Utilizing the realistic continuum description of twisted bilayer ${\mathrm{MoTe}}_2$ and many-body exact diagonalization calculation, we establish that the second moiré band of twisted bilayer ${\mathrm{MoTe}}_2$, at a small twist angle of approximately $2^{\circ }$, serves as an optimal platform for achieving the long-sought non-Abelian fractional quantum anomalous Hall states without the need for external magnetic fields. Across a wide parameter range, our exact diagonalization calculations reveal that the half-filled second moiré band demonstrates the ground state degeneracy and spectral flows, which are consistent with the Pfaffian state in the first Landau level. We further elucidate that the emergence of the non-Abelian state is deeply connected to the remarkable similarity between the second moiré band and the first Landau level. Essentially, the band not only exhibits characteristics akin to the first Landau level, $\frac{1}{2\pi }{\int }_{\mathrm{BZ}}{\mathrm{d}}^2\mathbf{k}\mathrm{tr}\eta \left(\mathbf{k}\right)\approx 3$ where ${\eta }_{ab}\left(\mathbf{k}\right)$ is the Fubini-Study metric of the band, but also that its projected Coulomb interaction closely mirrors the Haldane pseudopotentials of the first Landau level. Motivated by this observation, we introduce a metric of “first Landau level”-ness of a band, which quantitatively measures the alignment of the projected Coulomb interaction with the Haldane pseudopotentials in Landau levels. This metric is then compared with the global phase diagram of the half-filled second moiré band, revealing its utility in predicting the parameter region of the non-Abelian state. In addition, we uncover that the first and third moiré bands closely resemble the lowest and second Landau levels, revealing a remarkable sequential equivalence between the moiré bands and Landau levels. We finally discuss the potential implications on experiments.

According to the bulk-edge correspondence, a one-dimensional strip in the quantum anomalous Hall system typically exhibits two gapless chiral states on two edges characterized by a Chern number. Here, we introduce a model that exhibits what we call “half-antichiral” edge modes in a composite bilayer system comprising a Haldane model layer and a modified Haldane model layer. These states propagate in the same direction along the same edge of the strip and are compensated by the counterpropagating modes that reside in the bulk. In the presence of strong layer coupling, with the assistance of the chiral edge state in the layer of the Haldane model, the half-antichiral edge states of the whole system exhibit strong immunity to disorder, thereby creating a bi-conductance plateau. Interestingly, throughout this process, we observe a topological hidden phase transition where two valence bands with Chern number $C=\pm (1+1)$ evolve into one valence band with a high Chern number $C=\pm 2$ and one trivial valence band with $C=0$, which is closely related to the biconductance plateau. These findings open up possibilities for the development of layer-assisted topological states and novel topological phase transitions in systems with a high Chern number.

We study the appearance of a chiral edge mode on the two-dimensional (2D) surface of a 3D topological insulator (TI). The edge mode appears along the 1D boundary with a magnetic insulator (MI), dependent on the angle $\theta$ which the magnetization $M$ makes with the normal to the surface and on the chemical potential mismatch $\delta \mu$ across the TI-MI interface (assuming $1>\delta \mu /M\equiv sin\varphi )$. The propagation along the interface is chiral, with velocity $vcos(\theta -\varphi )$ smaller than the Dirac fermion velocity $v$. In momentum space the edge mode is an arc state, extending over the finite momentum interval that connects the Dirac point of the gapless Dirac fermions with the magnetic band gap. An electric field parallel to the boundary pumps charge between TI and MI via this arc state.

Due to their robustness, the implementation of geometric phases provides a reliable and controllable way to manipulate the phase of a spin wave, thereby paving the way toward functional magnonics-based data processing devices. Moreover, geometric phases in spin waves are interesting from a fundamental perspective as they contain information about spin wave band structures and play an important role in magnon Hall effects. In this paper, we propose to directly measure geometric phases in spin wave systems using the magnetic field sensing capabilities of nitrogen-vacancy (NV) centers. We demonstrate the general principles of this method on two systems in which spin waves acquire a geometric phase, namely, a wire with a magnetic domain wall and a system with position-dependent anisotropy axes, and explicitly show how this phase can be deduced from the NV center signal.

The shape of magnetic nanoparticles (MNPs) greatly affects their dynamics and their potential as heating agents, e.g., for magnetic hyperthermia treatment of cancer. To investigate shape effects theoretically, we present a computationally efficient model of a uniformly magnetized, spheroid-shaped MNP, suspended in liquid at finite temperature, where the magnetic dynamics are coupled to mechanical rotation. Using exact solutions for the shape-dependent input parameters we vary the aspect ratio from a flat disk, through a sphere to a thin needle shape. By computing the energy absorption rate under an alternating magnetic field, and decomposing the dissipated energy into a frictional and magnetic loss channel, we determine the main heating mechanism in different parameter regimes. We find a critical aspect ratio for maximizing frictional losses, which yields the largest total absorption for a broad range of intermediate applied fields. Depending on the applied field strength, this may increase the absorption rate by over 200% relative to both spherical and highly elongated particles. For stronger fields (larger than about half the anisotropy field given maximal shape anisotropy), magnetic losses dominate for all shapes and extreme elongation is preferable.

We investigate the properties of the recently observed “demon” mode, a 3D acoustic plasmon, in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ with an emphasis on evaluating its role for the pairing interactions in this superconductor. The demon mode is a low-energy electronic excitation, and it has been suggested that it could contribute to a reduced Coulomb repulsion and even a possible attractive interaction between electrons. In this study we explicitly calculate the dynamically screened Coulomb interaction for ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ by using a renormalized tight-binding band structure and the random phase approximation for the dielectric function. Although the focus here is on ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, this material is considered mainly as a prototype system, having an observed demon mode, and our results should be considered as a guide for applications to other systems. Our calculations show that there are regions in $\left(\mathbf{q},\omega \right)$ space where the Coulomb interaction becomes attractive. We find that although the demon mode is not capable of producing a total attractive electron-pairing interaction in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, it does contribute to a significant reduction in the Coulomb repulsion at the relevant pairing energy scale.

Monte Carlo methods have led to profound insights into the strong-coupling behavior of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of ${\mathbb{Z}}_N$ lattice gauge theories in $(2+1)$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For ${\mathbb{Z}}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the ${\mathbb{Z}}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.

We examine the low-energy excitations in the vicinity of the quantum critical point in ${\mathrm{LiHoF}}_4$, a physical realization of the transverse-field Ising model, focusing on the long-range fluctuations which soften to zero energy at the ferromagnetic quantum phase transition. Microwave spectroscopy in tunable loop-gap resonator structures identifies and characterizes the soft mode and higher-energy electronuclear states. We study these modes as a function of frequency and magnetic fields applied transverse and parallel to the Ising axis. These are understood in the context of a theoretical model of a soft electronuclear mode that interacts with soft photons as well as soft phonons. We identify competing infrared divergences at the quantum critical point, coming from the photons and the electronuclear soft mode. It is an incomplete cancellation of these divergences that leads to the muted but distinct signatures observed in the experiments. The application of a longitudinal magnetic field gaps the soft mode. Measurements well away from the quantum critical point reveal a set of “Walker” modes associated with ferromagnetic domain dynamics.

In this study, we propose that the signatures of spin fractionalization in quantum magnets can be identified through a detailed analysis of the temperature dependence of the asymmetric Fano lineshape of optical phonons overlapping with a continuum of spin excitations. We focus on the hyperhoneycomb magnet $\beta \text{−}{\text{Li}}_2{\text{IrO}}_3$, a promising candidate for being in proximity to a three-dimensional Kitaev quantum spin liquid. The Raman response in $\beta \text{−}{\text{Li}}_2{\text{IrO}}_3$ notably displays a distinctive asymmetric Fano lineshape in the 24 meV Raman-active optical phonon. This asymmetry arises from the interaction between the discrete phonon mode and the spin excitation continuum, which could be fractionalized if the material is indeed near a quantum spin-liquid phase. Our theoretical model considers the coupling of this optical phonon to Majorana fermions in the Kitaev model on the hyperhoneycomb lattice. Our findings reveal that the temperature-dependent Fano lineshape is consistent with the fractionalization of spins into Majorana fermions and $\mathbb{Z}{}_2$ fluxes.

It was recently discovered that, depending on their symmetries, collinear antiferromagnets may break spin degeneracy in momentum space, even in the absence of spin-orbit coupling. Such systems, dubbed altermagnets, have electronic bands with a spin-momentum texture set mainly by the combined crystal-magnetic symmetry. This discovery motivates the question of which novel physical properties derive from altermagnetic order. Here we show that one consequence of altermagnetic order is a fluctuation-driven piezomagnetic response. Using two Heisenberg models of $d$-wave altermagnets, a checkerboard one and one for rutiles, we determine the fluctuation-induced piezomagnetic coefficients considering temperature-induced transversal spin fluctuations. We establish in addition that magnetic fluctuations induce an anisotropic thermal spin conductivity.

We investigate the intrinsic microscopic mechanism of photon upconversion in air-suspended single-walled carbon nanotubes through photoluminescence and upconversion photoluminescence spectroscopy. Nearly linear excitation power dependence of upconversion photoluminescence intensity is observed, indicating a one-photon process as the underlying mechanism. In addition, we find a strongly anisotropic response to the excitation polarization, which reflects the intrinsic nature of the upconversion process. In upconversion photoluminescence excitation spectra, three peaks are observed, which are similar to photoluminescence sidebands of the $K$-momentum dark singlet exciton. The features in the upconversion photoluminescence excitation spectra are well reproduced by our second-order exciton-phonon interaction model, enabling the determination of phonon energies and relative amplitudes. The analysis reveals that the upconversion photoluminescence can be described as a reverse process of the sideband emission linked to the $K$-momentum phonon modes. The validity of our model is further reinforced by temperature-dependent upconversion photoluminescence excitation measurements reflecting variations in the phonon population. Our findings underscore the pivotal role of the resonant exciton-phonon coupling in pristine carbon nanotubes and present potential for advanced optothermal technologies by engineering the excitation pathways.

Recent experiments reported the realization of a heavy Fermi liquid in AB-stacked ${\mathrm{MoTe}}_2$/${\mathrm{WSe}}_2$ heterobilayers. In this paper, we show that the AB-stacked heterobilayer configuration is particularly suited to realize topological Kondo semimetal and topological Kondo insulator ground states at a doping of two holes per moiré unit cell. The small lattice mismatch between the ${\mathrm{MoTe}}_2$ and ${\mathrm{WSe}}_2$ monolayers and the different bandwidths of their highest lying moiré valence bands means that, in the experimentally relevant range of hole dopings, the ${\mathrm{MoTe}}_2$ layer is effectively a Mott insulator with only low-lying magnetic excitations Kondo-coupled to more itinerant electrons in the ${\mathrm{WSe}}_2$. The crucial consequence of the AB-stacking configuration is that the interlayer tunneling connects orbitals of opposite parity in the two layers, leading to a chiral Kondo coupling. We show that the chiral Kondo coupling favors a topological Kondo semimetal at filling $\nu =1+1$, with a nonquantized spin Hall conductance arising from edge modes, whose spectrum and overlap with bulk states we determine. We further show that a spatially random strain field that locally breaks the rotation symmetry can convert the Kondo semimetal to a narrow gap topological Kondo insulator featuring a quantized spin Hall conductance.

Orbital magnetism arises due to the coherent cyclotron motion of band electrons. System-bath entanglement is expected to disrupt this coherent electronic motion and quench orbital magnetism. Here, we show that a suitably tailored bath can lead to an enhancement of the orbital diamagnetic susceptibility of a multiband electron system and can even convert an orbital paramagnetic response into a diamagnetic one as the system-bath coupling is increased. We also demonstrate how a van Hove singularity in the bath density of states can be exploited to generate a giant enhancement of the orbital magnetic susceptibility. Our work opens doors to the possibility of controlling the orbital magnetic response of band electron systems through bath engineering.

Topological Hall effect (THE) in materials can arise as a result of the interaction of the conduction electrons with the underlying nontrivial spin texture that generates an emergent magnetic field in addition to the applied field that stabilizes the texture. Here we report the observation of THE below the Néel temperature of 16.5 K in an antiferromagnet ${\mathrm{GdNi}}_{0.4}{\mathrm{Si}}_{1.6}$ that crystallizes in centrosymmetric $P6/mmm$ structure. The presence of skyrmion lattice phase (SkL) in this material has been probed through ac and dc magnetic susceptibility $({\chi }_{\mathrm{ac}} \text{and} {\chi }_{\mathrm{dc}})$ measurements, transport properties, and by tracking the change of isothermal magnetic entropy ($\mathrm{\Delta }{S}_{\mathrm{M}}$). Magnetic phase diagrams have been constructed based on ${\chi }_{\mathrm{dc}}$, topological Hall resistivity, and $\mathrm{\Delta }{S}_{\mathrm{M}}$; all of these suggest the presence of SkL phase in this compound. Our results summarize the thermodynamic and transport properties that are produced from such a magnetic phase.

Electrically manipulating the magnetization of ferrimagnetic insulators, without reliance on an external magnetic field, offers potential for the advancement of fast and energy-efficient spintronic devices. In this paper, we report efficient field-free spin-orbit torque switching in the $\mathrm{T}{\mathrm{m}}_3\mathrm{F}{\mathrm{e}}_5{\mathrm{O}}_{12}/\mathrm{Pt}$ heterostructure epitaxially grown on a vicinal ${\mathrm{Y}}_3\left(\mathrm{S}{\mathrm{c}}_2\mathrm{G}{\mathrm{a}}_3\right){\mathrm{O}}_{12}$ (7 7 10) substrate with its surface having a ${10}^{\circ }$ miscut angle relative to the (111) orientation. The magnetic easy axis is identified to be approximately along the [443] direction, deviating from the film normal by ${17}^{\circ }$. This magnetic tilting breaks the in-plane magnetic symmetry and thus leads to the magnetization switching in zero field when the current is applied orthogonal to the miscut direction. Moreover, we observe that the anomalous Hall resistance, typically used to monitor the $\mathrm{T}{\mathrm{m}}_3\mathrm{F}{\mathrm{e}}_5{\mathrm{O}}_{12}$ magnetization state, becomes entangled with the transverse effect of the spin Hall magnetoresistance under an in-plane field. The resulting Hall resistance (and even its polarity) in response to the current-induced magnetization switching is significantly modified by the in-plane field. The dynamics of zero-field switching is simulated numerically based on the macrospin model. This work paves the way in the development of spintronic devices utilizing magnetic insulators.

${\mathrm{CaPd}}_2{\mathrm{As}}_2$ is known to superconduct below $T_c=1.27\left(3\right)$ K. In this work we examine whether the time-reversal symmetry (TRS) is preserved or broken upon entering the superconducting state in ${\mathrm{CaPd}}_2{\mathrm{As}}_2$, and probe its superconducting gap structure using muon spin relaxation and rotation ($\mu \mathrm{SR}$) measurements in zero field (ZF) and transverse field (TF), respectively. The analysis of ZF-$\mu \mathrm{SR}$ spectra reveals an increase in muon spin relaxation rate ${\lambda }_{\mathrm{ZF}}$ in the superconducting (SC) state attesting the presence of a weak magnetic field. The appearance of spontaneous magnetic field indicates the breaking of time-reversal symmetry state upon entering the SC state of ${\mathrm{CaPd}}_2{\mathrm{As}}_2$. The analysis of TF-$\mu \mathrm{SR}$ spectra provides information about the superconducting gap structure of ${\mathrm{CaPd}}_2{\mathrm{As}}_2$ which is found to have a single-band isotropic $s$-wave symmetry. We find an isotropic energy gap $\mathrm{\Delta }\left(0\right)=0.160\left(1\right)$ meV corresponding to $2\mathrm{\Delta }\left(0\right)/k_{\mathrm{B}}{T}_c=3.37\left(3\right)$ which is close to the weak-coupling BCS value of 3.53. The analysis of TF $\mu \mathrm{SR}$ also provides an estimate of effective penetration depth which is found to be ${\lambda }_{\mathrm{eff}}\left(0\right)=415\left(16\right)$ nm. Our $\mu \mathrm{SR}$ data thus find evidence for TRS breaking in ${\mathrm{CaPd}}_2{\mathrm{As}}_2$ with an $s$-wave singlet paring which is not expected for a conventional superconductor.

Competing and intertwined orders are ubiquitous in strongly correlated electron systems, such as the charge, spin, and superconducting orders in the high-$T_{\mathrm{c}}$ cuprates. Recent scanning tunneling microscopy (STM) measurements provide evidence for a charge density wave (CDW) that coexists with superconductivity in the heavy fermion metal ${\mathrm{UTe}}_2$. This CDW persists up to at least 7.5 K, and, as a CDW breaks the translational symmetry of the lattice, its disappearance is necessarily accompanied by a thermodynamic phase transition. We report high-precision thermodynamic measurements of the elastic moduli of ${\mathrm{UTe}}_2$. We observe no signature of a phase transition in the elastic moduli down to a level of 1 part in ${10}^7$, strongly implying the absence of bulk CDW order in ${\mathrm{UTe}}_2$. We suggest that the CDW and associated pair density wave observed by STM may be confined to the surface of ${\mathrm{UTe}}_2$.

The long-sought pair density wave (PDW) is an exotic phase of matter in which charge density wave (CDW) order is intertwined with the amplitude or phase of coexisting, superconducting order. Originally predicted to exist in copper-oxides, circumstantial evidence for PDW order now exists in a variety of materials. Recently, scanning tunneling microscopy (STM) studies have reported evidence for a three-component CDW at the surface of the heavy-fermion superconductor, ${\mathrm{UTe}}_2$, persisting below its superconducting transition temperature [Aishwarya et al., Nature 618, 928933 (2023); Gu et al., Nature 618, 921927 (2023); LaFleur et al., Nat. Commun. 15, 4456 (2024)]. Here, we use hard x-ray diffraction measurements on crystals of ${\mathrm{UTe}}_2$ at $T=1.9$ and 12 K to search for a bulk signature of this CDW. Using STM measurements as a constraint, we calculate the expected locations of CDW superlattice peaks and sweep a large volume of reciprocal space in search of a signature. We fail to find any evidence for a CDW near any of the expected superlattice positions in many Brillouin zones. We estimate an upper bound on the CDW lattice distortion of $u_{\text{max}}\lesssim 4\times {10}^{-3}\AA$. Our results suggest that the CDW observed in STM is either purely electronic, somehow lacking a signature in the lattice, or is restricted to the material surface.

We study low-temperature phases and edge-state conductance of an interacting composite $(1+1/n)$ Abelian helical edge state made of a regular helical liquid carrying charge $e$ and a (fractionalized) helical liquid carrying charge $e/n$. A systematic framework is developed for these composite $(1+1/n)$ Abelian helical edge states with $n=1,2,3$, incorporating symmetry-allowed interaction and disorder. For $n=1$, the system is made of two regular helical Luttinger liquids. For $n=2$, the composite edge state consists of a regular helical Luttinger liquid and a fractional topological insulator (the Abelian $Z_4$ topological order) edge state arising from half-filled conjugated Chern bands. The composite edge state with $n=2$ is pertinent to the recent twisted ${\mathrm{MoTe}}_2$ experiment at ${\nu }_{\text{tot}}=3$, suggesting a possible fractional topological insulator with an edge-state conductance $\frac{3}{2}\frac{e^2}{h}$. For $n=3$, we consider a regular helical Luttinger liquid and a pair of time-reversal Laughlin $\nu =\frac{1}{3}$ fractional quantum Hall edge states. Using bosonization, we identify relevant perturbations and construct generic phase diagrams in the presence of weak Rashba spin-orbit coupling. In addition to a phase of free bosons, we find a time-reversal symmetry-breaking localized insulator, two perfect positive drag phases (due to different mechanisms), a perfect negative drag phase (for $n=2,3$), a time-reversal symmetric Anderson localization (only for $n=1$), and a disorder-dominated metallic phase analogous to the $\nu =\frac{2}{3}$ disordered fractional quantum Hall edges (only for $n=3$). We further compute the two-terminal edge-state conductance, the primary experimental characterization for the (fractional) topological insulator. Remarkably, the negative drag phase gives rise to an unusual edge-state conductance $(1-1/n)\frac{e^2}{h}$, which is not directly associated with the filling factor. We further investigate the effect of an applied in-plane magnetic field. For $n>1$, the applied magnetic field can result in a phase with localization only in the regular helical liquid channel, and the edge-state conductance is $\frac{1}{n}\frac{e^2}{h}$, providing another testable signature. Our work establishes a systematic understanding of the composite $(1+1/n)$ Abelian helical edge, paving the way for future experimental and theoretical studies.

Altermagnets feature vanishing net magnetization, like antiferromagnets, but exhibit time-reversal symmetry breaking and momentum-dependent spin-split band structures. Motivated by the fact that all proposed altermagnets have paramagnetic states with multiple magnetic ions in the unit cell, we develop a class of realistic minimal models for altermagnetism through a comparative analysis of the magnetic atom Wyckoff site symmetry and the space group symmetry. Specifically, we develop electronic models for all centrosymmetric space groups with magnetic atoms occupying inversion symmetric Wyckoff positions with multiplicity two. These forty models include monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic materials and describe $d$-wave, $g$-wave, and $i$-wave altermagnetism. We further define and examine an altermagnetic susceptibility and mean field instabilities within a Hubbard model to reveal that these models have altermagnetic ground states. We shed insight on why most altermagnets form in nonsymmorphic space groups. We also provide the symmetry-required form of the spin-orbit coupling and show it yields a Berry curvature that is linear in this coupling for all forty models. We apply our models to representative cases of ${\mathrm{RuO}}_2, {\mathrm{MnF}}_2, {\mathrm{FeSb}}_2, \kappa$-Cl, CrSb, and MnTe.