Physical Properties of an Aperiodic Monotile with Graphene-like Features, Chirality, and Zero Modes.

The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i) the spectral function displays striking similarities to that of graphene, including sixfold symmetry and Dirac-like features; (ii) unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii) the spectrum has a macroscopic number of degenerate states at zero energy; (iv) when the magnetic flux per plaquette (ϕ) is half of the flux quantum, zero modes are found localized around the reflected "anti-hats"; and (v) its Hofstadter spectrum is periodic in ϕ, unlike for other quasicrystals. Our work serves as a basis to study wave and electron propagation in possible experimental realizations of the Hat, which we suggest.

Disorder-Induced Magnetotransport Anomalies in Amorphous and Textured Co1-xSix Semimetal Thin Films.

In recent times the chiral semimetal cobalt monosilicide (CoSi) has emerged as a prototypical, nearly ideal topological conductor hosting giant, topologically protected Fermi arcs. Exotic topological quantum properties have already been identified in CoSi bulk single crystals. However, CoSi is also known for being prone to intrinsic disorder and inhomogeneities, which, despite topological protection, risk jeopardizing its topological transport features. Alternatively, topology may be stabilized by disorder, suggesting the tantalizing possibility of an amorphous variant of a topological metal, yet to be discovered. In this respect, understanding how microstructure and stoichiometry affect magnetotransport properties is of pivotal importance, particularly in case of low-dimensional CoSi thin films and devices. Here we comprehensively investigate the magnetotransport and magnetic properties of ≈25 nm Co1-xSix thin films grown on a MgO substrate with controlled film microstructure (amorphous vs textured) and chemical composition (0.40 < x < 0.60). The resistivity of Co1-xSix thin films is nearly insensitive to the film microstructure and displays a progressive evolution from metallic-like (dρxx/dT > 0) to semiconducting-like (dρxx/dT < 0) regimes of conduction upon increasing the silicon content. A variety of anomalies in the magnetotransport properties, comprising for instance signatures consistent with quantum localization and electron-electron interactions, anomalous Hall and Kondo effects, and the occurrence of magnetic exchange interactions, are attributable to the prominent influence of intrinsic structural and chemical disorder. Our systematic survey brings to attention the complexity and the challenges involved in the prospective exploitation of the topological chiral semimetal CoSi in nanoscale thin films and devices.

Non-Hermitian Physics without Gain or Loss: The Skin Effect of Reflected Waves.

Physically, one tends to think of non-Hermitian systems in terms of gain and loss: the decay or amplification of a mode is given by the imaginary part of its energy. Here, we introduce an alternative avenue to the realm of non-Hermitian physics, which involves neither gain nor loss. Instead, complex eigenvalues emerge from the amplitudes and phase differences of waves backscattered from the boundary of insulators. We show that for any strong topological insulator in a Wigner-Dyson class, the reflected waves are characterized by a reflection matrix exhibiting the non-Hermitian skin effect. This leads to an unconventional Goos-Hänchen effect: due to non-Hermitian topology, waves undergo a lateral shift upon reflection, even at normal incidence. Going beyond systems with gain and loss vastly expands the set of experimental platforms that can access non-Hermitian physics and show signatures associated with non-Hermitian topology.