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Chiral symmetry is a fundamental property with profound implications for the properties of elementary particles, that implies a spectral symmetry (i.e. E => -E ) in their dispersion relation. In condensed matter physics, chiral symmetry is frequently associated with superconductors or materials hosting Dirac fermions such as graphene or topological insulators. There, chiral symmetry is an emergent low-energy property, accompanied by an emergent spectral symmetry. While the chiral symmetry can be broken by crystal distortion or external perturbations, the spectral symmetry frequently survives. As the presence of spectral symmetry does not necessarily imply chiral symmetry, the question arises how these two properties can be experimentally differentiated. Here, we demonstrate how a system with preserved spectral symmetry can reveal underlying broken chiral symmetry using topological defects. Our study shows that these defects induce a spectral imbalance in the Landau level spectrum, providing direct evidence of symmetry alteration at topological domain walls. Using high-resolution STM/STS we demonstrate the intricate interplay between chiral and translational symmetry which is broken at step edges in topological crystalline insulator Pb$_{1-x}$Sn$_x$Se. The chiral symmetry breaking leads to a shift in the guiding center coordinates of the Landau orbitals near the step edge, thus resulting in a distinct chiral flow of the spectral density of Landau levels. This study underscores the pivotal role of topological defects as sensitive probes for detecting hidden symmetries, offering profound insights into emergent phenomena with implications for fundamental physics., Comment: 13 pages, 3 figures, Supplementary Material

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 behaviour of such edge channels in Pb$_{1-x}$Sn$_{x}$Se 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., Comment: 8 pages, 5 figures (main text) and 5 pages, 6 figures (Supplementary Material)

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 $90^{o}$. The results are discussed in terms of overlapping wave functions with $p_x; p_y$ orbital character., Comment: 6 pages, 3 figures

The optical reflectivity of Pb$_{0.865}$Sn$_{0.135}$Se and Pb$_{0.75}$Sn$_{0.25}$Se solid solutions was measured in the THz spectral region energetically corresponding to bulk optical phonon excitations and in the temperature range from 40 K to 280 K. The analysis of Pb$_{0.75}$Sn$_{0.25}$Se data performed within the dynamic dielectric function formalism revealed a new effect due to the electron-phonon coupling resulting in resonant changes of LO phonon frequency for energy gap equal to zero or to LO phonon energy. This effect is absent for Pb$_{0.865}$Sn$_{0.135}$Se that exhibits an open energy gap with trivial band ordering at all temperatures. These results show that reflectivity in the THz range constitute a versatile experimental method for precise determination of band inversion in narrow-gap topological materials. For Pb$_{0.75}$Sn$_{0.25}$Se the transition from trivial insulator to topological crystalline insulator phase takes place at temperature T$_0$ = (172 $\pm$ 2) K., Comment: 12 pages, 5 figures

High quality p-type PbTe-CdTe monocrystalline alloys containing up to 10 at.$\%$ of Cd are obtained by self-selecting vapor transport method. Mid infrared photoluminescence experiments are performed to follow the variation of the fundamental energy gap as a function of Cd content. The Hall mobility, thermoelectric power, thermal conductivity and thermoelectric figure of merit parameter $ZT$ are investigated experimentally and theoretically paying particular attention to the two-valence band structure of the material. It is shown that the heavy-hole band near the $\Sigma$ point of the Brillouin zone plays an important role and is responsible for the Pb$_{1-x}$Cd$_x$Te hole transport at higher Cd-content. Our data and their description can serve as the standard for Pb$_{1-x}$Cd$_x$Te single crystals with $x$ up to 0.1. It is shown, that monocrystalline Pb$_{1-x}$Cd$_x$Te samples with relatively low Cd content of about 1 at.\% and hole concentration of the order of 10$^{20}$ cm$^{-3}$ may exhibit $ZT \approx$ 1.4 at 600 K., Comment: 11 pages, 12 figures

The 'double Dirac cone' 2D topological interface states found on the (001) faces of topological crystalline insulators such as Pb$_{1-x}$Sn$_{x}$Se 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 ultra-high 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 Pb$_{1-x}$Sn$_{x}$Se(001) crystals overgrown with PbSe, realizing trivial/topological heterostructures. We demonstrate that the valley interaction that splits the two Dirac cones at each $\bar{X}$ 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.

Point-contact spectroscopy of several non-superconducting topological materials reveals a low temperature phase transition that is characterized by a Bardeen-Cooper-Schrieffer-type of criticality. We find such a behavior of differential conductance for topological surfaces of non-magnetic and magnetic Pb$_{1-y-x}$Sn$_y$Mn$_x$Te. We examine a possible contribution from superconducting nanoparticles, and show to what extent our data are consistent with Brzezicki's et al. theory [arXiv:1812.02168], assigning the observations to a collective state adjacent to atomic steps at topological surfaces., Comment: 15 pages, 27 figures (with Supplemental Material)

We demonstrate that the metallic topological surface states wrap on all sides the 3D topological crystalline insulator SnTe. This is achieved by studying oscillatory quantum magneto-transport and magnetization at tilted magnetic fields which enables us to observe simultaneous contributions from neighbouring sample sides. Taking into account pinning of the Fermi energy by the SnTe reservoir we successfully describe theoretically the de Haas-van Alphen oscillations of magnetization. The determined \pi-Berry phase of surface states confirms their Dirac fermion character. We independently observe oscillatory contributions of magneto-transport and magnetization originating from the bulk SnTe reservoir of high hole density. It is concluded that the bulk and surface Landau states exist in parallel. Our main result that the bulk reservoir is surrounded on all sides by the topological surface states has an universal character., Comment: 5 pages, 2 figures, 12 pages supplemental material

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 non-trivial 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.

The transverse Nernst Ettingshausen (N-E) effect and electron mobility in Pb$_{1-x}$Sn$_x$Se alloys are studied experimentally and theoretically as functions of temperature and chemical composition in the vicinity of vanishing energy gap $E_g$. The study is motivated by the recent discovery that, by lowering the temperature, one can change the band ordering from trivial to nontrivial one in which the topological crystalline insulator states appear at the surface. Our work presents several new aspects. It is shown experimentally and theoretically that the bulk N-E effect has a maximum when the energy gap $E_g$ of the mixed crystal goes through zero value. This result contradicts the claim made in the literature that the N-E effect changes sign when the gap vanishes. We successfully describe $dc$ transport effects in the situation of extreme band's nonparabolicity which, to the best of our knowledge, has never been tried before. A situation is reached in which both two-dimensional bands (topological surface states) and three-dimensional bands are linear in electron \textbf{k} vector. Various scattering modes and their contribution to transport phenomena in Pb$_{1-x}$Sn$_x$Se are analyzed. As the energy gap goes through zero, some transport integrals have a singular (nonphysical) behaviour and we demonstrate how to deal with this problem by introducing damping., Comment: 23 pages, 6 figures

Ferromagnetic resonance (FMR) study of magnetic anisotropy is presented for thin layers of IV-VI diluted magnetic semiconductor Ge1-xMn xTe with x=0.14 grown by molecular beam epitaxy (MBE) on KCl (001) substrate with a thin PbTe buffer. Analysis of the angular dependence of the FMR resonant field reveals that an easy magnetization axis is located near to the normal to the layer plane and is controlled by two crystal distortions present in these rhombohedral Ge1-xMnxTe layers: the ferroelectric distortion with the relative shift of cation and anion sub-lattices along the [111] crystal direction and the biaxial in-plane, compressive strain due to thermal mismatch.

Since the advent of topological insulators hosting symmetry-protected Dirac surface states, efforts have been made to gap these states in a controllable way. A new route to accomplish this was opened up by the discovery of topological crystalline insulators (TCIs) where the topological states are protected by real space crystal symmetries and thus prone to gap formation by structural changes of the lattice. Here, we show for the first time a temperature-driven gap opening in Dirac surface states within the TCI phase in (Pb,Sn)Se. By using angle-resolved photoelectron spectroscopy, the gap formation and mass acquisition is studied as a function of composition and temperature. The resulting observations lead to the addition of a temperature- and composition-dependent boundary between massless and massive Dirac states in the topological phase diagram for (Pb,Sn)Se (001). Overall, our results experimentally establish the possibility to tune between a massless and massive topological state on the surface of a topological system., Comment: 5 pages, 3 figures

The recent discovery of a topological phase transition in IV-VI narrow-gap semiconductors has revitalized the decades-old interest in the bulk band inversion occurring in these materials. Here we systematically study the (001) surface states of Pb{1-x}Sn{x}Se mixed crystals by means of angle-resolved photoelectron spectroscopy in the parameter space 0 <= x <= 0.37 and 300 K >= T >= 9 K. Using the surface-state observations, we monitor directly the topological phase transition in this solid solution and gain valuable information on the evolution of the underlying fundamental band gap of the system. In contrast to common model expectations, the band-gap evolution appears to be nonlinear as a function of the studied parameters, resulting in the measuring of a discontinuous band inversion process. This finding signifies that the anticipated gapless bulk state is in fact not a stable configuration and that the topological phase transition therefore exhibits features akin to a first-order transition., Comment: article + supplemental figures

We present angle resolved photoemission spectroscopy measurements of the surface states on in-situ grown (111) oriented films of Pb$_{1-x}$Sn$_{x}$Se, a three dimensional topological crystalline insulator. We observe surface states with Dirac-like dispersion at $\bar{\Gamma}$ and $\bar{M}$ in the surface Brillouin zone, supporting recent theoretical predictions for this family of materials. We study the parallel dispersion isotropy and Dirac-point binding energy of the surface states, and perform tight-binding calculations to support our findings. The relative simplicity of the growth technique is encouraging, and suggests a clear path for future investigations into the role of strain, vicinality and alternative surface orientations in (Pb,Sn)Se compounds., Comment: 5 pages, 4 figures

We study the nature of (001) surface states in Pb_{0.73}Sn_{0.27}Se in the newly discovered topological-crystalline-insulator (TCI) phase as well as the corresponding topologically trivial state above the band-gap-inversion temperature. Our calculations predict not only metallic surface states with a nontrivial chiral spin structure for the TCI case, but also nonmetallic (gapped) surface states with nonzero spin polarization when the system is a normal insulator. For both phases, angle- and spin-resolved photoelectron spectroscopy measurements provide conclusive evidence for the formation of these (001) surface states in Pb_{0.73}Sn_{0.27}Se, as well as for their chiral spin structure., Comment: 6 pages, 2 figures

Topological insulators are a novel class of quantum materials in which time-reversal symmetry, relativistic (spin-orbit) effects and an inverted band structure result in electronic metallic states on the surfaces of bulk crystals. These helical states exhibit a Dirac-like energy dispersion across the bulk bandgap, and they are topologically protected. Recent theoretical proposals have suggested the existence of topological crystalline insulators, a novel class of topological insulators in which crystalline symmetry replaces the role of time-reversal symmetry in topological protection [1,2]. In this study, we show that the narrow-gap semiconductor Pb(1-x)Sn(x)Se is a topological crystalline insulator for x=0.23. Temperature-dependent magnetotransport measurements and angle-resolved photoelectron spectroscopy demonstrate that the material undergoes a temperature-driven topological phase transition from a trivial insulator to a topological crystalline insulator. These experimental findings add a new class to the family of topological insulators. We expect these results to be the beginning of both a considerable body of additional research on topological crystalline insulators as well as detailed studies of topological phase transitions., Comment: v2: published revised manuscript (6 pages, 3 figures) and supplementary information (5 pages, 8 figures)

We present the studies of magnetic properties of Ge/1-x/Cr/x/Te diluted magnetic semiconductor with changeable chemical composition 0.016 \leq x \leq 0.061. A spin-glass state (at T \leq 35 K) for x = 0.016 and 0.025 and a ferromagnetic phase (at T < 60 K) for x \geq 0.030 are observed. The long range carrier-mediated magnetic interactions are found to be responsible for the observed magnetic ordering for x < 0.045, while for x \geq 0.045 the spinodal decomposition of Cr ions leads to a maximum and decrease of the Curie temperature, TC, with increasing x. The calculations based on spin waves model are able to reproduce the observed magnetic properties at a homogeneous limit of Cr alloying, e.g. x < 0.04, and prove that carrier mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is responsible for the observed magnetic states. The value of the Cr-hole exchange integral, Jpd, estimated via fitting of the experimental results with the theoretical model, is in the limits 0.77...0.88 eV., Comment: 8 pages, 7 figures