Using complementary polarized and unpolarized single-crystal neutron diffraction, we have investigated the temperature-dependent magnetic structures of ${\mathrm{Eu}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{Fe}}_2{\mathrm{As}}_2$. Upon 50% dilution of the Eu sites with isovalent ${\mathrm{Ca}}^{2+}$, the Eu sublattice is found to be still long-range ordered below $T_{\text{Eu}}=10$ K, in the $A$-type antiferromagnetic (AFM) structure. The moment size of ${\mathrm{Eu}}^{2+}$ spins is estimated to be as large as $6.74\left(4\right){\mu }_B$ at 2.5 K. The Fe sublattice undergoes a spin-density-wave transition at $T_{\text{SDW}}=192\left(2\right)$ K and displays an in-plane AFM structure above $T_{\text{Eu}}$. However, at 2.5 K, the ${\mathrm{Fe}}^{2+}$ moments are found to be ordered in a canted AFM structure with a canting angle of $14{\left(4\right)}^{\circ }$ out of the $ab$ plane. The spin reorientation of Fe below the AFM ordering temperature of Eu provides direct evidence of a strong interplay between the two magnetic sublattices in ${\mathrm{Eu}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{Fe}}_2{\mathrm{As}}_2$.

We study the dc conductivity of iron-based superconductors within the orbital-selective spin fluctuation scenario. Within this approach, the anisotropy of spin fluctuations below the spin-nematic transition at $T_S$ is also responsible for the orbital ordering, induced by nematic self-energy corrections to the quasiparticle dispersion. As a consequence, the anisotropy of the dc conductivity below $T_S$ is determined not only by the anisotropy of the scattering rates as expected within a spin-nematic scenario, but also by the modification of the Fermi velocity due to the orbital reconstruction. More interestingly, it turns out that these two effects contribute to the dc-conductivity anisotropy with opposite signs. By using realistic band-structure parameters we compute the conductivity anisotropy for both 122 and FeSe compounds, discussing the possible origin of the different dc-conductivity anisotropy observed experimentally in these two families of iron-based superconductors.

We study novel three-dimensional gapped quantum phases of matter which support quasiparticles with restricted mobility, including immobile “fracton” excitations. So far, most existing fracton models may be instructively viewed as generalized Abelian lattice gauge theories. Here, by analogy with Dijkgraaf-Witten topological gauge theories, we discover a natural generalization of fracton models, obtained by twisting the gauge symmetries. Introducing generalized gauge transformation operators carrying an extra phase factor depending on local configurations, we construct a plethora of exactly solvable three-dimensional models, which we dub “twisted fracton models.” A key result of our approach is to demonstrate the existence of rich non-Abelian fracton phases of distinct varieties in a three-dimensional system with finite-range interactions. For an accurate characterization of these novel phases, the notion of being inextricably non-Abelian is introduced for fractons and quasiparticles with one-dimensional mobility, referring to their new behavior of displaying braiding statistics that is, and remains, non-Abelian regardless of which quasiparticles with higher mobility are added to or removed from them. We also analyze these models by embedding them on a 3-torus and computing their ground-state degeneracies, which exhibit a surprising and novel dependence on the system size in the non-Abelian fracton phases. Moreover, as an important advance in the study of fracton order, we develop a general mathematical framework which systematically captures the fusion and braiding properties of fractons and other quasiparticles with restricted mobility.

Two-dimensional materials are ideal platforms to explore new physical phenomena and reveal unique optical properties. Excitonic and quasiparticle effects are strongly enhanced by the reduced screening. The response to a perturbing electromagnetic field is dominated by in-plane light polarization. The quantum confinement of the atomic sheets in normal direction also allows out-of-plane pair excitations, which are ruled by selection rules and local-field effects. We apply the GW approximation and the Bethe-Salpeter equation to investigate optical transitions for light polarization both parallel and normal to the atomic planes. Prototypical systems range from semimetals to large-gap insulators such as graphene, graphene oxide, boron nitride, and molybdenum disulfide. For the considered materials, the out-of-plane absorption edge and the first van Hove singularities are blueshifted in dependence of the effective sheet thickness, while the intensity of the optical conductivity is reduced by orders of magnitude.

We have theoretically investigated the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in Weyl semimetals (WSMs) with tilted dispersion in the framework of the Matsubara Green's function. It is shown that there emerges a sharp peak or dip of the RKKY interaction at the phase boundary, which can unambiguously characterize the phase transition from type-I to type-II WSMs. Distinct responses of the RKKY interaction to the tilted parameter $A$ in two phases are revealed to distinguish different Weyl phases. Moreover, we find that a nonzero Dzyaloshinskii-Moriya term survives even for Fermi energy at the Weyl points, which is completely contributed by the tilting effect and is distinguished from the previous mechanism. Consequently, the RKKY interaction provides richer signatures superior to usual conductivity to probe Weyl phases with tilted dispersion since it involves a contribution from both the Fermi surface and the Fermi sea. We have performed an analysis with both the analytical formula and numerical calculations.

We study the effect of electron-acoustic phonon interactions in twisted bilayer graphene on resistivity in the high-temperature transport and superconductivity in the low-temperature phase diagram. We theoretically show that twisted bilayer graphene should have an enhanced and strongly twist-angle dependent linear-in-temperature resistivity in the metallic regime with the resistivity magnitude increasing as the twist angle approaches the magic angle. The slope of the resistivity versus temperature could approach one hundred ohm per kelvin with a strong angle dependence, but with a rather weak dependence on the carrier density. This higher-temperature density-independent linear-in-$T$ resistivity crosses over to a $T^4$ dependence at a low density-dependent characteristic temperature, becoming unimportant at low temperatures. This angle-tuned resistivity enhancement arises from the huge increase in the effective electron-acoustic phonon coupling in the system due to the suppression of graphene Fermi velocity induced by the flat-band condition in the moiré superlattice system. Our calculated temperature dependence is reminiscent of the so-called “strange metal” transport behavior except that it is arising from the ordinary electron-phonon coupling in a rather unusual parameter space due to the generic moiré flat-band structure of twisted bilayer graphene. We also show that the same enhanced electron-acoustic phonon coupling also mediates effective attractive interactions in $s,p,d$, and $f$ pairing channels with a theoretical superconducting transition temperature on the order of $\sim 5$ K near magic angle. The fact that ordinary acoustic phonons can produce exotic non-$s$-wave superconducting pairing arises from the unusual symmetries of the system.

Layered transition metal dichalcogenides (TMDCs) host a variety of strongly bound exciton complexes that control the optical properties in these materials. Apart from spin and valley, layer index provides an additional degree of freedom in a few-layer-thick film. Here we show that in a few-layer TMDC film, the wave functions of the conduction and valence-band-edge states contributing to the $K$ ($K^{\prime }$) valley are spatially confined in the alternate layers––giving rise to direct (quasi-)intralayer bright exciton and lower-energy interlayer dark excitons. Depending on the spin and valley configuration, the bright-exciton state is further found to be a coherent superposition of two layer-induced states, one (E type) distributed in the even layers and the other (O type) in the odd layers. The intralayer nature of the bright exciton manifests as a relatively weak dependence of the exciton binding energy on the thickness of the few-layer film, and the binding energy is maintained up to 50 meV in the bulk limit––which is an order of magnitude higher than conventional semiconductors. Fast Stokes energy transfer from the intralayer bright state to the interlayer dark states provides a clear signature in the layer-dependent broadening of the photoluminescence peak, and plays a key role in the suppression of the photoluminescence intensity observed in TMDCs with thickness beyond a monolayer.

We employ a minimal atomistic friction model to investigate the commensuration at interfaces when a large number of atoms are involved. As the normal load at the interface increases, we found a smooth transition from the ultralow friction (superlubricity) regime to the high-frictional motion via a gradual growth of the commensurate region where only a fraction of the atoms adjust their atomic arrangement according to the substrate surface potential. The center of mass of the sliding particle may lack the perfect periodicity of the conventional stick-slip motion in this partial commensuration state. The commensurate region is assigned as the effective contact, based on which the scaling behavior of friction can be explained in analogy to the classical Amontons law of friction. The revealed emergent state for large atomic sliders would be beneficial to studies on extending the fundamental frictional investigations to larger length scales.

We report the finding of the analogous valley Hall effect in phononic systems arising from mirror symmetry breaking, in addition to spatial inversion symmetry breaking. We study topological phases of plates and spring-mass models in kagome and modified kagome arrangements. By breaking the inversion symmetry it is well known that a defined valley Chern number arises. We also show that effectively, breaking the mirror symmetry leads to the same topological invariant. Based on the bulk-edge correspondence principle, protected edge states appear at interfaces between two lattices with different valley Chern numbers. By means of a plane wave expansion method and the multiple scattering theory for periodic and finite systems, respectively, we computed the Berry curvature, the band inversion, mode shapes, and edge modes in plate systems. We also find that appropriate multipoint excitations in finite system gives rise to propagating waves along a one-sided path only.

The existence of a quantum butterfly effect in the form of exponential sensitivity to small perturbations has been under debate for a long time. Lately, this question has gained increased interest due to the proposal to probe chaotic dynamics and scrambling using out-of-time-order correlators. In this work we study echo dynamics in the Sachdev-Ye-Kitaev model under effective time reversal in a semiclassical approach using the truncated Wigner approximation, which accounts for nonvanishing quantum fluctuations that are essential for the dynamics. We demonstrate that small imperfections introduced in the time-reversal procedure result in an exponential divergence from the perfect echo, which allows us to identify a Lyapunov exponent ${\lambda }_L$. In particular, we find that ${\lambda }_L$ is twice the Lyapunov exponent of the semiclassical equations of motion. This behavior is attributed to the growth of an out-of-time-order double commutator that resembles an out-of-time-order correlator.

We theoretically address the problem of cubic B20 helimagnets with a small concentration $c\ll 1$ of defect bonds in external magnetic field $\mathbf{H}$, which is relevant to mixed B20 compounds at small dopant concentrations. We assume that the Dzyaloshinskii-Moriya interaction and the exchange coupling constant are changed on imperfect bonds which leads to distortion of the conical spiral ordering. In a one-impurity problem we find that the distortion of the spiral pitch is long ranged and it is governed by the Poisson equation for an electric dipole. The variation of the cone angle is described by the screened Poisson equation for two electric charges with the screening length being of the order of the spiral period. We calculate corrections to the spiral vector and to the cone angle at finite $c$. The correction to the spiral vector is shown to be independent of $H$. We demonstrate that diffuse neutron scattering caused by disorder appears in the elastic cross section as power-law decaying tails centered at magnetic Bragg peaks.

We studied the transport of ${}^4\mathrm{He}$ atoms through 2.5-mm-thick solid ${}^4\mathrm{He}$ samples sandwiched between two superfluid leads with five different tailor-made sample cells. Measurements in a cell with a barrier at the center of the solid samples and in a cell filled with silica aerogel establish the causal relation between the observed mass flow and the dislocation network in the solid sample. Comparing the results from these cells and prior measurements on solid samples with thicknesses of 2 cm and $8\mu \mathrm{m}$ reveals that the mass flow rate decreases logarithmically with the thickness of the solid ${}^4\mathrm{He}$. Interestingly, the mass flow exhibits both superfluid and bosonic Luttinger liquid characteristics at low temperature.

Within the ground-state auxiliary-field quantum Monte Carlo technique, we introduce discrete Hubbard-Stratonovich transformations (HSTs) that are also suitable for spatially inhomogeneous trial functions. The discrete auxiliary fields introduced here are coupled to local spin or charge operators fluctuating around their Hartree-Fock values. The formalism can be considered a generalization of the discrete HSTs by J. E. Hirsch [Phys. Rev. B 28, 4059 (1983)] or a compactification of the shifted-contour auxiliary-field Monte Carlo formalism by N. Rom et al. [Chem. Phys. Lett. 270, 382 (1997)]. An improvement of the acceptance ratio is found for a real auxiliary field, while an improvement of the average sign is found for a purely imaginary auxiliary field. Efficiencies of the different HSTs are tested in the single-band Hubbard model at and away from half filling by studying the staggered magnetization and energy expectation values, respectively.

We study theoretically spontaneous currents and magnetic field induced in a superconductor-ferromagnet (S-F) bilayer due to direct and inverse proximity effects. There are two types of contributions to the induced currents. One is the Meissner current, which appears even in the absence of an external magnetic field due to the magnetic moment in the ferromagnet and to the magnetization in the superconductor. The second contribution is due to a space-dependent magnetization in the superconductor which is induced by the inverse proximity effect over a distance of the order of the superconducting correlation length ${\xi }_S$. In contrast, the magnetic induction $B$, caused by the Meissner currents, penetrates the S film over the London length ${\lambda }_S$. Even though ${\lambda }_S$ usually considerably exceeds the correlation length, the amplitude and sign of $B$ at distances much larger than ${\xi }_S$ depend crucially on the strength of the exchange energy in the ferromagnet and on the magnetic moment induced in the S layer.

Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong density wave fluctuations in two dimensions. While the weak-coupling theory finds the fully gapped chiral state to be energetically stable, we show that strong density wave fluctuations result in an additional contribution to the free energy of a superconductor with multicomponent order parameters, which generally favors nematic superconductivity. Our theory sheds light on the recent observation of rotational symmetry breaking in the superconducting state of twisted bilayer graphene.

Due to the intrinsic complexity of the quantum many-body problem, quantum Monte Carlo algorithms and their corresponding Monte Carlo configurations can be defined in various ways. Configurations corresponding to few Feynman diagrams often lead to severe sign problems. On the other hand, computing the configuration weight becomes numerically expensive in the opposite limit in which many diagrams are grouped together. Here we show that for continuous-time quantum Monte Carlo in the hybridization expansion the efficiency can be substantially improved by dividing the local impurity trace into fragments, which are then sampled individually. For this technique, which also turns out to preserve the fermionic sign, a modified update strategy is introduced in order to ensure ergodicity. Our (super)state sampling is particularly beneficial to calculations with many $d$ orbitals and general local interactions, such as full Coulomb interaction. For illustration, we reconsider the simple albeit well-known case of a degenerate three-orbital model at low temperatures. This allows us to quantify the coherence properties of the “spin-freezing” crossover, even close to the Mott transition.

We synthesized the $5d^1$ transition-metal oxides $A\mathrm{Os}{\mathrm{O}}_4\left(A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}\right)$ by solid-state reaction, and performed structure determination and magnetic and heat capacity measurements. It was found that they crystallize in a scheelite ($A=\mathrm{K}$ and Rb) or a quasischeelite structure ($A=\mathrm{Cs}$) comprising distorted diamond lattices of septivalent Os ($d^1$) ions tetrahedrally coordinated by four oxide ions without local inversion symmetry; hence an antisymmetric spin-orbit coupling is expected in the crystals. The K and Rb compounds have Weiss temperatures of $\theta =-66$ and $-18\mathrm{K}$, effective magnetic moments of ${\mu }_{\mathrm{eff}}=1.44$ and $1.45{\mu }_{\mathrm{B}}/\mathrm{Os}$, and antiferromagnetic transition temperatures of $T_{\mathrm{N}}=36.9$ and 21.0 K, respectively. In contrast, the Cs compound has $\theta =12\mathrm{K}$ and ${\mu }_{\mathrm{eff}}=0.8{\mu }_{\mathrm{B}}/\mathrm{Os}$ without magnetic transition above 2 K, instead exhibiting a first-order structural transition at $T_{\mathrm{s}}=152.5\mathrm{K}$. The decline of the Os moment from $1.73{\mu }_{\mathrm{B}}/\mathrm{Os}$ for the simple $d^1$ spin, particularly for Cs, is likely to originate from the antiparallel orbital moment, although the spin-orbit coupling is generally quenched in the low-lying $e$ orbitals.

Recent neutron-scattering measurements indicate that ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ forms an antiferromagnetic stripe phase near $x\approx 0.5$ in a Mott insulating state. This copper concentration is well in excess of that required for superconductivity, $x<0.04$. We have investigated the development of magnetism in this compound by using ${}^{23}\mathrm{Na}$ nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation measurements performed on single crystals ($x=0.13$, 0.18, 0.24, and 0.39). We find multiple inequivalent Na sites, each of which is associated with a different number of nearest-neighbor Fe sites occupied by a Cu dopant. We show that the distribution of Cu substituted for Fe is random in-plane for low concentrations ($x=0.13$ and 0.18) but deviates from this with increasing Cu doping. As is characteristic of many pnictide compounds, there is a spin pseudogap that increases in magnitude with dopant concentration. This is correlated with a corresponding increase in orbital NMR frequency shift, indicating a change in valence from ${\mathrm{Cu}}^{2+}$ to a ${\mathrm{Cu}}^{1+}$ state as $x$ exceeds 0.18, concomitant with the change of ${\mathrm{Fe}}^{2+}$ to ${\mathrm{Fe}}^{3+}$ resulting in the formation of magnetic clusters. However, for $x\le 0.39$ there is no evidence of long-range static magnetic order.

Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q=\pi$ in $t_{2g}^4$ spin-orbit coupled three-orbital Hubbard models at electronic density $n=4$. In parallel, experiments involving iridates with noninteger valence states for the Ir ions are starting to attract considerable attention. In this publication, using the density matrix renormalization group technique we present evidence for the existence of an excitonic condensate at $n=3.5$ in a one-dimensional Hubbard model with a degenerate $t_{2g}$ sector, when in the presence of spin-orbit coupling. At intermediate Hubbard $U$ and spin-orbit $\lambda$ couplings, we found an excitonic condensate at the unexpected momentum $q=\pi /2$ involving $j_{\mathrm{eff}}=3/2,m=\pm 1/2$, and $j_{\mathrm{eff}}=1/2,m=\pm 1/2$ bands in the triplet channel, coexisting with an also unexpected block magnetic order. We also present the entire $\lambda$ vs $U$ phase diagram, at a fixed and robust Hund coupling. Interestingly, this new “block excitonic phase” is present even at large values of $\lambda$, unlike the $n=4$ excitonic phase discussed before. Our computational study helps to understand and predict the possible magnetic phases of materials with $d^{3.5}$ valence and robust spin-orbit coupling.

In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological nature of one-dimensional (1D) bound states localized at step edges of the (001) surface of a topological crystalline insulator ${\mathrm{Pb}}_{0.7}{\mathrm{Sn}}_{0.3}\mathrm{Se}$, both theoretically and experimentally. We show that the topological stability of the step-edge states arises from an emergent particle-hole symmetry of the surface low-energy physics, and demonstrate the experimental signatures of the particle-hole symmetry breaking. We also reveal the effects of an external magnetic field on the 1D bound states. Our work suggests the possibility of similar topological step-edge modes in other topological materials with a rocksalt structure.