Session X43: New Developments in Topological Materials

Two-dimensional topological superconductivity in Pb/Co/Si(111)

The examination of supposedly well-known condensed matter systems through the prism of topology has led to the discovery of new quantum phenomena that were previously overlooked. Just like insulators can present topological phases characterized by Dirac edge states, superconductors can exhibit topological phases characterized by Majorana edge states. In particular, one-dimensional topological superconductors are predicted to host zero energy Majorana fermions at their extremities. Zero bias anomalies localized at the edge of proximity induced superconducting wires were recently interpreted as fingerprints of the emergence of topological superconductivity [1,2].

By contrast, two-dimensional (2D) superconductors have a one-dimensional boundary which would naturally lead to propagating Majorana edge states characterized by a Dirac-like dispersion. We have recently observed some hint of dispersive Majorana edge states in a single atomic layer Pb superconductor. This material has strong triplet correlations but is not topological by itself [3]. We will show that by applying a Zeeman field with the help of a buried Co-Si nano-magnet one can provoke a transition to a topological state [4].

In addition to their dispersive edge states, 2D topological superconductors are also supposed to support localized Majorana bound states in their vortex cores. We will show that some recent measurements seem to support this theoretical prediction [5].

References
[1] V. Mourik et al., Science 336, 1003 (2012)
[2] S. Nadj-Perge, et al., Science 346, 602 (2014)
[3] C. Brun et al., Nature Phys. 444, 10 (2014)
[4] G. C. Ménard, et al., Nature Comm, 8, 2040 (2017)
[5] G. C. Ménard, et al., arXiv:1810.09541   

Fractional Excitonic Insulator

We argue that a correlated fluid of electrons and holes can exhibit a fractional quantum Hall effect at zero magnetic field analogous to the Laughlin state at filling 1/m. We introduce a variant of the Laughlin wavefunction for electrons and holes and show that for m=1 it describes a Chern insulator that is the exact ground state of a free fermion model with p_x + i p_y excitonic pairing. For m>1 we develop a composite fermion mean field theory, and we will give several pieces of evidence that our wavefunction correctly describes this phase. We will present physical arguments that the m=3 state can be realized in a system with C₆ rotational symmetry in which energy bands with angular momentum that differ by 3 cross at the Fermi energy. This leads to a gapless state with (p_x + i p_y)³ excitonic pairing, which we argue is conducive to forming the fractional excitonic insulator in the presence of interactions. Prospects for numerics on model systems and band structure engineering to realize this phase in real materials will be discussed.

Yichen Hu, Jörn W.F. Venderbos and C.L. Kane, Phys. Rev. Lett. 121, 126601 (2018).   

New invariants, complete classification and fast diagnosis for topological crystalline insulators

Topological crystalline insulators have nontrivial band topology jointly protected by onsite symmetries of time reversal and charge conservation, as well as by spatial symmetries of lattice. Different types of lattice symmetries correspond to different topological invariants in the bulk and distinct characteristic surface states. We discuss newly discovered Z₂ invariants in 3D protected by rotation (screw) symmetry, inversion symmetry and roto-reflection symmetry, respectively. Each of the new invariants in the bulk is related to the (d-2)-dimensional edge states on the boundary. With the new invariants, we establish a complete classification of topological crystalline insulators for each of the 230 space groups in 3D, along with explicit, microscopic constructions for each class. To search for corresponding materials for the topological states in these new classes, we have established quantitative mappings from symmetry eigenvalues of valence bands to topological invariants all space groups. Applying these mappings, we have developed a fully automated diagnosis algorithm for all nonmagnetic crystals. The algorithm is applied to diagnosing 39519 materials, in which 8056 are found topological.   

Observation of tunable Dirac interface states in topological crystalline insulator superlattice

Topological crystalline insulators (TCIs) are unique topological systems. Their Dirac surface band structure - tightly linked to the crystal symmetries - can be tuned using a variety of external knobs. By stacking TCI Pb_1-xSn_xSe in a superlattice of alternating trivial and non-trivial topology, we dramatically enhance the optical response of its topological Dirac states and succeed in demonstrating the tuning of their energy gap with temperature. We use magnetooptical infrared Landau level spectroscopy to probe the band structure of those topological states in MBE grown high mobility TCI/trivial superlattices for magnetic fields up to 15T and temperatures between 4.2K and 200K. By simply varying the sample temperature, we show that one can tune the penetration depth of surface states into the TCI layer and the inter-surface hybridization across this layer. As a result, we observe a tuning of the Dirac gap over a range extending from 5meV to 60meV. We pave the way for further realization of tunable quantum phases using TCI superlattices.   

Wilson Loops, Wyckoff Positions, and Wannier Functions: New Developments in Stable and Fragile Topology

The interplay of topology and geometry has been -- and continues to be -- a rich area of study for condensed matter physics. Recently, we have realized that spatial symmetries allow for the stabilization of topological phases much more exotic than those that can be found with time-reversal symmetry alone. Examples include topological crystalline insulators, "hourglass Fermion" phases, and Dirac and double-Weyl semimetals. In this talk, I will review recent developments in the theory of band representations which highlight the role of Wannier functions and holonomy in explaining the origins of topological crystalline behavior. I will show how this relates to several new ideas, such as symmetry indicators, topological phases with high co-dimension boundary states, and the "fragile" topology of isolated groups of bands. Finally, I will discuss how non-symmorphic symmetries can protect novel topological surface states, which can be diagnosed through the holonomy of Bloch functions.