The Rosenzweig-Porter (RP) model has garnered much attention in the last decade, as it is a simple analytically tractable model showing both ergodic-nonergodic extended and Anderson localization transitions. Thus, it is a good toy model to understand the Hilbert-space structure of many-body localization phenomenon. In our Letter, we present analytical evidence, supported by exact numerics, that demonstrates the controllable tuning of the phase diagram in the RP model by employing on-site potentials with a nontrivial fractal dimension instead of the conventional random disorder. We demonstrate that such disorder extends the fractal phase and creates an unusual dependence of fractal dimensions of the eigenfunctions. Furthermore, we study the fate of level statistics in such a system to understand how these changes are reflected in the eigenvalue statistics.

The non-Hermitian skin effect (NHSE) refers to the extensive number of eigenstates of a non-Hermitian system that are localized in open boundaries. Here, we predict a universal phenomenon that the local particle-hole(-like) symmetry (PHS) leads to nonlocal pairs of skin modes distributed on different boundaries, manifesting a nonlocalization of the local PHS, which is unique to non-Hermitian systems. We develop a generic theory for the emergent nonlocal symmetry-protected NHSE by connecting the non-Hermitian system to an extended Hermitian Hamiltonian in a quadruplicate Hilbert space, which maps the skin modes to the topological zero modes, and the PHS to an emergent nonlocal symmetry in the perspective of many body physics. The predicted nonlocal NHSE is robust against perturbations. We propose optical Raman lattice models to observe the predicted phenomena in all physical dimensions, which are accessible with cold-atom experiments.

We analyze the quantum antiferromagnet on the maple leaf lattice in the presence of a magnetic field. Starting from its exact dimer ground state and for a magnetic field strength of the order of the local dimer spin-exchange coupling, we perform a strong-coupling expansion and extract an effective hard-core boson model. The interplay of effective many-body interactions, suppressed single-particle dynamics, and correlated hopping gives way to an intriguing series of superfluid to insulator transitions which correspond to magnetization plateaus in terms of the maple leaf spin degrees of freedom. While we find plateaus at intermediate magnetization to be dominated by bosonic density wave order, we conjecture plateau formation from multiboson bound states due to correlated hopping for lower magnetization.

We demonstrate that checkerboard magnet-superconductor hybrid (MSH) systems possess a rich phase diagram exhibiting both strong topological superconducting (STSC) and topological nodal point superconducting (TNPSC) phases. We show that TNPSC phases exist both for ferromagnetic and antiferromagnetic systems, yielding a plethora of qualitatively different edge mode structures. Checkerboard MSH systems also facilitate the emergence of STSC phases, which can be induced even in the limit of vanishing magnetization. Our results provide a new path for the quantum engineering of topological superconducting phases using atomic manipulation techniques.

The pyrochlore magnet ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ has attracted much attention as a quantum spin ice candidate whose novelty derives in part from the dipolar-octupolar nature of the ${\mathrm{Ce}}^{3+}$ pseudospin-1/2 degrees of freedom it possesses. We report heat capacity measurements on single crystal samples of ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ down to $T\sim 0.1\mathrm{K}$ in a magnetic field along the $[1,\overline{1},0]$ direction. These measurements show that the broad hump in the zero-field heat capacity moves higher in temperature with increasing field strength and is split into two separate humps by the $[1,\overline{1},0]$ magnetic field at $\sim 2\mathrm{T}$. These separate features are due to the decomposition of the pyrochlore lattice into effectively decoupled chains for fields in this direction: One set of chains ($\alpha$ chains) is polarized by the field while the other ($\beta$ chains) remains free. This situation is similar to that observed in the classical spin ices ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, but with the twist that here the strong transverse exchange interactions produce substantial quantum effects. Our theoretical modeling suggests that the $\beta$ chains are close to a critical state, with nearly-gapless excitations. We also report elastic and inelastic neutron scattering measurements on single crystal ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ in $[1,\overline{1},0]$ and $[0,0,1]$ magnetic fields at temperatures down to $T=0.03\mathrm{K}$. The elastic scattering behaves consistently with the formation of independent chains for a $[1,\overline{1},0]$ field, while the $[0,0,1]$ field produces a single field-induced elastic magnetic Bragg peak at $(0,2,0)$ and equivalent wavevectors, indicating a polarized spin ice state for fields above $\sim 3\mathrm{T}$. For both $[1,\overline{1},0]$ and $[0,0,1]$ magnetic fields, our inelastic neutron scattering results show an approximately-dispersionless continuum of scattering that increases in both energy and intensity with increasing field strength. By modeling the complete set of experimental data using numerical linked cluster and semiclassical molecular dynamics calculations, we demonstrate the dominantly multipolar nature of the exchange interactions in ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ and the smallness of the parameter $\theta$, which controls the mixing between dipolar and octupolar degrees of freedom. These results support previous estimates of the microscopic exchange parameters and place strong constraints on the theoretical description of this prominent spin ice candidate.

We investigate the magneto-optical response of Co to an ultrashort laser excitation by x-ray resonant magnetic reflectivity (XRMR) employing circular polarization. The time-resolved reflectivities detected for opposite sample magnetization are separated into magnetic and nonmagnetic contributions, which contain information about the structural, electronic, and magnetic properties of the sample. Different response times of the different contributions are observed. The experimental results are reproduced numerically by two different simulation approaches. On the one hand, we use a purely thermal model, a time-dependent heat-induced loss of macroscopic magnetization, and an inhomogeneous laser-induced strain profile. On the other hand, we employ time-dependent density-functional theory to calculate the transient optical response to the laser-induced excitation and from that the reflected intensities. While both methods are able to reproduce the time dependence of the magnetic signal, the ultrafast nonmagnetic change in reflectivity is captured satisfactorily only in simulations of the transient optical response function and has thus to be assigned to electronic effects. The energy dependence of the magnetic circular dichroism is investigated in the simulations, highlighting a dependence of the observable on the probing energy. Finally, a phenomenological explanation of the dynamics measured in dichroic x-ray reflectivity in the different channels is offered.

A microscopic elastic model allowing a symmetry breaking upon a spin transition is developed based on competing interactions between the nearest and next-nearest neighbors. The model yields a structurally degenerated high-spin state with a diamond-shaped cell and a nondegenerated low-spin state with a square-shaped cell. We investigated the effect of the symmetry change of the unit cell on the thermoinduced spin transition by monitoring the ratio of the elastic energies involved in the nearest and next-nearest neighbors. The simulations are performed on a deformable two-dimensional lattice made of spins $S=\pm 1$ (representing the high-spin and low-spin molecules) coupled with springs. The numerical resolution of the model is based on the Monte Carlo metropolis approach, running on spins and positions variables. The simulations of the thermoinduced spin transition disclose asymmetric thermal hysteresis loops with quite different domain distributions on the heating and cooling branches. The analysis of the magnetic and structural properties pointed out that the spin transition with symmetry breaking is dependent on the sign of the thermal gradient. We demonstrated that the nucleation and growth process of spin domains might contrast with the structural self-organization of the lattice according to the energetic contribution of the symmetry breaking. Indeed, the examination of the spatial organization aspects revealed that the structural and elastic anisotropy in the lattice hinders the long-range character of the intermolecular interactions. The lattice configurations show a labyrinthlike structure during a transition from high-symmetry to low-symmetry phases and a multidomain structure upon a transition in the other way around regardless of the spin state in both phases. Furthermore, we found that thermal fluctuations have a crucial role depending on the thermal gradient and on the direction of evolution of the symmetry (reducing or increasing). We demonstrated that stepped and even incomplete spin transitions could be obtained by adjusting the elastic contribution responsible for the symmetry breaking.

Actinide-bearing intermetallics display unusual electronic, magnetic, and physical properties that arise from the complex behavior of their $5f$ electron orbitals. Temperature ($T$) effects on actinide intermetallics are well studied, but high-pressure ($P$) properties and phase stabilities are known for only a handful of compositions. Furthermore, almost no data exist for simultaneous high $P$ and high $T$. We performed ambient-$T$ diamond-anvil cell x-ray diffraction experiments to study the behavior of the intermetallic ${\mathrm{U}}_6\mathrm{Fe}$ upon compression up to 82 GPa. ${\mathrm{U}}_6\mathrm{Fe}$ remains stable in the tetragonal $I4/mcm$ structure over this pressure range. We also performed ambient-$P$, low-$T$ diffraction and heat capacity measurements to constrain ${\mathrm{U}}_6\mathrm{Fe}$'s thermal behavior. These data were combined with calculations and fitted to a Mie-Grüneisen/Birch-Murnaghan thermal equation of state with the following parameter values at ambient $P$: bulk modulus $B_0=124.0$ GPa, pressure derivative $B_0^{\prime }=5.6$, Grüneisen parameter ${\mathrm{\Gamma }}_0=2.028$, volume exponent $q=0.934$, Debye temperature ${\theta }_0=175\mathrm{K}$, and unit-cell volume $V_0=554.4{\mathrm{\AA }}^3$. We report $T$-dependent thermal expansion coefficients and bond lengths of ${\mathrm{U}}_6\mathrm{Fe}$, which demonstrate the anisotropic compressibility and negative thermal expansion of the crystallographic $c$ axis. Additionally, density-functional theory calculations indicate increased delocalization of ${\mathrm{U}}_6\mathrm{Fe}$ bonds at high $P$.

We discuss spin-wave transport in anisotropic ferromagnets with an emphasis on the zeros of the band edges as a function of a magnetic field. An associated divergence of the magnon spin should be observable by enhanced magnon conductivities in nonlocal configurations, especially in two-dimensional ferromagnets.

The recent report of near-ambient conditions superconductivity in a nitrogen-doped lutetium hydride has inspired a large number of experimental studies with contradictory results. We model from first principles the physical properties of the possible parent structures of the reported superconductors, ${\mathrm{LuH}}_2$ and ${\mathrm{LuH}}_3$. We show that only the phonon band structure of ${\mathrm{LuH}}_3$ can explain the reported Raman spectra due to the presence of hydrogens at the interstitial octahedral sites. However, this structure is stabilized by anharmonicity only above 6 GPa. We find that the intriguing color change with pressure in the reported superconductor is consistent with the optical properties of ${\mathrm{LuH}}_2$, which are determined by the presence of an undamped interband plasmon. The plasmon blueshifts with pressure and modifies the color of the sample without requiring any structural phase transition. Our findings suggest that the main component in the experiments is ${\mathrm{LuH}}_2$ with some extra hydrogen atoms at octahedral sites. Neither ${\mathrm{LuH}}_2$ nor ${\mathrm{LuH}}_3$ superconducts at high temperatures.

Doping a Mott insulator gives rise to unconventional superconducting correlations. Here we address the interplay between $d$-wave superconductivity and Mott physics using the two-dimensional Hubbard model with cellular dynamical mean-field theory on a $2\times 2$ plaquette. Our approach is to study superconducting correlations from the perspective of a cluster quantum impurity model embedded in a self-consistent bath. At the level of the cluster, we calculate the probabilities of the possible cluster electrons configurations. Upon condensation, we find an increased probability that cluster electrons occupy a four-electron singlet configuration, enabling us to identify this type of short-range spin correlation as key to superconducting pairing. The increased probability of this four-electron singlet comes at the expense of a reduced probability of a four-electron triplet with no significant probability redistribution of fluctuations of charges. This allows us to establish that superconductivity at the level of the cluster primarily involves a reorganization of short-range spin correlations rather than charge correlations. We gain information about the bath by studying the spectral weight of the hybridization function. Upon condensation, we find a transfer of spectral weight leading to the opening of a superconducting gap. We use these insights to interpret the signatures of superconducting correlations in the density of states of the system and in the zero-frequency spin susceptibility.

The material class of kagome metals has rapidly grown and has been established as a field to explore the interplay between electronic topology and magnetism. In this work, we report a combined theoretical and experimental study of the anomalous Hall effect of the ferromagnetic kagome metal ${\mathrm{Fe}}_3\mathrm{Sn}$. The compound orders magnetically at 725 K and presents an easy-plane anisotropy. Hall measurements in single crystals below room temperature yield an anomalous Hall conductivity ${\sigma }_{xy}\sim 500{\left(\mathrm{\Omega }\text{cm}\right)}^{-1}$, which is found to depend weakly on temperature. This value is in good agreement with the band-intrinsic contribution obtained by density-functional calculations. Our calculations also yield the correct magnetic anisotropy energy and predict the existence of Weyl nodes near the Fermi energy.

We study the electronic spectral function of a metal in the vicinity of an antiferromagnetic (AFM) quantum critical point, focusing on a situation where the bare bandwidth of the spin fluctuations is significantly smaller than the Fermi energy. In this limit, we identify a range of energies where the fermionic quasiparticles near the “hot spots” on the Fermi surface are strongly scattered by the quantum critical fluctuations, whereas the damping of the AFM fluctuations by the electrons is negligible. Within a one-loop approximation, there is a parameter range where the $T=0$ spectral function at the hot spots has a “precursor gap” feature, with a local maximum at a finite frequency. However, we find that the ratio of the bare spin-wave velocity to the Fermi velocity required to obtain a precursor gap is smaller by about an order of magnitude than the value in the electron-doped cuprate superconductors. Hence, our results cannot easily account for the recent angle-resolved photoemission experiments in this system [He et al., Proc. Natl. Acad. Sci. USA 116, 3449 (2019)]. At lower frequencies, the Landau damping of the AFM fluctuations becomes important, and the electronic spectral function has the familiar ${\omega }^{-1/2}$ singularity. Our one-loop perturbative results are supported by a numerical Monte Carlo simulation of electrons coupled to an undamped, nearly critical AFM mode.

We introduce and classify nonequivalent commensurate stackings for bilayer dice or ${\mathcal{T}}_3$ lattices. For each of the four stackings with vertical alignment of sites in two layers, a tight-binding model and an effective model describing the properties in the vicinity of the threefold band-crossing points are derived. Focusing on these band-crossing points, we found that although the energy spectrum remains always gapless, depending on the stacking, different types of quasiparticle spectra arise. They include those with flat, tilted, anisotropic semi-Dirac, and $C_3$-corrugated energy bands. We use the derived tight-binding models to calculate the density of states and the spectral function. The corresponding results reveal drastic redistribution of the spectral weight due to the interlayer coupling that is unique for each of the stackings.

We calculate optical conductivity for bilayer dice lattices in commensurate vertically aligned stackings. The interband optical conductivity reveals a rich activation behavior unique for each of the four stackings. We found that the intermediate energy band, which corresponds to the flat band of a single-layer dice lattice, plays a different role for different stackings. The interband selection rules, which are crucial for the single-layer lattice, may become lifted in bilayer lattices. The results for effective and tight-binding models are found to be in qualitative agreement for some of the stackings and the reasons for the discrepancies for others are identified. Our findings propose optical conductivity as an effective tool to distinguish between different stackings in bilayer dice lattices.

Controlling tunnel coupling between quantum antidots (QADs) in the quantum Hall (QH) regime is problematic. We propose and demonstrate a scheme for tunable tunnel coupling between two QADs by utilizing a cotunneling process via a localized state as a third QAD. The effective tunnel coupling can be tuned by changing the localized level even with constant nearest-neighbor tunnel couplings. We systematically study the variation of transport characteristics in the effectively triple QAD system at the Landau level filling factor $\nu =2$. The tunable tunnel coupling is clarified by analyzing the anticrossing of Coulomb blockade peaks in the charge stability diagram, in agreement with numerical simulations based on the master equation. The scheme is attractive for studying coherence and interaction in QH systems.

We consider electron-hole Cooper pair condensation in a heterostructure formed by a topological insulator (TI) film and a quantum well. We argue that the helical nature of the Dirac electronic states at the TI surface results in the presence of two competing degenerate pairing channels. The corresponding paired states have an unconventional symmetry in the order parameter describing the Cooper pair condensate, can be classified by the topological Chern invariant, and are topologically distinct. We discuss possible manifestations of the nontrivial topology, including the formation of chiral states at the domain walls separating two distinct states, quantized anomalous transport phenomena, and connections with chiral topological superconductivity.

Anisotropic magnetic exchange interactions lead to a surprisingly rich variety of magnetic properties. Considering the spin-orbit coupling (SOC) as perturbation, we extract the general expression of a bilinear spin Hamiltonian, including isotropic exchange interaction, antisymmetric Dzyaloshinskii-Moriya (DM) interaction, and symmetric $\mathrm{\Gamma }$ term. We derive the expressions for the second-order SOC contribution to DM interaction, and reveal that the essential distinction between the DM and $\mathrm{\Gamma }$ term is from their different hopping processes, rather than the different orders of SOC. Based on combining the magnetic force theorem and linear-response approach, we present a method of calculating anisotropic magnetic interactions, which now has been implemented in the open source software WienJ. Furthermore, we introduce another method which could calculate the first- and second-order SOC contribution to the DM interaction separately, and overcome some shortcomings of previous methods. Our methods are successfully applied to several typical weak ferromagnets for $3d$, $4d$, and $5d$ transition-metal oxides. We also predict the conditions where the DM interactions proportional to $\lambda$ approximately vanish while the DM interactions proportional to ${\lambda }^2$ are nonzero, and believe that it may exist in certain magnetic materials.