In an effort to improve the spin coupling in single-molecule magnets, we rationally designed a new building-block molecule with significantly enhanced spin coupling compared to a previously established molecule. We relate this to a stabilization of aromaticity in the central connecting carbon ring, promoting the spin-polarization mechanism. This correlation between magnetic and electronic properties is supported by bulk measurements as well as submolecularly resolved scanning tunneling microscopy and spectroscopy experiments, where we found distinct differences in the local density of states distribution of the two molecules, especially at the central carbon ring. While the established molecule exhibits localized, spatially decoupled and even switchable states, the improved building block exhibits symmetric local density of states delocalized over the entire molecule, also revealing that this main characteristic electronic property is preserved upon adsorption on a metal surface. Due to their planar geometry, these molecules can serve as model systems for scanning-probe based studies of molecular magnetism.

We discuss the simulation of the low-energy effective field theory (EFT) for graphene in the presence of an external magnetic field. Our fully nonperturbative calculation uses methods of lattice gauge theory to study the theory using a hybrid Monte Carlo approach. We investigate the phenomenon of magnetic catalysis in the context of graphene by studying the chiral condensate which is the order parameter characterizing the spontaneous breaking of chiral symmetry. In the EFT, the symmetry-breaking pattern is given by $U\left(4\right)\to U\left(2\right)\times U\left(2\right)$. We also comment on the difficulty, in this lattice formalism, of studying the time-reversal-odd condensate characterizing the ground state in the presence of a magnetic field. Finally, we study the mass spectrum of the theory, in particular the Nambu-Goldstone mode as well as the Dirac quasiparticle, which is predicted to obtain a dynamical mass.

Plastic deformation of metallic glasses performed well below the glass transition temperature leads to the formation of shear bands as a result of shear localization. It is believed that shear banding originates from individual stress concentrators having quadrupolar symmetry. To elucidate the underlying mechanisms of shear-band formation, microstructural investigations were carried out on sheared zones using transmission electron microscopy. Here we show evidence of a characteristic signature present in shear bands manifested in the form of sinusoidal density variations. We present an analytical solution for the observed postdeformation state derived from continuum mechanics using an alignment of quadrupolar stress-field perturbations for the plastic events. Since we observe qualitatively similar features for three different types of metallic glasses that span the entire range of characteristic properties of metallic glasses, we conclude that the reported deformation behavior is generic for all metallic glasses, and thus has far-reaching consequences for the deformation behavior of amorphous solids in general.

The typical medium dynamical cluster approximation (TMDCA) is reformulated in the language of multiple scattering theory to make possible first-principles calculations of the electronic structure of substitutionally disordered alloys including the effect of Anderson localization. The TMDCA allows for a systematic inclusion of nonlocal multisite correlations and at the same time provides an order parameter, the typical density of states, for the Anderson localization transition. The relation between the dynamical cluster approximation and the multiple scattering theory is analyzed, and is illustrated for a tight-binding model.

We investigate nonequilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover) near the temperature $T_{\mathrm{u}}=0.282J$ of the equilibrium ${\mathbb{Z}}_2$-vortex unbinding. We show that starting from the high-temperature initial state, due to the presence of ${\mathbb{Z}}_2$ vortices in the system being considered, in a broad temperature range $T<T_{\mathrm{u}}$ the dynamic properties in the intermediate time range are similar to those of the two-dimensional XY model below the Berezinskii-Kosterlitz-Thouless transition. The interaction of ${\mathbb{Z}}_2$ vortices with spin-wave degrees of freedom does not emerge until rather long times.

The mean-field theory for disordered electron systems without interaction is widely and successfully used to describe equilibrium properties of materials over the whole range of disorder strengths. However, it fails to take into account the effects of quantum coherence and information of localization. Vertex corrections due to multiple backscatterings may drive the electrical conductivity to zero and make expansions around the mean field in strong disorder problematic. Here, we present a method for the calculation of two-particle quantities which enables us to characterize the metal-insulator transitions in disordered electron systems by using the typical medium dynamical cluster approximation. We show how to include vertex corrections and information about the mobility edge in the typical mean-field theory. We successfully demonstrate the application of the developed method by showing that the conductivity formulated in this way properly characterizes the metal-insulator transition in disordered systems.

We have systematically investigated the evolution of the magnetic structure of the bilayer ruthenate $\mathrm{C}{\mathrm{a}}_3{\left(\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x\right)}_2{\mathrm{O}}_7$ induced upon Mn doping. For $0<x\le 0.03$, the materials exhibit the same spin structure as that of the parent compound at low temperature, while an incommensurate cycloidal magnetic structure emerges at $T$ slightly above the metal-insulator transition (MIT) temperature $\left(T_{\mathrm{MIT}}\right)$. In contrast, for $x\ge 0.04$ the ground state becomes a G-type antiferromagnetic Mott insulator. Furthermore, we have observed magnetic-field-induced transitions in $\mathrm{C}{\mathrm{a}}_3{\left(\mathrm{R}{\mathrm{u}}_{0.96}\mathrm{M}{\mathrm{n}}_{0.04}\right)}_2{\mathrm{O}}_7$, which is positioned at the phase boundary. Below $T_{\mathrm{MIT}}$, the magnetic transition is accompanied by a structural transition, as well as a dramatic change in the electronic properties from a Mott insulator to a localized phase. On the contrary, an incommensurate-to-commensurate spin structure transition is observed for $T_{\mathrm{MIT}}<T<T_{\mathrm{ICM}}$. Our results suggest strong competing magnetic tendencies in this bilayer ruthenate system that are very susceptible to $3d$ transition-metal substitution and magnetic field.

We present a theoretical study of field-induced magnetic phases in the honeycomb Kitaev-Heisenberg model, which is believed to describe the essential physics of Mott insulators with strong spin-orbit coupling such as $A_2{\mathrm{IrO}}_3$ and $\alpha \text{−}{\mathrm{RuCl}}_3$. We obtain a rich finite temperature phase diagram in which the competition between the Zeeman coupling and thermal fluctuations gives rise to both collinear zigzag phases and noncoplanar magnetic orders. Our large-scale classical Monte Carlo simulations also unveil intriguing commensurate-incommensurate transitions and multiple-$\mathbf{Q}$ incommensurate phases at high field. Experimental implications are also discussed.

Spinons are among the generic excitations in one-dimensional spin systems; they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show that a representation in terms of hopping and Bogoliubov spinon processes, which we call “spinon-pair” operators, and their combination is possible. We refer to such a representation as second quantized form. Neglecting terms which change the number of spinons yields the variational results. Treating the bilinear and quartic terms by continuous unitary transformations leads to considerably improved results. Thus, we provide the proof of principle that systems displaying massive spinons as elementary excitations can be treated in second quantization based on spinon-pair representation.

We present a quantum model which provides enhanced understanding of recent transverse magnetic focusing experiments on graphene $p\text{−}n$ junctions. Spatially resolved flow maps of local particle current density show quantum interference and $p\text{−}n$ junction filtering effects, which are crucial to explaining the device operation. The Landauer-Büttiker formula is used alongside dephasing edge contacts to give exceptional agreement between simulated nonlocal resistance and the recent experiment by Chen et al. [Science 353, 1522 (2016)]. The origin of positive and negative focusing resonances and off-resonance characteristics are explained in terms of quantum transmission functions. Our model also captures subtle features from experiment, such as the $p\text{−}{p}^{-}$ to $p\text{−}{p}^{+}$ transition and the second $p\text{−}n$ focusing resonance.

Electrically gating of trilayer graphene (TLG) opens a band gap offering the possibility to electrically engineer TLG quantum dots. We study the energy levels of such quantum dots and investigate their dependence on a perpendicular magnetic field $B$ and different types of stacking of the graphene layers. The dots are modeled as circular and confined by a truncated parabolic potential which can be realized by nanostructured gates or position-dependent doping. The energy spectra exhibit the intervalley symmetry $E_K^e\left(m\right)=-E_{K^{\prime }}^h\left(m\right)$ for the electron $\left(e\right)$ and hole $\left(h\right)$ states, where $m$ is the angular momentum quantum number and $K$ and $K^{\prime }$ label the two valleys. The electron and hole spectra for $B=0$ are twofold degenerate due to the intervalley symmetry $E_K\left(m\right)=E_{K^{\prime }}[-(m+1)]$. For both ABC $[\alpha =1.5$ (1.2) for large (small) $R]$ and ABA $\left(\alpha =1\right)$ stackings, the lowest-energy levels show approximately a $R^{-\alpha }$ dependence on the dot radius $R$ in contrast with the $1/R^3$ one for ABC-stacked dots with infinite-mass boundary. As functions of the field $B$, the oscillator strengths for dipole-allowed transitions differ drastically for the two types of stackings.

In-plane composite structures constructed of the stripes or core/shells of single-layer GaN and AlN, which are joined commensurately, display a diversity of electronic properties that can be tuned by the size of their constituents. In heterostructures, the dimensionality of the electrons changes from two dimensional (2D) to one dimensional (1D) upon their confinements in wide constituent stripes, leading to the type-I band alignment and hence multiple quantum well structure in the direct space. The $\delta$ doping of one wide stripe by another narrow stripe results in local narrowing or widening of the band gap. A single quantum well structure is acquired from the finite-size AlN-GaN-AlN junctions. In a patterned array of GaN/AlN core/shells, the dimensionality of the electronic states is reduced from two dimensional to zero dimensional, forming multiple quantum dots in large GaN cores, while 2D electrons propagate in multiply connected AlN shell as if they are in a supercrystal. A consistent and detailed discussion of the effects of confinement in momentum and direct spaces is provided. As a result of confinement, the variation of the band gap in the direct space is found to be rather different from the edges of the conduction and valence bands inferred from the band edges of constituent 2D single-layer GaN and AlN. Even if all the results in this study pertain to the free-standing single-layer composite structures, the effects of the different substrates over which these composites can grow are examined in detail. This study unveils the potential of composite structures in designing novel nanomaterials. These predictions are obtained from first-principles calculations based on density functional theory on 2D GaN and AlN compound semiconductors which were synthesized recently.

Circular dichroism (CD) of a single-wall carbon nanotube (SWNT) is calculated as a function of the wavelength of light. Because of the symmetry between the $K$ and $K^{\prime }$ points in the hexagonal Brillouin zone, the conventional theory for CD intensity gives a zero value in which the absorption probability near the $K$ point for right-handed circular polarized light and that near the $K^{\prime }$ point for left-handed circular polarized light cancel each other. Considering the phase differences of the light for carbon atoms of a nanotube, which are beyond so-called dipole approximation, a formulation of CD for a SWNT is presented. Analytic and numerical calculations show (1) the alternating sign of the CD intensity at $E_{ii}$ ($i=1,2,3,...$) van Hove singular energies and (2) opposite sign of the CD values as a function of wavelength of the light for different types and handedness of nanotubes, which reproduce the experimental results. In the metallic SWNTs, we predict the opposite sign of CD values for split $E_{ii}^{+}$ and $E_{ii}^{-}$.

In the search for states with non-Abelian statistics, we explore the fractional quantum Hall effect in a system of two-dimensional (2D) charge carrier holes. We propose a method of mapping states of holes confined to a finite width quantum well in a perpendicular magnetic field to states in a spherical shell geometry. We take into account strong coupling between the spin and motion of charge parallel and perpendicular to the 2D layer. This method gives the single-particle hole states used in the exact diagonalization of systems with a small number of holes in the presence of Coulomb interactions, density matrix renormalization group, and topological entanglement entropy calculations. The hole quantum Hall state at half filling of the ground state in a magnetic field near the crossing of single-hole states is likely the Moore-Read Pfaffian state.

The pairing of composite fermions (CFs), i.e., electron-flux quasiparticles, is commonly proposed to explain the even-denominator fractional quantum Hall state observed at $\nu =5/2$ in the first excited $\left(N=1\right)$ Landau level (LL) of a two-dimensional electron system (2DES). While well established to exist in the lowest $\left(N=0\right)$ LL, much is unknown about CFs in the $N=1$ LL. Here we carry out geometric resonance measurements to detect CFs at $\nu =5/2$ by subjecting the 2DES to a one-dimensional density modulation. Our data, taken at a temperature of 0.3 K, reveal no geometric resonances for CFs in the $N=1$ LL. In stark contrast, we observe clear signatures of such resonances when $\nu =5/2$ is placed in the $N=0$ LL of the antisymmetric subband by varying the 2DES width. This finding implies that the CFs' mean free path is significantly smaller in the $N=1$ LL compared to the $N=0$ LL. Our additional data as a function of in-plane magnetic field highlight the role of subband index and establish that CFs at $\nu =5/2$ in the $N=0$ LL are more anisotropic in the symmetric subband than in the antisymmetric subband.

We investigate transport and thermoelectric properties of hybrid systems based on a single-level quantum dot and one superconducting lead. The other lead is generally normal-metallic ferromagnet. In the latter case, single-particle transport is spin polarized. Our main interest is in the interplay of Andreev tunneling of Cooper pairs and single-particle tunneling. The latter is responsible for relatively large thermopower and figure of merit due to a diverging density of single-particle states at the superconducting gap edges. A system with ferromagnetic and superconducting leads can also reveal spin thermoelectric phenomena. A finite superconducting gap is considered within the BCS theory, and the thermoelectric coefficients are calculated by means of nonequilibrium Green's function technique within Hartree-Fock–type approximation with respect to the intradot Coulomb interaction.

The magnetic ground state of the quasi-one-dimensional spin-1 antiferromagnetic chain is sensitive to the relative sizes of the single-ion anisotropy $\left(D\right)$ and the intrachain $\left(J\right)$ and interchain $\left(J^{\prime }\right)$ exchange interactions. The ratios $D/J$ and $J^{\prime }/J$ dictate the material's placement in one of three competing phases: a Haldane gapped phase, a quantum paramagnet, and an $XY$-ordered state, with a quantum critical point at their junction. We have identified $\left[\mathrm{Ni}\left({\mathrm{HF}}_2\right){\left(\mathrm{pyz}\right)}_2\right]{\mathrm{SbF}}_6$, where pyz = pyrazine, as a rare candidate in which this behavior can be explored in detail. Combining neutron scattering (elastic and inelastic) in applied magnetic fields of up to 10 tesla and magnetization measurements in fields of up to 60 tesla with numerical modeling of experimental observables, we are able to obtain accurate values of all of the parameters of the Hamiltonian $[D=13.3(1)$ K, $J=10.4\left(3\right)$ K, and $J^{\prime }=1.4\left(2\right)$ K], despite the polycrystalline nature of the sample. Density-functional theory calculations result in similar couplings $(J=9.2$ K, $J^{\prime }=1.8$ K) and predict that the majority of the total spin population resides on the Ni(II) ion, while the remaining spin density is delocalized over both ligand types. The general procedures outlined in this paper permit phase boundaries and quantum-critical points to be explored in anisotropic systems for which single crystals are as yet unavailable.

We have investigated crystal structure and magnetic properties of three $S=1{\mathrm{V}}^{3+}$ Ising-like anisotropic kagome lattice antiferromagnets, ${\mathrm{Cs}}_2\mathrm{K}{\mathrm{V}}_3{\mathrm{F}}_{12},{\mathrm{Cs}}_2\mathrm{Na}{\mathrm{V}}_3{\mathrm{F}}_{12}$, and ${\mathrm{Rb}}_2\mathrm{Na}{\mathrm{V}}_3{\mathrm{F}}_{12}$, using single crystals. Each compound crystallizes in a monoclinic system and has a slightly distorted kagome lattice. Although the magnetic properties are similar, the details depend on the magnitude of magnetic anisotropy. The magnetization and magnetic susceptibility are highly anisotropic owing to anisotropic $g$ factors and Ising-like single ion anisotropy originating from partially unquenched orbital moments of ${\mathrm{V}}^{3+}$, and the easy axis of Ising-like anisotropy is perpendicular to the kagome plane. In contrast to disordered ground states in the isostructural ${\mathrm{Ti}}^{3+}$ $\left(S=1/2\right)$ compounds, the ${\mathrm{V}}^{3+}$ $\left(S=1\right)$ compounds exhibit antiferromagnetic ordering with distorted ${120}^{\circ }$ structure or other nearly coplanar magnetic structure whose basal spin plane includes the easy axis, which is mainly due to large magnetic anisotropy and decrease of quantum fluctuation. Moreover, when magnetic fields are applied perpendicular to the kagome plane, magnetization curves of them show distinct 1/3 and 2/3 magnetization plateaus, which are stabilized by Ising-like single ion anisotropy. In particular, the 2/3 magnetization plateaus are notable magnetic phenomena in kagome lattice antiferromagnets and are due to the combination of spin frustration, Ising-like single ion anisotropy, and the small monoclinic distortion of kagome lattices.

We study a two-orbital $t\text{−}{J}_1\text{−}{J}_2$ model, originally developed to describe iron-based superconductors at low energies, in the presence of bond disorder (via next-nearest-neighbor $J_2$-bond dilution). By using the Bogoliubov–de Gennes approach, we self-consistently calculate the local pairing amplitudes and the corresponding density of states, which demonstrate a change of dominant pairing symmetry from $s_{\pm }$ wave to $d$ wave when increasing disorder strength as long as $J_1\lesssim J_2$. Moreover, the combined pairing interaction and strong bond disorder lead to the formation of $s_{\pm }$-wave “islands” with length scale of the superconducting coherence length embedded in a $d$-wave “sea.” This picture is further complemented by the disorder-averaged pair-pair correlation functions, distinct from the case with potential disorder, where the “sea” is insulating. Due to this inevitable formation of spatial inhomogeneity, the superconducting $T_c$ determined by the superfluid density ${\rho }_s\left(T\right)$ obviously deviates from the value predicted by the conventional Abrikosov-Gorkov theory, where the pairing amplitudes are viewed as uniformly suppressed as the disorder increases.

We clarify the topology of ${}^{3}P_2$ superfluids which are expected to be realized in the inner cores of neutron stars and cubic odd-parity superconductors. ${}^{3}P_2$ phases include uniaxial/biaxial nematic phases and nonunitary ferromagnetic and cyclic phases. Here, we show that all the phases are accompanied by different types of topologically protected gapless fermions: surface Majorana fermions in nematic phases and a quartet of (single) itinerant Majorana fermions in the cyclic (ferromagnetic) phase. Using the superfluid Fermi liquid theory, we also demonstrate that dihedral-two and -four biaxial nematic phases are thermodynamically favored in the weak coupling limit under a magnetic field. It is shown that the tricritical point exists on the phase boundary between these two phases and may be realized in the core of realistic magnetars. We unveil the intertwining of symmetry and topology behind the mass acquisition of surface Majorana fermions in nematic phases.