We model bent graphene as a large-radius (>1 nm) single-walled carbon nanotube in order to uncover the origin of its bending rigidity. An analytic formula based on the Hückel molecular orbital theory connects the finite resistance to bending directly to the curvature-induced torsional misalignment of the $\pi$ orbitals no longer of pure $p$ character. The analytical predictions are supported by direct density functional theory-based tight-binding objective molecular dynamics calculations. Our tight-binding theory also gives useful insight into modeling graphene bending with continuum plate mechanics and classical interatomic potentials.

We have performed an ab initio investigation of the electronic properties of the graphene sheet adsorbed by Ru adatoms (Ru/graphene). For a particular set of triangular arrays of Ru adatoms, we find the formation of four (spin-polarized) Dirac cones attributed to a suitable overlap between two hexagonal lattices: one composed by the C sites of the graphene sheet, and the other formed by the surface potential induced by the Ru adatoms. Upon the presence of spin-orbit coupling (SOC) nontrivial band gaps take place at the Dirac cones promoting several topological phases. Depending on the Ru concentration, the system can be topologically characterized among the phases (i) quantum spin Hall (QSH), (ii) quantum anomalous Hall (QAH), (iii) metal, (iv) or trivial insulator. For each concentration, the topological phase is characterized by the ab initio calculation of the Chern number.

We investigate a resonantly modulated harmonic mode, dispersively coupled to a nonequilibrium few-level quantum system. We focus on the regime where the relaxation rate of the system greatly exceeds that of the mode, and develop a quantum adiabatic approach for analyzing the dynamics. Semiclassically, the dispersive coupling leads to a mutual tuning of the mode and system into and out of resonance with their modulating fields, leading to multistability. In the important case where the system has two energy levels and is excited near resonance, the compound system can have up to three metastable states. Nonadiabatic quantum fluctuations associated with spontaneous transitions in the few-level system lead to switching between the metastable states. We provide parameter estimates for currently available systems.

We numerically investigate critically delocalized wave functions in models of two-dimensional Dirac fermions, subject to vector potential disorder. These describe the surface states of three-dimensional topological superconductors, and can also be realized through long-range correlated bond randomness in artificial materials like molecular graphene. A “frozen” regime can occur for strong disorder in these systems, wherein a single wave function presents a few localized peaks separated by macroscopic distances. Despite this rarefied spatial structure, we find robust correlations between eigenstates at different energies, at both weak and strong disorder. The associated level statistics are always approximately Wigner-Dyson. The system shows generalized Chalker (quantum critical) scaling, even when individual states are quasilocalized in space. We confirm analytical predictions for the density of states and multifractal spectra. For a single Dirac valley, we establish that finite energy states show universal multifractal spectra consistent with the integer quantum Hall plateau transition. A single Dirac fermion at finite energy can therefore behave as a “Quantum Hall critical metal.” For the case of two valleys and non-Abelian disorder, we verify predictions of conformal field theory. Our results for the non-Abelian case imply that both delocalization and conformal invariance are topologically protected for multivalley topological superconductor surface states.

Two-dimensional surface-scattering dynamics are central in the physics of topological insulators. Numerous electrical and optical measurements have evidenced that the origins of novel optoelectronic response can be traced back to Dirac surface-electron dynamics. Intrinsic surface dynamics, however, remain elusive because these experiments cannot access the frequencies of the surface-scattering rate. Time-resolved terahertz spectroscopy is the only apparatus for directly probing the collective response of low-energy electronic transitions. Here, by utilizing ultrafast optical-pump terahertz-probe spectroscopy, we discovered anomalous characteristics of the surface-scattering dynamics. Upon photoexcitation, the surface-scattering rate is increased and results in negative dynamic conductance at low temperature. Surprisingly, the differential changes of the surface-scattering rate are strongly reduced by photoexcited electrons at elevated temperature. We find that this nontrivial surface-electron dynamics is due to opening a carrier-relaxation channel from bulk to the surface state—one distinct characteristic of topological insulators. Our observations reveal unexpected surface dynamics of hot Dirac electrons, providing experimental a priori knowledge toward ultrafast optoelectronic operations.

The Mott-Anderson transition in the disordered charge-transfer model displays several new features in comparison to what is found in the disordered single-band Hubbard model, as recently demonstrated by large-scale computational (statistical dynamical mean-field theory) studies. Here we show that a much simpler typical medium theory approach (TMT-DMFT) to the same model is able to capture most qualitative and even quantitative aspects of the phase diagram, the emergence of an intermediate electronic Griffiths phase, and the critical behavior close to the metal-insulator transition. The conceptual and mathematical simplicity of the TMT-DMFT formulation thus makes it possible to gain useful new insight into the mechanism of the Mott-Anderson transition in these models.

Third-harmonic generation may be dramatically enhanced in monolayer graphene by inserting it in a properly designed structure. In addition, placing graphene within the defect layer of an asymmetric, one-dimensional photonic crystal triggers nearly 100% narrowband absorption. We demonstrate that the improved field localization within the defect state enhances third-harmonic generation by nearly five orders of magnitude compared with bare monolayer graphene. Saturation of the third-order susceptibility plays a role at both fundamental and third-harmonic frequencies. We discuss the benefits of including graphene within the structure for both signals.

In quasi-two-dimensional electron systems of layered transition metal dichalcogenides (TMDs) there is still controversy about the nature of the transitions to charge-density wave (CDW) phases, i.e., whether they are described by a Peierls-type mechanism or by a lattice-driven model. By performing scanning tunneling microscopy experiments on canonical TMD-CDW systems, we image the electronic modulation and the lattice distortion separately in $2\mathrm{H}\text{−}\mathrm{Ta}{\mathrm{S}}_2$, $\mathrm{Ta}{\mathrm{Se}}_2$, and $\mathrm{Nb}{\mathrm{Se}}_2$. Across the three materials, we found dominant lattice contributions instead of the electronic modulation expected from Peierls transitions, in contrast to the CDW states, which show the hallmark of contrast inversion between filled and empty states. Our results imply that periodic lattice distortion plays a vital role in the formation of CDW phases in TMDs and illustrate the importance of taking into account the more complicated lattice degrees of freedom when studying correlated electron systems.

We performed ${}^{13}\mathrm{C}$-NMR experiment and measured spin-lattice relaxation rate divided by temperature $1/T_{1}T$ near the superconducting (SC) transition temperature $T_c$ in $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Br ($\kappa$-Br salt), and $\kappa$-(BEDT-TTF)${}_2$Cu(NCS)${}_2$ ($\kappa$-NCS salt). We observed the reduction of $1/T_{1}T$ starting at the temperature higher than $T_c$ in $\kappa$-Br salt. Microscopic observation of the quasiparticle density of states in the fluctuating SC state revealed the effects of short-range Cooper pairs induced in the normal state to the quasiparticle density of states. We also performed systematic measurements in the fields both parallel and perpendicular to the conduction plane in $\kappa$-Br and $\kappa$-NCS salts, and confirmed that the reduction of $1/T_{1}T$ above $T_c$ is observed only in $\kappa$-Br salt regardless of the external field orientation.

A numerically efficient methodology that allows for relativistic calculations including spin-orbit coupling for spatially anisotropic potentials is employed to study the energetics and electronic properties of In/Si(111)($4\times 1$)/($8\times 2$) nanowires within density-functional theory. For the subtle total energy balance between the metallic In zigzag chain structure observed at room temperature and the insulating In hexagons that form below the critical temperature, scalar-relativistic corrections to the kinetic energy are clearly far more important than the spin-orbit coupling. On the other hand, a relativistic treatment including spin-orbit coupling is required to describe correctly the electronic band structure that shows a large, strongly anisotropic $k$-point-dependent spin splitting of the In-related states at the $X$ point of the surface Brillouin zone. Suitably combined with the metal-insulator transition, the resulting quasi-1D Rashba effect may be used for spin filtering.

We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. The starting point is a microscopic description of the system in terms of a many-body quantum master equation, where coherent and driven-dissipative dynamics occur on an equal footing. An equivalent Keldysh real-time functional integral reformulation opens up the problem to a practical evaluation using the tools of quantum field theory. In particular, we develop a functional renormalization group approach to quantitatively explore the universality class of this stationary nonequilibrium system. Key results comprise the emergence of an asymptotic thermalization of the distribution function, while manifest nonequilibrium properties are witnessed in the response properties in terms of a new, independent critical exponent. Thus, the driven-dissipative microscopic nature is seen to bear observable consequences on the largest length scales. The absence of two symmetries present in closed equilibrium systems—underlying particle number conservation and detailed balance, respectively—is identified as the root of this new nonequilibrium critical behavior. Our results are relevant for broad ranges of open quantum systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases.

The exact ground state of the reduced BCS Hamiltonian is investigated numerically for large system sizes and compared with the BCS ansatz. A “canonical” order parameter is found to be equal to the largest eigenvalue of Yang's reduced density matrix in the thermodynamic limit. Moreover, the limiting values of the exact analysis agree with those obtained for the BCS ground state. Exact results for the ground-state energy, level occupations, and a pseudospin-pseudospin correlation function are also found to converge to the BCS values already for relatively small system sizes. However, discrepancies persist for a pair-pair correlation function, for interlevel correlations of occupancies and for the fidelity susceptibility, even for large system sizes where these quantities have visibly converged to well-defined limits. Our results indicate that there exist nonperturbative corrections to the BCS predictions in the thermodynamic limit.

The local structures around Nb and Pb in the prototypical relaxor ferroelectric Pb(Mg${}_{1/3}$Nb${}_{2/3}$)O${}_3$ (PMN) were investigated by x-ray fluorescence holography. The separate atomic images of nearest Pb around Nb revealed acute and obtuse rhombohedral structures of the crystal unit cells. The Pb-Pb correlated images showed a local structure of body-center-like $2a_0\times 2a_0\times 2a_0$ superlattice, proving a rigid three-dimensional network structural model combining the two kinds of rhombohedrons. The Pb atoms in the networks are positionally stable, while the other Pb atoms are fluctuating. This superstructure and the fluctuating Pb and Nb atoms are believed to play an important role in the relaxor behavior of PMN at the atomic level.

X-ray absorption near-edge structure and extended x-ray absorption fine structure spectroscopy at the Ru $K$ edge of Ru-doped PbSc${}_{0.5}$Ta${}_{0.5}$O${}_3$ (PST-Ru), PbSc${}_{0.5}$Nb${}_{0.5}$O${}_3$ (PSN-Ru), and 0.9PbZn${}_{1/3}$Nb${}_{2/3}$O${}_3$-0.1PbTiO${}_3$ (PZN-0.1PT-Ru) as well as at the Ta $L_3$ edge of PST-Ru and the Nb $K$ edge of PSN-Ru was applied to study the short- and intermediate-range atomic arrangements in perovskite-type (ABO${}_3$) relaxor ferroelectrics. The compounds were also analyzed by complementary Raman scattering, visible/near-visible absorption spectroscopy, and synchrotron x-ray single-crystal diffraction. The results show that Ru is octahedrally coordinated in all three relaxor host matrices but the average oxidation state of Ru in PST-Ru and PSN-Ru is ∼4.4, whereas it is ∼3.8 in PZN-0.1PT-Ru. In PbSc${}_{0.5}$$B^{\prime \prime }$${}_{0.5}$O${}_3$ ($B^{\prime \prime }$ = Ta, Nb) Ru substitutes for the $B^{\prime \prime }$ cations in the form of isolated point defects, while in PZN-0.1PT-Ru Ru replaces adjacent $A$ and $B$ sites, forming a chainlike structural species of face-sharing elongated octahedra. Chemical 1:1 $B$-site order as well as dynamic $B$O${}_6$ tilting is observed around both the Ru dopant and the major $B^{\prime \prime }$ cation in PST-Ru and PSN-Ru regardless of the fact that according to x-ray diffraction at ambient conditions, the average structure is cubic with weak or no long-range chemical order. Pb cations are off-center displaced from the prototypic cubic $A$ site for all three compounds and in Ru-doped PbSc${}_{0.5}$$B^{\prime \prime }$${}_{0.5}$O${}_3$ the $B$O${}_6$ tilt angle correlates with the degree of coherent $B$-Pb distances.

Solid understanding of current induced torques is a key to the development of current and voltage controlled magnetization dynamics in ultrathin magnetic heterostructures. To evaluate the size and direction of such torques, or effective fields, a number of methods have been employed. Here, we examine the adiabatic (low-frequency) harmonic Hall voltage measurement that has been used to study the effective field. We derive an analytical formula for the harmonic Hall voltages to evaluate the effective field for both out of plane and in-plane magnetized systems. The formula agrees with numerical calculations based on a macrospin model. Two different in-plane magnetized films, Pt|CoFeB|MgO and CuIr|CoFeB|MgO are studied using the formula developed. The effective field obtained for the latter system shows relatively good agreement with that estimated using spin torque switching phase diagram measurements reported previously. Our results illustrate the versatile applicability of harmonic Hall voltage measurement for studying current induced torques in magnetic heterostructures.

We present a detailed study for the finite-frequency current noise of a Kondo quantum dot in the presence of a magnetic field by using a recently developed real-time functional renormalization group approach [C. P. Moca, P. Simon, C. H. Chung, and G. Zaránd, Phys. Rev. B 83, 201303(R) (2011)]. The scaling equations are modified in an external magnetic field; the couplings and nonlocal current vertices become strongly anisotropic, and develop new singularities. Consequently, in addition to the natural emission threshold frequency, $\hslash \omega =\left|eV\right|$, a corresponding singular behavior is found to emerge in the noise spectrum at frequencies $\hslash \omega \approx |eV\pm B|$. The predicted singularities are measurable with present-day experimental techniques.

We study the effects of electron-electron interactions on the steady-state characteristics of a hexagonal molecular ring in a magnetic field as a model for a benzene molecular junction. The system is driven out of equilibrium by applying a bias voltage across two metallic leads. We employ a model Hamiltonian approach to evaluate the effects of on-site as well as nearest-neighbor density-density–type interactions in a physically relevant parameter regime. Results for the steady-state current, charge density, and magnetization in three different junction setups (para, meta, and ortho) are presented. Our findings indicate that interactions beyond the mean-field level renormalize voltage thresholds as well as current plateaus. Electron-electron interactions lead to substantial charge redistribution as compared to the mean-field results. We identify a strong response of the circular current on the electronic structure of the metallic leads. Our results are obtained by steady-state cluster perturbation theory, a systematically improvable approximation to study interacting molecular junctions out of equilibrium, even in magnetic fields. Within this framework, general expressions for the current, charge density, and magnetization in the steady state are derived. The method is flexible and fast and can straightforwardly be applied to effective models as obtained from ab initio calculations.

The deposition of alkaline earths onto Ge(100) surfaces leads to well-ordered arrays of narrow trenches and elongated plateaus that extend for thousands of angstroms. Using scanning tunneling microscopy (STM) in conjunction with density functional theory (DFT), the atomic scale details of these nanostructures are revealed and the driving force responsible for their formation is evaluated. The STM data reveal a dramatic contrast reversal when the polarity of the imaging bias is switched. An energetically favorable structure for the plateaus was found using DFT that can reproduce all of the observed features. This structure is based upon a double dimer vacancy model in which Sr atoms displace two Ge dimers from the surface. Interestingly, the ordered plateau-trench structure is unique to Ge(100) despite the structural and chemical similarities to the Si(100) surface.

We observe spatial confinement of Dirac states on epitaxial graphene quantum dots with low-temperature scanning tunneling microscopy after using oxygen as an intercalant to suppress the surface state of Ir(111) and to effectively decouple graphene from its metal substrate. We analyze the confined electronic states with a relativistic particle-in-a-box model and find a linear dispersion relation. The oxygen-intercalated graphene is $p$ doped [$E_{\mathrm{D}}=\left(0.64\pm 0.07\right)$ eV] and has a Fermi velocity close to the one of free-standing graphene [$v_{\mathrm{F}}=\left(0.96\pm 0.07\right)\times {10}^6$ m/s].