Topological Crystalline Insulator Research Articles

Multiple Magnetic Topological Phases in the van der Waals Crystal Mn(Bi,Sb)4Se7.

Magnetic topological materials have drawn markedly attention recently due to the strong coupling of their novel topological properties and magnetic configurations. In particular, the MnBi2Te4/(Bi2Te3)n family highlights the researches of multiple magnetic topological materials. Via first-principles calculations, we predict that Mn(Bi, Sb)4Se7, the close relatives of MnBi2Te4/(Bi2Te3)n family, are topological nontrivival in both antiferromagnetic and ferromagnetic configurations. In the antiferromagnetic ground state, Mn(Bi, Sb)4Se7 are simultaneously topological insulators and axion insulators. Massless Dirac surface states emerge on the surfaces parallel to the z axis. In ferromagnetic phases, they are axion insulators. Particularly, when the magnetization direction is along the x axis, they are also topological crystalline insulators. Mirror-symmetry-protected gapless surface states exist on the mirror-invariant surfaces. Hence, the behaviors of surface states are strongly dependent on the magnetization directions and surface orientations. Our work provides more opportunities for the study of magnetic topological physics.

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.

Consequences of average time-reversal symmetry in disordered antiferromagnetic topological insulators

Average symmetry protects the topological surface states of topological (crystalline) insulators with time-reversal symmetry from disorder-induced localization. However, the nature of such average symmetry for magnetic topological insulators and, in particular, its connection to surface transport await inspection. Here, we investigate the impact of imperfect magnetic order on an antiferromagnetic topological insulator, which is a solid with a bulk axion field $\ensuremath{\theta}=\ensuremath{\pi}$. We find that the disordered topological surfaces of an antiferromagnetic topological insulator can be generally gapped and localized. The behavior of topological surfaces is now controlled by a mesoscopic average time-reversal symmetry that requires a magnetically imperfect system to be divisible into finite and magnetically neutral slabs. In the presence of this mesoscopic average time-reversal symmetry, the topological surface states will be gapless in the thermodynamic limit and tend to delocalize at a single energy similar to the delocalization transition in the chiral universality class. The notion of average-symmetry-induced delocalization is thus extended to account for magnetic topological insulators, and the spectroscopic and transport signatures clarified herein are relevant to future experimental investigations.

Experimental observation of geometric effect on the electron diffraction of quasi-one-dimensional nanostructures

One-dimensional (1D) nanostructures, such as nanowires, constitute building blocks for nanoscience and nanotechnology. Their fundamental physical properties are dictated by their crystalline structures, which are often characterized by transmission electron microscopy (TEM). Theoretically, the shape of a nanostructure can affect its electron diffraction pattern; however, for 1D nanostructures, an experimental observation of this geometric effect has not been reported. Here, we demonstrate unambiguously the first experimental observation of this geometric effect in electron diffraction from nanowires of iridium dioxide (IrO2) and lead tin telluride (Pb1-xSnxTe), which are topological semimetals and topological crystalline insulators, respectively. Grown by chemical vapor deposition, the nanowires are single-crystalline and have well defined facets with nearly rectangular cross-sections. Diffraction spot splitting was observed in electron diffraction patterns when the e-beam was not perpendicular to the major facets of the nanowires. Atomic-resolution scanning TEM studies rule out other possible origins of the splitting, including twin domains and non-uniform strain. Theoretical calculations of electron diffraction capturing the nanowire geometry show good agreement with the experimental results, including the diffraction order dependence of the peak splitting. The observation of this geometric effect offers a non-destructive approach to characterizing the thickness of the one-dimensional nanostructures.

Confined vs. extended Dirac surface states in topological crystalline insulator nanowires

Confining two dimensional Dirac fermions on the surface of topological insulators has remained an outstanding conceptual challenge. Here we show that Dirac fermion confinement is achievable in topological crystalline insulators (TCI), which host multiple surface Dirac cones depending on the surface termination and the symmetries it preserves. This confinement is most dramatically reflected in the flux dependence of these Dirac states in the nanowire geometry, where different facets connect to form a closed surface. Using SnTe as a case study, we show how wires with all four facets of the \langle 100 \rangle‹100› type display novel Aharonov-Bohm oscillations, while nanowires with the four facets of the \langle 110 \rangle‹110› type such oscillations are absent due to strong confinement of the Dirac states to each facet separately. Our results place TCI nanowires as a versatile platform for confining and manipulating Dirac surface states.

Symmetry-resolved entanglement of C2 -symmetric topological insulators

For a many-body system of arbitrary dimension, we consider fermionic ground states of noninteracting Hamiltonians invariant under a ${C}_{2}$ cyclic group. The absolute difference $\mathrm{\ensuremath{\Delta}}$ between the number of occupied symmetric and antisymmetric single-particle states is a topological invariant in this case. We prove lower bounds on the configurational and the number entropy based on this invariant. Entanglement entropies are particularly important for identifying topological phases protected by spatial symmetries because they lack gapless boundary modes in general. In topological crystalline insulators, the topological invariant $\mathrm{\ensuremath{\Delta}}$ and the entropy bounds can be directly determined from high-symmetry points in the Brillouin zone.

Ferroic Berry Curvature Dipole in a Topological Crystalline Insulator at Room Temperature.

The physics related to Berry curvature is now a central research topic in condensed matter physics. The Berry curvature dipole (BCD) is a significant and intriguing condensed matter phenomenon that involves inversion symmetry breaking. However, the creation and controllability of BCDs have so far been limited to far below room temperature (RT), and nonvolatile (i.e., ferroic) BCDs have not yet been discovered, hindering further progress in topological physics. In this work, we demonstrate a switchable and nonvolatile BCD effect at RT in a topological crystalline insulator, Pb1-xSnxTe (PST), which is attributed to ferroic distortion. Surprisingly, the magnitude of the ferroic BCD is several orders of magnitude greater than that of the nonferroic BCDs that appear, for example, in transition metal dichalcogenides. The discovery of this ferroic and extraordinarily large BCD in PST could pave the way for further progress in topological materials science and the engineering of novel topological devices.

Noncollinear twisted RKKY interaction on the optically driven SnTe(001) surface

The nontrivial spin texture on the (001) surface of topological crystalline insulator SnTe hosts exotic scientific importance and spintronic applications. Here, we study the effects of weak Floquet optical driving on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities on a doped SnTe(001) surface. Due to peculiar spin-orbit hybridization, we find a noncollinear twisted RKKY interaction with XYZ-Heisenberg, symmetric in-plane, and asymmetric Dzyaloshinskii-Moriya (DM) terms. We see that contributions from the $z$ $(x)$ component of the XYZ-Heisenberg (DM) interaction are dominant for most parameters. The interactions, including DM terms that are responsible for interesting spin textures, require doping in most cases. We propose to modify the interactions in situ via optical control of band structure, and thereby doping. A notable aspect of this control protocol is breaking of electron-hole symmetry, which stems from the DM interaction.

Mechanisms for magnetic skyrmion catalysis and topological superconductivity

We propose an alternative route to stabilize magnetic skyrmion textures which does not require Dzyaloshinkii-Moriya interactions, magnetic anisotropy, or an external Zeeman field. Instead, it solely relies on the emergence of flux in the system's ground state. We discuss scenarios that lead to a nonzero flux and identify the magnetic skyrmion ground states which become accessible in its presence. Moreover, we explore the chiral superconductors obtained for the surface states of a topological crystalline insulator when two types of magnetic skyrmion crystals coexist with a pairing gap. Our work opens perspectives for engineering topological superconductivity in a minimal fashion and promises to unearth functional topological materials and devices which may be more compatible with electrostatic control than the currently explored skyrmion-Majorana platforms.

Pressure-induced superconductivity in the weak topological insulator BiSe

Layered BiSe in the trigonal $P\overline{3}m1$ phase is a weak topological insulator and a candidate topological crystalline insulator. Here using structural, spectroscopic, resistance measurements at high pressure and density functional theory calculations, we report that BiSe exhibits a rich phase diagram with the emergence of superconductivity above 7 GPa. Structural transitions into SnSe-type energetically tangled orthorhombic structures and, subsequently, into a CsCl-type cubic structure having distinct superconducting properties are identified at 8 and 13 GPa, respectively. Superconductivity is preserved as the system transforms back to the trigonal phase upon release of pressure. Spin-orbit coupling plays a significant role in enhancement of ${T}_{c}$ in the trigonal and cubic phases. In the orthorhombic $Cmcm$ phase, ${T}_{c}$ decreases monotonically with increasing pressure, whereas unusual pressure-independent ${T}_{c}$ is observed in the cubic $Pm\overline{3}m$ phase. Theoretical analysis reveals topological surface states in the cubic phase. The emergence of superconductivity within the topological phases makes BiSe a candidate topological superconductor.

Superior Performances of Self-Driven Near-Infrared Photodetectors Based on the SnTe:Si/Si Heterostructure Boosted by Bulk Photovoltaic Effect.

The upsurge of new materials that can be used for near-infrared (NIR) photodetectors operated without cooling is crucial. As a novel material with a small bandgap of ≈0.28eV, the topological crystalline insulator SnTe has attracted considerable attention. Herein, this work demonstrates self-driven NIR photodetectors based on SnTe/Si and SnTe:Si/Si heterostructures. The SnTe/Si heterostructure has a high detectivity D* of 3.3 × 1012 Jones. By Si doping, the SnTe:Si/Si heterostructure reduces the dark current density and increases the photocurrent by ≈1 order of magnitude simultaneously, which improves the detectivity D* by ≈2 orders of magnitude up to 1.59×1014 Jones. Further theoretical analysis indicates that the improved device performance may be ascribed to the bulk photovoltaic effect (BPVE), in which doped Si atoms break the inversion symmetry and thus enable the generation of additional photocurrents beyond the heterostructure. In addition, the external quantum efficiency (EQE) measured at room temperature at 850nm increases by a factor of 7.5 times, from 38.5% to 289%. A high responsivity of 1979mA W-1 without bias and fast rising time of 8 µs are also observed. The significantly improved photodetection achieved by the Si doping is of great interest and may provide a novel strategy for superior photodetectors.

Coexistence of All-Order Topological States in a Three-Dimensional Phononic Topological Crystalline Insulator.

Classical-wave topological materials lacking intrinsic half-integer spins are less robust while more tunable. Here, we explore a single 3-dimensional phononic topological crystalline insulator that simultaneously exhibits a whole family of first-order quadratic surface, second-order hinge, and third-order corner states within the same bandgap. Such a topological crystalline insulator hosting all-order phases originates from the different topological nature when hierarchically projected onto different facets and lower dimensions, thus free from trivial cladding crystals. Our work offers an ideal platform for either robust wave propagation or localization in on-demand dimensions and may facilitate dimension division multiplexing technology.

Surface Morphology and Electronic Properties of SnTe Films Prepared by Molecular Beam Epitaxy

SnTe is receiving a lot of attention as a topological crystalline insulator. Herein, SnTe films are grown directly on GaAs (100) substrates by molecular beam epitaxy. The surface morphology and electronic properties are measured by atomic force microscopy and Hall effect measurement, respectively. Considering previous X‐ray diffraction results, the samples grown with high beam‐intensity ratios show hexagonal Te segregation in the films, which deteriorates the surface morphology and decreases the conductivity. By suppressing the supply of Te, better surface morphology and electrical properties are obtained.

Anyonic topological order in twisted equivariant differential (TED) K-theory

While the classification of noninteracting crystalline topological insulator phases by equivariant K-theory has become widely accepted, its generalization to anyonic interacting phases — hence to phases with topologically ordered ground states supporting topological braid quantum gates — has remained wide open. On the contrary, the success of K-theory with classifying noninteracting phases seems to have tacitly been perceived as precluding a K-theoretic classification of interacting topological order; and instead a mix of other proposals has been explored. However, only K-theory connects closely to the actual physics of valence electrons; and self-consistency demands that any other proposal must connect to K-theory. Here, we provide a detailed argument for the classification of symmetry protected/enhanced [Formula: see text]-anyonic topological order, specifically in interacting 2d semi-metals, by the twisted equivariant differential (TED) K-theory of configuration spaces of points in the complement of nodal points inside the crystal’s Brillouin torus orbi-orientifold. We argue, in particular, that : (1) topological 2d semi-metal phases modulo global mass terms are classified by the flat differential twisted equivariant K-theory of the complement of the nodal points; (2) [Formula: see text]-electron interacting phases are classified by the K-theory of configuration spaces of [Formula: see text] points in the Brillouin torus; (3) the somewhat neglected twisting of equivariant K-theory by “inner local systems” reflects the effective “fictitious” gauge interaction of Chen, Wilczeck, Witten and Halperin (1989), which turns fermions into anyonic quanta; (4) the induced [Formula: see text]-anyonic topological order is reflected in the twisted Chern classes of the interacting valence bundle over configuration space, constituting the hypergeometric integral construction of monodromy braid representations. A tight dictionary relates these arguments to those for classifying defect brane charges in string theory [H. Sati and U. Schreiber, Anyonic defect branes in TED-K-theory, arXiv:2203.11838], which we expect to be the images of momentum-space [Formula: see text]-anyons under a nonperturbative version of the AdS/CMT correspondence.

Transport property of topological crystalline insulator SnTe (100) and ferrimagnetic insulator heterostructures

• High quality SnTe/RE3Fe5O12 (RE=Eu, Y) epitaxial heterostructures were prepared. • Domain disorder is induced by Fe atom diffusion in SnTe through magnetic interface. • Two different magnetoelectrical transport in two heterostructures are observed. • Linear magnetoresistance and nonlinear Hall appear in SnTe/Eu 3 Fe 5 O 12 . Topological crystalline insulator (TCI) SnTe is a potential material for quantum electronic devices because of its attractive inherent sensitivity of band topology and highly mobile characteristic of Dirac fermions. The proximity effect at the interface of SnTe film can affect the topological surface transport and may result in novel quantum magneto-electric effects. Here, we study the magnetoelectrical transport properties of SnTe thin films grown on ferrimagnetic insulators Eu 3 Fe 5 O 12 (110) (EuIG (110)) and Y 3 Fe 5 O 12 (111) (YIG (111)) single-crystal underlayers by molecular beam epitaxy. Linear magnetic resistance (LMR) is observed in SnTe/EuIG heterostructures in the low field range, which is different from the weak antilocalization (WAL) characteristic of SnTe/YIG heterostructures. Especially, the double carrier characteristic with the coexistence of holes and electrons in SnTe/EuIG heterostructure is quite different from the holes as main carriers in SnTe/YIG, although the SnTe layer remains the same crystal plane (100) in the two heterostructures. The LMR in SnTe/EuIG is attributed to the topological surface Dirac electrons and disordered domain distribution in the SnTe layer which is in sharp contrast to the WAL of SnTe/YIG with ordered domain distribution in the SnTe layer. The present studies of transport properties not only provide a fundamental understanding of the transport mechanism of TCI and magnetite insulator heterostructure but also display the promising application probability for tunable topological electronic devices.

Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry

A two-dimensional topological crystalline insulator (TCI) with a single unit cell (u.c.) thickness is demonstrated here. To that end, one first shows that tetragonal (C 4 in-plane) symmetry is not a necessary condition for the creation of zero-energy metallic surface states on TCI slabs of finite-thicknesses, because zero-energy states persist even as all the in-plane rotational symmetries—furnishing topological protection—are completely removed. In other words, zero-energy levels on the model are not due to (nor are they protected by) topology. Furthermore, effective two-fold energy degeneracies taking place at few discrete k-points away from zero energy in the bulk Hamiltonian—that are topologically protected—persist at the u.c. thickness limit. The chiral nature of the bulk TCI Hamiltonian permits creating a square Hamiltonian, whose topological properties remarkably hold invariant at both the bulk and at the single u.c. thickness limits. The identical topological characterization for bulk and u.c.-thick phases is further guaranteed by a calculation involving Pfaffians. This way, a two-atom-thick TCI is deployed hereby, in a demonstration of a topological phase that holds both in the bulk, and in two dimensions.

Highly Tunable Beyond-Room-Temperature Intrinsic Ferromagnetism in Cr-Doped Topological Crystalline Insulator SnTe Crystals.

The combination of topological phase and intrinsic beyond-room-temperature ferromagnetism is expected to realize the quantum anomalous Hall effect at a high temperature. However, no beyond-room-temperature intrinsic ferromagnetism has been reported in either topological insulator or topological crystalline insulator (TCI) so far. Here, we report Cr-doping in TCI-phase SnTe crystals which possess highly tunable beyond-room-temperature intrinsic ferromagnetism including Tc, magnetic moment, and coercivity by varying Cr contents and crystal thickness. With the increase of the Cr content, the Tc increases by 159 K from 221 to 380 K and the saturation magnetic moments increase by ∼23.6 times from 0.018 to 0.421 μB/f.u. This intrinsic beyond-room-temperature ferromagnetism is fully demonstrated by the anomalous Hall effect and magneto-optical Kerr effect in a single CrxSn1-xTe nanosheet. Moreover, the room-temperature tunneling magnetoresistance effect has been realized by using a CrxSn1-xTe flake, a Fe thin film, and a commercially compatible ultrathin AlOx tunneling barrier. This work indicates a great potential of CrxSn1-xTe crystals in room-temperature magnetoelectronic and spintronic devices.

Spin-polarization of topological crystalline and normal insulator Pb[formula omitted]Sn[formula omitted]Se (111) epilayers probed by photoelectron spectroscopy

The helical spin texture on the surface of topological crystalline insulators (TCI) makes these materials attractive for application in spintronics. In this work, spin-polarization and electronic structure of surface states of (111)-oriented Pb1−xSnxSe TCI epitaxial films are examined by angle- as well as spin-resolved photoemission spectroscopy (SR-ARPES). High-quality epilayers with various Sn content are grown by the molecular beam epitaxy (MBE) method. Topological-normal insulator transition manifesting itself as band gap opening is observed. It is shown that the gap opening can be induced not only by changing the Sn content of the epilayer but also depositing a transition metal (TM) on its surface. In the latter case, the observed gaping of the surface states is caused by change in surface composition and not by magnetism. We also show that helical spin polarization is present not only for samples of topological composition but also for trivial ones (with an open band gap). The observed spin polarization reaches a value of 30% for the in-plane spin component and is almost absent for the out-of-plane one. We believe that our work will pave the way for the application of surface states not only of topological but also normal insulators based on lead–tin chalcogenides in spin-charge conversion devices.

Controlling Sound Wave Propagation in Topological Crystalline Insulators and Rainbow-Trapping

Topological crystalline insulators (TCIs) capable of supporting topological states protected by spatial symmetries have given rise to a promising platform for wave manipulation due to their robustness. Unfortunately, the methods to control the group velocity of topological states in classical wave systems are rarely discussed, which is an important issue in practical applications. In this work, we propose a method to change the frequency and propagation speed of topological edge states through on-site potential and realize a prototype of topological rainbow concentrator in a resonant acoustic system at subwavelength, which can separate different frequency components of propagating sound waves. The concepts of classical wave systems are combined with condensed matter physics, and the rigorous correspondence of TCIs and their analogs in acoustic resonant systems is demonstrated to design topological acoustic devices. Further, the implementation of controlling the group velocity of topological states precisely in a two-dimensional Su-Schrieffer-Heeger model is presented in detail, which can be extended to other TCI models and higher dimensions. We hope this work will enlarge possible applications of topological phenomena and the manufacture of acoustic devices.

Pressure-induced topological and structural phase transitions in natural van der Waals heterostructures from the (SnTe)m(Bi2Te3)n homologous family: Raman spectroscopy, x-ray diffraction, and density functional theory

A new class of van der Waals heterostructures of ${(\mathrm{SnTe})}_{\mathrm{m}}{({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})}_{\mathrm{n}}$ (with $m=1,2,.\phantom{\rule{0.16em}{0ex}}.$ and $n=1,2,.\phantom{\rule{0.16em}{0ex}}.$), consisting of a topological crystalline insulator SnTe and a topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ are emerging with exciting properties and applications, such as in thermoelectrics. Our study examines the stability of these heterostructures ($m$ = 1 and $n$ = 1,2) under pressure using Raman scattering, synchrotron x-ray diffraction, and density functional theory. Raman studies as a function of pressure carried out at room temperature reveal a phase transition in the pressure regime of 3--5 GPa for both the compounds, which is shown to be associated with an electronic topological transition involving change in the ${\mathrm{Z}}_{2}$ topological invariant. In addition to the electronic changes, our Raman experiments indicate that rhombohedral ($R\overline{3}m$) ${\mathrm{SnBi}}_{2}{\mathrm{Te}}_{4}$ undergoes structural transition at $\ensuremath{\sim}6.0$ to a possible monoclinic phase and another transition at $\ensuremath{\sim}12.0$ GPa. Raman and x-ray diffraction experiments on trigonal ($P\overline{3}m1$) ${\mathrm{SnBi}}_{4}{\mathrm{Te}}_{7}$ show two structural transitions at $\ensuremath{\sim}9.5$ GPa to a monoclinic phase followed by one to cubic phase at $\ensuremath{\sim}14.1$ GPa. Our analysis of electronic structure reveals that the phase transition at 9.5 GPa in ${\mathrm{SnBi}}_{4}{\mathrm{Te}}_{7}$ is accompanied by an insulator to semimetal transition.