With recent advances in the areas of nanostructure fabrication and molecular spintronics the idea of using single molecule magnets as building blocks for the next generation electronic devices becomes viable. A particular example represents a metal-organic complex in which organic ligands surround a rare-earth element or transition metal. Recently, it was explicitly shown that the relative position of the ligands with respect to each other can be reversibly changed by the external voltage without any need of the chemical modification of the sample. This opens a way of the electrical tuning of the Kondo effect in such metal-organic complexes. In this work, we present a detailed and systematic analysis of this effect in ${\mathrm{TbPc}}_2$ from an ab initio perspective and compare the obtained results with the existing experimental data.

Surface plasmon polaritons in planar graphene superlattices with one-dimensional periodic mo-dulation of the band gap were studied. The interminiband contribution to the optical conductivity of this system was found by the equation of motion method for two cases: the Fermi level falls within one of the minigaps and the Fermi level is located within one of the minibands. It was shown that the optical conductivity of the system varies significantly in these cases. The spectra of surface plasmon polaritons in the system differs for them.

We investigate the Cooper pair splitting based on crossed Andreev reflection in a two-dimensional narrow superconductor coupled to two leads, where the two leads are van der Waals (vdW) spin valves formed by inserting bilayer graphene (BLG) between two antiparallel insulating ferromagnetic layers. In this BLG-based $n$-type vdW spin valve/superconductor/$p$-type vdW spin valve junction with edge-contact geometry, when controlling the Fermi energy and the interlayer electric field in BLG independently by top- and bottom-gate voltages in the vdW spin valve region, we first demonstrate that the two electrons of perfect Cooper pair splitting can remain nonlocal valley entanglement. This effect can be explained as follows: When both the two antiparallel insulating ferromagnetic layers and the interlayer electric field are taken into account, BLG exhibits a spin-splitting but valley-degenerate band gap near the Dirac point. Thus, our setups allow the Cooper pair in the BCS scenario to serve as a natural source of valley entanglement. We further predict large oscillations of cross conductance as a function of the doping of the superconductor, the junction length, and the bias voltage. Our results may provide a tool for realizing fast nonlocal switching of the valley-entanglement state.

One of the main features of Weyl semimetals is the existence of Fermi arc surface states at their surface, which cannot be realized in pure two-dimensional systems in the absence of many-body interactions. Due to the gapless bulk of the semimetal, it is, however, challenging to observe clear signatures from the Fermi arc surface states. Here, we propose to detect such novel surface states via perfect negative refraction that occurs between two adjacent open surfaces with properly orientated Fermi arcs. Specifically, this phenomenon visibly manifests in nonlocal transport measurement, where the negative refraction generates a return peak in the real-space conductance. This provides a unique signature of the Fermi arc surface states. We discuss the appearance of this peak in both inversion- and time-reversal-symmetric Weyl semimetals, where the latter exhibits conductance oscillations due to multiple negative refraction scattering events.

We predict a two-dimensional monolayer polymorph of boron nitride in an orthorhombic structure (o-${\mathrm{B}}_2{\mathrm{N}}_2)$ using first-principles calculations. Structural optimization, phonon dispersion, and molecular dynamics calculations show that o-${\mathrm{B}}_2{\mathrm{N}}_2$ is thermally and dynamically stable. o-${\mathrm{B}}_2{\mathrm{N}}_2$ is a semiconductor with a direct band gap of 1.70 eV according to calculations based on hybrid functionals. The structure has high optical absorption in the visible range in the armchair direction while low absorption in the zigzag direction. This anisotropy is also present in electronic and mechanical properties. The in-plane stiffness of o-${\mathrm{B}}_2{\mathrm{N}}_2$ is very close to that of hexagonal boron nitride. The diatomic building blocks of this structure hint at its possible synthesis from precursors having B-B and N-N bonds.

We theoretically study the electronic structure of small-angle twisted bilayer graphene with a large potential asymmetry between the top and bottom layers. We show that the emergent topological channels known to appear on the triangular AB-BA domain boundary do not actually form a percolating network, but instead, they provide independent, perfect one-dimensional eigenmodes propagating in three different directions. Using the continuum-model Hamiltonian, we demonstrate that an applied bias causes two well-defined energy windows which contain sparsely distributed one-dimensional eigenmodes. The origin of these energy windows can be understood using a two-band model of the intersecting electron and hole bands of single-layer graphene. We also use the tight-binding model to implement the lattice deformations in twisted bilayer graphene and discuss the effect of lattice relaxation on the one-dimensional eigenmodes.

The $\epsilon -{\text{Fe}}_2{\text{O}}_3$ magnetic structure has been analyzed using the synchrotron radiation source. Time spectra of nuclear forward scattering for isolated nanoparticles with an average size of 8 nm immobilized in a xerogel matrix have been recorded in the temperature range of $4–300\mathrm{K}$ in applied magnetic fields of $0–4\mathrm{T}$ in the longitudinal direction at the European Synchrotron Radiation Facility (ESRF, Grenoble, France). It has been found that the external magnetic field does not qualitatively change the $H_{\mathrm{hf}}\left(\mathrm{T}\right)$ behavior, but makes a strong opposite impact on the hyperfine fields in the nonequivalent iron sites, leading to the divergence of $H_{\mathrm{hf}}$ polar angle dependences below 80 K. A complete diagram of the $\epsilon -{\text{Fe}}_2{\text{O}}_3$ magnetic structure in the temperature range of $4–300\mathrm{K}$ is proposed. At 300 K, the $\epsilon -{\text{Fe}}_2{\text{O}}_3$ compound is confirmed to be a collinear ferrimagnet. The experimental results show that the magnetic transition at $150–80\mathrm{K}$ leads to the formation of a noncollinear magnetic structure. Furthermore, in the range of the 80–4 K, the ground state of a magnetic spiral is established. The experimental results are supplemented by the analysis of the exchange interactions and temperature dependence of the magnetization in a magnetic field of 7 T.

In the seminal work by G. Eilenberger, Z. Phys. 214, 195 (1968), a closed-form expression for the free energy of inhomogeneous spin-singlet superconductor in terms of quasiclassical propagators has been suggested. However, deriving this expression and generalizing it for superconductors or superfluids with general matrix structure, e.g., spin-triplet correlations, has remained problematic. Starting from the Luttinger-Ward formulation, we discuss here the general solution. Besides ordinary superconductors with various scattering mechanisms, the obtained free-energy functional can be used for systems, such as superfluid ${}^3\mathrm{He}$ and superconducting systems with spatially inhomogeneous exchange field or spin-orbit coupling. Using this result, we derive the simplified expression for the free energy in the diffusive and hydrodynamic limits. As an example of using this formalism, we show that impurity scattering restores the first-order phase transition in superconductor-ferromagnetic insulator bilayers making this system similar to the bulk superconductor with the homogeneous built-in exchange field.

We study the motion of a slow quantum impurity in one-dimensional environments focusing on systems of strongly interacting bosons and weakly interacting fermions. While at zero temperature the impurity motion is frictionless, at low temperatures finite friction appears. The dominant process is the scattering of the impurity off two fermionic quasiparticles. We evaluate the friction force and show that, at low temperatures, it scales either as the fourth or the sixth power of temperature, depending on the system parameters. This is a result of the scattering of the impurity off two fermionic quasiparticles that are situated around different Fermi points. It is the dominant process at low temperatures. We also evaluate the contribution to the friction force originating from the scattering of the impurity off two fermionic quasiparticles that are situated around different Fermi points. It behaves as the tenth power of temperature.

The pyrochlore lattice is associated with several potential and actual spin liquid phases as a result of its strong geometric frustration. At finite temperature, these can exhibit an unusually broad crossover regime to a conventional paramagnet. Here, we study this regime analytically by showing how a single-tetrahedron Hamiltonian can extrapolate beyond the first term of a high-temperature expansion and yield insights into the buildup of correlations. We discuss how this unusual behavior is brought about by the structure of the eigenspaces of the coupling matrix. Further interesting behavior can appear for parameter values located near phase transitions: we find coexistence of (111) rods and (220) peaks in the structure factor, as observed in neutron-scattering experiments on ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$.

We analytically calculate the intra- and intersurface dynamical density-density linear responses of ultrathin topological insulator films with finite tunneling between their top and bottom surfaces in both metallic and insulating regimes. Employing the random phase approximation we investigate the dispersions of in-phase and out-of-phase collective density modes of this system in the metallic regime. We find that in contrast to the bilayers of the conventional two-dimensional electron gas, where finite tunneling gaps out the out-of-phase mode, in topological insulator thin films, this mode remains linear at long wavelengths. Depending on different system parameters, the velocity of out-of-phase mode can be tuned to be larger or substantially smaller than the Fermi velocity of electrons on the isolated surfaces of the topological insulator. Finite tunneling generally reduces the energy of collective modes, making them more confined in space.

We show that time crystal phases, which are known to exist for disorder-based many-body localized systems, also appear in systems where localization is due to strong magnetic field gradients. Specifically, we study a finite Heisenberg spin chain in the presence of a gradient field, which can be realized experimentally in quantum dot systems using micromagnets or nuclear spin polarization. Our numerical simulations reveal time crystalline order over a broad range of realistic quantum dot parameters, as evidenced by the long-time preservation of spin expectation values and the asymptotic form of the mutual information. We also consider the undriven system and present several diagnostics for many-body localization that are complementary to those recently studied. Our results show that these nonergodic phases should be realizable in modest-sized quantum dot spin arrays using only demonstrated experimental capabilities.

We study heat conduction mediated by longitudinal phonons in one-dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find nontrivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that, suprisingly, the thermal conductance of a system with strong disorder, characterized by a “heavy-tailed” probability distribution, and with large impedance mismatch between the bath and the system, scales normally with the system size, i.e., in a manner consistent with Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.

We construct a coupled wire model for a sequence of non-Abelian quantum Hall states occurring at filling factors $\nu =2/(2M+q)$ with integers $M$ and even (odd) integers $q$ for fermionic (bosonic) states. They are termed $Z_2\times Z_2$ orbifold states, which have a topological order with a neutral sector described by the $c=1$ orbifold conformal field theory (CFT) at radius $R_{\mathrm{orbifold}}=\sqrt{p/2}$ with even integers $p$. When $p=2$, the state can be viewed as two decoupled layers of Moore-Read states, whose neutral sector is described by the Ising $\times$ Ising CFT and contains a $Z_2\times Z_2$ fusion subalgebra. We demonstrate that orbifold states with $p>2$, also containing a $Z_2\times Z_2$ fusion algebra, can be obtained by coupling together an array of $\mathrm{MR}\times \mathrm{MR}$ wires through local interactions. The corresponding charge spectrum of quasiparticles is also examined. The orbifold states constructed here are complementary to the $Z_4$ orbifold states, whose neutral edge theory is described by orbifold CFT with odd integer $p$ and contains a $Z_4$ fusion algebra.

Odd-frequency superconductivity is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. Majorana zero modes exhibit pure odd-frequency superconducting correlations due to their specific properties. Thus, by tunnel-coupling an array of Majorana zero modes to a spin-polarized wire, it is in principle possible to engineer a bulk one-dimensional odd-frequency spinless $s$-wave superconductor. We point out here that each tunnel coupling element, being dependent on a large number of material-specific parameters, is generically complex with sample variability in both its magnitude and phase. Using this, we demonstrate that, upon averaging over phase disorder, the induced superconducting, including odd-frequency, correlations in the spin-polarized wire are significantly suppressed. We perform both a rigorous analytical evaluation of the disorder-averaged $T$ matrix in the wire, as well as numerical calculations based on a tight-binding model, and find that the anomalous, i.e., superconducting, part of the $T$ matrix is highly suppressed with phase disorder. We also demonstrate that this suppression is concurrent with the filling of the single-particle excitation gap by smearing the near-zero-frequency peaks, due to formation of bound states that satisfy phase-matching conditions between spatially separated Majorana zero modes. Our results convey important constraints on the parameter control needed in practical realizations of Majorana zero mode structures and suggest that the achievement of a bulk one-dimensional odd-$\omega$ superconductivity from Majorana zero modes demand full control of the system parameters.

The construction and classification of symmetry-protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Very recently, a complete classification and construction of space-group SPT phases were also proposed for interacting bosonic systems. In this Rapid Communication, we attempt to generalize this classification and construction scheme systematically into interacting fermion systems. In particular, we construct and classify point-group SPT phases for two-dimensional (2D) interacting fermion systems via lower-dimensional block-state decorations. We discover several intriguing fermionic SPT states that can only be realized in interacting fermion systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for 2D interacting fermion systems. Finally, the potential experimental realization of these different classes of point-group SPT phases in 2D correlated superconductors is addressed.

The temperature-induced structure variation and its effect on physical properties is pivotal in material preparation for devices application. Motivated by surface scanning tunnel microscope (STM) measurement of $T_d-{\mathrm{MoTe}}_2$ single crystal at low temperature, temperature dependent electronic structure, lattice dynamics, and topological properties are explored to understand the microscopic origin of the observed anisotropic negative thermal expansion and abnormal STM images below 70 K. Remarkably, we find that the nonequivalent Te atoms in $T_d-{\mathrm{MoTe}}_2$ have qualitatively different contributions to both phonon spectra and electronic structures. The in-plane longitudinal acoustic mode and the ${\mathrm{Te}}_{\left(2\right)}$ atoms are found to play an important role in uniaxial negative thermal expansion and the temperature dependent electronic phase transition, respectively. Interestingly, under the scalar relativistic approximation, a band renormalization occurs, accompanied by a Dirac phase transition from type II to type I, upon cooling below 70 K. Introducing spin-orbit coupling induces a temperature dependent semimetal–semiconductor transition. Our results explain the experimental phenomena very well: abnormal surface STM image below 70 K does not originate from the displacement of the Te atoms but the band renormalization owing to strong electron-lattice coupling.