Nanohardness and Young's Modulus of Pb1-xCdxTe Crystals Grown by the SSVG and MBE Methods.

The nanohardness and Young's modulus of Pb1-xCdxTe single crystals prepared by the self-selecting vapor growth (SSVG) method and thick, MBE-grown layers with a total Cd content of up to 7% metal atoms were studied using the nanoindentation technique; the nanohardness and Young's modulus were calculated by the Oliver and Pharr method. Significant hardening of SSVG crystals with increasing number of Cd atoms replacing Pb atoms in the formed solid solution was observed, and low anisotropy of the nanohardness and Young's modulus were found. The CdTe solubility limit in the solid solution grown using an MBE equal to 2.1% was demonstrated; even for the significantly higher total Cd concentration in the layer, the possible presence of precipitates was not detected. Significant differences were found for both the energy of elastic crystal deformation and Young's modulus determined for samples grown using the two methods. An increase in nanohardness with an increase in the number of Cd atoms outside the cation sublattice was shown. The different ratios of hardening mechanisms acting simultaneously in the analyzed crystals in various ranges of Cd concentrations were demonstrated and discussed. The observed effects were attributed to the much higher concentration of point defects in MBE-grown layers than in SSVG crystals, in particular, the interstitial Cd-Te vacancy complexes effectively hampering nucleation and propagation of dislocations in the former case.

Interaction Effects in a 1D Flat Band at a Topological Crystalline Step Edge.

Step edges of topological crystalline insulators can be viewed as predecessors of higher-order topology, as they embody one-dimensional edge channels embedded in an effective three-dimensional electronic vacuum emanating from the topological crystalline insulator. Using scanning tunneling microscopy and spectroscopy, we investigate the behavior of such edge channels in Pb1-xSnxSe under doping. Once the energy position of the step edge is brought close to the Fermi level, we observe the opening of a correlation gap. The experimental results are rationalized in terms of interaction effects which are enhanced since the electronic density is collapsed to a one-dimensional channel. This constitutes a unique system to study how topology and many-body electronic effects intertwine, which we model theoretically through a Hartree-Fock analysis.

Systematic Investigation of the Coupling between One-Dimensional Edge States of a Topological Crystalline Insulator.

The interaction of spin-polarized one-dimensional (1D) topological edge modes localized along single-atomic steps of the topological crystalline insulator Pb_{0.7}Sn_{0.3}Se(001) has been studied systematically by scanning tunneling spectroscopy. Our results reveal that the coupling of adjacent edge modes sets in at a step-to-step distance d_{ss}≤25 nm, resulting in a characteristic splitting of a single peak at the Dirac point in tunneling spectra. Whereas the energy splitting exponentially increases with decreasing d_{ss} for single-atomic steps running almost parallel, we find no splitting for single-atomic step edges under an angle of 90°. The results are discussed in terms of overlapping wave functions with p_{x}, p_{y} orbital character.

Fragility of the Dirac Cone Splitting in Topological Crystalline Insulator Heterostructures.

The "double Dirac cone" 2D topological interface states found on the (001) faces of topological crystalline insulators such as Pb1-xSnxSe feature degeneracies located away from time reversal invariant momenta and are a manifestation of both mirror symmetry protection and valley interactions. Similar shifted degeneracies in 1D interface states have been highlighted as a potential basis for a topological transistor, but realizing such a device will require a detailed understanding of the intervalley physics involved. In addition, the operation of this or similar devices outside of ultrahigh vacuum will require encapsulation, and the consequences of this for the topological interface state must be understood. Here we address both topics for the case of 2D surface states using angle-resolved photoemission spectroscopy. We examine bulk Pb1-xSnxSe(001) crystals overgrown with PbSe, realizing trivial/topological heterostructures. We demonstrate that the valley interaction that splits the two Dirac cones at each X̅ is extremely sensitive to atomic-scale details of the surface, exhibiting non-monotonic changes as PbSe deposition proceeds. This includes an apparent total collapse of the splitting for sub-monolayer coverage, eliminating the Lifshitz transition. For a large overlayer thickness we observe quantized PbSe states, possibly reflecting a symmetry confinement mechanism at the buried topological interface.

Robust spin-polarized midgap states at step edges of topological crystalline insulators.

Topological crystalline insulators are materials in which the crystalline symmetry leads to topologically protected surface states with a chiral spin texture, rendering them potential candidates for spintronics applications. Using scanning tunneling spectroscopy, we uncover the existence of one-dimensional (1D) midgap states at odd-atomic surface step edges of the three-dimensional topological crystalline insulator (Pb,Sn)Se. A minimal toy model and realistic tight-binding calculations identify them as spin-polarized flat bands connecting two Dirac points. This nontrivial origin provides the 1D midgap states with inherent stability and protects them from backscattering. We experimentally show that this stability results in a striking robustness to defects, strong magnetic fields, and elevated temperature.