Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well characterized by now, their presence in fractional dimensions remains vastly unexplored. Here, we theoretically show that a special class of crystalline phases, namely, higher-order topological phases that via an extended bulk-boundary correspondence feature robust gapless modes on lower-dimensional boundaries, such as corners and hinges, can be found on a representative family of fractional materials: quantum fractals. To anchor this general proposal, we demonstrate realizations of second-order topological insulators and superconductors, supporting charged and neutral Majorana corner modes on planar Sierpiński carpet and triangle fractals, respectively. These predictions can be experimentally tested on designer electronic fractal materials, as well as on various highly tunable metamaterial platforms, such as photonic and acoustic lattices.

We approximately solve the Schrödinger equation for two-dimensional Wannier-Mott excitons in the effective-mass approximation and derive an expression for the exciton energy levels, hence the exciton binding energy. The electron-hole interaction is described by the Rytova-Keldysh potential in a logarithmic approximation. From the derived expression, we introduce approximate expressions to experimentally determine the exciton binding energy (along with the quasiparticle band gap), the screening length, and the exciton reduced mass from measured exciton transition energies of the ground state ($1s$), and the first ($2s$) and the second ($3s$) excited states. Our results agree well with experimental data and theoretical calculations.

We explore topological transitions in the type of propagation of surface electromagnetic modes in massive anisotropic tilted two-dimensional (2D) Dirac systems. The presence of tilting and mass gives rise to an indirect band gap that strongly modifies the joint density of states compared to the gapless system. New Van Hove singularities appear, and the interplay between intra- and interband transitions leads to an anisotropic optical conductivity with imaginary parts acquiring opposite signs in orthogonal directions, opening the possibility of having hyperbolic propagation of plasmons. Isofrequency contours and low plasmon losses, as obtained from the dispersion relation, show that transitions between purely anisotropic quasielliptical and well-defined, highly directional, hyperbolic modes are attainable only when tilt and mass coexist via frequency and Fermi level variation. This behavior could be probed in massive tilted 2D Dirac materials like the organic-layered compound $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ [BEDT-TTF = (bis-(ethylenedithio)tetrathiafulvalene)] or ${\mathrm{WTe}}_2$, in which hyperbolic plasmons were recently observed, through far-infrared absorption, optical nanoscopy, and similar current tools in graphene plasmonics.

We study the dynamical behavior of the mean-square displacement of height fluctuations of freestanding graphene using a phase-field-crystal model introduced recently. We find that the dynamic scaling behavior obtained numerically at long times is well described by the scaling theory of polymerized membranes. The critical exponent characterizing the power-law increase with time depends only on the equilibrium roughening exponent $\xi$ as $\alpha =\xi /(1+\xi )$. For sufficiently long times it crosses over to linear behavior for finite-size systems. The critical exponent $\alpha$ is in good agreement with the anomalous diffusion exponent observed experimentally in graphene, suggesting this is a property that could also be observable in other two-dimensional crystalline materials.

Molecular chirality detection and enantiomer discrimination are very important issues for many areas of science and technology, prompting intensive investigations via optical methods. However, these methods are hindered by the intrinsically weak nature of chiro-optical signals. Here, we investigate and demonstrate the potential of gain materials and of combined gain-loss media to enhance these signals. Specifically, we show that the proper combination of a thin chiral layer with a gain-loss bilayer can lead to large enhancements of both the circular dichroism (CD) response and the dissymmetry factor $g$ compared with the chiral layer alone. The most pronounced enhancements are obtained in the case of a parity-time ($\mathit{PT}$) symmetric gain-loss bilayer, while deviations from the exact $\mathit{PT}$ symmetry lead to only moderate changes of the CD and $g$ response, demonstrating also the possibility of tuning the system response by tuning the gain layer properties. In the case of $\mathit{PT}$-symmetric gain-loss bilayers, we found that the largest CD enhancement is obtained at the system lasing threshold, while the $g$ enhancements are at the anisotropic transmission resonances of the systems. Our results clearly demonstrate the potential of gain materials in chirality detection. Moreover, our gain-involving approach can be applied in conjunction with most of the nanophotonics/nanostructures-based approaches that have already been proposed for chirality sensing, further enhancing the performance/output of both approaches.

In candidate Kitaev materials, the off-diagonal $\mathrm{\Gamma }$ and ${\mathrm{\Gamma }}^{\prime }$ interactions are identified to come from the spin-orbit coupling and trigonal distortion, respectively. They have generated intense research efforts because of their intimate relation to the field-induced magnetically disordered state reported in $\alpha \text{−}{\mathrm{RuCl}}_3$. Theoretically, while a plethora of field-induced phases has been proposed in the honeycomb lattice, a stable intermediate phase that can survive in a wide parameter region regardless of the underlying phases is still lacking. Here we focus on the interplay of an out-of-plane magnetic field and a symmetry-allowed ${\mathrm{\Gamma }}^{\prime }$ term due to trigonal distortion in the dominant antiferromagnetic $\mathrm{\Gamma }$ region. By using multifaceted approaches ranging from classical Monte Carlo and semiclassical spin-wave theory to density-matrix renormalization group, we identify an intriguing spin-flop phase in the presence of magnetic field and antiferromagnetic ${\mathrm{\Gamma }}^{\prime }$ interaction, before it eventually enters into a fully polarized state. As the ${\mathrm{\Gamma }}^{\prime }$ interaction approaches the size of $\mathrm{\Gamma }$ one, the $\mathrm{\Gamma }\text{−}{\mathrm{\Gamma }}^{\prime }$ model maps to the easy-axis XXZ antiferromagnet, where the spin-flop phase can be understood as a superfluid phase in the extended Bose-Hubbard model. Our finding thus demonstrates an exciting path from the honeycomb $\mathrm{\Gamma }$ model towards a $U\left(1\right)$-symmetric XXZ antiferromagnet in a magnetic field.

We theoretically study a short single-channel Josephson junction between superconductors in the trivial and topological phases. The junction is assumed to be biased by a small current and subjected to quasiparticle poisoning. We find that the presence of quasiparticles leads to a voltage signal from the Josephson junction that can be observed both in the trivial and topological phases. Quite remarkably, these voltage signatures are sufficiently different in the two phases such that they can serve as means to clearly distinguish between trivial Andreev and topological Majorana bound states in the system. Moreover, these voltage signatures, in the trivial and topological phases, would allow one to directly measure the quasiparticle poisoning rates and test various approaches for protection against quasiparticle poisoning.

The interest in Be as an impurity in GaN stems from the challenge to understand why GaN can be doped $p$ type with Mg, while this does not work for Be. While theory has actually predicted an acceptor level for Be that is shallower than Mg, it was also argued that Be is not a suitable acceptor because its amphoteric nature, i.e., its tendency to occupy substitutional Ga as well as interstitial sites, would be considerably more pronounced than for Mg and hence lead to self-compensation. Using the emission channeling technique at the ISOLDE/CERN facility, we determined the lattice location of ${}^{11}\mathrm{Be}$ $\left(t_{1/2}=13.8\mathrm{s}\right)$ in different doping types of GaN as a function of implantation temperature. We find within an accuracy of 0.08 Å that the location of interstitial Be is the one predicted by theory. The room temperature interstitial fraction of ${}^{11}\mathrm{Be}$ was correlated with the GaN doping type, being highest (up to ∼80%) in $p$ type and lowest in $n$-GaN, thus giving direct evidence for the amphoteric character of Be. We find that interstitial ${}^{11}\mathrm{Be}$ fractions are generally much higher than for Mg, which confirms that indeed self-compensation should be considerably more pronounced for Be. With rising implantation temperature, an increasing conversion of interstitial to substitutional Be is observed, involving at least two clearly identifiable steps at 50–150 °C and 350–500 °C. This suggests that the migration of interstitial Be may be subject to two different activation energies.

Spin transport in ferromagnetic insulator/heavy metal heterojunctions has attracted much attention because of its rich physics and potential applications. Here, we report an anomalous anisotropic magnetoresistance (AMR) at low temperature in a ${\mathrm{Tm}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}\text{/Pt}$ bilayer, which has often been neglected for its weak signal compared with spin Hall magnetoresistance. In our study, the magnetic proximity effect is weak above 50 K so that the AMR signal is mainly caused by ordinary magnetoresistance and spin-related scattering. However, at low temperatures, the AMR changes dramatically due to the weak localization (WL) and weak anti-localization (WAL) related to the quantum diffusion mechanism. Moreover, the dominated mechanism changes from WL to WAL in a Cu-inserted structure of TmIG/Cu/Pt without the magnetic proximity exchange coupling at the interfaces, accompanied by an AMR variation from negative to positive. Our study reveals the quantum correction effect on the AMR, which provides a possible explanation of the complex resistive behavior at low temperatures.

We use a hydrodynamic approach to investigate dynamic spin susceptibility of the antiferromagnetic spin-$1/2$ Heisenberg chain with a uniform Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field. We find that transverse (with respect to the magnetic field) spin susceptibility harbors two (respectively, three) spin excitation modes when the magnetic field is parallel (respectively, orthogonal) to the DM axis. In all cases, the marginally irrelevant backscattering interaction between the spinons creates a finite energy splitting between optical branches of excitations at $k=0$. Additionally, for the orthogonal geometry, the two lower spin branches exhibit avoided crossing at finite momentum which is determined by the total magnetic field (the sum of the external and internal molecular fields) acting on spinons. Our approximate analytical calculations compare well with numerical results obtained using matrix-product-state (MPS) techniques. Physical consequences of our findings for the electron spin resonance experiments are discussed in detail.

A Dirac nodal-line phase as a quantum state of topological materials, usually occur in three-dimensional or, at least, two-dimensional materials with sufficient symmetry operations that could protect the Dirac band crossings. Here, we report a combined theoretical and experimental study on the electronic structure of the quasi-one-dimensional ternary telluride ${\mathrm{TaPtTe}}_5$, which is corroborated as being in a robust nodal-line phase with fourfold degeneracy. Our angle-resolved photoemission spectroscopy measurements show that two pairs of linearly dispersive Dirac-like bands exist in a very large energy window, which extend from a binding energy of $\sim 0.75$ eV to across the Fermi level. The crossing points are at the boundary of Brillouin zone and form Dirac-like nodal lines. Using first-principles calculations, we demonstrate the existing of nodal surfaces on the $k_y=\pm \pi$ plane in the absence of spin-orbit coupling (SOC), which are protected by nonsymmorphic symmetry in ${\mathrm{TaPtTe}}_5$. When SOC is included, the nodal surfaces are broken into several nodal lines. By theoretical analysis, we conclude that the nodal lines along $Y\text{−}T$ and the ones connecting the $R$ points are nontrivial and protected by nonsymmorphic symmetry against SOC.

Frustrated Mott insulators such as transition metal dichalcogenides present an ideal platform for the experimental realization of externally tuned insulator-metal transition. In this paper, we present the first nonperturbative numerical investigation of the disorder-induced insulator-metal transition in a two-dimensional frustrated Mott insulator. Our approach is generic and captures the essential physics of Mott insulator-metal transition in geometrically frustrated lattices. For concreteness, we have compared our results with the experimental observations on copper (Cu) intercalated 1T-${\mathrm{TaS}}_2$. Based on the magnetic, spectroscopic, and transport signatures, we have mapped out the thermal phase diagram of Cu intercalated 1T-${\mathrm{TaS}}_2$ and established that over a regime of moderate disorder strength this material hosts an antiferromagnetic metal. Moreover, the insulator-metal transition in this system is not tied to the loss of magnetic correlations, thereby giving rise to two quantum critical points. The emergent non-Fermi liquid metal is governed by resilient quasiparticles, that survive as the relevant low energy excitations even after the break down of the Fermi liquid description. The transport and spectroscopic signatures discussed in this letter are expected to serve as important benchmarks for future experiments on this and related class of materials.

We report an inelastic neutron scattering study (INS) on the low-energy crystal electric field (CEF) excitations of ${\mathrm{Pr}}_{2-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_{4+\delta }$ single crystals at various temperatures. The observed low-$E$ CEF level of the O-doped sample $(x=0,\delta \approx 0.24)$ at $\sim 5.5\mathrm{meV}$ appears at significantly lower energy than that of the Sr-doped sample $(x=0.5,\delta =0.0)$ at $\sim 8.5\mathrm{meV}$. Applying the point charge (PC) model calculation, this has been interpreted as an effect of the interstitial oxygen via lowering the local symmetry and modifying the CEF environment of the central rare earth ${\mathrm{Pr}}^{3+}$ $\left({}^{3}H_4\right)$ ions.

The interaction between electronic and vibrational degrees of freedom is an important mechanism in nonequilibrium charge transport through molecular nanojunctions. While adiabatic polaron-type coupling has been studied in great detail, new transport phenomena arise for nonadiabatic coupling scenarios corresponding to a breakdown of the Born-Oppenheimer approximation. Employing the numerically exact hierarchical equations of motion approach, we analyze the effect of nonadiabatic electronic-vibrational coupling on electron transport in molecular junctions considering a series of models with increasing complexity. The results reveal a significant influence of nonadiabatic coupling on the transport characteristics and a variety of interesting effects, including negative differential conductance. The underlying mechanisms are analyzed in detail.

Symmetry fractionalization on topological excitations is one of the most remarkable quantum phenomena in topological orders with symmetry, i.e., symmetry-enriched topological phases. While much progress has been theoretically and experimentally made in two dimensions (2D), the understanding on symmetry fractionalization in 3D is far from complete. A long-standing challenge is to understand symmetry fractionalization on looplike topological excitations, which are spatially extended objects. In this paper, we construct a powerful topological-field-theoretical framework approach for 3D topological orders, which leads to a systematic characterization and classification of symmetry fractionalization. For systems with Abelian gauge groups ($G_g$) and Abelian symmetry groups ($G_s$), we successfully establish equivalence classes that lead to a finite number of patterns of symmetry fractionalization, although there are notoriously infinite number of Lagrangian-descriptions of the system. Based on this, we compute topologically distinct types of fractional symmetry charges carried by particles. Then, for each type, we compute topologically distinct statistical phases of braiding processes among loop excitations and external symmetry fluxes. As a result, we are able to unambiguously list all physical observables for each pattern of symmetry fractionalization. We present detailed calculations on many concrete examples. As an example, we find that the symmetry fractionalization in an untwisted ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ topological order with ${\mathbb{Z}}_2$ symmetry is classified by ${\left({\mathbb{Z}}_2\right)}^6\oplus {\left({\mathbb{Z}}_2\right)}^2\oplus {\left({\mathbb{Z}}_2\right)}^2\oplus {\left({\mathbb{Z}}_2\right)}^2$. If the topological order is twisted, the classification reduces to ${\left({\mathbb{Z}}_2\right)}^6$ in which particle excitations always carry integer charge. Inspired by the field-theoretical analysis, we find that our classification of symmetry fractionalization with twist $\omega$ can be formally organized into an algebraic formalism: ${⨁}_{{\nu }_i}{\mathcal{H}}^4(G_g{⋋}_{{\nu }_i}{G}_s,U\left(1\right))/{\mathrm{\Gamma }}_{\omega }\left({\nu }_i\right),$ where anomaly-free symmetry fractionalization on particles ${\nu }_i\in {\mathcal{H}}_{non}^2(G_s,G_g)$. Despite the lack of detailed dependence of ${\mathrm{\Gamma }}_{\omega }\left({\nu }_i\right)$ on $\omega$ and ${\nu }_i$, the present field-theoretical approach allows us to efficiently calculate and understand ${\mathrm{\Gamma }}_{\omega }\left({\nu }_i\right)$. Several future directions are presented at the end of this paper.

We study the effect of carrier doping to the Mott insulator on the Penrose tiling, aiming at clarifying the interplay between quasiperiodicity and strong electron correlations. We numerically solve the Hubbard model on the Penrose-tiling structure within a real-space dynamical mean-field theory, which can deal with a spatial inhomogeneity as well as a singular self-energy necessary to describe the Mott insulator. We find that the strong correlation effect produces a charge distribution unreachable by a static mean-field approximation. In a small doping region, the spectrum shows a site-dependent gap just above the Fermi energy, which is generated by a singularly large self-energy emergent from the Mott physics and regarded as a real-space counterpart of the momentum-dependent pseudogap observed in a square-lattice Hubbard model.

We show that artificial neural networks (ANNs) can, to high accuracy, determine the topological invariant of a disordered system given its two-dimensional real-space Hamiltonian. Furthermore, we describe a “renormalization-group” (RG) network, an ANN which converts a Hamiltonian on a large lattice to another on a small lattice while preserving the invariant. By iteratively applying the RG network to a “base” network that computes the Chern number of a small lattice of set size, we are able to process larger lattices without retraining the system. We therefore show that it is possible to compute real-space topological invariants for systems larger than those on which the network was trained. This opens the door for computation times significantly faster and more scalable than previous methods.

Photoluminescence and stimulated emission spectroscopies were performed on transparent aluminum nitride (AlN) substrates grown by hydride vapor-phase epitaxy. The stimulated emission was observed from cryogenic to room temperatures and its origin was assigned on the basis of the spontaneous emission spectra and existing theories. Two stimulated emission mechanism crossovers were also found. One was a temperature-induced crossover from a purely excitonic mechanism to a carrier-involved mechanism, which is a universal behavior in semiconducting materials. The other was an excitation-power–induced crossover from an exciton–exciton scattering mechanism to a phonon-mediated mechanism, which is a unique behavior attributed to the peculiar excitonic structure (negative crystal-field splitting and positive electron–hole exchange interaction energies) of AlN.

In contrast to the intensively investigated transition metal dichalcogenides like ${\mathrm{MoS}}_2$, ${\mathrm{ReS}}_2$ crystals possess a reduced in-plane symmetry, leading to anisotropic optical properties. Here, we report on the impact of strain on the Raman response of a ${\mathrm{ReS}}_2$ monolayer. Since mechanical strain can be used to shift the Raman-active phonon frequencies, we apply uniaxial tensile strain of up to 0.74% along the Re-chain direction ($x$ axis) of the atomically thin crystal and measure the Raman response with the scattered light polarized parallel and perpendicular to the strain direction along the $x$ axis. Complementarily, we carry out ab initio calculations to determine the phonon energies and Raman intensities under strain. We find a shift to lower energies for all phonon modes when tensile strain is applied to the monolayer. The determined gauge factors/Grüneisen parameters are in good agreement between experiment and theory. Our study demonstrates that the optomechanical properties of ${\mathrm{ReS}}_2$ can be tuned by external straining, which is of importance for potential future strain-sensor applications, e.g., in the biomedical sector.

Recent progress in the controllable functionalization of graphene surfaces enables the experimental realization of complex functionalized graphene nanostructures, such as Sierpinski carpet (SC) fractals. Herein, we model the SC fractals formed by hydrogen and fluorine functionalized patterns on graphene surfaces, namely, H-SC and F-SC, respectively. We then reveal their electronic properties and quantum transport features. From the calculated results of the total and local densities of state, we find that states in H-SC and F-SC have two characteristics: (i) low-energy states inside about $|E/t|\le 1$ (with $t$ as the nearest-neighbor hopping) are localized inside free graphene regions due to the insulating properties of functionalized graphene regions and (ii) high-energy states in F-SC have two special energy ranges including $-2.3<E/t<-1.9$ with localized holes only inside free graphene areas and $3<E/t<3.7$ with localized electrons only inside fluorinated graphene areas. The two characteristics are further verified by the real-space distributions of normalized probability density. We analyze the fractal dimension of their quantum conductance spectra and find that conductance fluctuations in these structures follow the Hausdorff dimension. We calculate their optical conductivity and find that several additional conductivity peaks appear in high-energy ranges due to the adsorbed H or F atoms.