In this work we conduct a close-up investigation into the nature of near-field heat transfer (NFHT) of two graphene sheets in parallel-plate geometry. We develop a fully microscopic and quantum approach using the nonequilibrium Green's function method. A Caroli formula for heat flux is proposed and numerically verified. We show that our near-field-to-black-body heat flux ratios generally exhibit $1/d^{\alpha }$ dependence, with an effective exponent $\alpha \approx 2.2$, at long distances exceeding 100 nm and up to one micron; in the opposite $d\to 0$ limit, the values converge to a range within an order of magnitude. We justify this feature by noting it is owing to the breakdown of local conductivity theory, which predicts a $1/d$ dependence. Furthermore, from the numerical result, we find that in addition to thermal wavelength ${\lambda }_{th}$ a shorter distance scale $\sim 10-100$ nm, comparable to the graphene thermal length $\left(\hslash v_F/k_{B}T\right)$ or Fermi wavelength $\left(k_F^{-1}\right)$, marks the transition point between the short- and long-distance transfer behaviors; within that point, a relatively large variation of heat flux in response to doping level becomes a typical characteristic. The emergence of such large variation is tied to relative NFHT contributions from the intra- and interband transitions. Beyond that point, scaling of thermal flux $\propto 1/d^{\alpha }$ can be generally observed.

It has been shown that long-range $p$-wave superconductivity in a Kitaev chain can be engineered via an ac field with a high frequency [M. Benito et al., Phys. Rev. B 90, 205127 (2014)]. For its experimental realization, however, theoretical understanding of Floquet engineering with a broader range of driving frequencies becomes important. In this paper, focusing on the ac-driven tunneling interactions of a Kitaev chain, we investigate effects from the leading correction to the high-frequency limit on the emergent $p$-wave superconductivity. Importantly, we find new engineered long-range $p$-wave pairing interactions that can significantly alter the ones in the high-frequency limit at long interaction ranges. We also find that the leading correction additionally generates nearest-neighbor $p$-wave pairing interactions with a renormalized pairing energy, long-range tunneling interactions, and, in particular, multiple pairs of Floquet Majorana edge states that are destroyed in the high-frequency limit.

We study two-magnon excitations in resonant inelastic x-ray scattering (RIXS) at the transition-metal $K$ edge. Instead of working with effective Heisenberg spin models, we work with a Hubbard-type model ($d\text{−}p$ model) for a typical insulating cuprate ${\mathrm{La}}_2{\mathrm{CuO}}_4$. For the antiferromagnetic ground state within the spin density wave (SDW) mean-field formalism, we calculate the dynamical correlation function within the random-phase approximation (RPA), and then obtain two-magnon excitation spectra by calculating the convolution of it. Coupling between the $K$-shell hole and the magnons in the intermediate state is calculated by means of diagrammatic perturbation expansion in the Coulomb interaction. The calculated momentum dependence of RIXS spectra agrees well with that of experiments. A notable difference from previous calculations based on the Heisenberg spin models is that RIXS spectra have a large two-magnon weight near the zone center, which may be confirmed by further careful high-resolution experiments.

We study the concept of entanglement distance between two quantum states, which quantifies the amount of information shared between their reduced density matrices (RDMs). Using analytical arguments combined with density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we show that for gapless systems the entanglement distance has power law dependence on the energy separation and subsystem size, with ${\alpha }_E$ and ${\alpha }_{\ell }$ exponents, respectively. Using conformal field theory (CFT) we find ${\alpha }_E=2$ and ${\alpha }_{\ell }=4$ for Abelian theories with $c=1$, as in the case of free fermions. For non-Abelian CFTs ${\alpha }_E=0$, and ${\alpha }_{\ell }$ is twice the conformal dimension of the thermal primary fields. For instance, for $Z_3$ parafermion CFT ${\alpha }_E=1$ and ${\alpha }_{\ell }=4/5$. For gapped 1+1 dimensional (1+1D) fermion systems, we show that the entanglement distance divides the low energy excitations into two branches with different values of ${\alpha }_E$ and ${\alpha }_{\ell }$. These two branches are related to momentum transfers near zero and $\pi$. We also demonstrate that the entanglement distance reaches its maximum for degenerate states related through nonlocal operators such as Wilson loops. For example, degenerate ground states (GSs) of 2+1D topological states have maximum entanglement distance. In contrast, degenerate GSs related through confined anyon excitations such as genons have minimum entanglement distance. Various implications of this concept for quantum simulations are discussed. Finally, based on the ideas developed we discuss the computational complexity of DMRG algorithms that are capable of finding all degenerate GSs.

We present a systematic density functional theory (DFT) plus Hubbard $U$ study of structural trends and the stability of different magnetically ordered states across the rare-earth nickelate series, $R{\mathrm{NiO}}_3$, with $R$ from Lu to La. In particular, we investigate how the magnetic order, the change of the rare-earth ion, and the Hubbard interaction $U$ are affecting the bond-length disproportionation between the nickel sites. Our results show that structural parameters can be obtained that are in very good agreement with present experimental data and that $\mathrm{DFT}+U$ is in principle able to capture the most important structural trends across the nickelate series. However, the amplitude of the bond-length disproportionation depends very strongly on the specific value used for the Hubbard $U$ parameter and also on the type of magnetic order imposed in the calculation. Regarding the relative stability of different magnetic orderings, a realistic antiferromagnetic order, consistent with the experimental observations, is favored for small $U$ values and becomes more and more favorable compared to the ferromagnetic state towards the end of the series (i.e., towards $R=\mathrm{Pr}$). Nevertheless, it seems that the stability of the ferromagnetic state is generally overestimated within the $\mathrm{DFT}+U$ calculations. Our work provides a profound starting point for more detailed experimental investigations and also for future studies using more advanced computational techniques such as, e.g., DFT combined with dynamical mean-field theory.

The phase stabilities and ordering tendencies in the quaternary full-Heusler alloys NiCoMnAl and NiCoMnGa have been investigated by in situ neutron diffraction, calorimetry, and magnetization measurements. NiCoMnGa was found to adopt the $\mathrm{L}{2}_1$ structure, with distinct Mn and Ga sublattices but a common Ni-Co sublattice. A second-order phase transition to the $\mathrm{B}2$ phase with disorder also between Mn and Ga was observed at $1160\text{K}$. In contrast, in NiCoMnAl slow cooling or low-temperature annealing treatments are required to induce incipient $\mathrm{L}{2}_1$ ordering, otherwise the system displays only $\mathrm{B}2$ order. Linked to $\mathrm{L}{2}_1$ ordering, a drastic increase in the magnetic transition temperature was observed in NiCoMnAl, while annealing affected the magnetic behavior of NiCoMnGa only weakly due to the low degree of quenched-in disorder. First principles calculations were employed to study the thermodynamics as well as order-dependent electronic properties of both compounds. It was found that a near half-metallic pseudogap emerges in the minority spin channel only for the completely ordered Y structure. However, this structure is energetically unstable compared to a tetragonal structure with alternating layers of Ni and Co, which is predicted to be the low-temperature ground state. The experimental inaccessibility of the totally ordered structures is explained by kinetic limitations due to the low ordering energies.

The study of Weyl semimetals (WSMs) lies at the forefront of the nontrivial topological phenomena in condensed-matter physics. In this work, we study the effect of on-site repulsive Hubbard interaction on the WSM system with a nonzero tilt at half filling. Within the Hartree-Fock mean-field approximation, we treat the Hubbard interaction self-consistently and find that the Fock exchange field vanishes, while the Hartree field can renormalize the topological mass, the tilt, and the Fermi velocity of the Weyl cones. When the renormalized tilt is larger than the renormalized Fermi velocity, the Hubbard interaction will induce the quantum phase transition from a type-I WSM to a type-II WSM. We then provide the interaction-induced phase diagrams of WSMs in different parametric spaces, in which the antiferromagnetic order at strong interaction is also considered. In addition, we analyze another model hosting two pairs of Weyl nodes, and similar results are obtained. The implications of these results are discussed.

Using first-principles computations, we discuss topological properties of germanene in buckled as well as planar honeycombs with asymmetric passivation via hydrogen and nitrogen (GeHN) atoms. GeHN in the planar structure is found to harbor a quantum anomalous Hall (QAH) insulator phase. Our analysis indicates that the buckled GeHN also possesses a QAH phase under tensile strain. We computed the associated Chern numbers and edge states to confirm the presence of the QAH state. In particular, chiral edge bands connecting conduction and valence bands were found at the edges of a planar zigzag GeHN nanoribbon. By considering a range of buckling distances, we demonstrate how the system undergoes the transition from the trivial to the QAH phase between the buckled and planar structures. Finally, we show CdTe(111) to be a suitable substrate for supporting buckled germanene in the QAH phase. Our results suggest that functionalized germanene could provide a robust QAH-based platform for spintronics applications.

Near-field thermal radiation mediated by surface plasmons in parallel graphene nanodisk dimers is studied using a semianalytical model under the electrostatic approximation. The radiative heat transfer between two disks as a function of the distance between them in coaxial and coplanar configurations is first considered. Three regimes are identified and their extents determined using nondimensional analysis. When the edge-to-edge separation is smaller than the disk diameter, near-field coupling and surface plasmon hybridization lead to an enhancement of the radiative heat transfer by up to four orders of magnitude compared to the Planck blackbody limit. A mismatch in the disk diameters affects the plasmonic mode hybridization and can either diminish or enhance the near-field radiation. Destructive interference between eigenmodes that emerge when the relative orientation between disks is varied can induce a twofold reduction in the radiative heat transfer. In all configurations, the radiative heat transfer properties can be controlled by tuning the disk size/orientation, the substrate optical properties, and graphene's doping concentration and electron mobility.

The thermal radiation properties of guided surface plasmons in one-dimensional co-planar graphene nanodisk arrays are predicted using a semi-analytical electrostatic model. The plasmonic band structure contains nonlocalized dispersion bands that are well-described by the electrostatic model for disk diameters smaller than 200 nm. A nondimensional model is proposed that enables systematic analysis of the waveguiding properties based on scaling laws. The thermal transport is dominated by the lowest-order radial modes and can be controlled by tuning the disk size, the substrate optical properties, and graphene's doping concentration and electron mobility. The maximum predicted thermal conductivity and thermal diffusivity are 4.$5{\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ and $1.3\times {10}^{-3}{\mathrm{m}}^2$/s, orders of magnitude larger than predictions of thermal transport by guided surface plasmon- or phonon-polaritons in other materials. The results suggest that graphene surface plasmons, which can be thermally-activated at room temperature, are a suitable platform for tunable and fast thermal transport, with potential application as photon-based thermotronic interconnects.

Two-particle backscattering in time-reversal-invariant interacting helical electron systems can lead to the formation of quasiparticles with charge $e/2$. We propose a way to detect such states by means of the Josephson effect in the presence of proximity-induced superconductivity. In this case, the existence of $e/2$ charges leads to an $8\pi$-periodic component of the Josephson current which can be identified through measurement of Shapiro steps in Josephson junctions. In particular, we show that even when there is weak explicit time-reversal symmetry breaking, which causes the two-particle backscattering to be a subleading effect at low energies, its presence can still be detected in driven, current-biased Shapiro step measurements. The disappearance of some of these steps as a function of the drive frequency is directly related to the existence of non-Abelian zero-energy states. We suggest that this effect can be measured in current state-of-the-art Rashba wires.

Relaxor ferroelectric materials, such as $\mathrm{Pb}\left[{\left(\mathrm{M}{\mathrm{g}}_{0.33}\mathrm{N}{\mathrm{b}}_{0.67}\right)}_{1\text{−}x}\mathrm{T}{\mathrm{i}}_x\right]{\mathrm{O}}_3$ (PMN-PT) with generic stoichiometry, undergo a ferroelectric-to-paraelectric phase transition as a function of temperature. The exact transition characterized by Curie temperature ($T_c$) varies as a function of chemistry ($x$), i.e., the concentration of Ti. In this study, we investigated the structural phase transition by exploring the temperature dependence of the single-crystal elastic properties of $\mathrm{Pb}\left[{\left(\mathrm{M}{\mathrm{g}}_{0.33}\mathrm{N}{\mathrm{b}}_{0.67}\right)}_{0.7}\mathrm{T}{\mathrm{i}}_{0.3}\right]{\mathrm{O}}_3$, i.e., $x\approx 0.3$. We used resonant ultrasound spectroscopy to determine the elasticity at elevated temperatures, from which $T_c=398\pm 5\mathrm{K}$ for PMN-PT ($x\approx 0.3$) was determined. We report the full elastic constant tensor ($C_{ij}=\{C_{11},C_{12},C_{44}$}), acoustic attenuation ($Q^{-1}$), longitudinal ($V_P$) and shear ($V_S$) sound velocities, and elastic anisotropy of PMN-PT as a function of temperature for $400<T<871\mathrm{K}$. Temperature trends of the elastic constants $C_{11},C_{44}$ and bulk modulus indicate that at $T>T_c$ the material first stiffens and reaches maxima in the vicinity of the Burns temperature ($T_b\sim 673\mathrm{K}$), followed by a more typical gradual softening of the elastic constants. Similar temperature-dependent anomalies are also observed with anisotropy and $Q^{-1}$, with minima in the vicinity of $T_b$. We used the temperature dependence of $C_{ij}$, $Q^{-1}$, $V_P,V_S$, and anisotropy to infer the evolution of polar nanoregions as the material evolved from $T>T_c$.

A 1D anharmonic chain with a single impurity particle is used to study the vibrational energy localization. Numerical and asymptotic solutions for the symmetric anharmonic localized mode are both presented. The numerical results reveal that the energy localization strengthens with decreasing impurity mass or with increasing anharmonicity. In the weak-anharmonicity limit, the energy localization is close to the harmonic results and varies linearly with respect to the anharmonicity parameter. In the strong-anharmonicity limit, the localized structure tends towards a constant value that is independent of anharmonicity, but as a function of impurity mass. We finally analyze the stability of this symmetric impurity mode, and evidence a stable asymmetric mode as the result of a bifurcation from the symmetric mode for the case of the large impurity mass.

We present low-temperature transport measurements of ${\mathrm{C}}_{60}$-based single-molecule transistors fabricated using ferromagnetic break junction devices with planar elliptical leads, revealing a gate-modulated single-channel spin-$\frac{1}{2}$ Kondo effect. The shape anisotropy and dipole interaction of the source and drain electrodes allows for the relative alignment of their respective magnetic moments to be switched between a parallel and an antiparallel configuration. Both the ferromagnetism of the electrodes and the manipulation of their magnetization are shown to impact the magnetotransport in the Kondo regime in a manner consistent with analytical results, but with a magnitude highly sensitive to the precise electrode-molecule geometry and associated coupling asymmetry.

Neutron diffraction and muon spin relaxation ($\mu \mathrm{SR}$) studies are presented for the newly characterized polymorph of ${\mathrm{NiNb}}_2{\mathrm{O}}_6 (\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6)$ with space group ${P4}_2/n$ and $\mu \mathrm{SR}$ data only for the previously known columbite structure polymorph with space group $Pbcn$. The magnetic structure of the ${P4}_2/n$ form was determined from neutron diffraction using both powder and single-crystal data. Powder neutron diffraction determined an ordering wave vector $\vec{k}=(\frac{1}{2},\frac{1}{2},\frac{1}{2})$. Single-crystal data confirmed the same $\vec{k}$ vector and showed that the correct magnetic structure consists of antiferromagnetically coupled chains running along the $a$ or $b$ axis in adjacent ${\mathrm{Ni}}^{2+}$ layers perpendicular to the $c$ axis, which is consistent with the expected exchange interaction hierarchy in this system. The refined magnetic structure is compared with the known magnetic structures of the closely related trirutile phases, ${\mathrm{NiSb}}_2{\mathrm{O}}_6$ and ${\mathrm{NiTa}}_2{\mathrm{O}}_6$. $\mu \mathrm{SR}$ data finds a transition temperature of $T_N\sim 15\mathrm{K}$ for this system, while the columbite polymorph exhibits a lower $T_N=5.7\left(3\right)$ K. Our $\mu \mathrm{SR}$ measurements also allowed us to estimate the critical exponent of the order parameter $\beta$ for each polymorph. We found $\beta =0.25\left(3\right)$ and 0.16(2) for the $\beta$ and columbite polymorphs, respectively. The single-crystal neutron scattering data give a value for the critical exponent $\beta =0.28\left(3\right)$ for $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$, in agreement with the $\mu \mathrm{SR}$ value. While both systems have $\beta$ values less than 0.3, which is indicative of reduced dimensionality, this effect appears to be much stronger for the columbite system. In other words, although both systems appear to be well described by $S=1$ spin chains, the interchain interactions in the $\beta$ polymorph are likely much larger.

We investigate in detail antiferromagnetic (AF) and superconducting (SC) phases as well as their coexistence in the two-dimensional Kondo lattice model on a square lattice, which is a paradigmatic model for heavy-fermion materials. The results presented are mainly obtained using the variational cluster approximation (VCA) and are complemented by analytical findings for the equations of motion of pairing susceptibilities. A particularly interesting aspect is the possibility to have $s$-wave SC near half-filling as reported by Bodensiek et al. [Phys. Rev. Lett. 110, 146406 (2013)] When doping the system, we identify three regions which correspond to an AF metallic phase with small Fermi surface at weak coupling, an AF metal with a different Fermi surface topology at intermediate coupling, and a paramagnetic metal with a large Fermi surface at strong coupling. The transition between these two AF phases is found to be discontinuous at lower fillings, but turns to a continuous one when approaching half-filling. In the quest for $s$-wave superconductivity, only solutions are found which possess mean-field character. No true superconducting solutions caused by correlation effects are found in the $s$-wave channel. In contrast, we clearly identify robust $d$-wave pairing away from half-filling. However, we show that only by treating antiferromagnetism and superconductivity on equal footing, artificial superconducting solutions at half-filling can be avoided. Our VCA findings support scenarios previously identified by variational Monte Carlo approaches and are a starting point for future investigations with VCA and further approaches such as cluster-embedding methods.

Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing the few-body models that can be easily accessed by theoretical or experimental means, to accurately capture the ground-state properties of infinite many-body systems in higher dimensions. The general idea is to embed a small bulk of the infinite model in an “entanglement bath” so that the many-body effects can be faithfully mimicked. The approach we propose is efficient, simple, flexible, sign-problem free, and it directly accesses the thermodynamic limit. The numerical results of the spin models on honeycomb and simple cubic lattices show that the ground-state properties including quantum phase transitions and the critical behaviors are accurately captured by only $O\left(10\right)$ physical and bath sites. Moreover, since the few-body Hamiltonian only contains local interactions among a handful of sites, our work provides different ways of studying the many-body phenomena in the infinite strongly correlated systems by mimicking them in the few-body experiments using cold atoms/ions, or developing quantum devices by utilizing the many-body features.

We discuss the universal spin dynamics in quasi-one-dimensional systems including the real spin in narrow-gap semiconductors like InAs and InSb, the valley pseudospin in staggered single-layer graphene, and the combination of real spin and valley pseudospin characterizing single-layer transition metal dichalcogenides (TMDCs) such as ${\mathrm{MoS}}_2$, ${\mathrm{WS}}_2$, ${\mathrm{MoS}}_2$, and ${\mathrm{WSe}}_2$. All these systems can be described by the same Dirac-like Hamiltonian. Spin-dependent observable effects in one of these systems thus have counterparts in each of the other systems. Effects discussed in more detail include equilibrium spin currents, current-induced spin polarization (Edelstein effect), and spin currents generated via adiabatic spin pumping. Our work also suggests that a long-debated spin-dependent correction to the position operator in single-band models should be absent.