Density-functional-theory-based electronic structure calculations are carried out to elucidate the origins of the observed electronic properties of molybdenum hollandite K${}_2$Mo${}_8$O${}_{16}$. We find that the Mo${}_4$ cluster in the double Mo chains behaves as a “superatom,” a hypothetical big atom with a single composite molecular orbital, and that the system can be regarded as a solid of the superatoms condensed into a simple monoclinic structure with four superatoms per unit cell, thereby yielding four energy bands near the Fermi level at half filling. Based on an effective model proposed, we argue that K${}_2$Mo${}_8$O${}_{16}$ is a Mott insulator with one electron per superatom, which exhibits strongly frustrated antiferromagnetic spin correlations in the superatomic crystal.

We investigate the expansion of bosons and fermions in a homogeneous lattice after a sudden removal of the trapping potential using exact numerical methods. As a main result, we show that in one dimension, both bosonic and fermionic Mott insulators expand with the same velocity, irrespective of the interaction strength, provided the expansion starts from the ground state of the trapped gas. Furthermore, their density profiles become identical during the expansion; the asymptotic density dynamics is identical to that of initially localized, noninteracting particles, and the asymptotic velocity distribution is flat. The expansion velocity for initial correlated Mott insulating states is therefore independent of the interaction strength and particle statistics. Interestingly, this nonequilibrium dynamics is sensitive to the interaction driven quantum phase transition in the Bose-Hubbard model; while being constant in the Mott phase, the expansion velocity decreases in the superfluid phase and vanishes for large systems in the noninteracting limit. These results are compared to the setup of a recent experiment [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)], where the trap opening was combined with an interaction quench from infinitely strong interactions to finite values. In the latter case, the interaction quench breaks the universal dynamics in the asymptotic regime and the expansion depends on the interaction strength. We carry out an analogous analysis for a two-component Fermi gas, with similar observations. In addition, we study the effect of breaking the integrability of hard-core bosons in different ways; while the fast ballistic expansion from the ground state of Mott insulators in one dimension remains unchanged for finite interactions, we observe strong deviations from this behavior on a two-leg ladder even in the hard-core case. This change in dynamics bares similarities with the dynamics in the dimensional crossover from one to two dimensions observed in the aformentioned experimental study.

The split silicon-vacancy (SiV) defect in diamond is an electrically and optically active color center. Recently, it has been shown that this color center is bright and can be detected at the single defect level. In addition, the SiV defect shows a nonzero electronic spin ground state that potentially makes this defect an alternative candidate for quantum optics and metrology applications beside the well-known nitrogen-vacancy color center in diamond. However, the electronic structure of the defect, the nature of optical excitations and other related properties are not well understood. Here we present advanced ab initio study on SiV defect in diamond. We determine the formation energies, charge transition levels, and the nature of excitations of the defect. Our study unravels the origin of the dark or shelving state for the negatively charged SiV defect associated with the 1.68-eV photoluminescence center.

We present theoretical results on the relationship between the rotational diffusion coefficient of a nanodiamond undergoing Brownian motion and the configuration of nitrogen vacancy centers (NVCs) contained in the particle. Through exact calculations and simulations, we obtain the fluorescence intensity autocorrelation function that is measured in optically detected magnetic resonance experiments conducted at single-particle level. We relate the autocorrelation function to the rotational diffusion coefficient and discuss the influence of different NVC configurations on the outcome of measurements. We believe that our results can be useful in interpreting observations on nanodiamonds that contain multiple nitrogen vacancy centers.

We show that the thermoelectric properties of nanoscale junctions featuring states near the Fermi level strongly depend on the type of resonance generated by such states, which can be either Fano- or Breit-Wigner-like. We give general expressions for the thermoelectric coefficients generated by the two types of resonances and calculate the thermoelectric properties of these systems, which encompass most nanoelectronics junctions. We include simulations of real junctions where metalloporphyrins dithiolate molecules bridge gold electrodes and prove that for some metallic elements the thermoelectric properties show a large variability with respect to the position of the resonance near the Fermi level. We find that the thermopower and figure of merit are largely enhanced when the resonance gets close to the Fermi level and reach values higher than typical values found in other nanoscale junctions. The specific value and temperature dependence are determined by a series of factors such as the strength of the coupling between the state and other molecular states, the symmetry of the state, the strength of the coupling between the molecule and the leads and the spin-filtering behavior of the junction.

The effective theory for bilayer graphene (BLG), subject to parallel/in-plane magnetic fields, is derived. With a sizable magnetic field the trigonal warping becomes irrelevant, and one ends up with two Dirac points in the vicinity of each valley in the low-energy limit, similar to the twisted BLG. Combining twisting and parallel field thus gives rise to a Dirac system with tunable Fermi velocity and cutoff. If the interactions are sufficiently strong, several fully gapped states can be realized in these systems, in addition to the ones in a pristine setup. Transformations of the order parameters under various symmetry operations are analyzed. The quantum critical behavior of various phase transitions driven by the twisting and the magnetic field is reported. The effects of an additional perpendicular field and possible ways to realize the new massive phases are highlighted.

We show that the fractional quantum Hall effect can be phenomenologically described as a special flow of a quantum incompressible Euler liquid. This flow consists of a large number of vortices of the same chirality. In this approach each vortex is identified with an electron while the fluid is neutral. We show that the Laughlin wave function naturally emerges as a stationary flow of the system of vortices in quantum fluid dynamics. Here we develop the hydrodynamics of the vortex liquid and are able to consistently quantize it. As a demonstration of the efficiency of the hydrodynamics we show how subtle features of the fractional quantum Hall effect such as effects of Lorentz shear stress, the structure function, the Hall current in a nonuniform magnetic field, and Hall conductance in a curved spatial landscape naturally follow from the hydrodynamics approach.

Using exact diagonalization and tensor network techniques, we compute the gap for the Affleck-Kennedy-Lieb-Tasaki (AKLT) Hamiltonian in one and two spatial dimensions. Tensor network methods are used to extract physical properties directly in the thermodynamic limit, and we support these results using finite-size scalings from exact diagonalization. Studying the AKLT Hamiltonian perturbed by an external field, we show how to obtain an accurate value of the gap of the original AKLT Hamiltonian from the field value at which the ground state verifies $e_0<0$, which is a quantum critical point. With the tensor network renormalization group methods we provide direct evidence of a finite gap in the thermodynamic limit for the AKLT models in the one-dimensional chain and two-dimensional hexagonal and square lattices. This method can be applied generally to Hamiltonians with rotational symmetry, and we also show results beyond the AKLT model.

It is known that zigzag graphene edge is able to support edge states: There is a nondispersive single-electron band localized near the zigzag edge. However, it is generally believed that no edge states exist near the unmodified armchair edge, while they do appear if the edge is subjected to suitable modifications (e.g., chemical functionalization). We explicitly present two types of edge modification which support the localized states. Unlike zigzag edge states, which have zero energy and show no dispersion, properties of the armchair localized states depend sensitively on the type of edge modification. Under suitable conditions they demonstrate pronounced dispersion. While the zigzag edge state wave function decays monotonously when we move away from the edge, the armchair edge state wave function shows nonmonotonous decay. Such states may be observed in scanning tunneling spectroscopy experimentally.

We investigate the effect of an in-plane ac electric field coupled to electrons in the honeycomb lattice and show that it can be used to manipulate the Dirac points of the electronic structure. We find that the position of the Dirac points can be controlled by the amplitude and the polarization of the field for high-frequency drivings, providing a new platform to achieve their merging, a topological transition which has not been observed yet in electronic systems. Importantly, for lower frequencies we find that the multiphoton absorptions and emissions processes yield the creation of additional pairs of Dirac points. This provides an additional method to achieve the merging transition by just tuning the frequency of the driving. Our approach, based on Floquet formalism, is neither restricted to specific choice of amplitude or polarization of the field, nor to a low-energy approximation for the Hamiltonian.

We study the coupling between elastic membrane distortions and Dirac electrons in a dynamical sheet of graphene. This coupling can be understood in terms of an effective gauge field acting on electrons, which has two contributions: (quasi)static and purely dynamic, of the Berry-phase origin, both in general engendering fictitious electric and magnetic fields. The static gauge potential (along with the electromagnetic field that it parametrizes) is known to be of opposite sign at the $K$ and $K^{\prime }$ valleys, while we find the same dynamic gauge potential at the two valleys, similarly to the true electromagnetic field. The mechanical fluctuations can thus mediate an indirect coupling between charge and valley degrees of freedom.

We investigate the electrical conductivity of spin-polarized graphene in the presence of short-ranged magnetic scatterers within the relaxation time approximation and the semiclassical Boltzmann approach. Spin-flip scattering of the itinerant electrons from the majority spin subband into the minority one results in a minimum in the electrical resistivity at a finite temperature. While this behavior is reminiscent of the renowned Kondo effect, it has an entirely different origin and differs from the Kondo effect in several aspects. In particular, unlike the Kondo effect, this is a single particle phenomenon, and it does not require antiferromagnetic coupling between the magnetic moments of impurities and spins of the itinerant electrons.

We study the spin-phonon drag effect in the magnetothermal transport of spin-$\frac{1}{2}$ two-leg ladders coupled to lattice degrees of freedom. Using a bond-operator description for the triplon excitations of the spin ladder and magnetoelastic coupling to acoustic phonons, we employ the time convolutionless projection operator method to derive expressions for the diagonal and off-diagonal thermal conductivities of the coupled two-component triplon-phonon system. We find that for magnetoelastic coupling strengths and diagonal scattering rates relevant to copper-oxide spin ladders the drag heat conductivity can be of similar magnitude as the diagonal triplon heat conductivity. Moreover, we show that the drag and diagonal conductivities display very similar overall temperature dependencies. Finally, the drag conductivity is shown to be rather susceptible to external magnetic fields.

Based on the minimum two-orbital model and the phase diagram recently proposed by Tai et al. [Europhys. Lett. 103, 67001 (2013)] for both electron- and hole-doped 122 iron-based superconducting compounds, we use the Bogoliubov-de-Gennes equations to perform a comprehensive investigation of the evolution of the Fermi surface (FS) topology in the presence of the collinear spin-density-wave (SDW) order as the doping is changed. In the parent compound, the ground state is the SDW order, where the FS is not completely gapped, and two types of Dirac cones, one electron-doped and the other hole-doped emerge in the magnetic Brillouin zone. Our findings are qualitatively consistent with recent angle-resolved photoemission spectroscopy and magnetoresistivity measurements. We also examine the FS evolution of both electron- and hole-doped cases and compare them with measurements, as well as with those obtained by other model Hamiltonians.

Vacancy dynamics in oxides are vital for understanding redox reactions and resulting memristive effects or catalytic activity. We present a method to track and drive vacancies which we apply to metadynamics simulation of oxygen vacancies (V${}_{\mathrm{O}}{}^{2+}$) in rutile, demonstrating its effectiveness. Using the density-functional based tight-binding method, it is possible to explore the free energy hyperplane of oxygen vacancies in TiO${}_2$. We show that the migration of V${}_{\mathrm{O}}{}^{2+}$ in TiO${}_2$ is governed by the jump with the highest degree of topological interconnection. Free energy profiles are consistent with minimum energy paths.

To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU($N$) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU($N$) Néel and valence-bond solid phases is characterized for $N=2$, 3, and 4 on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size ($L=256$) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y\equiv 1/\nu$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field ${\Psi }^2$ for the SU(3) model.

We study the phase transition from a topological to a normal insulator with concentration $x$ in (Bi${}_{1-x}$In${}_x{)}_2$Se${}_3$ and (Bi${}_{1-x}$Sb${}_x{)}_2$Se${}_3$ in the Bi${}_2$Se${}_3$ crystal structure. We carry out first-principles calculations on small supercells, using this information to build Wannierized effective Hamiltonians for a more realistic treatment of disorder. Despite the fact that the spin-orbit coupling (SOC) strength is similar in In and Sb, we find that the critical concentration $x_{\mathrm{c}}$ is much smaller in (Bi${}_{1-x}$In${}_x{)}_2$Se${}_3$ than in (Bi${}_{1-x}$Sb${}_x{)}_2$Se${}_3$. For example, the direct supercell calculations suggest that $x_{\mathrm{c}}$ is below $12.5\%$ and above 87.5$\%$ for the two alloys, respectively. More accurate results are obtained from realistic disordered calculations, where the topological properties of the disordered systems are understood from a statistical point of view. Based on these calculations, $x_c$ is around $17\%$ for (Bi${}_{1-x}$In${}_x{)}_2$Se${}_3$, but as high as 78%–83% for (Bi${}_{1-x}$Sb${}_x{)}_2$Se${}_3$. In (Bi${}_{1-x}$Sb${}_x{)}_2$Se${}_3$, we find that the phase transition is dominated by the decrease of SOC, with a crossover or “critical plateau” observed from around 78$\%$ to 83$\%$. On the other hand, for (Bi${}_{1-x}$In${}_x{)}_2$Se${}_3$, the In 5$s$ orbitals suppress the topological band inversion at low-impurity concentration, therefore accelerating the phase transition. In (Bi${}_{1-x}$In${}_x{)}_2$Se${}_3$ we also find a tendency of In atoms to segregate.

We consider the activation of phase jumps in a one-dimensional Bose-Einstein condensate. Our system includes a nonlocal interaction term which mimics, for example, a dipole-blockaded Rydberg system. In the mean-field limit the condensate can form superfluid droplets, arranged periodically on a line, thus displaying a supersolidlike ground state. Under an imposed velocity, phase jumps will develop. We study these phase jumps numerically and analytically, and are able to write down a relationship between the velocity, the width of the density peaks, the number of phase jumps, and $\Lambda$, a parameter that determines the number of peaks in the condensate.

We propose that the nonequilibrium current measured in the $a$-$b$ plane of an underdoped cuprate (in either the strange metal or pseudogap regime) in contact with either an overdoped cuprate or a standard Fermi liquid can be used to diagnose how different the pseudogap and strange metals are from a Fermi liquid. Naively, one expects the strange metal to be more different from a Fermi liquid than the pseudogap is. We compute the expected nonequilibrium transport signal with the three Green's functions that are available in the literature: (1) marginal Fermi-liquid theory, (2) the phenomenological ansatz for the pseudogap regime, and (3) the Wilsonian reduction of the Hubbard model which contains both the strange metal and pseudogap. All three give linear $I$-$V$ curves at low bias voltages. Significant deviations from linearity at higher voltages obtain only in the marginal Fermi-liquid approach. The key finding, however, is that $I$-$V$ curves for the strange metal/Fermi-liquid contact exceed that of the pseudogap/Fermi-liquid system. If this is borne out experimentally, this implies that the strange metal is less orthogonal to a Fermi liquid than the pseudogap is. Within the Wilsonian reduction of the Hubbard model, this result is explained in terms of a composite-particle picture. Namely, the pseudogap corresponds to a confinement transition of the charge degrees of freedom present in the strange metal. In the strange metal the composite excitations break up and electron quasiparticles scatter off bosons. The bosons here, however, do not arise from phonons but from the charge degrees of freedom responsible for dynamical spectral weight transfer.

The influence of bulk inversion asymmetry in $\left[001\right]$ and $\left[013\right]$ grown HgTe quantum wells is investigated theoretically. The bulk inversion asymmetry leads to an anticrossing gap between two zero-mode Landau levels in a HgTe topological insulator, i.e., the quantum well with inverted band structure. It is found that this is the main contribution to the anticrossing splitting observed in recent experimental magnetospectroscopic measurements. The relevant optical transitions involve different subbands, but the electron-electron interaction induced depolarization shift is found to be negligibly small. It is also found that the splitting of this anticrossing only depends weakly on the tilting angle when the magnetic field is tilted away from the perpendicular direction to the quantum well. Thus, the strength of bulk inversion asymmetry can be determined via a direct comparison between the theoretical calculated one-electron energy levels and experimentally observed anticrossing energy gap.