We examine the low frequency spin susceptibility of the paramagnetic phase of the quantum Ising chain in a transverse field at temperatures well below the energy gap. We find that the imaginary part is dominated by rare quantum processes in which the number of quasiparticles changes by an odd number. We obtain exact results for the NMR relaxation rate in the low temperature limit for the integrable model with nearest-neighbor Ising interactions, and derive exact universal scaling results applicable to generic Ising chains near the quantum critical point. These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system ${\mathrm{CoNb}}_2{\mathrm{O}}_6$.

We report on high-field magnetotransport ($B$ up to 35 T) on a gated superlattice based on single-layer graphene aligned on top of hexagonal boron nitride. The large-period moiré modulation ($\approx 15$ nm) enables us to access the Hofstadter spectrum in the vicinity of and above one flux quantum per superlattice unit cell ($\mathrm{\Phi }/{\mathrm{\Phi }}_0=1$ at $B=22$ T). We thereby reveal, in addition to the spin-valley antiferromagnet at $\nu =0$, two insulating states developing in positive and negative effective magnetic fields from the main $\nu =1$ and $\nu =-2$ quantum Hall states, respectively. We investigate the field dependence of the energy gaps associated with these insulating states, which we quantify from the temperature-activated peak resistance. Referring to a simple model of local Landau quantization of third-generation Dirac fermions arising at $\mathrm{\Phi }/{\mathrm{\Phi }}_0=1$, we describe the different microscopic origins of the insulating states and experimentally determine the energy-momentum dispersion of the emergent gapped Dirac quasiparticles.

In this work, we examine the topological phases that can arise in triangular lattices with disconnected elementary band representations. We show that, although these phases may be “fragile” with respect to the addition of extra bands, their topological properties are manifest in certain nontrivial holonomies (Wilson loops) in the space of nontrivial bands. We introduce an eigenvalue index for fragile topology, and we show how a nontrivial value of this index manifests as the winding of a hexagonal Wilson loop; this remains true even in the absence of time-reversal or sixfold rotational symmetry. Additionally, when time-reversal and twofold rotational symmetry are present, we show directly that there is a protected nontrivial winding in more conventional Wilson loops. Crucially, we emphasize that these Wilson loops cannot change without closing a gap to the nontrivial bands. By studying the entanglement spectrum for the fragile bands, we comment on the relationship between fragile topology and the “obstructed atomic limit” of Bradlyn et al. [Nature (London) 547, 298 (2017)]. We conclude with some perspectives on topological matter beyond the K-theory classification.

Studying the prototypical ferromagnetic superconductor ${\mathrm{UGe}}_2$ we demonstrate the potential of the modulated intensity by zero effort (MIEZE) technique—a novel neutron spectroscopy method with ultrahigh energy resolution of at least $1\mu \mathrm{eV}$—for the study of quantum matter. We reveal purely longitudinal spin fluctuations in ${\mathrm{UGe}}_2$ with a dual nature arising from $5f$ electrons that are hybridized with the conduction electrons. Local spin fluctuations are perfectly described by the Ising universality class in three dimensions, whereas itinerant spin fluctuations occur over length scales comparable to the superconducting coherence length, showing that MIEZE is able to spectroscopically disentangle the complex low-energy behavior characteristic of quantum materials.

Surface-modulated magnonic crystals are the natural link between continuous films with sinusoidal spin-wave eigenmodes and one-dimensional magnonic crystals composed of individual nanowires. Nevertheless, the transformation process of the spin-wave modes in this transition remains unclear. Here, spin-wave modes in their entire transition from a flat film to a “full” (one-dimensional) magnonic crystal are studied by ferromagnetic resonance (FMR) and micromagnetic simulations. For this purpose, the surface of a prepatterned thin permalloy film was sequentially ion milled resulting in hybrid structures, referred to as surface-modulated magnonic crystals, with increasing modulation depth. After each step, FMR measurements were carried out in backward-volume and Damon-Eshbach geometry. The evolution of each spin-wave resonance is studied together with the corresponding mode profile obtained by micromagnetic simulations. Simple rules describing the transition of the modes from the film to the modes of the full magnonic crystal are provided, unraveling the complexity of spin-wave states in these hybrid systems.

We study the emission of individual quantum dots in CdTe/ZnTe samples doped with a low concentration of Cr. In addition to dots with a photoluminescence (PL) split by the exchange interaction with a magnetic Cr atom, we observe another type of dots with a complex PL structure composed of a minimum of six lines on the exciton and biexciton and three lines on the charged excitons. In these dots, the linear polarization dependence and the magnetic field dependence of the PL behave like three similar quantum dots emitting at slightly different energies. Cross-correlation intensity measurements show that these emission lines are not independent but exchange intensities in a timescale of a few hundred nanoseconds depending on the optical excitation power. We attribute this PL structure to charge fluctuations of a Cr atom located in the vicinity the CdTe dots in the ZnTe barrier. We present a model which confirms that the presence of a single charge fluctuating between −e (${\mathrm{Cr}}^{+}$), 0 (${\mathrm{Cr}}^{2+}$), and +e (${\mathrm{Cr}}^{3+}$) and located a few nm away from the dot explains the observation of three emission energies. We finally show that the interaction between the confined carriers and the nearby fluctuating localized charge can be modified by an applied static electric field which modulates the splitting of the emission lines.

We study a topological band degeneracy in non-Hermitian systems with parity-time ($\mathcal{P}\mathcal{T}$) and parity-particle-hole ($CP$) symmetries. In $d$-dimensional non-Hermitian systems, it is shown that $(d-1)$-dimensional exceptional surfaces can appear from band touching thanks to $\mathcal{P}\mathcal{T}$ or $CP$ symmetry. We investigate the topological stability and zero-gap quasiparticles for the exceptional surfaces due to the band degeneracy. We also demonstrate the band degeneracy by using lattice models of a topological semimetal and a superconductor.

Non-Hermitian (NH) Hamiltonians have become an important asset for the effective description of various physical systems that are subject to dissipation. Motivated by recent experimental progress on realizing the NH counterparts of gapless phases such as Weyl semimetals, here we investigate how NH symmetries affect the occurrence of exceptional points (EPs), that generalize the notion of nodal points in the spectrum beyond the Hermitian realm. Remarkably, we find that the dimension of the manifold of EPs is generically increased by one as compared to the case without symmetry. This leads to nodal surfaces formed by EPs that are stable as long as a protecting symmetry is preserved, and that are connected by open Fermi volumes. We illustrate our findings with analytically solvable two-band lattice models in one and two spatial dimensions, and show how they are readily generalized to generic NH crystalline systems.

Many-body-localized (MBL) systems do not thermalize under their intrinsic dynamics. The athermality of MBL, we propose, can be harnessed for thermodynamic tasks. We illustrate this ability by formulating an Otto engine cycle for a quantum many-body system. The system is ramped between a strongly localized MBL regime and a thermal (or weakly localized) regime. The difference between the energy-level correlations of MBL systems and of thermal systems enables mesoscale engines to run in parallel in the thermodynamic limit, enhances the engine's reliability, and suppresses worst-case trials. We estimate analytically and calculate numerically the engine's efficiency and per-cycle power. The efficiency mirrors the efficiency of the conventional thermodynamic Otto engine. The per-cycle power scales linearly with the system size and inverse-exponentially with a localization length. This work introduces a thermodynamic lens onto MBL, which, having been studied much recently, can now be considered for use in thermodynamic tasks.

Various device-based experiments have indicated that electron transfer in certain chiral molecules may be spin dependent, a phenomenon known as the chiral induced spin selectivity (CISS) effect. However, due to the complexity of these devices and a lack of theoretical understanding, it is not always clear to what extent the chiral character of the molecules actually contributes to the magnetic-field-dependent signals in these experiments. To address this issue, we report here an electron transmission model that evaluates the role of the CISS effect in two-terminal and multiterminal linear-regime electron transport experiments. Our model reveals that for the CISS effect, the chirality-dependent spin transmission is accompanied by a spin-flip electron reflection process. Furthermore, we show that more than two terminals are required in order to probe the CISS effect in the linear regime. In addition, we propose two types of multiterminal nonlocal transport measurements that can distinguish the CISS effect from other magnetic-field-dependent signals. Our model provides an effective tool to review and design CISS-related transport experiments, and to enlighten the mechanism of the CISS effect itself.

Spin interactions of magnetic impurities mediated by conduction electrons is one of the most interesting and potentially useful routes to ferromagnetism in condensed matter. In recent years, such systems have received renewed attention due to the advent of materials in which Dirac electrons are the mediating particles, with prominent examples being graphene and topological insulator surfaces. In this paper, we demonstrate that such systems can host a remarkable variety of behaviors, in many cases controlled only by the density of electrons in the system. Uniquely characteristic of these systems is an emergent long-range form of the spin stiffness when the Fermi energy $\mu$ resides at a Dirac point, becoming truly long-range as the magnetization density becomes very small. It is demonstrated that this leads to screened Coulomb-like interactions among domain walls, via a subtle mechanism in which the topology of the Dirac electrons plays a key role: the combination of attraction due to bound in-gap states that the topology necessitates and repulsion due to scattering phase shifts yields logarithmic interactions over a range of length scales. We present detailed results for the bound states in a particularly rich system, a topological crystalline insulator surface with three degenerate Dirac points and one energetically split off. This system allows for distinct magnetic ground states, which are either twofold or sixfold degenerate, with either short-range or emergent long-range interactions among the spins in both cases. Each of these regimes is accessible, in principle, by tuning the surface electron density via a gate potential. A study of the Chern number associated with different magnetic ground states leads to predictions for the number of in-gap states that different domain walls should host, which we demonstrate using numerical modeling are precisely borne out. The nonanalytic behavior of the stiffness on magnetization density is shown to have a strong impact on the phase boundary of the system and opens a pseudogap regime within the magnetically ordered region. We thus find that the topological nature of these systems, through its impact on domain wall excitations, leads to unique behaviors distinguishing them markedly from their nontopological analogs.

The high-pressure magnetic properties of the iodo-substituted bisdiselenazolyl radical ferromagnet IBPSSEt have been studied by vibrating-coil SQUID magnetometry. The magnetic state at a pressure ($P$) of approximately 2 GPa has the highest Curie temperature ($T_{\mathrm{C}}$) of 27.5 K, and displays an ideal three-dimensional (3D) ferromagnetic interaction network. The value of $T_{\mathrm{C}}$ observed by ac magnetic susceptibility measurements is consistent with that obtained from dc measurements below approximately 4 GPa. Field-cooled dc measurements at more elevated pressures reveal a slow evolution of magnetic ordering, so that at $P>6$ GPa the structure may be described in terms of a 1D ferromagnetic chain with predominantly antiferromagnetic lateral (interchain) interactions, in accord with the results of density functional theory calculations.

High-order topological insulators are a recent development extending the topological theory of charge polarization to higher multipole moments. In these systems, the presence of a nontrivial $n$-dimensional bulk results in boundary modes of a dimension $n-2$ or lower. Since their theoretical proposal, several experimental realizations of high-order topological insulators have been reported. However, high-order topological transitions have not been observed. In this Rapid Communication, we report on the observation of a high-order topological transition in a quadrupole topological insulator implemented in an LC circuit with nonlinear couplings. This system presents the ability to confine electromagnetic energy in its corner states, with a localization length that can be tuned over a broad range through the use of an external bias voltage. Additionally, we provide an experimental characterization and an effective theory for the boundary states, further corroborating their topological nature by direct measurement of the winding number.

Weakly bound systems, like noble-gas dimers or two-dimensional layered materials (graphite, hexagonal boron nitride, or transition-metal dichalcogenides), exhibit excited electronic states of a particular nature. These so-called exciplex states combine on-site (or intralayer) and charge-transfer (or interlayer) configurations in a well-balanced way. We show by ab initio many-body perturbation theory that the energy and composition of the exciplex states depend sensitively on the bond length or interlayer distance of the material. When the constituents approach each other, the charge-transfer contribution increases and the excitation is redshifted to lower energy. If the system is excited into the exciplex state, then a covalent-like bond results. In consequence, noble-gas dimers form excimer complexes, while layered materials exhibit interlayer contraction.

Following the recent success of realizing exciton-polariton condensates in cavities, we examine the hybridization of cavity photons with the closest analog of excitons within a superconductor, states called Bardasis-Schrieffer modes. Although these modes do not typically couple linearly to light, one can engineer a coupling with an externally imposed supercurrent, leading to the formation of hybridized Bardasis-Schrieffer-polariton states, which we obtain both as poles of the bosonic Green's function and through the derivation of an effective Hamiltonian picture for the model. These new excitations have nontrivial overlap with both the original photon states and $d$-wave superconducting fluctuations. We conjecture that a phase-coherent density of these objects could produce a finite $d$-wave component of the superconducting order parameter—an $s\pm id$ superconducting state.

Topological semimetals, extending the topological classification from insulators to metals, have greatly enriched our understanding of topological states in condensed matter. This is particularly true for topological nodal-line semimetals (TNLSs). In the present paper, we identify layered materials as promising candidates for hosting TNLSs. Based on first-principles calculations and effective model analysis, we propose that layered ferromagnetic rare-earth-metal monohalides LnX (Ln = La, Gd; X = Cl, Br) exhibit long pursued topological phases. Specifically, single-layer LaX and single-layer GdX are ideal two-dimensional (2D) Weyl semimetals and large-gap 2D quantum anomalous Hall insulators (QAHIs), with band gaps up to 61 meV, respectively. In addition, 3D LaX and 3D GdX are TNLSs with a pair of mirror-symmetry protected nodal lines and 3D QAHIs, respectively. The nodal lines in 3D LaX extending through the whole Brillouin zone (BZ) are fairly robust against strong spin-orbit coupling (SOC) and located close to the Fermi level, providing a novel platform toward exploring the exotic properties in nodal-line fermions as well as related device designs.

We study the band structure of twinned and detwinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ using angle-resolved photoemission spectroscopy. The combination of measurements in the ordered and normal states along four high-symmetry momentum directions $\mathrm{\Gamma }$/$Z\text{−}X/Y$ enables us to identify the complex reconstructed band structure in the ordered state in great detail. We clearly observe the nematic splitting of the $d_{xz}$ and $d_{yz}$ orbitals as well as folding due to magnetic order with a wave vector of $(\pi ,\pi ,\pi )$. We are able to assign all observed bands. In particular we suggest an assignment of the electron bands different from previous reports. The high-quality spectra allow us to achieve a comprehensive understanding of the band structure of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$.

The thermal Hall conductance is a universal and topological property which characterizes the fractional quantum Hall (FQH) state. The quantized value of the thermal Hall conductance has only recently been measured experimentally in integer quantum Hall (IQH) and FQH regimes, however, the existing setup is not able to detect if the thermal current is counterpropagating or copropagating with the charge current. Furthermore, although there is experimental evidence for heat transfer between the edge modes and the bulk, the current theories do not take this dissipation effect into consideration. In this Rapid Communication, we construct phenomenological rate equations for the heat currents which include equilibration processes between the edge modes and energy dissipation to an external thermal bath. Solving these equations in the limit where the temperature bias is small, we compute the temperature profiles of the edge modes in a FQH state, from which we infer the two-terminal thermal conductance of the state as a function of the coupling to the external bath. We show that the two-terminal thermal conductance depends on the coupling strength, and can be nonuniversal when this coupling is very strong. Furthermore, we propose an experimental setup to examine this theory, which may also allow the determination of the sign of the thermal Hall conductance.

We investigate the dc resistivity and Hall effect of the quasi-two-dimensional organic materials $\kappa –{\left(\mathrm{ET}\right)}_{2}X$, where $X={\mathrm{Ag}}_2{\left(\mathrm{CN}\right)}_3$ and $\text{B}{\left(\mathrm{CN}\right)}_4$ and compare them with the results for $X={\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$. All three compounds are considered to be quantum-spin-disordered Mott insulators. Despite high similarities in chemical composition and crystal structure, large differences in the dc resistivity and Hall coefficient are found. While around room temperature the dc transport properties are dominantly determined by the strength of the electron correlations, upon reducing the temperature, dc transport happens by hopping due to inherent disorder. The most disordered compound with $X={\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$ turns out to have the lowest dc resistivity and the highest charge carrier density, i.e., in the phase diagram it is located closest to the metal-insulator transition. The least disordered compound with $X=\text{B}{\left(\mathrm{CN}\right)}_4$ shows the highest resistivity and the lowest carrier density, i.e., lies farthest from the metal-insulator transition. We explain such counterintuitive behavior within the theory of Mott-Anderson localization as a consequence of disorder-induced localized states within the correlation gap.

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes $N$ below the correlation volume $N_{\xi }$ and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length $\xi \sim ln{N}_{\xi }$ that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast “diffusion,” which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. Spectral correlations in the delocalized phase near the transition are characterized by level number variance ${\mathrm{\Sigma }}_2\left(\omega \right)$ crossing over, with increasing frequency $\omega$, from ergodic behavior ${\mathrm{\Sigma }}_2=\left(2/{\pi }^2\right)ln\omega /\mathrm{\Delta }$ to ${\mathrm{\Sigma }}_2\propto {\omega }^2$ at ${\omega }_c\sim {\left(N{N}_{\xi }\right)}^{-1/2}$ and finally to Poissonian behavior ${\mathrm{\Sigma }}_2=\omega /\mathrm{\Delta }$ at ${\omega }_{\xi }\sim N_{\xi }^{-1}$. We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate $d\to \infty$ limit of the Anderson model in $d$ spatial dimensions.