In this work, we study the effect of engineered disorder on the local magnetic response of proximity-coupled superconducting island arrays by comparing scanning superconducting quantum interference device (SQUID) susceptibility measurements to a model in which we treat the system as a network of one-dimensional (1D) superconductor–normal-metal–superconductor Josephson junctions, each with a Josephson coupling energy $E_J$ determined by the junction length or distance between islands. We find that the disordered arrays exhibit a spatially inhomogeneous diamagnetic response which, for low local applied magnetic fields, is well described by this junction network model, and we discuss these results as they relate to inhomogeneous 2D superconductors. Our model of the static magnetic response of the arrays does not fully capture the onset of nonlinearity and dissipation with increasing applied field, as these effects are associated with vortex motion due to the dynamic nature of the scanning SQUID susceptometry measurement. This work demonstrates a model 2D superconducting system with engineered disorder, and it highlights the impact of dissipation on the local magnetic properties of 2D superconductors and Josephson junction arrays.

The interplay between electron-electron interactions and structural ordering can yield exceptionally rich correlated electronic phases. We have used scanning tunneling microscopy to investigate bulk $1T\text{−}{\mathrm{TaSe}}_2$ and have uncovered surprisingly diverse correlated surface states thereof. These surface states exhibit the same in-plane charge-density wave ordering but dramatically different electronic ground states ranging from insulating to metallic. The insulating variety of surface state shows signatures of a decoupled surface Mott layer. The metallic surface states, on the other hand, exhibit zero-bias peaks of varying strength that suggest Kondo phases arising from coupling between the Mott surface layer and the metallic bulk of $1T\text{−}{\mathrm{TaSe}}_2$. The surface of bulk $1T\text{−}{\mathrm{TaSe}}_2$ thus constitutes a rare realization of the periodic Anderson model covering a wide parameter regime, thereby providing a model system for accessing different correlated phenomena in the same crystal. Our results highlight the central role played by strong correlations in this material family.

We investigate the effects of disorder characterizing a superconducting thin film on the proximity-induced superconductivity generated by the film (in, e.g., a semiconductor) based on the exact numerical analysis of a three-dimensional microscopic model. To make the problem numerically tractable, we use a recursive Green's function method in combination with a “patching approach” that exploits the short-range nature of the interface Green's function in the presence of disorder. As a result of the Fermi surface mismatch between the superconductor (SC) and the semiconductor (SM) in combination with the confinement-induced quantization of the transverse SC modes, the proximity effect induced by a clean SC film is typically one to three orders of magnitude smaller that the corresponding quantity for a bulk SC and exhibits huge thickness-dependent variations. The presence of disorder has competing effects: on the one hand, it enhances the proximity-induced superconductivity and suppresses its strong thickness dependence, on the other hand, it generates proximity-induced effective disorder in the SM. The effect of proximity-induced disorder on the topological superconducting phase and the associated Majorana modes is studied nonperturbatively.

Random flux is commonly believed to be incapable of driving full metal-insulator transitions in noninteracting systems. Here we show that random flux can after all induce a full metal–band insulator transition in the two-dimensional Su-Schrieffer-Heeger model. Remarkably, we find that the resulting insulator can be an extrinsic higher-order topological insulator with zero-energy corner modes in proper regimes, rather than a conventional Anderson insulator. Employing both level statistics and finite-size scaling analysis, we characterize the metal–band insulator transition and numerically extract its critical exponent as $\nu =2.48\pm 0.08$. To reveal the physical mechanism underlying the transition, we present an effective band structure picture based on the random-flux averaged Green's function.

${\mathrm{RbFe}}^{2+}{\mathrm{Fe}}^{3+}{\mathrm{F}}_6$ is an example of an antiferromagnet with charge ordering of the octahedrally coordinated ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions. As well as different spin values, ${\mathrm{Fe}}^{2+}$ $(S=2)$ and ${\mathrm{Fe}}^{3+}$ $(S=\frac{5}{2})$ possess differing orbital ground states with ${\mathrm{Fe}}^{2+}$ having an orbital degeneracy with an effective orbital angular momentum of $l=1$. The resulting low-temperature magnetic structure is noncollinear with the spins aligned perpendicular to nearest neighbors [S. W. Kim et al. Chem. Sci. 3, 741 (2012)]. The combination of an orbital degeneracy and noncollinear spin arrangements introduces the possibility for unusual types of excitations such as amplitude modes of the order parameter. In this paper we investigate this by applying a multilevel analysis to model neutron spectroscopy data [M. Songvilay et al. Phys. Rev. Lett. 121, 087201 (2018)]. In particular, we discuss the possible origins of the momentum and energy broadened continuum scattering observed in terms of amplitude fluctuations allowed through the presence of an orbital degree of freedom on the ${\mathrm{Fe}}^{2+}$ site. We extend previous spin-orbit exciton models based on a collinear spin structure to understand the measured low-energy excitations and also to predict and discuss possible amplitude mode scattering in ${\mathrm{RbFe}}^{2+}{\mathrm{Fe}}^{3+}{\mathrm{F}}_6$.

We show that the Migdal-Eliashberg theory loses validity at a finite value ${\lambda }_c$ of the electron-phonon coupling $\lambda$ regardless of the underlying model Hamiltonian. The value of ${\lambda }_c$ is approximately between 3.0 and 3.7. The new phase that emerges at $\lambda >{\lambda }_c$ breaks the lattice translational symmetry. Depending on the filling fraction and crystal symmetry, it is an insulator or a Fermi liquid. Its characteristic feature is a gap or a pronounced depression of the fermionic density of states near the Fermi level. We establish the breakdown from within the Migdal-Eliashberg theory by demonstrating that the normal state specific heat is negative for $\lambda \ge 3.7$ and the quasiparticle lifetime vanishes in the strong coupling limit. At fixed $\lambda >{\lambda }_c$, the transition to the new phase occurs at a critical temperature higher than the superconducting transition temperature. In addition, there is a first-order phase transition between the new phase and the superconducting state as we vary $\lambda$ across ${\lambda }_c$ at fixed temperature. We put forward a new theory—lattice-fermionic theory of superfluidity—that bridges the gap between the Migdal-Eliashberg approach and the physics at stronger coupling. At small $\lambda$, our theory reduces to the Migdal-Eliashberg theory, and past ${\lambda }_c$, it describes the new phase and a range of other phenomena.

We derive a general low-energy theory for twisted moiré heterostructures comprised of Dirac materials. We apply our theory to heterostructures on the surface of a three-dimensional topological insulator (3D TI). First, we consider the interface between two 3D TIs arranged with a relative twist angle. We prove that if the two TIs are identical, then a necessary condition for a perturbative magic angle where the Dirac cone velocity vanishes is to have an interlayer spin-flipping hopping term. Without this term, the Dirac cone velocities can still be significantly renormalized, decreasing to less than half of their original values, but they will not vanish. Second, we consider graphene on the surface of a TI arranged with a small twist angle. Again, a magic angle is unachievable with only a spin-flipping hopping term; under such conditions, the Dirac cone is renormalized, but only moderately. In both cases, our perturbative results are verified by computing the band structure of the continuum model. The enhanced density of states that results from decreasing the surface Dirac cone velocity provides a tunable route to realizing interacting topological phases.

Polarization-dependent reflectivity measurements were carried out over a broad frequency range on single-crystalline ZrGeSe and ZrGeS compounds, which are closely related to the prototype nodal-line semimetal ZrSiS. These measurements revealed the strongly anisotropic character of both ZrGeSe and ZrGeS, with a reduced plasma frequency for the out-of-plane direction $\mathbf{E}\parallel c$ as compared with the in-plane direction $\mathbf{E}\parallel ab$. For $\mathbf{E}\parallel ab$, the optical conductivity spectrum consists of two Drude terms followed by a shoulder or plateaulike behavior and a distinct U shape at higher energies, while for $\mathbf{E}\parallel c$, one Drude term is followed by a peaklike behavior, and the U shape of the profile is less developed. Under external pressure, two prominent excitations appear in the out-of-plane optical conductivity spectrum of ZrGeSe, whose frequency position and oscillator strength show a weak anomaly at $\sim 3$ GPa. Overall, the pressure-induced changes in the profile of the $\mathbf{E}\parallel c$ conductivity spectrum are much enhanced $>\sim 3$ GPa. We compare our results to those recently reported for ZrSiS in a quantitative manner.

We studied the low-energy electronic response of the prototypical correlated metal ${\mathrm{SrVO}}_3$ in the ultraclean and disordered limit using infrared spectroscopy and density functional theory plus dynamical mean field theory calculations ($\mathrm{DFT}+\mathrm{DMFT}$). A strong optical excitation at 70 meV is observed in the optical response of the ultraclean samples but is hidden by the low-energy Drude-like response from intraband excitations in the more disordered samples. $\mathrm{DFT}+\mathrm{DMFT}$ calculations reveal that this optical excitation originates from interband transitions between the bands split by orbital off-diagonal hopping, which has often been ignored in cubic systems, such as ${\mathrm{SrVO}}_3$. A memory function analysis of the optical data shows that this interband transition can lead to deviations of optical self-energy from the expected Fermi-liquid behavior. Our findings demonstrate that analysis schemes employed to extract many-body effects from optical spectra may be oversimplified to study the true electronic ground state and that improvements in material quality can guide efforts to refine theoretical approaches.

Determining and explaining the presence of a gap at a magnon crossing point is a critical step to characterize the topological properties of a material. An inelastic neutron scattering study of a single crystal is a powerful experimental technique to probe the magnetic excitation spectra of topological materials. Here, we show that when the scattering intensity rapidly disperses in the vicinity of a crossing point, such as a Dirac point, the apparent topological gap size is extremely sensitive to experimental conditions including sample mosaic, resolution, and momentum integration range. We demonstrate these effects using comprehensive neutron scattering measurements of ${\mathrm{CrCl}}_3$. Our measurements confirm the gapless nature of the Dirac magnon in ${\mathrm{CrCl}}_3$, but also reveal an artificial, i.e., extrinsic, magnon gap unless the momentum integration range is carefully controlled. Our study provides an explanation of the discrepancies between spectroscopic and first-principles estimates of Dirac magnon gap sizes and provides guidelines for accurate measurement of topological magnon gaps.

Thin films of ${\mathrm{Mn}}_4\mathrm{N}$ and related ternary metallic perovskites with perpendicular anisotropy are interesting for spintronics, but their magnetic structures differ from the triangular ferrimagnetism of the bulk. A temperature-independent anomalous Hall conductivity of $-90{\mathrm{\Omega }}^{–1}\mathrm{c}{\mathrm{m}}^{–1}$ was found in ${\mathrm{Mn}}_4\mathrm{N}$ films, in addition to the normal temperature-dependent contribution. Based on known spin structures of bulk ${\mathrm{Mn}}_{3}Z\mathrm{N}$ compounds and the distance dependence of the Mn-Mn exchange for first- and second-neighbor Mn-Mn pairs, we propose a topological noncollinear spin structure for the ${\mathrm{Mn}}_4\mathrm{N}$ films with perpendicular anisotropy. The Letter shows how a small change in symmetry of the spin structure can influence the magnetotransport properties of frustrated ferrimagnetic films.

We study the temperature dependence of electrical resistivity for currents directed along all crystallographic axes of the spin-triplet superconductor ${\mathrm{UTe}}_2$. We focus particularly on an accurate determination of the resistivity along the $c$ axis (${\rho }_c$) by using a generalized Montgomery technique that allows extraction of crystallographic resistivity components from a single sample. In contrast to expectations from the observed highly anisotropic band structure, our measurement of the absolute values of resistivities in all current directions reveals a surprisingly nearly isotropic transport behavior at temperatures above Kondo coherence, with ${\rho }_c\sim {\rho }_b\sim 2{\rho }_a$, that evolves to reveal qualitatively distinct behaviors on cooling. The temperature dependence of ${\rho }_c$ exhibits a peak at a temperature much lower than the onset of Kondo coherence observed in ${\rho }_a$ and ${\rho }_b$, consistent with features in magnetotransport and magnetization that point to a magnetic origin. A comparison to the temperature-dependent evolution of the scattering rate observed in angle-resolved photoemission spectroscopy experiments provides important insights into the underlying electronic structure necessary for building a microscopic model of superconductivity in ${\mathrm{UTe}}_2$.

We analyze triply degenerate nodal points [or triple points (TPs) for short] in energy bands of crystalline solids. Specifically, we focus on spinless band structures, i.e., when spin-orbit coupling is negligible, and consider TPs formed along high-symmetry lines in the momentum space by a crossing of three bands transforming according to a one-dimensional (1D) and a two-dimensional (2D) irreducible corepresentation (ICR) of the little cogroup. The result is a complete classification of such TPs in all magnetic space groups, including the nonsymmorphic ones, according to several characteristics of the nodal-line structure at and near the TP. We show that the classification of the presently studied TPs is exhausted by 13 magnetic point groups (MPGs) that can arise as the little cogroup of a high-symmetry line and which support both 1D and 2D spinless ICRs. For 10 of the identified MPGs, the TP characteristics are uniquely determined without further information; in contrast, for the 3 MPGs containing sixfold rotational symmetry, two types of TPs are possible, depending on the choice of the crossing ICRs. The classification result for each of the 13 MPGs is illustrated with first-principles calculations of a concrete material candidate.

We present a thorough experimental study of the three-dimensional hyperhoneycomb Kitaev magnet $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$, using a combination of inelastic neutron scattering (INS), time-domain terahertz spectroscopy (TDTS), and heat capacity measurements. The main results include a massive low-temperature reorganization of the INS spectral weight that evolves into a broad peak centered around 12 meV, and a distinctive peak in the terahertz data at 2.8(1) meV. A detailed comparison to powder-averaged spin-wave theory calculations reveals that the positions of these two features are controlled by the anisotropic $\mathrm{\Gamma }$ coupling and the Heisenberg exchange $J$, respectively. The refined microscopic spin model places $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ in close proximity to the Kitaev spin liquid phase.

We consider dielectric cavities whose radiation space is restricted by two parallel metallic planes. The TM solutions of the Maxwell equations of the system are equivalent to the solutions of periodical arrays of dielectric cavities. The system readily allows to achieve bound states in the continuum (BICs) of any type including topological BICs as dependent on position and orientation of the cavities relative to the planes and that extremely facilitates experimental studies in comparison to infinite arrays of the cavities. We show the effect of merging of topologically protected BICs that pushes the square asymptotic of the $Q$ factor into the power degree 4 or even 6.

We have studied the structural and magnetic properties of $\mathrm{Tb}\left({\mathrm{Fe}}_{0.2}{\mathrm{Mn}}_{0.2}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_{0.2}{\mathrm{Ni}}_{0.2}\right){\mathrm{O}}_3$ (T5BO) high-entropy oxide perovskite (HEOP) thin films. Using synchrotron-based x-ray absorption spectroscopy, employing x-ray magnetic circular dichroism, we performed an element-sensitive study of epitaxial T5BO thin films. The measurements reveal a magnetic multiphase with variable ferromagnetic ordering of all transition metal elements, providing a promising route towards designer ferroic properties in Tb-based HEOP thin films.

Interfaces between specific complex oxides host two-dimensional electron systems (2DESs) with strong electron-electron interactions. This combination yields a rich phenomenology, including an apparently intrinsic electronic phase separation (EPS). We designed an experiment to study the origins and magnitude of EPS in oxide 2DESs in more detail. We measure the capacitance between the 2DES at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface and an electrode on top of the ${\mathrm{LaAlO}}_3$ as a function of applied gate voltage. Our measurements reveal a significant reduction of this capacitance in the region of the phase diagram where the charge-carrier density is low. The tunnel conductance is reduced as well, which implies that part of the interface becomes insulating. These measurements allow us to directly estimate the magnitude of the EPS at a carrier density of several ${10}^{13}{\text{cm}}^{-2}$, higher than the nominal carrier density in most experiments. The pattern in the capacitance-voltage measurements reflecting the local metal-insulator transitions suggests that the main driver for EPS is a strong variation of the electrostatic potential with a non-normal probability distribution. We study the effect of this in-plane potential variation on the electronic properties of the 2DES by mapping the full superconducting dome as a function of both backgate and topgate voltage. This map shows that, once insulating patches emerge, the global critical temperature $T_{\mathrm{c}}$ falls, while the onset temperature—i.e., highest local $T_{\mathrm{c}}$—remains fairly constant.

Using Monte Carlo simulations and finite-size scaling analysis, we show that the $q$-state clock model with $q=6$ on a simple cubic lattice with open surfaces has a rich phase diagram; in particular, it has an extraordinary-log phase, in addition to the ordinary and extraordinary transitions at the bulk critical point. We prove numerically that the presence of the intermediate extraordinary-log phase is due to the emergence of an O(2) symmetry in the surface state before the surface enters the $Z_q$ symmetry-breaking region as the surface coupling is increased at the bulk critical point, while O(2) symmetry emerges for the bulk. The critical behaviors of the extraordinary-log transition, as well as the ordinary transition and the special transition separating the ordinary and extraordinary-log transitions, are obtained.

The recent “honeycomb code” is a fault-tolerant quantum memory defined by a sequence of checks, which implements a nontrivial automorphism of the toric code. We argue that a general framework to understand this code is to consider continuous adiabatic paths of gapped Hamiltonians and we give a conjectured description of the fundamental group and second and third homotopy groups of this space in two spatial dimensions. A single cycle of such a path can implement some automorphism of the topological order of that Hamiltonian. We construct such paths for arbitrary automorphisms of two-dimensional doubled topological order. Then, realizing this in the case of the toric code, we turn this path back into a sequence of checks, constructing an automorphism code closely related to the honeycomb code.

The surface of a Weyl semimetal famously hosts an exotic topological metal that contains open Fermi arcs rather than closed Fermi surfaces. In this work, we show that the surface is also endowed with a feature normally associated with strongly interacting systems, namely, Luttinger arcs, defined as zeros of the electron Green's function. The Luttinger arcs connect surface projections of Weyl nodes of opposite chirality and form closed loops with the Fermi arcs when the Weyl nodes are undoped. Upon doping, the ends of the Fermi and Luttinger arcs separate and the intervening regions get filled by surface projections of bulk Fermi surfaces. Remarkably, unlike Luttinger contours in strongly interacting systems, the precise shape of the Luttinger arcs can be determined experimentally by removing a surface layer. We use this principle to sketch the Luttinger arcs for Co and Sn terminations in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. The area enclosed by the Fermi and Luttinger arcs approximately equals the surface particle density in weakly coupled systems while the correction is governed by the interlayer couplings and the perimeter of the Fermi-Luttinger loop.