We present the phonon dispersion of bulk ${\mathrm{MoS}}_2$ in the high-symmetry directions of the Brillouin zone, determined by inelastic x-ray scattering. Our results underline the two-dimensional nature of ${\mathrm{MoS}}_2$. In combination with state-of-the-art first-principles calculations, we determine the phonon displacement patterns, symmetry properties, and scattering intensities. The results will be the basis for future experimental and theoretical work regarding electron-phonon interactions, intervalley scattering, as well as phonons in related 2D materials.

$\pi /8$ phase gates (magic gates or T gates) are crucial to augment topological systems based on Majorana zero modes to full quantum universality. We present a scheme based on a combination of projective measurements and nonadiabatic evolution that effectively cancels smooth control errors when implementing phase gates in Majorana-based systems. Previous schemes based on adiabatic evolution are susceptible to problems arising from small but finite dynamical phases that are generically present in topologically unprotected gates. A measurement-only approach eliminates dynamical phases. For nonprotected gates, however, forced-measurement schemes are no longer effective, which leads to low success probabilities of obtaining the right succession of measurement outcomes in a measurement-only implementation. We show how to obtain a viable measurement-based scheme which dramatically increases the success probabilities by evolving the system nonadiabatically with respect to the degenerate subspace in between measurements. We outline practical applications of our scheme in recently proposed quantum computing designs based on Majorana tetrons and hexons.

We report on the occurrence of knotted metallic band structures as stable topological phases in non-Hermitian (NH) systems. These knotted NH metals are characterized by open Fermi surfaces, known in mathematics as Seifert surfaces, that are bounded by knotted lines of exceptional points. Quite remarkably, and in contrast to the situation in Hermitian systems, no fine tuning or symmetries are required in order to stabilize these exotic phases of matter. By explicit construction, we derive microscopic tight-binding models hosting knotted NH metals with strictly short-ranged hopping, and investigate the stability of their topological properties against perturbations. Building up on recently developed experimental techniques for the realization of NH band structures, we discuss how the proposed models may be experimentally implemented in photonic systems.

We suggest a pump-probe method for studying semiconductor spin dynamics based on pumping of carrier spins by a pulse of oscillating radiofrequency (rf) magnetic field and probing by measuring the Faraday rotation of a short laser pulse. We demonstrate this technique on $n$-GaAs and observe the onset and decay of coherent spin precession during and after the course of rf pulse excitation. We show that the rf field resonantly addresses the electron spins with Larmor frequencies close to that of the rf field. This opens the opportunity to determine the homogeneous spin coherence time $T_2$, that is inaccessible directly in standard all-optical pump-probe experiments.

High-resolution resonant inelastic x-ray scattering (RIXS) has proven particularly effective in the determination of crystal field and spin excitations in cuprates. Its strength lies in the large Cu $L_3$ resonance and in the fact that the scattering cross section follows quite closely the single-ion model predictions, both in the insulating parent compounds and in the superconducting doped materials. However, the spectra become increasingly broader with (hole) doping, hence resolving and assigning spectral features has proven challenging even with the highest energy resolution experimentally achievable. Here we have overcome this limitation by measuring the polarization dependence of the RIXS spectra as a function of momentum transfer and doping in thin films of ${\mathrm{NdBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$. Besides confirming the previous assignment of $dd$ and spin excitations (magnon, bimagnon) in the antiferromagnetic insulating parent compound, we unequivocally single out the actual spin-flip contribution at all dopings. We also demonstrate that the softening of $dd$ excitations is mainly attributed to the shift of the $xy$ peak to lower energy loss. These results provide a definitive assessment of the RIXS spectra of cuprates and demonstrate that RIXS measurements with polarization control are practically feasible and highly informative.

We study the dynamics and readout of topological qubits encoded by zero-energy Majorana bound states in a topological superconductor. We take into account bosonic modes due to the electromagnetic environment which couple the Majorana manifold to above-gap continuum quasiparticles. This coupling causes the degenerate ground state of the topological superconductor to be dressed in a polaronlike manner by quasiparticle states and bosons, and the system to become gapless. Topological protection and hence full coherence is only maintained if the qubit is operated and read out within the low-energy spectrum of the dressed states. We discuss reduction of fidelity and/or visibility if this condition is violated by a quantum-dot readout that couples to the bare (undressed) Majorana modes. For a projective measurement of the bare Majorana basis, we formulate a Bloch-Redfield approach that is valid for weak Majorana-environment coupling and takes into account constraints imposed by fermion-number-parity conservation. Within the Markovian approximation, our results essentially confirm earlier theories of finite-temperature decoherence based on Fermi's golden rule. However, the full non-Markovian dynamics reveals, in addition, the fidelity reduction by a projective measurement. Using a spinless nanowire model with $p$-wave pairing, we provide quantitative results characterizing these effects.

Hexagonal boron nitride ($h\mathrm{BN}$) is the supporting substrate of choice for two-dimensional material devices because it is atomically flat and chemically inert. However, due to the small size of mechanically exfoliated $h\mathrm{BN}$ flakes, electronic structure studies of two-dimensional materials supported by $h\mathrm{BN}$ using angle-resolved photoemission spectroscopy (ARPES) are challenging. Here we investigate the electronic band structure of a Bernal-stacked bilayer graphene sheet on a hexagonal boron nitride (BLG/$h\mathrm{BN}$) flake using nanospot ARPES (nanoARPES). By fitting high-resolution energy vs momentum electronic band spectra, we extract the tight-binding parameters for BLG on $h\mathrm{BN}$. In addition, we reveal spatial variations of the alignment angle between BLG and $h\mathrm{BN}$ lattices via inhomogeneity of the electronic bands near the Fermi level. We confirmed these findings by scanning tunneling microscopy measurements obtained on the same device. Our results from spatially resolved nanoARPES measurements of BLG/$h\mathrm{BN}$ heterostructures are instrumental for understanding experiments that utilize spatial averaging techniques such as electronic transport and optical spectroscopy.

We report the infrared dielectric properties of $\alpha$-quartz in the temperature range from $1.5\mathrm{K}$ to $200\mathrm{K}$. Using an infrared free-electron laser, far-infrared reflectivity spectra of a single crystal $y$ cut were acquired along both principal axes, under two different incidence angles, in $S$ and $P$ polarization. These experimental data have been fitted globally for each temperature with a multioscillator model, allowing one to extract frequencies and damping rates of the ordinary and extraordinary, transverse and longitudinal optic phonon modes, and hence the temperature-dependent dispersion of the infrared dielectric function. The results are in line with previous high-temperature studies, allowing for a parametrized description of all temperature-dependent phonon parameters and the resulting dielectric function from $1.5\mathrm{K}$ up to the $\alpha \text{−}\beta$-phase transition temperature, $T_C=846\mathrm{K}$. Using these data, we predict remarkably high quality factors for polaritons in $\alpha$-quartz's hyperbolic spectral region at low temperatures.

The advancement of quantum optical science and technology with solid-state emitters such as nitrogen-vacancy (NV) centers in diamond critically relies on the coherence of the emitters' optical transitions. A widely employed strategy to create NV centers at precisely controlled locations is nitrogen ion implantation followed by a high-temperature annealing process. We report on experimental data directly correlating the NV center optical coherence to the origin of the nitrogen atom. These studies reveal low-strain, narrow-optical-linewidth $(<500$ MHz) NV centers formed from naturally occurring ${}^{14}\mathrm{N}$ atoms. In contrast, NV centers formed from implanted ${}^{15}\mathrm{N}$ atoms exhibit significantly broadened optical transitions $(>1$ GHz) and higher strain. The data show that the poor optical coherence of the NV centers formed from implanted nitrogen is not due to an intrinsic effect related to the diamond or isotope. These results have immediate implications for the positioning accuracy of current NV center creation protocols and point to the need to further investigate the influence of lattice damage on the coherence of NV centers from implanted ions.

We numerically study the formation of entanglement clusters across the many-body localization transition. We observe a crossover from strong many-body entanglement in the ergodic phase to weak local correlations in the localized phase, with continuous clusters throughout the phase diagram. Critical states close to the transition have a structure compatible with fractal or multiscale-entangled states, characterized by entanglement at multiple levels: small strongly entangled clusters are weakly entangled together to form larger clusters. The critical point therefore features subthermal entanglement and a power-law distributed cluster size. Upon entering the localized phase, the power-law distribution seems to persist with a varying power that crosses over into a stretched exponent before eventually becoming exponential deep in the localized phase. These results are in agreement with some of the recently proposed phenomenological renormalization-group schemes characterizing the many-body localized critical point, and serve to constrain other such schemes.

Macroscopic superconductivity in various ultrathin films at the ultimate two-dimensional limit, i.e., films with thickness of only one- or two-atomic layers supported by single-crystal surfaces, has manifested itself in experiments with only zero resistance but not yet with the Meissner effect due to the lack of a proper in situ technique, although both phenomena are the defining characteristics of a superconductor. Using a self-developed multifunctional scanning tunneling microscope, we succeeded in detecting not only the macroscopic supercurrent but also diamagnetic response of a two-atomic-layer indium film on a Si(111) surface. The diamagnetic measurements reveal that the low-temperature variation of penetration depth follows the Bardeen-Cooper-Schrieffer theory in the dirty limit. The magnitude of the pair-breaking interaction is determined to be 0.80 from the magnetic field dependence of the zero-temperature penetration depth, which implies that the pairing symmetry deviates slightly from an isotropic $s$ wave. The present work demonstrates that it is possible to observe the Meissner effect in ultrathin superconducting films that are vulnerable to air, which is very helpful for a detailed understanding of the microscopic pairing mechanism.

We report a detailed study of the microscopic effects of Cu intercalation on the charge density wave (CDW) in $1T-{\mathrm{Cu}}_x{\mathrm{TiSe}}_2$. Scanning tunneling microscopy and spectroscopy reveal a unique, Cu-driven spatial texturing of the charge-ordered phase, with the appearance of energy-dependent CDW patches and sharp $\pi$-phase shift domain walls ($\pi \mathrm{DWs}$). The energy and doping dependencies of the patchwork are directly linked to the inhomogeneous potential landscape due to the Cu intercalants. They imply a CDW gap with unusual features, including a large amplitude, the opening below the Fermi level, and a shift to higher binding energy with electron doping. Unlike the patchwork, the $\pi \mathrm{DWs}$ occur independently of the intercalated Cu distribution. They remain atomically sharp throughout the investigated phase diagram and occur in both superconducting and nonsuperconducting specimens. These results provide unique atomic-scale insight into the CDW ground state, questioning the existence of incommensurate CDW domain walls and contributing to understanding its formation mechanism and interplay with superconductivity.

A local model of the dielectric response of a metal predicts that singular surfaces, such as sharp-edged structures, have a continuous absorption spectrum and extreme concentration of energy at the singularity. Here, we show that nonlocality drastically alters this picture: The spectrum is now discrete and the energy concentration, though still substantial, is greatly reduced.

We report the experimental demonstration of an abnormal, opposite anticrossing effect in a photon-magnon-coupled system that consists of an yttrium iron garnet film and an inverted pattern of split-ring resonator structure (denoted as ISRR) in a planar geometry. It is found that the normal shape of anticrossing dispersion typically observed in photon-magnon coupling is changed to its opposite anticrossing shape just by changing the position/orientation of the ISRR's split gap with respect to the microstrip line axis along which ac microwave currents are applied. Characteristic features of the opposite anticrossing dispersion and its linewidth evolution are analyzed with the help of analytical derivations based on electromagnetic interactions. The observed opposite anticrossing dispersion is ascribed to the compensation of both intrinsic damping and coupling-induced damping in the magnon modes. This compensation is achievable by controlling the relative strength and phase of oscillating magnetic fields generated from the ISRR's split gap and the microstrip feeding line. The position/orientation of an ISRR's split gap provides a robust means of controlling the dispersion shape of anticrossing and its damping in a photon-magnon coupling, thereby offering more opportunity for advanced designs of microwave devices.

The many-body localization (MBL) phase transition is not a conventional thermodynamic phase transition. Thus, to define the phase transition, one should allow the possibility of taking the limit of an infinite system in a way that is not the conventional thermodynamic limit. We explore this for the so-called avalanche instability due to rare thermalizing regions in the MBL phase for systems with quenched randomness in two cases: for short-range interacting systems in more than one spatial dimension and for systems in which the interactions fall off with distance as a power law. We find an unconventional way of scaling these systems so that they do have a type of phase transition. Our arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension (or with sufficiently rapidly decaying power laws) is a transition where entanglement in the eigenstates begins to spread into some typical regions: The transition is set by when the avalanches start. Once this entanglement gets started, the system does thermalize. From this point of view, the much-studied case of one-dimensional MBL with short-range interactions is a special case with a different, and in some ways more conventional, type of phase transition.

We used high-resolution resonant inelastic x-ray scattering (RIXS) at the Ni $L_3$ edge to simultaneously investigate high-energy interband transitions characteristic of Ni-O bond ordering and low-energy collective excitations of the Ni spins in the rare-earth nickelates $R{\mathrm{NiO}}_3$ ($R=\mathrm{Nd}$, Pr, La) with pseudocubic perovskite structure. With the support of calculations based on a double-cluster model we quantify bond order (BO) amplitudes for different thin films and heterostructures and discriminate short-range BO fluctuations from long-range static order. Moreover we investigate magnetic order and exchange interactions in spatially confined $R{\mathrm{NiO}}_3$ slabs by probing dispersive magnon excitations. While our study of superlattices (SLs) grown in the (001) direction of the perovskite structure reveals a robust noncollinear spin spiral magnetic order with dispersive magnon excitations that are essentially unperturbed by BO modulations and spatial confinement, we find magnons with flat dispersions and strongly reduced energies in SLs grown in the ${\left(111\right)}_{\text{pc}}$ direction that exhibit collinear magnetic order. These results give insight into the interplay of different collective ordering phenomena in a prototypical $3d$ transition metal oxide and establish RIXS as a powerful tool to quantitatively study several order parameters and the corresponding collective excitations within one experiment.

We propose that the fracton models with subsystem symmetry can be a class of toy models for the holographic principle. The discovery of the anti–de Sitter/conformal field theory correspondence as a concrete construction of holography and the subsequent developments including the subregion duality and Ryu-Takayanagi formula of entanglement entropy have revolutionized our understanding of quantum gravity and provided powerful tool sets for solving various strongly coupled quantum field theory problems. To resolve many mysteries of holography, toy models can be very helpful. One example is the holographic tensor networks, which illuminate the quantum-error-correcting properties of gravity in the anti–de Sitter space. In this work we discuss a classical toy model featuring subsystem symmetries and immobile fracton excitations. We show that such a model defined on the hyperbolic lattice satisfies some key properties of the holographic correspondence. The correct subregion duality and Ryu-Takayanagi formula for mutual information are established for a connected boundary region. A naively defined black hole's entropy scales as its horizon area. We also present discussions on corrections for more complicated boundary subregions, the possible generalizations of the model, and a comparison with the holographic tensor networks.

Quantum dot molecules (QDMs) have widely tunable exciton transition energies and transition strengths that can be controlled with an applied electric field. We use these properties to demonstrate in situ tuning of the vacuum Rabi splitting for a quantum dot molecule embedded in a photonic crystal cavity. Both components of the anisotropic exchange doublet have a component parallel to the cavity and are strongly coupled. This produces two QDM-cavity polaritons with properties dominated by the cavity and a third mixed-spin hybrid state with little cavity component and unusual polarization.

While chiral magnetic skyrmions have been attracting significant attention in the past years, recently, a new type of chiral particle emerging in thin films—a chiral bobber—has been theoretically predicted and experimentally observed. Here, based on theoretical arguments, we uncover that these novel chiral states possess inherent transport fingerprints that allow for their unambiguous electrical detection in systems comprising several types of chiral states. We reveal that unique transport and orbital characteristics of bobbers root in the nontrivial magnetization distribution in the vicinity of the Bloch points, and demonstrate that tuning the details of the Bloch point topology can be used to drastically alter the emergent response properties of chiral bobbers to external fields, which bears great potential for spintronics applications and cognitive computing.

Quantum magnets with significant bond-directional Ising interactions, so-called Kitaev materials, have attracted tremendous attention recently in the search for exotic spin liquid states. Here we present a comprehensive set of measurements that enables us to investigate the crystal structures, ${\mathrm{Ir}}^{4+}$ single-ion properties, and magnetic ground states of the double perovskite iridates ${\mathrm{La}}_{2}B{\mathrm{IrO}}_6$ ($B=\text{Mg,}\text{Zn}$) and $A_2{\mathrm{CeIrO}}_6$ ($A=\text{Ba,}\text{Sr}$) with a large nearest-neighbor distance $>5$ Å between ${\mathrm{Ir}}^{4+}$ ions. Our neutron powder diffraction data on ${\mathrm{Ba}}_2{\mathrm{CeIrO}}_6$ can be refined in the cubic space group $Fm\overline{3}m$, while the other three systems are characterized by weak monoclinic structural distortions. Despite the variance in the noncubic crystal field experienced by the ${\mathrm{Ir}}^{4+}$ ions in these materials, x-ray absorption spectroscopy and resonant inelastic x-ray scattering are consistent with $J_{\mathrm{eff}}=1/2$ moments in all cases. Furthermore, neutron scattering and resonant magnetic x-ray scattering show that these systems host $A$-type antiferromagnetic order. These electronic and magnetic ground states are consistent with expectations for face-centered-cubic magnets with significant antiferromagnetic Kitaev exchange, which indicates that spacing magnetic ions far apart may be a promising design principle for uncovering additional Kitaev materials.