Non-Hermitian Floquet Topological Matter-A Review

The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matter due to its exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions.

Evidence of phase stability, topological phonon and temperature-induced topological phase transition in rocksalt SnS and SnSe

Both SnS and SnSe have been experimentally and theoretically confirmed as topological crystalline insulators in native rocksalt structure. Here, phononic structure, thermodynamic properties and temperature dependent electron-phonon interaction (EPI) have investigated for both the materials in rocksalt phase. Previously performed theoretical studies have predicted the phase instability of SnS in this crystal structure at ambient condition. But, after a detailed study performing on the phonon calculation of SnS, we have predicted the phase stability of SnS with considering the Sn 4porbitals as valence states inab-initiocalculation. The importance of long range Coulomb forces along with the themodynamical properties are also described in detailed for both materials. The computed value of Debye temperature (ΘD) for SnS (SnSe) is ∼315.0 K (∼201.7 K). The preliminary evidence of topological phonon is found alongX-Wdirection, where the linear band touching is observed as compared to type II Weyl phononic material ZnSe (Liuet al2021Phys. Rev.B103094306). The topological phase transition is seen for these materials due to EPI, where non-linear temperature dependent bandgap is estimated. The predicted value of transition temperature for SnS (SnSe) is found to be ∼700 K, where after this temperature the non-trivial to trivial topological phase is seen. The strength of EPI shows more stronger impact on the electronic structure of SnS than SnSe material. The reason of non-linear behaviour of bandgap with rise in temperature is discussed with the help of temperature dependent linewidths and lineshifts of conduction band and valence band due to EPI. The present study reveals the phase stability of SnS along with the comparative study of thermal effect on EPI of SnS and SnSe. Further, the possibility of temperature induced topological phase transition provides one of important behaviour to apply these two materials for device making application.

Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model

Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos by introducing asymmetry to its hopping amplitudes. The resulting nonreciprocal Maryland model is found to possess a real-to-complex spectrum transition at a finite amount of hopping asymmetry, through which it changes from a localized phase to a mobility edge phase. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found. A topological winding number is further introduced to characterize the transition between different phases. Our work introduces a unique type of non-Hermitian quasicrystal, which admits exactly obtainable phase diagrams, mobility edges, and holding no extended phases at finite nonreciprocity in the thermodynamic limit.

Phase-induced topological superconductivity in a planar heterostructure

Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A major cause of this ambiguity is the side effects of applying a magnetic field: induced in-gap states, vortices, and alignment issues. Here we propose a planar semiconductor-superconductor heterostructure as a platform for realizing topological superconductivity without applying a magnetic field to the two-dimensional electron gas hosting the topological state. Time-reversal symmetry is broken only by phase biasing the proximitizing superconductors, which can be achieved using extremely small fluxes or bias currents far from the quasi-one-dimensional channel. Our platform is based on interference between this phase biasing and the phase arising from strong spin-orbit coupling in closed electron trajectories. The principle is demonstrated analytically using a simple model, and then shown numerically for realistic devices. We show a robust topological phase diagram, as well as explicit wavefunctions of Majorana zero modes. We discuss experimental issues regarding the practical implementation of our proposal, establishing it as an accessible scheme with contemporary experimental techniques.

Topological transition in measurement-induced geometric phases

The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous and also underline the physics of robust topological phenomena such as the quantum Hall effect. Equivalently, a geometric phase may be induced through a cyclic sequence of quantum measurements. We show that the application of a sequence of weak measurements renders the closed trajectories, hence the geometric phase, stochastic. We study the concomitant probability distribution and show that, when varying the measurement strength, the mapping between the measurement sequence and the geometric phase undergoes a topological transition. Our finding may impact measurement-induced control and manipulation of quantum states-a promising approach to quantum information processing. It also has repercussions on understanding the foundations of quantum measurement.

Observation of Effective Pseudospin Scattering in ZrSiS

3D Dirac semimetals are an emerging class of materials that possess topological electronic states with a Dirac dispersion in their bulk. In nodal-line Dirac semimetals, the conductance and valence bands connect along a closed path in momentum space, leading to the prediction of pseudospin vortex rings and pseudospin skyrmions. Here, we use Fourier transform scanning tunneling spectroscopy (FT-STS) at 4.5 K to resolve quasiparticle interference (QPI) patterns at single defect centers on the surface of the line nodal semimetal zirconium silicon sulfide (ZrSiS). Our QPI measurements show pseudospin conservation at energies close to the line node. In addition, we determine the Fermi velocity to be ℏv_F = 2.65 ± 0.10 eV Å in the Γ-M direction ∼300 meV above the Fermi energy E_F and the line node to be ∼140 meV above E_F. More importantly, we find that certain scatterers can introduce energy-dependent nonpreservation of pseudospin, giving rise to effective scattering between states with opposite pseudospin deep inside valence and conduction bands. Further investigations of quasiparticle interference at the atomic level will aid defect engineering at the synthesis level, needed for the development of lower-power electronics via dissipationless electronic transport in the future.