We consider the Kondo effect, arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the $C_3$ rotation symmetry, and we retain only the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) $\propto 1/\left[\left|\omega \right|{ln}^2\left(\mathrm{\Lambda }/\left|\omega \right|\right)\right]$ near the Dirac point $\omega \to 0$ even though the bulk density of states vanishes linearly. We study the resulting three-impurity multichannel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-$1/2$ doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity.

In iron-based superconductors, both nematic and magnetic fluctuations are expected to enhance superconductivity and may originate from a quantum critical point hidden beneath the superconducting dome. The behavior of the nonsuperconducting state can be an important piece of the puzzle, motivating, in this paper, the use of high magnetic fields to suppress superconductivity and measure the nematic susceptibility of the normal state at low temperatures. We describe experimental advances which make it possible to measure a resistive gauge factor (which is a proxy for the nematic susceptibility) in the field-induced normal state in a 65 T pulsed magnet, and report measurements of the gauge factor of a micromachined single crystal of $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.926}{\mathrm{Co}}_{0.074}\right)}_2{\mathrm{As}}_2$ at temperatures down to 1.2 K. The nematic susceptibility increases monotonically in the field-induced normal state as the temperature decreases, consistent with the presence of a quantum critical point nearby in composition.

The valence band electronic structure of a ${\mathrm{BaTiO}}_3$-derived oxide quasicrystal (OQC) is studied by photoemission using momentum microscopy. An upward-dispersive ${\mathrm{O}}_{2p}$ band is identified, and it can be assigned to a combination of in-plane orbitals according to the symmetry and the overlap of the wave functions. In addition, the signature of ${\mathrm{Ti}}_{3d}$ states near the Fermi level is observed, which results in a metallic character of the OQC with $3d^1$ occupation. Our experiments reveal two-dimensional electronic states within the OQC based on a symmetry-adapted decomposition of photoelectron intensity distribution in the momentum space.

In this work we explore the interplay between global symmetry and the mobility of quasiparticle excitations. We show that fractonic matter naturally appears in a three-dimensional $U\left(1\right)$ gauge theory, enriched by global $U\left(1\right)$ and translational symmetries, via the mechanism of anyonic spin-orbit coupling. We develop a systematic understanding of such symmetry-enforced mobility restrictions in terms of the classification of $U\left(1\right)$ gauge theories enriched by $U\left(1\right)$ and translational symmetries. We provide a unified construction of these phases by gauging layered symmetry-protected topological phases.

Magnon spintronics is a prosperous field that promises beyond-CMOS technology based on elementary excitations of the magnetic order that act as information carriers for future computational architectures. Unidirectional propagation of spin waves is key to the realization of magnonic logic devices. However, previous efforts to enhance the magnetostatic surface spin wave nonreciprocity did not realize (let alone control) purely unidirectional propagation. Here we experimentally demonstrate excitation of unidirectional exchange spin waves by a nanoscale magnetic grating consisting of Co nanowires fabricated on an ultrathin yttrium iron garnet film. We explain and model the nearly perfect unidirectional excitation by the chirality of the magneto-dipolar interactions between the Kittel mode of the nanowires and the exchange spin waves of the film. Reversal of the magnetic configurations of film and nanowire array from parallel to antiparallel changes the direction of the excited spin waves. Our results raise the prospect of a chiral magnonic logic without the need to involve fragile surface states.

We examine the interplay of symmetry and topological order in $2+1$-dimensional topological quantum phases of matter. We present a precise definition of the topological symmetry group $\text{Aut}\left(\mathcal{C}\right)$, which characterizes the symmetry of the emergent topological quantum numbers of a topological phase $\mathcal{C}$, and we describe its relation with the microscopic symmetry of the underlying physical system. This allows us to derive a general framework to characterize and classify symmetry fractionalization in topological phases, including phases that are non-Abelian and symmetries that permute the quasiparticle types and/or are antiunitary. We develop a theory of extrinsic defects (fluxes) associated with elements of the symmetry group, extending previous results in the literature. This provides a general classification of $2+1$-dimensional symmetry-enriched topological (SET) phases derived from a topological phase of matter $\mathcal{C}$ with on-site symmetry group $G$. We derive a set of data and consistency conditions, the solutions of which define the algebraic theory of the defects, known as a $G$-crossed braided tensor category ${\mathcal{C}}_G^{\times }$. This allows us to systematically compute many properties of these theories, such as the number of topologically distinct types of defects associated with each group element, their fusion rules, quantum dimensions, zero modes, braiding exchange transformations, a generalized Verlinde formula for the defects, and modular transformations of the $G$-crossed extensions of topological phases. We also examine the promotion of the global on-site symmetry to a local gauge invariance (“gauging the symmetry”), wherein the extrinsic $G$ defects are turned into deconfined quasiparticle excitations, which results in a different topological phase ${\left({\mathcal{C}}_G^{\times }\right)}^G$. We present systematic methods to compute the properties of ${\left({\mathcal{C}}_G^{\times }\right)}^G$ when $G$ is a finite group. The quantum phase transition between the topological phases ${\left({\mathcal{C}}_G^{\times }\right)}^G$ and $\mathcal{C}$ can be understood to be a “gauge symmetry breaking” transition, thus shedding light on the universality class of a wide variety of topological quantum phase transitions. A number of instructive and/or physically relevant examples are studied in detail.

The deconfined quantum critical point (DQCP) was originally proposed as a continuous transition between two spontaneous symmetry breaking phases in 2D spin-1/2 systems. While great efforts have been spent on the DQCP for 2D systems, both theoretically and numerically, ambiguities among the nature of the transition are still not completely clarified. Here we shift the focus to a recently proposed 1D incarnation of DQCP in a spin-1/2 chain. By solving it with the variational matrix product state in the thermodynamic limit, a continuous transition between a valence-bond solid phase and a ferromagnetic phase is discovered. The scaling dimensions of various operators are calculated and compared with those from field theoretical description. At the critical point, two emergent $\mathrm{O}\left(2\right)$ symmetries are revealed, and the associated conserved current operators with exact integer scaling dimensions are determined with scrutiny. Our findings provide the low-dimensional analog of DQCP where unbiased numerical results are in perfect agreement with the controlled field theoretical predictions and have extended the realm of the unconventional phase transition as well as its identification with the advanced numerical methodology.

We introduce and solve a model of interacting electrons and phonons that is a natural generalization of the Sachdev-Ye-Kitaev model and that becomes superconducting at low temperatures. In the normal state, two non-Fermi-liquid fixed points with distinct universal exponents emerge. At weak coupling, superconductivity prevents the onset of low-temperature quantum criticality, reminiscent of the behavior in several heavy-electron and iron-based materials. At strong coupling, pairing of highly incoherent fermions sets in deep in the non-Fermi-liquid regime, a behavior qualitatively similar to that in underdoped cuprate superconductors. The pairing of incoherent time-reversal partners is protected by a mechanism similar to Anderson's theorem for disordered superconductors. The superconducting ground state is characterized by coherent quasiparticle excitations and higher-order bound states thereof, revealing that it is no longer an ideal gas of Cooper pairs, but a strongly coupled pair fluid. The normal-state incoherency primarily acts to suppress the weight of the superconducting coherence peak and reduce the condensation energy. Based on this, we expect strong superconducting fluctuations, in particular at strong coupling.

Searching for a Kitaev spin liquid phase motivated intense research on the honeycomb iridate materials. However, access to a spin liquid ground state has been hindered by magnetic ordering. ${\mathrm{Cu}}_2{\mathrm{IrO}}_3$ is a new honeycomb iridate without thermodynamic signatures of a long-range order. Here, we use muon spin relaxation to uncover the magnetic ground state of ${\mathrm{Cu}}_2{\mathrm{IrO}}_3$. We find a two-component depolarization with slow- and fast-relaxation rates corresponding to distinct regions with dynamic and static magnetism coexisting in the material. X-ray absorption spectroscopy and first-principles calculations identify a mixed copper valence as the origin of this behavior. Our results suggest that a minority of ${\mathrm{Cu}}^{2+}$ ions nucleate regions of static magnetism, whereas the majority of ${\mathrm{Cu}}^{+}/{\mathrm{Ir}}^{4+}$ on the honeycomb lattice give rise to a Kitaev spin liquid.

The iron-based superconductors are characterized by strong fluctuations due to high transition temperatures and small coherence lengths. We investigate fluctuation behavior in the magnetic iron-pnictide superconductor $\mathrm{Rb}\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{As}}_4$ by calorimetry and transport. We find that the broadening of the specific-heat transition in magnetic fields is very well described by the lowest-Landau-level scaling. We report calorimetric and transport observations for vortex-lattice melting, which is seen as a sharp drop of the resistivity and a step of the specific heat at the magnetic-field-dependent temperature. The melting line in the temperature–magnetic field plane lies noticeably below the upper-critical-field line and its location is in quantitative agreement with theoretical predictions without fitting parameters. Finally, we compare the melting behavior of $\mathrm{Rb}\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{As}}_4$ with other superconducting materials showing that thermal fluctuations of vortices are not as prevalent as in the high-temperature superconducting cuprates, yet they still noticeably influence the properties of the vortex matter.

The eigenstate thermalization hypothesis (ETH) is a conjecture on the nature of isolated quantum systems that implies thermal behavior of subsystems when it is satisfied. ETH has been tested in various local many-body interacting systems. We examine the validity of ETH scaling in a class of nonlocal disordered many-body interacting systems—the Sachdev-Ye-Kitaev (SYK) Majorana models—that may be tuned from chaotic behavior to integrability. Our analysis shows that ${\mathrm{SYK}}_4$ (with quartic couplings), which is maximally chaotic in the large system size limit, satisfies the standard ETH scaling while ${\mathrm{SYK}}_2$ (with quadratic couplings), which is integrable, does not. We show that the low-energy and high-energy properties are drastically different when the two Hamiltonians are mixed, as a result of ${\mathrm{SYK}}_2$ being an RG relevant perturbation.

We present a generalization of free-fermionic topological insulators that are composed of topological subsystems of differing dimensionality. These topological subsystems of nonzero codimension are embedded within a trivial insulating environment. A general procedure is described to isolate and classify such embedded topological insulators and we present three representative examples in varying dimensions and symmetry classes. Moreover, we demonstrate with concrete examples that the presence of periodically placed embedded topological insulators in an otherwise trivially classified system can lead to topologically nontrivial physical phenomena on crystalline defects, namely, topological surface/edge modes at stacking faults and partial edge dislocations.

The layered van der Waals antiferromagnet ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ has been predicted to combine the band ordering of archetypical topological insulators such as ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ with the magnetism of Mn, making this material a viable candidate for the realization of various magnetic topological states. We have systematically investigated the surface electronic structure of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$(0001) single crystals by use of spin- and angle-resolved photoelectron spectroscopy experiments. In line with theoretical predictions, the results reveal a surface state in the bulk band gap and they provide evidence for the influence of exchange interaction and spin-orbit coupling on the surface electronic structure.

In the triangular layered magnet ${\mathrm{PdCrO}}_2$ the intralayer magnetic interactions are strong; however, the lattice structure frustrates interlayer interactions. In spite of this, long-range, ${120}^{\circ }$ antiferromagnetic order condenses at $T_N=38$ K. We show here through neutron scattering measurements under in-plane uniaxial stress and in-plane magnetic field that this occurs through a spontaneous breaking of the threefold rotational symmetry of the nonmagnetic lattice, which relieves the interlayer frustration. We also show through resistivity measurements that uniaxial stress can suppress thermal magnetic disorder within the antiferromagnetic phase.

The existence of surface electromagnetic waves in the dielectric-metal interface is due to the sign change of real parts of permittivity across the interface. In this work, we demonstrate that the interface constructed by two semi-infinite photonic crystals with different signs of the imaginary parts of permittivity also supports surface electromagnetic eigenmodes with real eigenfrequencies, protected by $\mathcal{PT}$ symmetry of the loss-gain interface. Using a multiple scattering method and full wave numerical methods, we show that the dispersion of such interface states exhibits unusual features such as zigzag trajectories or closed loops. To quantify the dispersion, we establish a non-Hermitian Hamiltonian model that can account for the zigzag and closed-loop behavior for arbitrary Bloch momentums. The properties of the interface states near the Brillouin zone center can also be explained within the framework of effective medium theory. It is shown that turning points of the dispersion are exceptional points (EPs), which are characteristic features of non-Hermitian systems. When the permittivity of photonic crystal changes, these EPs can coalesce into higher-order EPs or anisotropic EPs. These interface modes hence exhibit and exemplify many complex phenomena related to exceptional point physics.

We present a combined study of zero-field ${}^{51}\mathrm{V}$ and ${}^{127}\mathrm{I}$ NMR at ambient pressure and specific heat and magnetization measurements under pressure up to 2.08 GPa on bulk single crystals of the van der Waals ferromagnet ${\mathrm{VI}}_3$. At ambient pressure, our results consistently demonstrate that ${\mathrm{VI}}_3$ undergoes a structural transition at $T_s\approx 78\mathrm{K}$, followed by two subsequent ferromagnetic transitions at $T_{\mathrm{FM}1}\approx 50\mathrm{K}$ and $T_{\mathrm{FM}2}\approx 36\mathrm{K}$ upon cooling. At lowest temperature $\left(T<T_{\mathrm{FM}2}\right)$, two magnetically ordered V sites exist, whereas only one magnetically ordered V site is observed for $T_{\mathrm{FM}1}<T<T_{\mathrm{FM}2}$. Whereas $T_{\mathrm{FM}1}$ is almost unaffected by external pressure, $T_{\mathrm{FM}2}$ is highly responsive to pressure and merges with the $T_{\mathrm{FM}1}$ line at $p\approx 0.6\mathrm{GPa}$. At even higher pressures $\left(p\approx 1.25\mathrm{GPa}\right)$, the $T_{\mathrm{FM}2}$ line merges with the structural transition at $T_s$ which becomes moderately suppressed with $p$ for $p<1.25\mathrm{GPa}$. Taken together, our data point toward a complex magnetic structure and an interesting interplay of magnetic and structural degrees of freedom in ${\mathrm{VI}}_3$.

We report the dynamics of the cuprate superconductor $\mathrm{La}{}_{2-x}{\mathrm{Sr}}_x\mathrm{CuO}{}_4$ $(x=0.14)$ after intense photoexcitation utilizing near-infrared ($800\mathrm{nm}$) optical pump-terahertz probe spectroscopy. In the superconducting state at $5\mathrm{K}$, we observed a redshift of the Josephson plasma resonance that sustains for hundreds of picoseconds after the photoexcitation, indicating the destruction of the $c$-axis superconducting coherence. We show that the metastable spectral features can be described by the photoinduced surface heating of the sample. We also demonstrate that the conventional analysis used to extract the spectra of the photoexcited surface region can give rise to artifacts in the nonequilibrium response.

Here we report the evolution of structural, magnetic, and transport properties in ${\mathrm{MnBi}}_{2-x}{\mathrm{Sb}}_x{\mathrm{Te}}_4\left(0\le x\le 2\right)$ single crystals. ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$, isostructural to ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, is successfully synthesized in single-crystal form. Magnetic measurements suggest an antiferromagnetic order below $T_N=19\mathrm{K}$ for ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$ with the magnetic moments aligned along the crystallographic $c$ axis. With increasing Sb content in ${\mathrm{MnBi}}_{2-x}{\mathrm{Sb}}_x{\mathrm{Te}}_4$, the $a$-lattice parameter decreases linearly following Vegard's law, while the $c$-lattice parameter shows little compositional dependence. The contraction along $a$ is caused by the reduction of the Mn-Te-Mn bond angle, while the Mn-Te bond length remains nearly constant. The antiferromagnetic ordering temperature slightly decreases from 24 K for ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ to 19 K for ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$. More dramatic change was observed for the critical magnetic fields required for the spin-flop transition and the moment saturation. Both critical fields decrease with increasing Sb content for $x\le 1.72$; a spin-flip transition occurs in ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$ at a small field of 3 kOe applied along the $c$ axis. In high magnetic fields, the saturation moment at 2 K shows significant suppression from $3.56{\mu }_B/\mathrm{Mn}$ for ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ to $1.57{\mu }_B/\mathrm{Mn}$ for ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$. Analysis of the magnetization data suggests that both the interlayer magnetic interaction and single-ion anisotropy decrease with increasing Sb content for $x\le 1.72$. The partial substitution of Bi by Sb also dramatically affects the transport properties. A crossover from $n$-type to $p$-type conducting behavior is observed around $x\approx 0.63$. Our results show close correlation between structural, magnetic, and transport properties in ${\mathrm{MnBi}}_{2-x}{\mathrm{Sb}}_x{\mathrm{Te}}_4$ and that partial substitution of Bi by Sb is an effective approach to fine tuning both the magnetism and transport properties of ${\mathrm{MnBi}}_{2-x}{\mathrm{Sb}}_x{\mathrm{Te}}_4$.

The exciton polariton (EP) is a half-light and half-matter quasiparticle that is promising for exploring both fundamental quantum phenomena as well as photonic applications. Van der Waals materials, such as transition-metal dichalcogenide (TMD), emerge as a promising nanophotonics platform due to its support of long propagative EPs even at room temperature. However, real-space studies have been limited to bulk crystal waveguides with a thickness no less than 60 nm. Here we report the nano-optical imaging of the transverse-electric EPs in ${\mathrm{WSe}}_2$ nanoflakes down to a few atomic layers, which can be turned on and off by tuning the polarization state of the excitation laser. Unlike previously studied transverse-magnetic modes that exist only in bulk TMD waveguides, we found that the transverse-electric EPs could reside in ultrathin ${\mathrm{WSe}}_2$ samples, owing to the alignment of the electric field with the in-plane dipole orientation of two-dimensional excitons. Furthermore, we show that the EP wavelength and propagation length can be largely controlled by varying laser energy and sample thickness. These findings open opportunities to realize near-infrared polaritonic devices and circuits truly at the atomically thin limit.

We report a study on the magnetotransport properties and on the Fermi surfaces (FS) of ZrSi(Se,Te) semimetals. Density-functional theory (DFT) calculations, in absence of spin orbit coupling (SOC), reveal that both the Se and the Te compounds display Dirac nodal lines (DNL) close to the Fermi level ${\varepsilon }_F$ at symmorphic and nonsymmorphic positions, respectively. We find that the geometry of their FSs agrees well with DFT predictions. ZrSiSe displays low residual resistivities, pronounced magnetoresistivity, high carrier mobilities, and a butterflylike angle-dependent magnetoresistivity (AMR), although its DNL is not protected against gap opening. As in ${\mathrm{Cd}}_3{\mathrm{As}}_2$, its transport lifetime is found to be ${10}^2$ to ${10}^3$ times larger than its quantum one. ZrSiTe, which possesses a protected DNL, displays conventional transport properties. Our evaluation indicates that both compounds most likely are topologically trivial. Nearly angle-independent effective masses with strong angle-dependent quantum lifetimes lead to the butterfly AMR in ZrSiSe