We identify the possibility of realizing higher order topological (HOT) phases in noncrystalline or amorphous materials. Starting from two- and three-dimensional crystalline HOT insulators, accommodating topological corner states, we gradually enhance structural randomness in the system. Within a parameter regime, as long as amorphousness is confined by an outer crystalline boundary, the system continues to host corner states, yielding amorphous HOT insulators. However, as structural disorder percolates to the edges, corner states start to dissolve into amorphous bulk, and ultimately the system becomes a trivial insulator when amorphousness plagues the entire system. These outcomes are further substantiated by computing the quadrupolar (octupolar) moment in two (three) dimensions. Therefore, HOT phases can be realized in amorphous solids, when wrapped by a thin (lithographically grown, for example) crystalline layer. Our findings suggest that crystalline topological phases can be realized even in the absence of local crystalline symmetry.

We investigate phonon-mediated Cooper pairing in flat electronic band systems by solving the full-bandwidth multiband Eliashberg equations for superconductivity in magic angle twisted bilayer graphene using a realistic tight-binding model. We find that Cooper pairing away from the Fermi level contributes decisively to superconductivity by enhancing the critical temperature and ensures a robust finite superfluid density. We show that this pairing yields particle-hole asymmetric superconducting domes in the temperature-gating phase diagram and gives rise to distinct spectroscopic signatures in the superconducting state. We predict several such features in tunneling and angle-resolved photoemission spectra for future experiments.

We use Nielsen's geometric approach to quantify the circuit complexity in a one-dimensional Kitaev chain across a topological phase transition. We find that the circuit complexities of both the ground states and nonequilibrium steady states of the Kitaev model exhibit nonanalytical behaviors at the critical points, and thus can be used to detect both equilibrium and dynamical topological phase transitions. Moreover, we show that the locality property of the real-space optimal Hamiltonian connecting two different ground states depends crucially on whether the two states belong to the same or different phases. This provides a concrete example of classifying different gapped phases using Nielsen's circuit complexity. We further generalize our results to a Kitaev chain with long-range pairing, and we discuss generalizations to higher dimensions. Our result opens up an avenue for using circuit complexity as a tool to understand quantum many-body systems.

We show an experimental evidence of the domination of absorption over scattering in absorbance spectra of detonation nanodiamonds. We perform absorbance measurements on the UV-vis spectrophotometer equipped with an integrating sphere and compare them with conventional absorbance spectra. Additionally, we measure the scattering light intensity at the cuvette side wall (scattering at ${90}^{\circ }$ angle). The obtained experimental data were interpreted using photon random-walk simulations in turbid media and the Kubelka-Munk approach. The scattering cross sections and indicatrices were obtained by Mie theory. We discover that despite being very close to the ${\lambda }^{-4}$ power law (like Rayleigh scattering) the light extinction by the primary 4-nm diamond crystallites is due to absorption only and scattering can be neglected. That is the reason why previously absorption and scattering contributions were confused. The scattering is governed only by the agglomerates of 100 nm and larger in size remaining in the hydrosols and their fraction can be effectively controlled by centrifugation. Only Mie theory reproduces correctly the close to ${\lambda }^{-2}$ scattering by the agglomerates accounting for the weird interplay between their size, fractal dimension, and dielectric properties. Finally, using the obtained absorbance spectra we estimate the fraction of nondiamond phase in nanodiamonds and their agglomerates.

The magnetic moment of a quantum dot can be screened by its coupling to a superconducting reservoir, depending on the hierarchy of the superconducting gap and the relevant Kondo scale. This screening-unscreening transition can be driven by electrostatic gating, tunnel coupling, and, as we demonstrate here, a magnetic field. We perform high-resolution spectroscopy of subgap excitations near the screening-unscreening transition of asymmetric superconductor-quantum dot-superconductor (S–QD–S) junctions formed by the electromigration technique. Our measurements reveal a re-entrant phase boundary determined by the competition between Zeeman energy and gap reduction with magnetic field. We further track the evolution of the phase transition with increasing temperature, which is also evinced by thermal replicas of subgap states.

Magnetic hopfions are topologically protected three-dimensional solitons that are constituted by a tube which exhibits a topologically nontrivial spin texture in the cross-section profile and is closed to a torus. Here we show that the hopfion's locally uncompensated emergent field leads to a topological Hall signature, although the topological Hall effect vanishes on the global level. The topological Hall signature is switchable by magnetic fields or electric currents and occurs independently of the anomalous and conventional Hall effects. It can therefore be exploited to electrically detect hopfions in experiments and even to distinguish them from other textures like skyrmion tubes. Furthermore, it can potentially be utilized in spintronic devices. Exemplarily, we propose a hopfion-based racetrack data storage device and simulate the electrical detection of the hopfions as carriers of information.

The observation of high-order harmonic generation (HHG) from bulk crystals is stimulating substantial efforts to understand the involved mechanisms and their analog to the intuitive three-step recollision model of gas-phase HHG. Here we explore the roles of electronic band structure and Coulomb interactions in solid-state HHG by studying the optical response of linear atomic chains and carbon nanotubes to intense ultrashort pulses. Specifically, we simulate electron dynamics by solving the single-particle density matrix equation of motion in the presence of intense ultrafast optical fields, incorporating tight-binding electronic states and a self-consistent electron-electron interaction. At this level of description, linear atomic chains constitute an idealized yet realistic one dimensional (1D) system in which to explore HHG that can advantageously be tuned to describe metals, regular insulators, and topological insulators. Our chain model readily provides insight on the temporal evolution of electronic states in reciprocal space, revealing the important role played by electron interactions in HHG, due in part to the presence of collective optical resonances. This model further predicts that doped semiconductors generate high harmonics more efficiently than their metallic and undoped counterparts. To complement this idealized system we also show results for HHG in more realistic quasi-1D structures such as carbon nanotubes, the behavior of which is found to be in good qualitative agreement with the atomic chains. Our findings apply directly to extreme nonlinear optical phenomena in atoms on surfaces, carbon-based structures, linear arrays of dopant atoms in semiconductors, and linear molecules, such as polycyclic aromatic hydrocarbon chains, and can be straightforwardly extended to optimize existing platforms for HHG or identify new solid-state alternatives in the context of nonlinear plasmonics.

The intrinsic mechanism of the spin-orbit coupling at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface remains a debatable issue. Rashba-type spin-orbit coupling is an appealing candidate that has been demonstrated by several magnetotransport results. On the other hand, the atomic spin-orbit coupling was also shown to play an important role, particularly when the Fermi level is close to the Lifshitz point. In this paper, we focus on the measurements of the anisotropic superconducting upper critical fields in gated ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ devices. By rigorous fittings of the $H_{c2}-T$ curves using both the Werthamer-Helfand-Hohenberg theory and Klemm-Luther-Beasley model, an upper limit of the spin-orbit scattering lifetime can be determined in the two-dimensional limit of the superconducting state. We found that the extracted spin-orbit scattering lifetime monotonically increases with the effective transport lifetime that spans over two orders of magnitude in the regime with sheet density close to and higher than that at the Lifshitz point. Those results suggest the dominant role of Elliott-Yafet type spin relaxation. The comparison to the weak localization fittings on magnetoconductance reveals a striking difference. Such a model dependence infers an electronic phase separation at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface, where the superconductivity originates from a selective $d$-subband occupancy.

Recently, the very first large-gap Kane-Mele quantum spin Hall insulator was predicted to be monolayer jacutingaite (${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$), a naturally occurring exfoliable mineral discovered in Brazil in 2008. The stacking of quantum spin Hall monolayers into a van-der-Waals layered crystal typically leads to a (0;001) weak topological phase, which does not protect the existence of surface states on the (001) surface. Unexpectedly, recent angle-resolved photoemission spectroscopy experiments revealed the presence of surface states dispersing over large areas of the 001-surface Brillouin zone of jacutingaite single crystals. The 001-surface states have been shown to be topologically protected by a mirror Chern number $C_M=-2$, associated with a nodal line gapped by spin-orbit interactions. Here, we extend the two-dimensional Kane-Mele model to bulk jacutingaite and unveil the microscopic origin of the gapped nodal line and the emerging crystalline topological order. By using maximally localized Wannier functions, we identify a large nontrivial second nearest-layer hopping term that breaks the standard paradigm of weak topological insulators. Complemented by this term, the predictions of the Kane-Mele model are in remarkable agreement with recent experiments and first-principles simulations, providing an appealing conceptual framework also relevant for other layered materials made of stacked honeycomb lattices.

We propose an implementation of a singlet-only spin qubit in a GaAs-based triple quantum dot with a (1, 4, 1) charge occupation. In the central multielectron dot, the interplay between Coulomb interaction and an out-of-plane magnetic field creates an energy spectrum with a tunable singlet-triplet splitting, which can be exploited to create a six-particle singlet-only qubit with a qubit splitting that can straightforwardly be tuned over tens of $\mu \mathrm{eV}$ by adjusting the external magnetic field. We confirm the full exchange-based electric control of the qubit and demonstrate its superior coherence properties due to its singlet-only nature.

We study the thermalization, after sudden and slow quenches, in an interacting model having a quantum phase transition from a Sachdev-Ye-Kitaev (SYK) non-Fermi liquid (NFL) to a Fermi liquid (FL). The model has SYK fermions coupled to noninteracting lead fermions and can be realized in a graphene flake connected to external leads. A sudden quench to the NFL leads to rapid thermalization via collapse-revival oscillations of the quasiparticle residue of the lead fermions. In contrast, the quench to the FL shows multiple prethermal regimes and much slower thermalization. In the slow quench performed over a time $\tau$, we find that the excitation energy generated has a remarkable intermediate-$\tau$ nonanalytic power-law dependence, ${\tau }^{-\eta }$ with $\eta <1$, which seemingly masks the dynamical manifestation of the initial residual entropy of the SYK fermions. Our study gives an explicit demonstration of the intriguing contrasts between the out-of-equilibrium dynamics of a NFL and a FL in terms of their thermalization and approach to adiabaticity.

Spin ice may be considered to be a model system for the investigation of pinch point scattering. We present very-high-resolution numerical simulations and an analytical theory of the pinch point profiles of the near-neighbor and dipolar spin ice models and find these to be in excellent agreement with each other and with existing theory. Most importantly, the pinch points of the dipolar spin ice model are infinitely sharp, as a result of unscreened dipolar fields. These results are compared to polarized neutron scattering measurements of the pinch point profiles in ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, considered to be an accurate realization of dipolar spin ice. In contrast to the numerical and analytical results, the experimental pinch point profiles are shown to be broadened in a manner that is quantitatively consistent with fully screened dipolar fields. This striking paradox is not easily resolved: Possible resolutions implicate quantum fluctuations or fundamental corrections to the theory of simulation or polarized neutron scattering. We further discuss our results in the context of spin ice's role as a model Coulomb fluid.

Antiferromagnets and ferromagnets are archetypes of the two distinct (type-A and type-B) ways of spontaneously breaking a continuous symmetry. Although type-B Nambu-Goldstone modes arise in various systems, the ferromagnet was considered pathological due to the stability and symmetry-breaking nature of its exact ground state. However, here we show that symmetry breaking in ferrimagnets closely resembles the ferromagnet. In particular, there is an extensive ground-state degeneracy, there is no Anderson tower of states, and the maximally polarized ground state is thermodynamically stable. Our results are derived analytically for the Lieb-Mattis ferrimagnet and numerically for the Heisenberg ferrimagnet. We argue that these properties are generic for type-B symmetry-broken systems, where the order parameter operator is a symmetry generator.

We construct a family of translationally invariant lattice models with a large number $\left(N\right)$ of orbitals at every site coupled together via single-electron tunneling. By tuning the relative strength of the electronic bandwidth and on-site interactions, which have a modified Sachdev-Ye-Kitaev form, we demonstrate a number of unusual features at strong coupling and in the large-$N$ limit. We find examples of (i) an intrinsic non-BCS superconducting instability arising out of an incoherent non-Fermi-liquid metal, and (ii) an instability of an incipient heavy Fermi-liquid metal to superconductivity with transition temperatures comparable to its renormalized bandwidth. At strong coupling, these solvable models display pairing instabilities that are not driven by any special “nesting” properties associated with an underlying Fermi surface.

We show that a slab of a three-dimensional inversion-symmetric higher-order topological insulator (HOTI) in class A is a 2D Chern insulator, and that in class AII is a 2D $Z_2$ topological insulator. We prove it by considering a process of cutting the three-dimensional inversion-symmetric HOTI along a plane and study the spectral flow in the cutting process. We show that the $Z_4$ indicators, which characterize three-dimensional inversion-symmetric HOTIs in classes A and AII, are directly related to the $Z_2$ indicators for the corresponding two-dimensional slabs with inversion symmetry, i.e., the Chern number parity and the $Z_2$ topological invariant, for classes A and AII, respectively. The existence of the gapless hinge states is understood from the conventional bulk-edge correspondence between the slab system and its edge states. Moreover, we also show that the spectral-flow analysis leads to another proof of the bulk-edge correspondence in one- and two-dimensional inversion-symmetric insulators.

In topology, a torus remains invariant under certain nontrivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter supported on a torus geometry in real space, these transformations encode the braiding statistics and fusion rules of emergent anyonic excitations and thus serve as a diagnostic of topological order. Moreover, modular transformations of higher genus surfaces, e.g., a torus with multiple handles, can enhance the computational power of a topological state, in many cases providing a universal fault-tolerant set of gates for quantum computation. However, due to the intrusive nature of modular transformations, which abstractly involve global operations, physical implementations of them in local systems have remained elusive. Here, we show that by engineering an effectively folded manifold corresponding to a multilayer topological system, modular transformations can be applied in a single shot by independent local unitaries, providing a novel class of transversal logical gates for fault-tolerant quantum computation. Specifically, we demonstrate that multilayer topological states with appropriate boundary conditions and twist defects allow modular transformations to be effectively implemented by a finite sequence of local SWAP gates between the layers. We further provide methods to directly measure the modular matrices, and thus the fractional statistics of anyonic excitations, providing a novel way to directly measure topological order. A more general theory of transversal gates and the deep connection to anyon symmetry transformation and symmetry-enriched topological orders are also discussed.

We discuss the stability of ferromagnetic long-range order in three-dimensional classical $XY$ ferromagnets upon substitution of a small subset of equally oriented bonds by impurity bonds, on which the ferromagnetic exchange $J_{\perp }>0$ is replaced by a strong antiferromagnetic coupling $J_{\mathrm{imp}}<0$. In the impurity-free limit, the effective low-energy Hamiltonian is that of spin waves. In the presence of a single, sufficiently strongly frustrating impurity bond, the ground state is twofold degenerate, corresponding to either clockwise or counterclockwise canting of the spins in the vicinity of the impurity bond. For a small but finite concentration of impurity bonds, the effective low-energy Hamiltonian is that of Ising variables encoding the sense of rotation of the local canting around the impurities. Those degrees of freedom interact pairwise through a dipolar interaction mediated by spin waves. A spatially random distribution of impurities leads to a ferromagnetic Ising ground state, which indicates the instability of the $XY$ ferromagnet towards a spiral state, with wave vector and transition temperature both proportional to the concentration of impurity bonds. This mechanism of spiral order by disorder is relevant for magnetic materials such as ${\mathrm{YBaCuFeO}}_5$, for which our theory predicts a ratio between the spiral ordering temperature and the modulus of the spiral wave vector close to the measured ones.

We study the superconductivity of spin-polarized electrons in centrosymmetric ferromagnetic metals. Due to the spin polarization and the Fermi statistics of electrons, the superconducting pairing function naturally has odd parity. According to the parity formula proposed by Fu, Berg, and Sato, odd-parity pairing leads to conventional first-order topological superconductivity when a normal metal has an odd number of Fermi surfaces. Here, we derive generalized parity formulas for the topological invariants characterizing the higher-order topology of centrosymmetric superconductors. Based on the formulas, we systematically classify all possible band structures of ferromagnetic metals that can induce inversion-protected higher-order topological superconductivity. Among them, doped ferromagnetic nodal semimetals are identified as the most promising normal-state platform for higher-order topological superconductivity. In two dimensions, we show that odd-parity pairing of doped Dirac semimetals induces a second-order topological superconductor. In three dimensions, odd-parity pairing of doped nodal-line semimetals generates a nodal-line topological superconductor with monopole charges. On the other hand, odd-parity pairing of doped monopole nodal-line semimetals induces a three-dimensional third-order topological superconductor. Our theory shows that the combination of superconductivity and ferromagnetic nodal semimetals opens up another avenue for future topological quantum computations using Majorana zero modes.

We classify subsystem symmetry-protected topological (SSPT) phases in $3+1$ dimensions $(3+1\text{D}$) protected by planar subsystem symmetries: short-range entangled phases which are dual to long-range entangled Abelian fracton topological orders via a generalized “gauging” duality. We distinguish between weak SSPTs, which can be constructed by stacking $2+1\text{D}$ SPTs, and strong SSPTs, which cannot. We identify signatures of strong phases, and show by explicit construction that such phases exist. A classification of strong phases is presented for an arbitrary finite Abelian group. Finally, we show that fracton orders realizable via $p$-string condensation are dual to weak SSPTs, while those dual to strong SSPTs exhibit statistical interactions prohibiting such a realization.

We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the half-filled, three-dimensional time-reversal-invariant Hofstadter model with finite spin-orbit coupling. Besides the weak and strong topological insulator phases we find a nodal line semimetal in the parameter regime between the two three-dimensional topological insulator phases. Using dynamical mean-field theory combined with the topological Hamiltonian approach we find stabilization of these three-dimensional topological states due to the Hubbard interaction. We study surface states which exhibit an asymmetry between left and right surfaces originating from the broken parity symmetry of the system. Our results set the stage for further research on inhomogeneous three-dimensional topological systems, proximity effects, topological Mott insulators, nontrivially linked nodal line semimetals, and circuit-based quantum simulators.