Recent experiments with strong THz fields in both conventional and unconventional superconductors have clearly evidenced a marked third-harmonic generation below the superconducting temperature $T_c$. Its interpretation challenged substantial theoretical work aimed at establishing the relative efficiency of quasiparticle excitations and collective modes in triggering such a resonant response. Here we compute the nonlinear current by implementing a time-dependent Bogoljubov–de Gennes approach, with the twofold aim to account nonperturbatively for the effect of local disorder, and to include the contribution of all collective modes, i.e., superconducting amplitude (Higgs) and phase fluctuations, and charge fluctuations. We show that, in agreement with previous work, already at small disorder the quasiparticle response is dominated by paramagnetic effects. We further demonstrate that paramagnetic processes mediate also the response of all collective modes, with a substantial contribution of charge/phase fluctuations. These processes, which have been overlooked so far, turn out to dominate the third-order current at strong disorder. In addition, we show that disorder strongly influences the polarization dependence of the nonlinear response, with a marked difference between the clean and the disordered case. Our results are particularly relevant for recent experiments in cuprates, whose band structure is in a first approximation reproduced by our lattice model.

The relaxation of a classical spin, exchange coupled to the local magnetic moment at an edge site of the one-dimensional spinful Su-Schrieffer-Heeger model, is studied numerically by solving the full set of equations of motion. A Lindblad coupling of a few sites at the opposite edge to an absorbing bath ensures that convergence with respect to the system size is achieved with only a moderate number of core sites. This allows us to numerically exactly study the long-time limit and to determine the parameter regimes where spin relaxation takes place. Corresponding dynamical phase diagrams for the topologically trivial and the nontrivial cases are constructed. The dynamical phase boundaries, the role of the topological edge state, and its internal Zeeman splitting for the spin-relaxation process, as well as incomplete spin relaxation on long time scales can be explained within the framework of a renormalized linear-response approach when explicitly taking retardation effects and nonequilibrium spin-exchange processes into account.

Quantum well states formed by $d$ electrons in metallic thin films are responsible for many fundamental phenomena that oscillate with layer thickness, such as magnetic anisotropy or magnetoresistance. Using momentum microscopy and angle-resolved photoemission, we mapped in unprecedented detail the quantized electronic states of Fe(001) in a broad photon energy range starting from soft x-ray (160 eV) down to vacuum ultraviolet (8.4 eV). We show that it is possible to simulate the experimentally observed photoemission spectra with high accuracy by using the ab initio electronic bulk band structure as the initial state, taking into account that free electron final electronic states are intrinsically broadened along the wave vector direction perpendicular to the sample surface. To simulate the thin-film case, we take into account a subset of the initial electronic states, which results in the reproduction of the quantized electronic structure observed in the experiment. In addition, we present results of the spin-sensitive measurements, which are confronted with the photoemission simulation that takes into account the spin degree of freedom. We demonstrate electronic states that can be responsible for the oscillations of the magnetic anisotropy in Fe(001) thin films with periods of about 5 and 9 monolayers. We show that these quantum well states change position in reciprocal space depending on the magnetization direction. Our photoemission simulation reproduces this effect, which highlights its origin in the relativistic bulk electronic band structure of bcc Fe. We also observed magnetization-dependent spin-orbit gaps with the symmetry lower than the bulk symmetry. We believe that the same method of simulating photoemission spectra might facilitate interpretation of the photoemission intensities measured for other three-dimensional materials, especially when the spin-polarized quantized electronic states are considered.

We explore attractive dipolar interaction in indirect excitons (IXs). For one layer of IXs in a single pair of coupled quantum wells (CQWs), the out-of-plane IX electric dipoles lead to repulsive dipolar interaction between IXs. The attractive dipolar interaction between IXs is realized in a two-CQW heterostructure with two IX layers in two separated CQW pairs. We found both in experimental measurements and theoretical simulations that increasing density of IXs in one layer causes a monotonic energy reduction for IXs in the other layer. We also found an in-plane shift of a cloud of IXs in one layer towards a cloud of IXs in the other layer. This behavior is qualitatively consistent with attractive dipolar interaction. The measured IX energy reduction and IX cloud shift are higher than the values given by the correlated liquid theory.

Understanding the spreading of quantum correlations in out-of-equilibrium many-body systems is one of the major challenges in physics. For isolated systems, a hydrodynamic theory explains the origin and spreading of entanglement via the propagation of quasiparticle pairs. However, when systems interact with their surrounding much less has been established. Here we show that the quasiparticle picture remains valid for open quantum systems: While information is still spread by quasiparticles, the environment modifies their correlation and introduces incoherent and mixing effects. For free fermions with gain/loss dissipation we provide formulas fully describing incoherent and quasiparticle contributions in the spreading of entropy and mutual information. Importantly, the latter is not affected by entanglement of the system with the external environment. The mutual information is exponentially damped at short times and eventually vanishes signaling the onset of a classical limit. The behavior of the logarithmic negativity is similar and this scenario is common to other dissipations. For weak dissipation, the presence of quasiparticles underlies remarkable scaling behaviors.

Polar materials can host a variety of topologically significant magnetic phases, which often emerge from a modulated magnetic ground state. Relatively few noncentrosymmetric tetragonal materials have been shown to host topological spin textures and new candidate materials are necessary to expand the current theoretical models. This manuscript reports on the anisotropic magnetism in the polar, tetragonal material ${\mathrm{NdCoGe}}_3$ via thermodynamic and neutron diffraction measurements. The previously reported $H-T$ phase diagram is updated to include several additional phases, which exist for both $H$ = 0 and with an applied field $H\perp c$. Neutron diffraction data reveal that the magnetic structures below $T_{N1}$ = 3.70 K and $T_{N2}$ = 3.50 K are incommensurate, with a ground-state magnetic order that is incommensurate in all directions with the propagation vector $\vec{k}$ = (0.494, 0.0044, 0.385) at 1.8 K. A unique magnetic structure solution is not achievable, but the possible single-$\vec{k}$ and multi-$\vec{k}$ spin models are discussed. These results demonstrate that ${\mathrm{NdCoGe}}_3$ hosts complicated magnetic order derived from modulated magnetic moments.

We present and implement a self-consistent $\mathrm{D}\mathrm{\Gamma }\mathrm{A}$ approach for multiorbital models and ab initio materials calculations. It is applied to the one-band Hubbard model at various interaction strengths with and without doping, to the two-band Hubbard model with two largely different bandwidths, and to ${\mathrm{SrVO}}_3$. The self-energy feedback reduces critical temperatures compared to dynamical mean-field theory, even to zero temperature in two dimensions. Compared to a one-shot, non-self-consistent calculation the nonlocal correlations are significantly reduced when they are strong. In case nonlocal correlations are weak to moderate as for ${\mathrm{SrVO}}_3$, one-shot calculations are sufficient.

It is well known that the ambient environment can dramatically renormalize the quasiparticle gap and exciton binding energies in low-dimensional materials, but the effect of the environment on the energy splitting of the spin-singlet and spin-triplet exciton states is less understood. A prominent effect is the renormalization of the exciton binding energy and optical strength (and hence the optical spectrum) through additional screening of the direct Coulomb term describing the attractive electron-hole interaction in the kernel of the Bethe-Salpeter equation. The repulsive exchange interaction responsible for the singlet-triplet splitting, on the other hand, is unscreened within formal many-body perturbation theory. However, Benedict argued that in practical calculations restricted to a subspace of the full Hilbert space, the exchange interaction should be appropriately screened by states outside of the subspace, the so-called $S$ approximation [L. X. Benedict, Phys. Rev. B 66, 193105 (2002)]. Here, we systematically explore the accuracy of the $S$ approximation for different confined systems, including a molecule and heterostructures of semiconducting and metallic layered materials. We show that the $S$ approximation is actually exact in the limit of small exciton binding energies (i.e., small direct term) and can be used to significantly accelerate convergence of the exciton energies with respect to the number of empty states, provided that a particular effective screening consistent with the conventional Tamm-Dancoff approximation is employed. We further find that the singlet-triplet splitting in the energy of the excitons is largely unaffected by the external dielectric environment for most quasi-two-dimensional materials.

We investigate the magnetic properties of $\mathrm{Li}\mathrm{Yb}{\mathrm{O}}_2$, containing a three-dimensionally frustrated, diamondlike lattice via neutron scattering, magnetization, and heat capacity measurements. The stretched diamond network of ${\mathrm{Yb}}^{3+}$ ions in $\mathrm{Li}\mathrm{Yb}{\mathrm{O}}_2$ enters a long-range incommensurate, helical state with an ordering wave vector $\mathbf{k}=(0.384,\pm 0.384,0)$ that “locks-in” to a commensurate $\mathbf{k}=(1/3,\pm 1/3,0)$ phase under the application of a magnetic field. The spiral magnetic ground state of $\mathrm{Li}\mathrm{Yb}{\mathrm{O}}_2$ can be understood in the framework of a Heisenberg $J_1-J_2$ Hamiltonian on a stretched diamond lattice, where the propagation vector of the spiral is uniquely determined by the ratio of $J_2/\left|J_1\right|$. The pure Heisenberg model, however, fails to account for the relative phasing between the Yb moments on the two sites of the bipartite lattice, and this detail as well as the presence of an intermediate, partially disordered, magnetic state below 1 K suggests interactions beyond the classical Heisenberg description of this material.

We propose a four-state quantum system, or quantum unit, that can be realized in superconducting heterostructures. The unit combines the states of a spin and an Andreev qubit providing the opportunity of quantum superpositions of their states. This functionality is achieved by tunnel coupling between a four-terminal superconducting heterostructure housing a Weyl point and a quantum dot. The quantum states in the vicinity of the Weyl point are extremely sensitive to small changes of superconducting phase; this gives rich opportunities for quantum manipulation. We establish an effective Hamiltonian for the setup and describe the peculiarities of the resulting spectrum. We concentrate on the four-state subspace and explain how to make a double qubit in this setup. We review various ways to achieve quantum manipulation in the unit: this includes resonant, adiabatic, diabatic manipulation and combinations of those. We provide detailed illustrations of designing arbitrary quantum gates in the unit.

We study the electronic structure of quasicrystals composed of incommensurate stacks of atomic layers. We consider two systems: A pair of square lattices with a relative twist angle of $\theta ={45}^{\circ }$ and a pair of hexagonal lattices with a relative twist angle of $\theta ={30}^{\circ }$, with various interlayer interaction strengths. This constitutes every two-dimensional bilayer quasicrystal system. We investigate the resonant coupling governing the quasicrystalline order in each quasicrystal symmetry, and we calculate the quasiband dispersion. The resonant interaction emerges in bilayer quasicrystals if all the dominant interlayer interactions occur between the atomic orbitals that have the same magnetic quantum number. Thus, not only the quasicrystal composed of the widely studied graphene but also those composed of transition metal dichalcogenides will exhibit the quasicrystalline states. We find that some quasicrystalline states, which are usually obscured by decoupled monolayer states, are more prominent, i.e., “exposed,” in the systems with strong interlayer interaction. We also show that we can switch the states between quasicrystalline configuration and its layer components by turning on and off the interlayer symmetry.

Chiral spin textures, such as skyrmions, merons, and vortices in ferromagnetic (FM)/antiferromagnetic (AFM) heterostructures are actively explored for utilization in future data storage and signal processing devices. Here, we present a systematic study of the magnetic vortex structures in soft-magnetic NiFe and exchange coupled NiFe/IrMn and IrMn/NiFe/IrMn disk structures. The annihilation of the magnetic vortex state is mediated by the creation and subsequent annihilation of the intermediate vortex-antivortex (V-AV) pairs. Using the combination of high-resolution in-field magnetic force microscopy (MFM) and magneto-optic Kerr effect magnetometry, we show a considerable enhancement in the stability of the intermediate V-AV state in exchange coupled NiFe/IrMn and IrMn/NiFe/IrMn disk structures. Analysis of the remanent high-resolution MFM images shows a significant increase in the effective vortex core radius and an additional distortion of the FM vortex structure in exchange coupled disks, most likely caused by the randomly distributed uncompensated spins at the surface of the AFM layer. We further suggest that the displacement of the vortex core from the center of the exchange coupled disks depend on the magnitude of the exchange bias field and AFM grain characteristics. Additionally, we present a summary of crucial magnetic vortex parameters and properties, such as effective core radius, core displacement, handedness, nucleation field, V-AV annihilation field, and interfacial exchange energy in exchange coupled disk structures.

The hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, is known to be realized in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Here, we demonstrate by means of Monte Carlo simulations that the hedgehog lattice is induced by not the DM interaction but by frustration in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, the breathing bond alternation is characterized by the ratio of the nearest-neighbor (NN) antiferromagnetic exchange interaction for large tetrahedra to that for small ones, $J_1^{\prime }/J_1$. A quadruple-$\mathbf{q}$ state with the ordering vector of $\mathbf{q}=(\pm \frac{1}{2},\pm \frac{1}{2},\pm \frac{1}{2})$, which is realized for a large third-NN antiferromagnetic interaction along the bond direction $J_3$, turns out to become the hedgehog-lattice state in the breathing case of $J_1^{\prime }/J_1<1$, while in the uniform case of $J_1^{\prime }/J_1=1$, it is a collinear state favored by thermal fluctuations. It is also found that in a magnetic field, the structure of the $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ hedgehog lattice is changed from cubic to tetragonal, resulting in a nonzero net spin chirality, which in a metallic system should yield a characteristic topological Hall effect.

${\mathrm{Fe}}_{1+x}\mathrm{Te}$ is a two-dimensional van der Waals antiferromagnet that becomes superconducting on anion substitution on the Te site. The properties of the parent phase of ${\mathrm{Fe}}_{1+x}\mathrm{Te}$ are sensitive to the amount of interstitial iron situated between the iron-tellurium layers. ${\mathrm{Fe}}_{1+x}\mathrm{Te}$ displays collinear magnetic order coexisting with low-temperature metallic resistivity for small concentrations of interstitial iron $x$ and helical magnetic order for large values of $x$. While this phase diagram has been established through scattering [see, for example, E. E. Rodriguez et al., Phys. Rev. B 84, 064403 (2011); S. Rößler et al., Phys. Rev. B 84, 174506 (2011)], recent scanning tunneling microscopy measurements [C. Trainer et al., Sci. Adv. 5, eaav3478 (2019)] have observed a different magnetic structure for small interstitial iron concentrations $x$ with a significant canting of the magnetic moments along the crystallographic $c$ axis of $\theta ={28}^{\circ }\pm 3^{\circ }$. In this paper, we revisit the magnetic structure of ${\mathrm{Fe}}_{1.09}\mathrm{Te}$ using spherical neutron polarimetry and scanning tunneling microscopy to search for this canting in the bulk phase, and we compare surface and bulk magnetism. The results show that the bulk magnetic structure of ${\mathrm{Fe}}_{1.09}\mathrm{Te}$ is consistent with collinear in-plane order ($\theta =0$ with an error of $\sim 5^{\circ }$). Comparison with scanning tunneling microscopy on a series of ${\mathrm{Fe}}_{1+x}\mathrm{Te}$ samples reveals that the surface exhibits a magnetic surface reconstruction with a canting angle of the spins of $\theta =29.8^{\circ }$. We suggest that this is a consequence of structural relaxation of the surface layer resulting in an out-of-plane magnetocrystalline anisotropy. The magnetism in ${\mathrm{Fe}}_{1+x}\mathrm{Te}$ displays different properties at the surface when the symmetry constraints of the bulk are removed.

As a consequence of the approximate spin-valley symmetry in graphene, the ground state of electrons in graphene at charge neutrality is a particular SU(4) quantum Hall ferromagnet to minimize their exchange energy. If only the Coulomb interaction is taken into account, this ferromagnet can appeal either to the spin degree of freedom or equivalently to the valley pseudo-spin degree of freedom. This freedom in choice is then limited by subleading energy scales that explicitly break the SU(4) symmetry, the simplest of which is given by the Zeeman effect that orients the spin in the direction of the magnetic field. In addition, there are also valley symmetry-breaking terms that can arise from short-range interactions or electron-phonon couplings. Here, we build upon the phase diagram, which has been obtained by Kharitonov [M. Kharitonov, Phys. Rev. B 85, 155439 (2012)], in order to identify the different skyrmions that are compatible with these types of quantum Hall ferromagnets. Similarly to the ferromagnets, the skyrmions at charge neutrality are described by the $\text{Gr}(2,4)$ Grassmannian at the center, which allows us to construct the skyrmion spinors. The different skyrmion types are then obtained by minimizing their energy within a variational approach, with respect to the remaining free parameters that are not fixed by the requirement that the skyrmion at large distances from their center must be compatible with the ferromagnetic background. We show that the different skyrmion types have a clear signature in the local, sublattice-resolved, spin magnetization, which is in principle accessible in scanning-tunneling microscopy and spectroscopy.

We measured spin Seebeck signals at the top and bottom surfaces of an antiferromagnetic ${\mathrm{Cr}}_2{\mathrm{O}}_3$ film, using a $\mathrm{Pt}/{\mathrm{Cr}}_2{\mathrm{O}}_3/\mathrm{Pt}$ trilayer. Our experimental data, combined with micromagnetic simulations, clearly demonstrate that the uncompensated sublattice at the top and bottom surfaces plays a decisive role in determining the symmetry of the spin Seebeck signals, providing fundamental insight for understanding the generation of spin Seebeck signal in antiferromagnetic materials.

Hamiltonian models based on a localized basis set are widely used in condensed matter physics, as, for example, for the calculation of electronic structures or transport properties. The presence of a weak and homogeneous magnetic field can be taken into account through Peierls phase factors on the hopping Hamiltonian elements. Here, we propose simple and convenient recipes to properly determine such Peierls phase factors for quasi-one-dimensional systems that are periodic or with periodic subcomponents (as in Hall bars, for example), and periodic two-dimensional systems. We also show some examples of applications of the formulas, and more specifically concerning the electronic structure of carbon nanotubes in magnetic fields, the integer quantum Hall effect in six-terminal bars obtained in two-dimensional electron gases, and the electronic structure of bumped graphene superlattices in the presence of a magnetic field.

Fractons are a type of emergent quasiparticle that cannot move freely in isolation, but can easily move in bound pairs. Similar phenomenology is found in boson-affected hopping models, encountered in the study of polaron systems and hole-doped Ising antiferromagnets, in which motion of a particle requires the creation or absorption of background bosonic excitations. In such models, individual low-energy quasiparticles cannot move freely, while bound pairs have drastically increased mobility. We show that boson-affected hopping models can provide a natural realization of fractons, either approximately or exactly, depending on the details of the system. We first consider a generic one-dimensional boson-affected hopping model, in which we show that single particles move only at sixth order in perturbation theory, while motion of bound states occurs at second order, allowing for a broad parameter regime exhibiting approximate fracton phenomenology. We explicitly map the model onto a fracton Hamiltonian featuring conservation of dipole moment via integrating out the mediating bosons. We then consider a special type of boson-affected hopping models with mutual hard-core repulsion between particles and bosons, experimentally accessible in hole-doped mixed-dimensional Ising antiferromagnets, in which the hole motion is one dimensional in an otherwise two-dimensional antiferromagnetic background. We show that this system exhibits perfect fracton behavior to all orders in perturbation theory. We suggest diagnostic signatures of fractonic behavior, opening a door to use already existing experimental tools to study their unusual physics, such as universal gravitation and restricted thermalization. As an example, gravitational attraction manifests as phase separation of holes in doped antiferromagnets. In studying these models, we identify simple effective one-dimensional microscopic Hamiltonians featuring perfect fractonic behavior, paving the way to future studies on fracton physics in lower dimensions, where a wealth of numerical and analytical tools already exist. In these Hamiltonians we identify pair-hopping interactions as the mechanism of dipole motion, and argue that this may provide a connection to topological edge states in boundary fractonic systems.

The magnetic state of heavy metal Pt thin films in proximity to the ferrimagnetic insulator ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ has been investigated systematically by means of x-ray magnetic circular dichroism and x-ray resonant magnetic reflectivity measurements combined with angle-dependent magnetotransport studies. To reveal intermixing effects as the possible cause for induced magnetic moments in Pt, we compare thin film heterostructures with different orders of the layer stacking and different interface properties. For standard Pt layers on ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ thin films, we do not detect any static magnetic polarization in Pt. These samples show an angle-dependent magnetoresistance behavior, which is consistent with the established spin Hall magnetoresistance. In contrast, for the inverted layer sequence, ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ thin films grown on Pt layers, Pt displays a finite induced magnetic moment comparable to that of all-metallic Pt/Fe bilayers. This magnetic moment is found to originate from finite intermixing at the ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}/\mathrm{Pt}$ interface. As a consequence, we found a complex angle-dependent magnetoresistance indicating a superposition of the spin Hall and the anisotropic magnetoresistance in these types of samples. Both effects can be disentangled from each other due to their different angle dependence and their characteristic temperature evolution.

The crystal-field ground-state wave function of ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ has been investigated with linearly polarized $M$-edge x-ray absorption spectroscopy from 250 mK to 250 K, thus covering the superconducting $(T_{\text{c}}=0.6 \mathrm{K})$, Kondo $(T_{\text{K}}\approx 20 \mathrm{K})$, and Curie-Weiss regimes. The comparison with full multiplet calculations shows that the temperature dependence of the experimental linear dichroism is well explained with a ${\mathrm{\Gamma }}_7^{\left(1\right)}$ crystal-field ground state and the thermal population of excited states at around 30 meV. The crystal-field scheme does not change throughout the entire temperature range thus making the scenario of orbital switching unlikely. Spectroscopic evidence for the presence of the Ce $4f^0$ configuration in the ground state is consistent with the possibility for a multiorbital character of the ground state. We estimate from the Kondo temperature and crystal-field splitting energies that several percents of the higher lying ${\mathrm{\Gamma }}_6$ state and ${\mathrm{\Gamma }}_7^{\left(2\right)}$ crystal-field states are mixed into the primarily ${\mathrm{\Gamma }}_7^{\left(1\right)}$ ground state. This estimate is also supported by renormalized band-structure calculations that uses the experimentally determined crystal-field scheme.