Spin-nematic and spin-smectic phases have been reported in magnetic materials, which break rotational symmetry while preserving translational symmetry along certain directions. However, until now the analogy to liquid crystals remained incomplete because no magnetic analog of cholesteric order was known. Here we show that the bilayer perovskite Sr$_3$Fe$_2$O$_7$, previously believed to adopt a simple single-$\mathbf{q}$ spin-helical order, hosts two distinct types of multi-$\mathbf{q}$ spin textures and the first "spin-cholesteric". Its ground state represents a novel multi-$\mathbf{q}$ spin texture with unequally intense spin modulations at the two ordering vectors. This is followed in temperature by the new "spin-cholesteric" phase with spontaneously broken chiral symmetry, in which the translational symmetry is broken only along one of the crystal directions while the weaker orthogonal modulation melts, giving rise to intense short-range dynamical fluctuations. Shortly before the transition to the paramagnetic state, vortex-crystal order spanned by two equivalent $\mathbf{q}$ vectors emerges. The "spin-cholesteric" phase completes the spin analogy with liquid crystals and renders Sr$_3$Fe$_2$O$_7$ a touchstone for studying transitions among multiple-$\mathbf{q}$ spin textures in a centrosymmetric host.

The superconducting order parameter is directly related to the pairing interaction, with the amplitude determined by the interaction strength, while the phase reflects the spatial structure of the interaction. However, given the large variety of materials and their rich physical properties within the iron-based high-Tc superconductors, the structure of the order parameter remains controversial in many cases. Here, we introduce Defect Bound State Quasi Particle Interference (DBS-QPI) as a new method to determine the superconducting order parameter. Using a low-temperature scanning tunneling microscope, we image in-gap bound states in the stoichiometric iron-based superconductor LiFeAs and show that the bound states induced by defect scattering are formed from Bogoliubov quasiparticles that have significant spatial extent. Quasiparticle interference from these bound states has unique signatures from which one can determine the phase of the order parameter as well as the nature of the defect, i.e. whether it is better described as a magnetic vs a nonmagnetic scatterer. DBS-QPI provides an easy but general method to characterize the pairing symmetry of superconducting condensates.

From first-principles calculations, we investigate the structural and electronic properties of the kagome metals AV3Sb5 (A = Cs, K, Rb) under isotropic and anisotropic pressure. Charge ordering patterns are found to be unanimously suppressed, while there is a significant rearrangement of p-type and m-type van Hove point energies with respect to the Fermi level. Already for moderate tensile strain along the V plane and compressive strain normal to the V layer, we find that a van Hove point can be shifted to the Fermi energy. Such a mechanism provides an invaluable tuning knob to alter the correlation profile in the kagome metal, and suggests itself for further experimental investigation. It might allow to reconcile possible multi-dome superconductivity in kagome metals not only from phonons, but also from the viewpoint of unconventional pairing.

Einstein is usually revered as the father of special and general relativity. In this article I demonstrate that he is also the father of Solid State Physics, or even his broader version known as Condensed Matter Physics (including liquids). His 1907 article on the specific heat of solids introduces, for the first time, the effect of lattice vibrations on the thermodynamic properties of crystals, in particular the specific heat. His 1905 article on the photoelectric effect and photoluminescence opened the fields of photoelectron spectroscopy and photoluminescence spectroscopy. Other important achievements include Bose-Einstein condensation and the Einstein relation between the difussion coefficient an mobility. In this article I discuss Einstein's papers relevant to these topics and their relevance to modern day condensed matter physics.

Recently resonant inelastic x-ray scattering experiments reported fine details of the charge excitations around the in-plane momentum ${\bf q}_{\parallel}=(0,0)$for various doping rates in electron-doped cuprates${\rm La_{2-x}Ce_xCuO_4}$. We find that those new experimental data are well captured by acoustic-like plasmon excitations in a microscopic study of the layered $t$-$J$ model with the long-range Coulomb interaction. The acoustic-like plasmon is not a usual plasmon typical to the two-dimensional system, but has a small gap proportional to the interlayer hopping $t_z$.

We analyze the electronic structure of different surface terminations for infinite-layer nickelates. Surface NiO$_2$ layers are found to be buckled, in contrast to planar bulk layers. While the rare-earth terminated surface fermiology is similar to the bulk limit of the nickelates, the NiO$_2$ terminated surface band structure is significantly altered, originating from the effect of absence of rare-earth atoms on the crystal field splitting. Contrary to the bulk Fermi surfaces, there are two Ni-$3d$ Fermi pockets, giving rise to enhanced spectral weight around the $\bar{\text{M}}$ point in the surface Brillouin zone. From a strong-coupling analysis, we obtain dominant extended $s$-wave superconductivity for the surface layer, as opposed to $d$-wave for the bulk. This finding distinguishes the nickelates from isostructural cuprates, where the analogous surface pairing mechanism is less pronounced. Our results are consistent with region-dependent gap structures revealed in recent STM measurements and provide an ansatz to interpret experimental data of surface-sensitive measurements on the infinite-layer nickelates.

Intercalation is a robust approach for modulating the properties of epitaxial graphene on SiC and stabilizing two-dimensional (2D) intercalant layers at the graphene/SiC interface. In this work, we present synchrotron-based angle resolved photoelectron spectroscopy (ARPES) measurements focussing on the band structure of intercalated Pb under a single layer of epitaxial graphene. The interlayer Pb exhibits a metallic character, a $(1 \times 1)$ registry with respect to SiC, and free electron-like bands to a first order. Divergences from the free electron approximation include various band splittings and gaps throughout the Pb Brillouin zone. Light polarization dependent ARPES measurements indicate a predominant out-of-plane orbital character for the Pb bands, suggesting potential interactions between the interlayer Pb and graphene's $\pi$ orbitals that may induce proximity effects in graphene. Density functional theory (DFT) calculations for a $(1 \times 1)$ Pb monolayer on SiC show a reasonable qualitative agreement with the experimentally observed interlayer bands as well as the polarization dependent measurements. Finally, temperature dependent ARPES measurements reveal that the nearly charge-neutral graphene layer involves charge transfer from both the interlayer Pb and the substrate SiC.

We explore the propagation of a single hole in the generalized quantum compass model which interpolates between fully isotropic antiferromagnetic (AF) phase in the Ising model and nematic order of decoupled AF chains for frustrated compass interactions. We observe coherent hole motion due to either interorbital hopping or due to the three-site effective hopping, while quantum spin fluctuations in the ordered background do not play any role.

At very high doping levels the van Hove singularity in the $\pi^*$ band of graphene becomes occupied and exotic ground states possibly emerge, driven by many-body interactions. Employing a combination of ytterbium intercalation and potassium adsorption, we $n$ dope epitaxial graphene on silicon carbide past the $\pi^*$ van Hove singularity, up to a charge carrier density of 5.5$\times$10$^{14}$ cm$^{-2}$. This regime marks the unambiguous completion of a Lifshitz transition in which the Fermi surface topology has evolved from two electron pockets into a giant hole pocket. Angle-resolved photoelectron spectroscopy confirms these changes to be driven by electronic structure renormalizations rather than a rigid band shift. Our results open up the previously unreachable beyond-van-Hove regime in the phase diagram of epitaxial graphene, thereby accessing an unexplored landscape of potential exotic phases in this prototype two-dimensional material.

A major obstacle to understanding high-Tc cuprates is that superconductivity precludes observing normal-state properties at low temperatures. One prime example is the normal-state spin susceptibility \c{hi}spin: although its decrease upon cooling far above Tc typifies pseudogap behavior, its behavior at low temperatures is generally unknown. Here, our measurements in high magnetic fields expose \c{hi}spin of YBa2Cu3Oy down to low temperatures. Even though superconductivity is suppressed by the field, we uncover two thermally-activated contributions alongside a residual \c{hi}spin(T=0) due to gapless excitations. We relate these two distinct gaps to short-range charge-density waves and to the formation of singlets as in certain quantum spin systems. Both phenomena thus contribute to the pseudogap at low temperature, supplementing short-lived antiferromagnetism that initiates pseudogap behavior at high temperatures. We therefore propose that the pseudogap ought to be regarded as a composite property and that, when not undergoing spin-stripe ordering, underdoped cuprates tend to form short-ranged spin singlets.

We classify interacting topological insulators and superconductors with order-two crystal symmetries (reflection and twofold rotation), focusing on the case where interactions reduce the noninteracting classification. We find that the free-fermion $\mathbb{Z}_2$ classifications are stable against quartic contact interactions, whereas the $\mathbb{Z}$ classifications reduce to $\mathbb{Z}_N$, where $N$ depends on the symmetry class and the dimension $d$. These results are derived using a quantum nonlinear $\sigma$ model (QNLSM) that describes the effects of the quartic interactions on the boundary modes of the crystalline topological phases. We use Clifford algebra extensions to derive the target spaces of these QNLSMs in a unified way. The reduction pattern of the free-fermion classification then follows from the presence or absence of topological terms in the QNLSMs, which is determined by the homotopy group of the target spaces. We show that this derivation can be performed using either a complex fermion or a real Majorana representation of the crystalline topological phases and demonstrate that these two representations give consistent results. To illustrate the breakdown of the noninteracting classification we present examples of crystalline topological insulators and superconductors in dimensions one, two, and three, whose surfaces modes are unstable against interactions. For the three-dimensional example, we show that the reduction pattern obtained by the QNLSM method agrees with the one inferred from the stability analysis of the boundary modes using bosonization.

Many natural and artificial reactions including photosynthesis or photopolymerization are initiated by stimulating organic molecules into an excited state, which enables new reaction paths. Controlling light-matter interaction can influence this key concept of photochemistry, however, it remained a challenge to apply this strategy to control photochemical reactions at the atomic scale. Here, we profit from the extreme confinement of the electromagnetic field at the apex of a scanning tunneling microscope (STM) tip to drive and control the rate of a free-base phthalocyanine phototautomerization with submolecular precision. By tuning the laser excitation wavelength and choosing the STM tip position, we control the phototautomerization rate and the relative tautomer population. This sub-molecular optical control can be used to study any other photochemical processes.

Using a generalized response theory we derive the electronic Raman response function for metals with anisotropic relaxation rates. The calculations account for the long--range Coulomb interaction and treat the collision operator within a charge conserving relaxation time approximation. We extend earlier treatments to finite wavenumbers ($|{\bf q}|\ll k_{\rm F}$) and incorporate inelastic electron--electron scattering besides elastic impurity scattering. Moreover we generalize the Lindhard density response function to the Raman case. Numerical results for the quasiparticle scattering rate and the Raman response function for cuprate superconductors are presented.

The identity of the fundamental broken symmetry (if any) in the underdoped cuprates is unresolved. However, evidence has been accumulating that this state may be an unconventional density wave. Here we carry out site-specific measurements within each CuO$_2$ unit-cell, segregating the results into three separate electronic structure images containing only the Cu sites (Cu(r)) and only the x/y-axis O sites (O$_x$(r) and O$_y$(r)). Phase resolved Fourier analysis reveals directly that the modulations in the O$_x$(r) and O$_y$(r) sublattice images consistently exhibit a relative phase of ${\pi}$. We confirm this discovery on two highly distinct cuprate compounds, ruling out tunnel matrix-element and materials specific systematics. These observations demonstrate by direct sublattice phase-resolved visualization that the density wave found in underdoped cuprates consists of modulations of the intra-unit-cell states that exhibit a predominantly d-symmetry form factor.

The coherence of an electronic spin in a semiconductor quantum dot decays due to its interaction with the bath of nuclear spins in the surrounding isotopes. This effect can be reduced by subjecting the system to an external magnetic field and by applying optical pulses. By repeated pulses in long trains the spin precession can be synchronized to the pulse period $T_\text{R}$. This drives the nuclear spin bath into states far from equilibrium leading to nuclear frequency focusing. In this paper, we use an efficient classical approach introduced in Phys. Rev. B $\textbf{96}$, 054415 (2017) to describe and to analyze this nuclear focusing. Its dependence on the effective bath size and on the external magnetic field is elucidated in a comprehensive study. We find that the characteristics of the pulse as well as the nuclear Zeeman effect influence the behavior decisively.

Heavy-fermion metals exhibit a plethora of low-temperature ordering phenomena, among them the so-called hidden-order phases that in contrast to conventional magnetic order are invisible to standard neutron diffraction. One of the oldest and structurally simplest hidden-order compounds, CeB6, became famous for an elusive phase that was attributed to the antiferroquadrupolar ordering of cerium-4f moments. In its ground state, CeB6 also develops a more usual antiferromagnetic (AFM) order. Hence, its essential low-temperature physics was always considered to be solely governed by AFM interactions between the dipolar and multipolar Ce moments. Here we overturn this established perspective by uncovering an intense ferromagnetic (FM) low-energy collective mode that dominates the magnetic excitation spectrum of CeB6. Our inelastic neutron-scattering data reveal that the intensity of this FM excitation by far exceeds that of conventional spin-wave magnons emanating from the AFM wave vectors, thus placing CeB6 much closer to a FM instability than could be anticipated. This propensity of CeB6 to ferromagnetism may account for much of its unexplained behavior, such as the existence of a pronounced electron spin resonance, and should lead to a substantial revision of existing theories that have so far largely neglected the role of FM interactions.

Here we present a combined study of the slightly underdoped novel pnictide superconductor Ba(1-x)K(x)Fe(2)As(2) by means of X-ray powder diffraction, neutron scattering, muon spin rotation (muSR), and magnetic force microscopy (MFM). Commensurate static magnetic order sets in below Tm ~ 70 K as inferred from the emergence of the magnetic (1 0 -3) reflection in the neutron scattering data and from the observation of damped oscillations in the zero-field-muSR asymmetry. Transverse-field muSR below Tc shows a coexistence of magnetically ordered and non-magnetic states, which is also confirmed by MFM imaging. We explain such coexistence by electronic phase separation into antiferromagnetic and superconducting/normal state regions on a lateral scale of several tens of nanometers. Our findings indicate that such mesoscopic phase separation can be considered an intrinsic property of some iron pnictide superconductors.

We study the magnetic interactions in Mott-Hubbard systems with partially filled $t_{2g}$-levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain "weak" ferromagnetism, with an anomalously large ferromagnetic moment, in Sr$_2$IrO$_4$.

The optimally doped and underdoped region of the $t-J$ model at large N (N is the number of spin components) is governed by the competition of d-wave superconductivity (SC) and a d Charge-Density Wave (d-CDW).The partial destruction of the Fermi surface by the d-CDW and the resulting density of states are discussed. Furthermore, c-axis conductances for incoherent and coherent tunneling are calculated, considering both an isotropic and an anisotropic in-plane momentum dependence of the hopping matrix element between the planes. The influence of self-energy effects on the conductances is also considered using a model where the electrons interact with a dispersionless, low-lying branch of bosons. We show that available tunneling spectra from break-junctions are best explained by assuming that they result from incoherent tunneling with a strongly anisotropic hopping matrix element of the form suggested by band structure calculations. The conductance spectra are then characterized by one single peak which evolves continuously from the superconducting to the d-CDW state with decreasing doping. The intrinsic c-axis tunneling spectra are, on the other hand, best explained by coherent tunneling. Calculated spectra show at low temperatures two peaks due to SC and d-CDW. With increasing temperature the BCS-like peak moves to zero voltage and vanishes at T$_c$,exactly as in experiment.Our results thus can explain why break junction and intrinsic tunneling spectra are different from each other. Moreover, they support a scenario of two competing order parameters in the underdoped region of high-T$_c$ superconductors.

In this paper the correlation between education, research and macroeconomic strength of countries at a global scale is analyzed on the basis of statistical data published by the UNIDO and OECD. It uses sets of composite indicators describing the economical performance and competitiveness as well as those relevant for human development, education, knowledge and technology achievement and correlates them. It turns out that for countries with a human development index (HDI) below 0.7 the basic education and technology achievement indices are the driving force for further development, whereas for the industrialized countries the knowledge index as a composite education and communication index has the strongest effect on the economic strength of a country as measured by the gross domestic product.