Schindler, F., et al.Higher-order topology in bismuth”. Nature Physics 14 (2018): , 14, 918-924. Web. Publisher's VersionAbstract
The mathematical field of topology has become a framework in which to describe the low-energy electronic structure of crystalline solids. Typical of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk–boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk–boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principles calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunnelling spectroscopy, we probe the signatures of the rotational symmetry of the one-dimensional states located at the step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.
Li, Jian, et al.Majorana spin in magnetic atomic chain systems”. Physical Review B 97.12 (2018): , 97, 12, 125119-1 - 125119-20. Web. Publisher's VersionAbstract
In this paper, we establish that Majorana zero modes emerging from a topological band structure of a chain of magnetic atoms embedded in a superconductor can be distinguished from trivial localized zero energy states that may accidentally form in this system using spin-resolved measurements. To demonstrate this key Majorana diagnostics, we study the spin composition of magnetic impurity induced in-gap Shiba states in a superconductor using a hybrid model. By examining the spin and spectral densities in the context of the Bogoliubov-de Gennes (BdG) particle-hole symmetry, we derive a sum rule that relates the spin densities of localized Shiba states with those in the normal state without superconductivity. Extending our investigations to a ferromagnetic chain of magnetic impurities, we identify key features of the spin properties of the extended Shiba state bands, as well as those associated with a localized Majorana end mode when the effect of spin-orbit interaction is included. We then formulate a phenomenological theory for the measurement of the local spin densities with spin-polarized scanning tunneling microscopy (STM) techniques. By combining the calculated spin densities and the measurement theory, we show that spin-polarized STM measurements can reveal a sharp contrast in spin polarization between an accidental-zero-energy trivial Shiba state and a Majorana zero mode in a topological superconducting phase in atomic chains. We further confirm our results with numerical simulations that address generic parameter settings.
Randeria, Mallika T., et al.Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference”. Nature Physics 14 (2018): , 14, 796-800. Web. Publisher's VersionAbstract
States with spontaneously broken symmetry can form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. Materials with several degenerate regions in the Brillouin zone—called valleys—offer a rich setting for the emergence of such states, which have potential electronic and optical applications1,2,3,4. To date, identification of these broken-symmetry phases has mostly relied on macroscopic transport or optical properties. Here we demonstrate a direct approach by visualizing the wavefunctions of bismuth surface states with a scanning tunnelling microscope. Strong spin–orbit coupling on the surface of bismuth leads to six degenerate, teardrop-shaped, hole valleys5. Our spectroscopic measurements reveal that exchange interactions fully lift this degeneracy at high magnetic field, and we are able to determine the nature of the valley ordering by imaging the broken-symmetry Landau level wavefunctions. The spatial features of singly degenerate Landau level wavefunctions near isolated defects contain unique signatures of interference between spin-textured valleys, which identify the electronic ground state as a quantum Hall ferroelectric. Our observations confirm the recent prediction6 that interactions in strongly anisotropic valley systems favour the occupation of a single valley, giving rise to emergent ferroelectricity in the surface state of bismuth.
Gyenis, A., et al.Visualizing heavy fermion confinement and Pauli-limited superconductivity in layered CeCoIn5”. Nature Communications 9 .549 (2018). Web. Publisher's VersionAbstract
Layered material structures play a key role in enhancing electron–electron interactions to create correlated metallic phases that can transform into unconventional superconducting states. The quasi-two-dimensional electronic properties of such compounds are often inferred indirectly through examination of bulk properties. Here we use scanning tunneling microscopy to directly probe in cross-section the quasi-two-dimensional electronic states of the heavy fermion superconductor CeCoIn5. Our measurements reveal the strong confined nature of quasiparticles, anisotropy of tunneling characteristics, and layer-by-layer modulated behavior of the precursor pseudogap gap phase. In the interlayer coupled superconducting state, the orientation of line defects relative to the d-wave order parameter determines whether in-gap states form due to scattering. Spectroscopic imaging of the anisotropic magnetic vortex cores directly characterizes the short interlayer superconducting coherence length and shows an electronic phase separation near the upper critical in-plane magnetic field, consistent with a Pauli-limited first-order phase transition into a pseudogap phase.
Papić, Z., et al.Imaging Anyons with Scanning Tunneling Microscopy”. Physical Review X 8011037 (2018). Web. Publisher's VersionAbstract
Anyons are exotic quasiparticles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-Abelian statistics—a property that would help realize fault-tolerant quantum computation. Non-Abelian anyons have long been predicted to occur in the fractional quantum Hall (FQH) phases that form in two-dimensional electron gases in the presence of a large magnetic field, such as the ν=5/2 FQH state. However, direct experimental evidence of anyons and tests that can distinguish between Abelian and non-Abelian quantum ground states with such excitations have remained elusive. Here, we propose a new experimental approach to directly visualize the structure of interacting electronic states of FQH states with the STM. Our theoretical calculations show how spectroscopy mapping with the STM near individual impurity defects can be used to image fractional statistics in FQH states, identifying unique signatures in such measurements that can distinguish different proposed ground states. The presence of locally trapped anyons should leave distinct signatures in STM spectroscopic maps, and enables a new approach to directly detect—and perhaps ultimately manipulate—these exotic quasiparticles.
Jeon, S., et al.Distinguishing a Majorana zero mode using spin resolved measurements”. Science eaan3670 (2017). Web. Publisher's VersionAbstract

One-dimensional topological superconductors host Majorana zero modes (MZMs), the non-local property of which could be exploited for quantum computing applications. We use spin-polarized scanning tunneling microscopy to show that MZMs realized in self-assembled Fe chains on the surface of Pb have a spin polarization that exceeds that stemming from the magnetism of these chains. This feature, captured by our model calculations, is a direct consequence of the nonlocality of the Hilbert space of MZMs emerging from a topological band structure. Our study establishes spin polarization measurements as a diagnostic tool to distinguish topological MZMs from trivial in-gap states of a superconductor.

Feldman, B. E., et al.High-resolution studies of the Majorana atomic chain platform”. Nature Physics 13 (2016): , 13, 286-291. Web. Publisher's Version
Gyenis, A., et al.Imaging electronic states on topological semimetals using scanning tunneling microscopy”. New Journal of Physics 18.105003 (2016). Web. Publisher's Version
Liu, M., et al.Large discrete jumps observed in the transition between Chern states in a ferromagnetic topological insulator”. Science Advances 29.7 (2016). Web. Publisher's Version
Feldman, B. E., et al.Observation of a nematic quantum Hall liquid on the surface of bismuth”. Science 354.6310 (2016). Web. Publisher's Version

Princeton University press release: "Unusual quantum liquid on crystal surface could inspire future electronics"

Gyenis, A., et al.Quasiparticle interference of heavy fermions in resonant x-ray scattering”. Science Advances 210 (2016). Web. Publisher's Version
Inoue, H., et al.Quasiparticle interference of the Fermi arcs and surface-bulk connectivity of Weyl semimetals”. Science 351.6278 (2016). Web. Publisher's Version

Princeton University press release: "Down the rabbit hole: how electrons travel through exotic new material (Science)"

Randeria, M. T., et al.Scanning Josephson spectroscopy on the atomic scale”. Physical Review B 93.16115R (2016). Web. Publisher's Version
Kushwaha, S. K., et al.Sn-doped Bi1.1 Sb 0.9Te2S, a bulk topological insulator with ideal properties”. Nature Communication 711456 (2016). Web. Publisher's Version
Li, J., et al.Two-dimensional chiral topological superconductivity in Shiba lattices”. Nature Communication 712297 (2016). Web. Publisher's Version
Das, P. K., et al.Layer-Dependent Quantum Cooperation of Electron and Hole States In the Anomalous Semimetal WTe2”. Nature Communication 710847 (2016). Web. Publisher's Version
Li, J., et al.Manipulating Majorana Zero Modes on Atomic Rings With External Magnetic Field”. Nature Communication 710395 (2016). Web. Publisher's Version
Neupert, T., A. Yazdani, and B. A. Bernevig. “Shiba Chains of Scalar Impurities on Unconventional Superconductors”. Physical Review B 93.094508 (2016). Web. Publisher's Version
Yazdani, A., E.H. Silva da Neto, and P. Aynajian. “Spectroscopic Imaging of Strongly Correlated Electronic States”. Annual Review of Condensed Matter Physics 711 (2016). Web. Publisher's Version
Kourtic, S., et al.Universal Signatures of Fermi Arcs in Quasiparticle Interference on the Surface of Weyi Semimetals”. Physical Review B Rapid Communication 93.041109 (2016). Web. Publisher's Version