less than 30 meV, requiring cryogenic operation temperatures in order to suppress detrimental bulk contributions to the edge conductance. Room-temperature functionalities, however, require much larger gaps. Here we show how this can be achieved by making use of a new QSH paradigm based on substrate-supported atomic monolayers of a high-Z element. Experimentally, the material is synthesized as honeycomb lattice of bismuth atoms, forming "bismuthene", on top of the wide-gap substrate SiC(0001). Consistent with the theoretical expectations, the spectroscopic signatures in experiment display a huge gap of ~0.8 eV in bismuthene, as well as conductive edge states. The analysis of the layer-substrate orbitals arrives at a QSH phase, whose topological gap - as a hallmark mechanism - is driven directly by the atomic spin-orbit coupling (SOC). Our results demonstrate how strained artificial lattices of heavy atoms, in contact with an insulating substrate, can be utilized to evoke a novel topological wide-gap scenario, where the chemical potential is located well within the global system gap, ensuring pure edge state conductance. We anticipate future experiments on topological signatures, such as transport measurements that probe the QSH effect via quantized universal conductance, notably at room temperature.

cond-mat.str-el↗