On the robustness of topological corner modes in photonic crystals

We analyze the robustness of corner modes in topological photonic crystals, taking a $C_6$-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry and Wilson loop calculations to demonstrate that the topological properties of the bulk crystal stem from an obstructed atomic limit phase. We then characterize the topological corner modes emerging within the gapped edge modes employing a semi-analytical model, determining the appropriate real space topological invariants. For the first time, we provide a detailed account of the effect of long-range interactions on the topological modes in photonic crystals, and we quantify their robustness to perturbations. We conclude that, while photonic long-range interactions inevitably break chiral symmetry, the corner modes are protected by lattice symmetries.Comment: v1: 6 pages, 4 figures (supp 10 pages, 3 figures, 1 table

Spectroscopic perspective on the interplay between electronic and magnetic properties of magnetically doped topological insulators

We combine low energy muon spin rotation (LE-$\mu$SR) and soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to study the magnetic and electronic properties of magnetically doped topological insulators, (Bi,Sb)$_2$Te$_3$. We find that one achieves a full magnetic volume fraction in samples of (V/Cr)$_x$(Bi,Sb)$_{2-x}$Te$_3$ at doping levels x $\gtrsim$ 0.16. The observed magnetic transition is not sharp in temperature indicating a gradual magnetic ordering. We find that the evolution of magnetic ordering is consistent with formation of ferromagnetic islands which increase in number and/or volume with decreasing temperature. Resonant ARPES at the V $L_3$ edge reveals a nondispersing impurity band close to the Fermi level as well as V weight integrated into the host band structure. Calculations within the coherent potential approximation of the V contribution to the spectral function confirm that this impurity band is caused by V in substitutional sites. The implications of our results on the observation of the quantum anomalous Hall effect at mK temperatures are discussed

Topological semimetals without quasiparticles

The interplay between interactions and topology in quantum materials is of extensive current interest. Strong correlations are known to be important for insulating topological states, as exemplified by the fractional quantum Hall effect. For the metallic case, whether and how they can drive topological states that have no free-electron counterparts is an open and pressing question. We introduce a general framework for lattice symmetries to constrain single-particle excitations even when they are not quasiparticles, and substantiate it in a periodic Anderson model with two channels of conduction electrons. We demonstrate that symmetry constrains correlation-induced emergent excitations to produce non-Fermi liquid topological phases. The loss of quasiparticles in these phases is manifested in a non-Fermi liquid form of spectral and transport properties, whereas its topological nature is characterized by surface states and valley and spin Hall conductivities. We also identify candidate materials to realize the proposed phases. Our work opens a door to a variety of non-Fermi liquid topological phases in a broad range of strongly correlated materials.Comment: 46 pages, 3 figures main text + 11 figures supplementary informatio

Unconventional Charge-to-Spin Conversion in Graphene/MoTe2 van der Waals Heterostructures

Spin-charge interconversion (SCI) is a central phenomenon to the development of spintronic devices from materials with strong spin-orbit coupling (SOC). In the case of materials with high crystal symmetry, the only allowed SCI processes are those where the spin-current, charge-current, and spin-polarization directions are orthogonal to each other. Consequently, standard SCI experiments are designed to maximize the signals arising from the SCI processes with conventional mutually orthogonal geometry. However, in low-symmetry materials, certain nonorthogonal SCI processes are also allowed. Since the standard SCI experiment is limited to charge current flowing only in one direction in the SOC material, certain allowed SCI configurations remain unexplored. Here, we perform a thorough SCI study in a graphene-based lateral spin valve combined with low-symmetry MoTe2. Due to a very low contact resistance between the two materials, we can detect SCI signals using both a standard configuration, where the charge current is applied along MoTe2, and a recently introduced [three-dimensional- (3D) current] configuration, where the charge-current flow can be controlled in three directions within the heterostructure. As a result, we observe three different SCI components, one orthogonal and two nonorthogonal, adding valuable insight into the SCI processes in low-symmetry materials. The large SCI signals obtained at room temperature, along with the versatility of the 3D-current configuration, provide feasibility and flexibility to the design of the next generation of spin-based devices.This work is supported by the Spanish MICINN under Projects No. RTI2018-094861-B-I00, No. PGC2018-101988-B-C21, No. PID2019-109905GB-C21, No. MAT2017-88377-C2-2-R, and the Maria de Maeztu Units of Excellence Programme (Grants No. MDM-2016-0618 and No. CEX2020-001038-M); the “Valleytronics” Intel Science Technology Center; the Gipuzkoa Regional Council under Projects No. 2021-CIEN-000037-01 and No. 2021-CIEN-000070-01; and the European Union H2020 under the Marie Sklodowska-Curie Actions (Grants No. 0766025-QuESTech and No. 794982-2DSTOP). N.O. thanks the Spanish MICINN for support from a Ph.D. fellowship (Grant No. BES-2017-07963). J.I.-A. acknowledges support from the “Juan de la Cierva-Formación” program by the Spanish MICINN (Grant No. FJC2018-038688-I) for a postdoctoral fellowship. R.C. acknowledges funding from Generalitat Valenciana through Grant No. CIDEGENT/2018/004 M.G.V. and I.R. thanks support from the Spanish MICINN (grant PID2019-109905GBC21), the German Research Foundation DFG (grant nr. GA3314/1-1-FOR 5249 QUAST) and the European Research Council ERC (Grant No. 101020833)

Pb9_9Cu(PO4)6_6(OH)2_2: Phonon bands, Localized Flat Band Magnetism, Models, and Chemical Analysis

In a series of recent reports, doped lead apatite (LK-99) has been proposed as a candidate ambient temperature and pressure superconductor. However, from both an experimental and theoretical perspective, these claims are largely unsubstantiated. To this end, our synthesis and subsequent analysis of an LK-99 sample reveals a multiphase material that does not exhibit high-temperature superconductivity. We study the structure of this phase with single-crystal X-ray diffraction (SXRD) and find a structure consistent with doped $\text{Pb}_{10}(\text{PO}_4)_6(\text{OH})_2$. However, the material is transparent which rules out a superconducting nature. From ab initio defect formation energy calculations, we find that the material likely hosts $\text{OH}^-$ anions, rather than divalent $\text{O}^{2-}$ anions, within the hexagonal channels and that Cu substitution is highly thermodynamically disfavored. Phonon spectra on the equilibrium structures reveal numerous unstable phonon modes. Together, these calculations suggest it is doubtful that Cu enters the structure in meaningful concentrations, despite initial attempts to model LK-99 in this way. However for the sake of completeness, we perform ab initio calculations of the topology, quantum geometry, and Wannier function localization in the Cu-dominated flat bands of four separate doped structures. In all cases, we find they are atomically localized by irreps, Wilson loops, and the Fubini-Study metric. It is unlikely that such bands can support strong superfluidity, and instead are susceptible to ferromagnetism (or out-of-plane antiferromagnetism) at low temperatures, which we find in ab initio studies. In sum, $\text{Pb}_{9}\text{Cu}(\text{PO}_4)_6(\text{OH})_2$ could more likely be a magnet, rather than an ambient temperature and pressure superconductor.Comment: 39 pages including appendices. Updated defect calculations and energy-dispersive X-ray spectroscopy dat

Spin texture induced by oxygen vacancies in strontium perovskite (001) surfaces: A theoretical comparison between SrTiO3 and SrHfO3

The electronic structure of SrTiO3 and SrHfO3 (001) surfaces with oxygen vacancies is studied by means of first-principles calculations. We reveal how oxygen vacancies within the first atomic layer of the SrTiO3 surface (i) induce a large antiferrodistortive motion of the oxygen octahedra at the surface, (ii) drive localized magnetic moments on the Ti 3d orbitals close to the vacancies, and (iii) form a two-dimensional electron gas localized within the first layers. The analysis of the spin texture of this system exhibits a splitting of the energy bands according to the Zeeman interaction, lowering of the Ti 3dxy level in comparison with dxz and dyz, and also an in-plane precession of the spins. No Rashba-like splitting for the ground state or for the ab initio molecular dynamics trajectory at 400 K is recognized as suggested recently by A. F. Santander-Syro et al. [Nat. Mater. 13, 1085 (2014)]. Instead, a sizable Rashba-like splitting is observed when the Ti atom is replaced by a heavier Hf atom with a much larger spin-orbit interaction. However, we observe the disappearance of the magnetism and the surface two-dimensional electron gas when full structural optimization of the SrHfO3 surface is performed. Our results uncover the sensitive interplay of spin-orbit coupling, atomic relaxations, and magnetism when tuning these Sr-based perovskites

Higher-order topology in bismuth

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