Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five of the ten Altland-Zirnbauer symmetry classes allow for the existence of such second-order topological insulators in two and three dimensions. We show that reflection symmetry can be employed to systematically generate examples of second-order topological insulators and superconductors, although the topologically protected states at corners (in two dimensions) or at crystal edges (in three dimensions) continue to exist if reflection symmetry is broken. A three-dimensional second-order topological insulator with broken time-reversal symmetry shows a Hall conductance quantized in units of e 2 /h.Introduction.-After the discovery of topological insulators and superconductors and their classification for the ten Altland-Zirnbauer symmetry classes [1][2][3], the concept of nontrivial topological band structures has been extended to materials in which the crystal structure is essential for the protection of topological phases [4]. This includes weak topological insulators [5], which rely on the discrete translation symmetry of the crystal lattice, and topological crystalline insulators [6], for which other crystal symmetries are invoked to protect a topological phase. Whereas the original strong topological insulators always have topologically protected boundary states, weak topological insulators or topological crystalline insulators have protected boundary states for selected surfaces/edges only.In a recent publication, Schindler et al. [7] proposed another extension of the topological insulator (TI) family: a higher-order topological insulator. Being crystalline insulators, these have well-defined faces and well-defined edges or corners at the intersections between the faces. An nth order topological insulator has topologically protected gapless states at the intersection of n crystal faces, but is gapped otherwise [7]. For example, a second-order topological insulator in two dimensions (d = 2) has zeroenergy states at corners, but a gapped bulk and no gapless edge states. Earlier examples of higher-order topological insulators and superconductors avant la lettre appeared in works by (see also [11,12]), who considered insulators and superconductors with protected corner states in d = 2 and d = 3 [13]. Sitte et al. showed that a threedimensional topological insulator in a magnetic field of generic direction also acquires the characteristics of a second-order topological Chern insulator, with chiral states moving along the sample edges [14].Since a second-order TI has a topologically trivial d-dimensional bulk, from a topological point of view its boundaries are essentially stand-alone (d − 1)-dimensional insulators, so that topologically protected states at corners (for d = 2) or edges (for d = 3) arise naturally as "domain walls" at the intersection of two boundaries if these ar...

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We combine scanning-tunneling-spectroscopy experiments probing magnetic impurities on a superconducting surface with a theoretical analysis of the tunneling processes between (superconducting) tip and substrate. We show that the current through impurity-induced Shiba bound states is carried by single-electron tunneling at large tip-substrate distances and Andreev reflections at smaller distances. The single-electron current requires relaxation processes, allowing us to extract information on quasiparticle transitions and lifetimes.

Ten isoindigo-based polymers were synthesized, and their photophysical and electrochemical properties and device performances were systematically investigated. The HOMO levels of the polymers were tuned by introducing different donor units, yet all polymers exhibited p-type semiconducting properties. The hole mobilities of these polymers with centrosymmetric donor units exceeded 0.3 cm 2 V −1 s −1 , and the maximum reached 1.06 cm 2 V −1 s −1 . Because of their low-lying HOMO levels, these copolymers also showed good stability upon moisture. AFM and GIXD analyses revealed that polymers with different symmetry and backbone curvature were distinct in lamellar packing and crystallinity. DFT calculations were employed to help us propose the possible packing model. Based on these results, we propose a design strategy, called "molecular docking", to understand the interpolymer π−π stacking. We also found that polymer symmetry and backbone curvature affect interchain "molecular docking" of isoindigo-based polymers in film, ultimately leading to different device performance. Finally, our design strategy maybe applicable to other reported systems, thus representing a new concept to design conjugated polymers for field-effect transistors.