Kagome-lattice magnets $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$ recently emerged as a new platform to exploit the interplay between magnetism and topological electronic states. Some of the most exciting features of this family are the dramatic dependence of the easy magnetization direction on the rare-earth specie, despite other magnetic and electronic properties being essentially unchanged, and the kagome geometry of the Mn planes that in principle can generate flat bands and Dirac points; gapping of the Dirac points by spin-orbit coupling has been suggested recently to be responsible for the observed anomalous Hall response in the member ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$. In this paper, we address both issues with ab initio calculations. We have discovered the significant role played by higher-order crystal-field parameters and rare-earth magnetic anisotropy constants in these systems. We demonstrate that the microscopic origin of rare-earth magnetic anisotropy can also be quantified and understood at various levels: ab initio, phenomenological, and analytical. In particular, using a simple and physically transparent analytical model based on perturbation theory, we are able to explain, with full quantitative agreement, the evolution of rare-earth magnetic anisotropy across the series. We analyze in detail the topological properties of Mn-dominated bands and demonstrate how they emerge from the multiorbital planar kagome model. We further show that, despite this fact, most of the topological features at the Brillouin zone corner K are strongly 3D and therefore cannot explain the observed quasi-2D anomalous Hall effect, while the most pronounced quasi-2D dispersion are too far removed from the Fermi level. By employing self-consistent calculations with ab initio many-body approaches, we demonstrate that the exchange-correlation effects beyond the density functional theory for itinerant Mn-$d$ electrons do not significantly alter the obtained electronic and magnetic structure. Therefore, we conclude that, contrary to previous claims, the most pronounced 2D kagome-derived topological band features bear little relevance to transport in $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$, albeit they may possibly be brought to focus by electron or hole doping.

We study bosonic topological phases constructed from electrons. In addition to a bulk excitation energy gap, these bosonic phases also have a fermion energy gap, below which all local excitations in the bulk and on the edge are even combinations of electrons. We focus on chiral phases, in which all low-energy edge excitations move in the same direction, that arise from the short-range entangled $E_8$ quantum Hall state, the bosonic analog of the filled lowest Landau level of electrons. The $E_8$ edge-state theory features an $E_8$ Kac-Moody symmetry that can be decomposed into ${\mathcal{G}}_A\times {\mathcal{G}}_B$ subalgebras, such as $\mathrm{SU}\left(3\right)\times E_6, \mathrm{SO}\left(M\right)\times \mathrm{SO}(16-M)$, and $G_2\times F_4$. (Here, $\left\{\mathrm{SO}\right(M\left)\right\}, \left\{\mathrm{SU}\right(N\left)\right\}$, and $\{E_8,G_2,F_4\}$ denote orthogonal, unitary, and exceptional Lie algebras.) Using these symmetry decompositions, we construct exactly solvable coupled-wire model Hamiltonians for families of long-range entangled ${\mathcal{G}}_A$ or ${\mathcal{G}}_B$ bosonic fractional quantum Hall states that “partially fill” the $E_8$ state and are pairwise related by a generalized particle-hole symmetry. These long-range entangled states feature either Abelian or non-Abelian topological order. Some support the emergence of nonlocal Dirac and Majorana fermions, Ising anyons, metaplectic anyons, Fibonacci anyons, as well as deconfined ${\mathbb{Z}}_2$ gauge fluxes and charges.

We prove a generic spin-statistics relation for the fractional quasiparticles that appear in Abelian quantum Hall states on the disk. The proof is based on an efficient way for computing the Berry phase acquired by a generic quasiparticle translated in the plane along a circular path, and on the crucial fact that once the gauge-invariant generator of rotations is projected onto a Landau level, it fractionalizes among the quasiparticles and the edge. Using these results we define a measurable quasiparticle fractional spin that satisfies the spin-statistics relation. As an application, we predict the value of the spin of the composite-fermion quasielectron proposed by Jain; our numerical simulations agree with that value. We also show that Laughlin's quasielectrons satisfy the spin-statistics relation, but carry the wrong spin to be the antianyons of Laughlin's quasiholes. We continue by highlighting the fact that the statistical angle between two quasiparticles can be obtained by measuring the angular momentum while merging the two quasiparticles. Finally, we show that our arguments carry over to the non-Abelian case by discussing explicitly the Moore-Read wave function.

Recently, Song and Bernevig [Phys. Rev. Lett. 129, 047601 (2022)] reformulated magic-angle twisted bilayer graphene as a topological heavy fermion problem, and used this reformulation to provide a deeper understanding for the correlated phases at integer fillings. In this work, we generalize this heavy-fermion paradigm to magic-angle twisted symmetric trilayer graphene, and propose a low-energy $f\text{−}c\text{−}d$ model that reformulates magic-angle twisted symmetric trilayer graphene as heavy localized $f$ modes coupled to itinerant topological semimetalic $c$ modes and itinerant Dirac $d$ modes. Our $f\text{−}c\text{−}d$ model well reproduces the single-particle band structure of magic-angle twisted symmetric trilayer graphene at low energies for displacement field $\mathcal{E}\in [0,300]\mathrm{meV}$. By performing Hartree-Fock calculations with the $f\text{−}c\text{−}d$ model for $\nu =0,-1,-2$ electrons per Moiré unit cell, we reproduce all the correlated ground states obtained from the previous numerical Hartree-Fock calculations with the Bistritzer-MacDonald-type model, and we find additional new correlated ground states at high displacement field. Based on the numerical results, we propose a simple rule for the ground states at high displacement fields by using the $f\text{−}c\text{−}d$ model, and provide analytical derivation for the rule at charge neutrality. We also provide analytical symmetry arguments for the (nearly) degenerate energies of the high-$\mathcal{E}$ ground states at all the integer fillings of interest, and make experimental predictions of which charge-neutral states are stabilized in magnetic fields. Our $f\text{−}c\text{−}d$ model provides a new perspective for understanding the correlated phenomena in magic-angle twisted symmetric trilayer graphene, suggesting that the heavy fermion paradigm of Song and Bernevig [Phys. Rev. Lett. 129, 047601 (2022)] should be the generic underpinning of correlated physics in multilayer moire graphene structures.

Two objects in relative motion without physical contact suffer a friction force, resulting from vacuum fluctuation. It is widely accepted that friction acts in the opposite direction of the relative velocity. Here, this study demonstrates the existence of negative friction, where the direction of friction is along the sliding direction, in a gain system. The system consists of a vacuum-separated silica sphere and a dielectric substrate covered by a graphene sheet (gain medium). The friction torque of the rotating sphere can be switched between positive and negative, depending on the quasi-Fermi energy of graphene. Negative vacuum friction can be achieved when the quasi-Fermi energy is large, and its magnitude is strongly dependent on the distance, temperature, and permittivity of the substrate. For moderate conditions, the torque generated by negative friction surpasses the resistance posed by the surrounding air, presenting a different approach for driving nanoparticles to an ultrahigh rotating speed.

We have experimentally studied the accuracy of the Jones-type reflection matrix $\mathbf{R}$ that describes light reflection from a magnetic sample exhibiting the magneto-optical (MO) Kerr effect (MOKE). For this purpose, we performed a comprehensive experimental study, utilizing generalized MO ellipsometry, which allows for the simultaneous measurement of all complex-valued elements of $\mathbf{R}$ for arbitrary magnetization vector orientations. For the collection of suitable datasets under appropriate test conditions, we also fabricated and utilized a thin film sample that exhibits a uniform magnetization state, whose vector orientation can be easily rotated by an applied magnetic field. This approach enabled us to systematically and simultaneously vary the MOKE coefficients of $\mathbf{R}$, which permitted us to verify the accuracy of $\mathbf{R}$ with high precision. While we observe the widely used standard formulation of $\mathbf{R}$ to be correct under most experimental conditions, we also found small systematic deviations for some specific cases. However, these deviations are not indicative of a limited correctness of $\mathbf{R}$, but instead, they are related to the material assumptions that are commonly made for the derivation of $\mathbf{R}$. For our specific sample here, the origin of the deviation is MO anisotropy, and upon considering this material property accurately, an exact description of all experimental results by $\mathbf{R}$ can be reestablished.

A report on the near-ambient superconductivity in a nitrogen-doped lutetium hydride has stimulated great interest in this material [Dasenbrock-Gammon et al., Nature (London) 615, 244 (2023)]. While its superconductivity is still a subject of debate, the structure of the claimed cubic phase remains uncertain. In this work, we study the effect of nitrogen doping and pressure on the energetic and dynamic stability of cubic $\mathrm{Lu}{\mathrm{H}}_3$. Our findings indicate that both pressure and nitrogen doping can enhance the stability of the cubic $\mathrm{Lu}{\mathrm{H}}_3$ phase. We propose a ${\mathrm{Lu}}_8{\mathrm{H}}_{21}\mathrm{N}$ structure that exhibits a stable phonon, reasonable thermodynamic stability at 1 GPa, and an x-ray diffraction pattern similar to the experimental data. However, we do not observe electron-phonon coupling in the zone-center phonon modes of these crystal structures.

Thermodynamic and magnetic studies on high-quality single crystals are used to investigate the magnetic phase diagram and magnetostructural coupling in the mixed-spin system ${\mathrm{Ni}}_{0.25}{\mathrm{Mn}}_{0.75}{\mathrm{TiO}}_3$. Clear anomalies in the thermal expansion at the spin ordering and spin reorientation temperatures,$T_N$ and $T_R$, evidence pronounced magnetoelastic effects. The magnetic entropy is released mainly above $T_N$ implying considerable short range magnetic order up to about $4\times T_N$. This is associated with a large regime of negative thermal expansion of the $c$ axis. Both $T_N$ and $T_R$ exhibit the same sign of uniaxial pressure dependence, which is positive (negative) for pressure applied along the $b$ $\left(c\right)$ axis. The magnetic phase diagrams are constructed and the uniaxial pressure dependencies of the ordering phenomena are determined. For magnetic fields $B\parallel b$ axis, a sign change and splitting of anomalies implies further magnetic phases. In addition to short-range magnetic order well above $T_N$, competing anisotropies yield a glasslike behavior as evidenced by a maximum in AC-$\chi$ $(T_{\mathrm{SG}}\simeq 3.7 \mathrm{K})$ and quasilinear temperature dependence of $c_{\mathrm{p}}$. High-field magnetization up to 50 T demonstrates that in addition to antiferromagnetically ordered spins there are also only weakly coupled moments at 2 K with a sizable amount of about 15% of all ${\mathrm{Mn}}^{2+}$ spins present in the material. The observed changes in the pressure dependence and the magnetostrictive effects shed light on the recently observed flop of electric polarization from $P\parallel c$ to $P\parallel a$ [Phys. Rev. B 90, 144429 (2014)], in particular, suggesting that the magnetoelectric effect is not directly related to magnetostriction.

Van Roosbroeck's equations constitute a versatile tool to determine the dynamics of electrons under time- and space-dependent perturbations. Extensively utilized in ordinary semiconductors, their potential to model devices made from topological materials remains untapped. Here, we adapt van Roosbroeck's equations to theoretically study the bulk response of a Weyl semimetal to an ultrafast and spatially localized light pulse in the presence of a quantizing magnetic field. We predict a transient oscillatory photovoltage that originates from the chiral anomaly. The oscillations take place at the plasma frequency (THz range) and are damped by intervalley scattering and dielectric relaxation. Our results illustrate the ability of van Roosbroeck's equations to unveil the interplay between electronic band topology and fast carrier dynamics in microelectronic devices.

${\mathrm{BaFe}}_2{\mathrm{As}}_2$ is the parent compound for a family of iron-based high-temperature superconductors as well as a prototypical example of the spin density wave (SDW) system. In this study, we perform an optical pump-probe study of this compound to systematically investigate the SDW order across the pressure-temperature phase diagram. The suppression of the SDW order by pressure manifests itself through the increase of relaxation time together with the decrease of the pump-probe signal and the pump energy necessary for complete vaporization of the SDW condensate. We have found that the pressure-driven suppression of the SDW order at low temperature occurs gradually, in contrast to the thermally induced SDW transition. Our results suggest that the pressure-driven quantum phase transition in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ (and probably other iron pnictides) is continuous and it is caused by the gradual worsening of the Fermi-surface nesting conditions.

The theoretical description of strongly correlated materials relies on the ability to simultaneously capture, on equal footing, the different competing energy scales. Unfortunately, existing approaches are either typically extremely computationally demanding, making systematic screenings of correlated materials challenging or are limited to a subset of observables of interest. The recently developed ghost Gutzwiller ansatz (gGut) has shown great promise to remedy this dichotomy. It is based on a self-consistency condition around the comparatively simple static one-particle reduced density matrix, yet has been shown to provide accurate static and dynamical observables in one-band systems. In this work, we investigate its potential role in the modeling of correlated materials, by applying it to several multiorbital lattice models. Our results confirm the accuracy at lower computational cost of the gGut, and show promise for its application to materials research.

Topological quantum chemistry (TQC) is a successful framework for identifying (noninteracting) topological materials. Based on the symmetry eigenvalues of Bloch eigenstates at maximal momenta, which are attainable from first principles calculations, a band structure can either be classified as an atomic limit, in other words adiabatically connected to independent electronic orbitals on the respective crystal lattice, or it is topological. For interacting systems, there is no single-particle band structure and hence, the TQC machinery grinds to a halt. We develop a framework analogous to TQC, but employing $n$-particle Green's function to classify interacting systems. Fundamentally, we define a class of interacting reference states that generalize the notion of atomic limits, which we call Mott atomic limits, and are symmetry protected topological states. Our formalism allows to fully classify these reference states (with $n=2$), which can themselves represent symmetry protected topological states. We present a comprehensive classification of such states in one dimension and provide numerical results on model systems. With this, we establish Mott atomic limit states as a generalization of the atomic limits to interacting systems.

The nonlinear optical response of bismuth (Bi) in the nonperturbative regime is studied by phase-resolved two-dimensional terahertz (THz) spectroscopy. A (111)-oriented rhombohedral Bi film of 45-nm thickness is excited by a pair of THz pulses with center frequencies of 1.1 THz, electric field amplitudes of 300 and 600 kV/cm, and pulse durations of 1 ps. The phase-resolved nonlinear signal field, emitted by the sample and recorded in a transmission geometry, allows for a separation of different components of the total nonlinear response, including higher harmonics of the THz pulses and pump-probe signals with few-picosecond decay times. The pump-probe signals originate from irreversible electron-hole pair generation and display a sixfold amplitude pattern in the azimuthal sample orientation. The linearly polarized pump pulses generate an unequal transient carrier population in the six $L$ valleys of the band structure, resulting in a reduction of symmetry of the excited crystal and a backfolding of phonons from the $X$ to the $\mathrm{\Gamma }$ point. Wave packets of back-folded acoustic phonons, which are displacively excited by the THz pump pulse, give rise to coherent pump-probe signals oscillating with a frequency of 0.8 THz.

For families of Hamiltonians defined by parts that are local, the most general definition of a symmetry algebra is the commutant algebra, i.e., the algebra of operators that commute with each local part. Thinking about symmetry algebras as commutant algebras allows for the treatment of conventional symmetries and unconventional symmetries (e.g., those responsible for weak ergodicity breaking phenomena) on equal algebraic footing. In this work, we discuss two methods for numerically constructing this commutant algebra starting from a family of Hamiltonians. First, we use the equivalence of this problem to that of simultaneous block diagonalization of a given set of local operators and discuss a probabilistic method that has been found to work with probability 1 for both Abelian and non-Abelian symmetries or commutant algebras. Second, we map this problem onto the problem of determining frustration-free ground states of certain Hamiltonians, and we use ideas from tensor network algorithms to efficiently solve this problem in one dimension. These numerical methods are useful in detecting standard and nonstandard conserved quantities in families of Hamiltonians, which includes examples of regular symmetries, Hilbert space fragmentation, and quantum many-body scars, and we show many such examples. In addition, they are necessary for verifying several conjectures on the structure of the commutant algebras in these cases, which we have put forward in earlier works. Finally, we also discuss similar methods for the inverse problem of determining local operators with a given symmetry or commutant algebra, which connects to existing methods in the literature. A special case of this construction reduces to well-known “Eigenstate to Hamiltonian” methods for constructing Hermitian local operators that have a given state as an eigenstate.

There have been substantial recent efforts, both experimentally and theoretically, to find a material realization of the Kitaev spin liquid—the ground state of the exactly solvable Kitaev model on the honeycomb lattice. Candidate materials are now plentiful, but the presence of non-Kitaev terms makes comparison between theory and experiment challenging. We rederive time-dependent Majorana mean-field theory and extend it to include quantum phase information, allowing the direct computation of the experimentally relevant dynamical spin-spin correlator, which reproduces exact results for the unperturbed model. In contrast to previous work, we find that small perturbations do not substantially alter the exact result, implying that $\alpha \text{−}\mathrm{RuCl}_3$ is perhaps farther from the Kitaev phase than originally thought. Our approach generalizes to any correlator and to any model where Majorana mean-field theory is a valid starting point.

We describe two approximation methods designed to capture the leading behavior of the low-energy tail of the momentum-dependent spectral density $A(\mathbf{k},E)$ and the tunneling density of states $D\left(E\right)$ for an injected particle, such as an electron or an exciton, interacting with a bath of phonons at a nonzero initial temperature $T$, including quantum corrections due to the nonzero frequencies of the relevant phonons. In our imaginary-time-dependent Hartree (ITDH) approximation, we consider a situation in which the particle is injected into a specified coherent state of the phonon system, and we show how one can use the ITDH approximation to obtain the correlation function $C\left(\tau \right)$ for that initial state. The thermal average $C\left(\tau \right)$ is obtained, in principle, by integrating the result over all possible initial phonon coherent states, weighted by a thermal distribution. However, in the low-energy tail, one can obtain a good first approximation by considering only initial states near the one that maximizes the integrand. Our second approximation, the fixed-wave-function (FWF) approximation, assumes that the wave function of the injected particle evolves instantaneously to a wave function which then is independent of time, while the phonon system continues to evolve due to interaction with the particle. We discuss how to invert the Laplace transform and how to obtain $A(\mathbf{k},E)$ as well as $D\left(E\right)$ from the imaginary-time analysis. The FWF approximation is used to calculate $D\left(E\right)$ for a one-dimensional continuum model of a particle interacting with acoustic phonons, and effects due to the quantum motion of phonons are observed. In the classical phonon limit, where the nuclear mass is taken to infinity while the elastic constants and other parameters are held fixed, the dominant behaviors of both the ITDH and FWF approximations in the low-energy tail reduce to that found in the past for a particle in a random potential with a Gaussian statistical distribution.

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In particular, at the critical measurement rate, we find that the entanglement of a subsystem of size $\ell$ scales as $S\sim \sqrt{\ell }$; moreover, the dynamical critical exponent $z=\infty$. The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents. We argue for this infinite-randomness scenario on general grounds and present numerical evidence that it captures some features of the universal critical properties of MIPT using large-scale simulations of Clifford circuits. These findings demonstrate that the relevance and irrelevance of perturbations to the MIPT can naturally be interpreted using a powerful heuristic known as the Harris criterion.

A growing body of work suggests that planar Josephson junctions fabricated using superconducting hybrid materials provide a highly controllable route toward one-dimensional topological superconductivity. Among the experimental controls are the in-plane magnetic field, phase difference across the junction, and carrier density set by electrostatic gate voltages. Here, we investigate wide planar Josephson junctions based on an epitaxial InAs/Al heterostructure, embedded in a superconducting loop, probed with integrated quantum point contacts (QPCs) at both ends of the junction. For a large range of gate voltages, a closing and reopening of the superconducting gap is observed that appears strongly correlated at the two ends of the junction. The reopening occurred roughly at in-plane magnetic field $B_{\parallel }\simeq 0.2\mathrm{T}$, was uniform across multiple devices, and tunable with phase bias. A narrower range of the junction gate voltage, covering roughly 10% of the operable gate space, supports a zero-bias conductance peak (ZBCP) that appears upon reopening of the gap. However, the height, shape, and even presence of ZBCPs typically differed between the ends, suggesting a weak end-to-end correlation. Theoretical modeling suggests an orbital-effect driven mechanism for the gap-reopening. Within this model, the gap reopening represents a topological phase transition when associated with a zero-energy state. While several features of the experimental data are captured by our model, the lack of end-to-end correlation of ZBCPs in the experiment suggests the absence of an uninterrupted topological phase along the junction, presumably due to disorder. Deliberately tuned local end dots show distinctly different phenomenology, particularly with respect to phase bias, providing a check on possible topological and nontopological interpretations.

The development and characterization of three-dimensional (3D) topological magnetic textures has become an important topic in modern magnetism both for fundamental and technological perspectives. Among the novel 3D spin textures, skyrmionic cocoons have been successfully stabilized in magnetic multilayers having a variable thickness of the ferromagnet in the vertical direction of the stack. These ellipsoidal 3D magnetic textures remain vertically confined in a fraction of the total thickness, whereas, coexisting with fully columnar skyrmions. Here, we use xray holography with about 15-nm lateral resolution to investigate how their properties depend on the field and temperature. We observe circular objects with different amplitude of contrast, which evidences the presence of different 3D objects located in various vertical parts of the multilayer. Moreover, whereas, sweeping an out-of plane magnetic field, we witness an attractive interaction between cocoons located at various heights, mainly due to the stray field, which impacts their horizontal positionings. The x-ray holography measurements also allow to determine the size of the cocoons at remanence, which at room temperature, possess diameters close to 100 nm on average. Combining this transmission technique with magnetic force microscopy and micromagnetic simulations gives a precise insight into the 3D distribution of the magnetization, which demonstrates the 3D nature of skyrmionic cocoons.

We investigate thermal Hall conductivity ${\kappa }_{xy}$ of a $J\text{−}K$ Kitaev-Heisenberg model with a Zeeman field in the (111) direction in light of the recent debate surrounding the possible reemergence of Ising topological order (ITO) and half-quantized ${\kappa }_{xy}/T$ upon field suppression of long-range magnetic order in Kitaev materials. We use the purification-based finite-temperature tensor network approach making no prior assumptions about the nature of the excitations: Majorana, visons, or spin waves. For purely Kitaev interactions and fields $h/K\gtrsim 0.02$ sufficient to degrade ITO, the peak ${\kappa }_{xy}/T$ monotonically decreases from half quantization associated with lower fields—a behavior reminiscent of vison fluctuation corrections. For higher fields $h/K\gtrsim 0.1,$ we find the results qualitatively consistent with a spin-wave treatment. In our $J\text{−}K$ model (with ferro-$K$ and antiferro-$J$), in the vicinity of field-suppressed magnetic order, we found ${\kappa }_{xy}/T$ to be significant, with peak magnitudes exceeding half quantization followed by a monotonic decrease with increasing $h.$ We thus conclude that the half-quantized thermal Hall effect in the vicinity of field-suppressed magnetic order in our model is a fine-tuning effect and is not associated with a Majorana Hall state with ITO.