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3D Dirac semimetals with square-net non-symmorphic symmetry, such as ternary ZrXY (X=Si, Ge; Y=S, Se, Te) compounds, have attracted significant attention owing to the presence of topological nodal lines, loops, or networks in their bulk. Orbital symmetry plays a profound role such materials as the different branches of the nodal dispersion can be distinguished by their distinct orbital symmetry eigenvalues. The presence of different eigenvalues suggests that scattering between states of different orbital symmetry may be strongly suppressed. Indeed, in ZrSiS, there has been no clear experimental evidence of quasiparticle scattering between states of different symmetry eigenvalue has been reported at small wave vector $q$. Here we show, using quasiparticle interference (QPI), that atomic step-edges in the ZrSiS surface facilitate quasiparticle scattering between states of different symmetry eigenvalues. This symmetry eigenvalue mixing quasiparticle scattering is the first to be reported for ZrSiS and contrasts quasiparticle scattering with no mixing of symmetry eigenvalues, where the latter occurs with scatterers preserving the glide mirror symmetry of the crystal lattice, e.g., native point defects in ZrSiS. Finally, we show that the electronic structure of the ZrSiS surface, including its unique floating band surface state (FBSS), can be tuned by a vertical electric field locally applied by the tip of a scanning tunneling microscope (STM), enabling control of a spin-orbit induced avoided crossing near the Fermi level by as much as 300%.

Ultra-low temperature scanning tunnelling microscopy and spectroscopy (STM/STS) achieved by dilution refrigeration can provide unrivalled insight into the local electronic structure of quantum materials and atomic-scale quantum systems. Effective isolation from mechanical vibration and acoustic noise is critical in order to achieve ultimate spatial and energy resolution. Here, we report on the design and performance of an ultra-low vibration (ULV) laboratory hosting a customized but otherwise commercially available 40mK STM. The design of the vibration isolation consists of a T-shaped concrete mass block (55t), suspended by actively controlled pneumatic springs, and placed on a foundation separated from the surrounding building in a "room-within-a-room" design. Vibration levels achieved are meeting the VC-M vibration standard at >3 Hz, reached only in a limited number of laboratories worldwide. Measurement of the STM's junction noise confirms effective vibration isolation on par with custom built STMs in ULV laboratories. In this tailored low-vibration environment, the STM achieves an energy resolution of 43ueV (144 mK), promising for the investigation and control of quantum matter at atomic length scales.

In one-dimensional (1D) systems, electronic interactions lead to a breakdown of Fermi liquid theory and the formation of a Tomonaga-Luttinger Liquid (TLL). The strength of its many-body correlations can be quantified by a single dimensionless parameter, the Luttinger parameter $K$, characterising the competition between the electrons' kinetic and electrostatic energies. Recently, signatures of a TLL have been reported for the topological edge states of quantum spin Hall (QSH) insulators, strictly 1D electronic structures with linear (Dirac) dispersion and spin-momentum locking. Here we show that the many-body interactions in such helical Luttinger Liquid can be effectively controlled by the edge state's dielectric environment. This is reflected in a tunability of the Luttinger parameter $K$, distinct on different edges of the crystal, and extracted to high accuracy from the statistics of tunnelling spectra at tens of tunneling points. The interplay of topology and many-body correlations in 1D helical systems has been suggested as a potential avenue towards realising non-Abelian parafermions.

Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Amongst them is the quantum spin Hall (QSH) insulator - a two-dimensional state of matter that arises from an interplay of topological band inversion and strong spin-orbit coupling, with large tunable bulk band gaps up to 800meV and gapless, one-dimensional edge states. Reviewing recent advances in materials science and engineering alongside theoretical description, this article surveys the QSH materials library with focus on their prospects for QSH-based device applications. In particular, this review discusses theoretical predictions of non-trivial superconducting pairing in the QSH state towards Majorana based topological quantum computing - the next frontier in QSH materials research.

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 $\hbar v_F = 2.65 \pm 0.10$ eV {\AA} in the {\Gamma}-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 non-preservation of pseudospins, giving rise to effective scattering between states with opposite valley 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.