While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a continuous low-energy Hamiltonian. Here we show that the generalized chiral symmetry can be rigorously defined for lattice fermions as well. A key concept is a continuous “algebraic deformation” of Hamiltonians, which generates lattice models with the generalized chiral symmetry from those with the conventional chiral symmetry. This enables us to explicitly express zero modes of the deformed Hamiltonian in terms of that of the original Hamiltonian. Another virtue is that the deformation can be extended to nonuniform systems, such as fermion-vortex systems and disordered systems. Application to fermion vortices in a deformed system shows how the zero modes for the conventional Dirac fermions with vortices can be extended to the tilted case.

As a promising candidate system to realize topological superconductivity, the system of a 3D topological insulator (TI) grown on top of the $s$-wave superconductor has been extensively studied. To access the topological superconductivity experimentally, the 3D TI sample must be thin enough to allow for Cooper pair tunneling to the exposed surface of TI. The use of magnetically ordered dopants to break time-reversal symmetry may allow the surface of a TI to host Majorana fermion, which are believed to be a signature of topological superconductivity. In this work, we study a magnetically-doped thin film TI-superconductor hybrid system. Considering the proximity induced order parameter in thin film of TI, we analyze the gap closing points of the Hamiltonian and draw the phase diagram as a function of relevant parameters: the hybridization gap, Zeeman energy, and chemical potential of the TI system. Our findings provide a useful guide in choosing relevant parameters to facilitate the observation of topological superconductivity in thin film TI-superconductor hybrid systems. In addition, we further perform numerical analysis on a TI proximity coupled to an $s$-wave superconductor and find that, due to the spin-momentum locked nature of the surface states in TI, the induced $s$-wave order parameter of the surface states persists even at large magnitude of the Zeeman energy.

A large photon drag effect of the massless Dirac fermions in intrinsic graphene is predicted for a graphene-on-plasmonic-layer system. The surface plasmons in the plasmonic layer enlarge the wave number of the photon hundreds times more than in vacuum. The evanescent field of the surface plasmons generates a directional motion of carriers in the intrinsic graphene because of the large momentum transfer from the surface plasmon to the excited carriers. A model Hamiltonian is developed on the assumption that the in-plane wavelength of the surface plasmons is much smaller than the mean free path of the carriers. The time evolution of the density matrix is solved by perturbation method as well as numerical integration. The nondiagonal density matrix elements with momentum transfer lead to a gauge current, which is an optically driven macroscopic direct current. The dependence of the macroscopic direct current on the incident direction and intensity of the laser field is studied.

The understanding of the fundamental geometric and electronic properties of metal-organic hybrid interfaces is a key issue on the way to improving the performance of organic electronic and spintronic devices. Here, we studied the adsorption heights of copper-II-phthalocyanine (CuPc) and 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) on a ${\mathrm{Pb}}_1{\mathrm{Ag}}_2$ surface alloy on Ag(111) using the normal-incidence x-ray standing waves technique. We find a significantly larger adsorption height of both molecules on the Pb-Ag surface alloy compared to the bare Ag(111) surface which is caused by the larger size of Pb. This increased adsorption height suppresses the partial chemical interaction of both molecules with Ag surface atoms. Instead, CuPc and PTCDA molecules bond only to the Pb atoms with different interaction strength ranging from a van der Waals–like interaction for CuPc to a weak chemical interaction with additional local bonds for PTCDA. The different adsorption heights for CuPc and PTCDA on ${\mathrm{Pb}}_1{\mathrm{Ag}}_2$ are the result of local site-specific molecule-surface bonds mediated by functional molecular groups and the different charge donating and accepting character of CuPc and PTCDA.

The opening of a band gap due to compressive uniaxial strain renders bulk HgTe a strong three-dimensional topological insulator with protected gapless surface states at any surface. By employing a six-band $\mathbf{k}·\mathbf{p}$ model, we determine the spin textures of the topological surface states of bulk HgTe uniaxially strained along the $\left(100\right)$ direction. We show that at the $\left(010\right)$ and $\left(001\right)$ surfaces, an increase in the strain magnitude triggers a topological phase transition where the winding number of the surface-state spin texture is flipped while the four topological invariants characterizing the bulk band structure of the material are unchanged.

The Purcell factor quantifies the change of the radiative decay of a dipole in an electromagnetic environment relative to free space. Designing this factor is at the heart of photonics technology, striving to develop ever smaller or less lossy optical resonators. The Purcell factor can be expressed using the electromagnetic eigenmodes of the resonators, introducing the notion of a mode volume for each mode. This approach allows an analytic treatment, reducing the Purcell factor and other observables to sums over eigenmode resonances. Calculating the mode volumes requires a correct normalization of the modes. We introduce an exact normalization of modes, not relying on perfectly matched layers. We present an analytic theory of the Purcell effect based on this exact mode normalization and the resulting effective mode volume. We use a homogeneous dielectric sphere in vacuum, which is analytically solvable, to exemplify these findings. We furthermore verify the applicability of the normalization to numerically determined modes of a finite dielectric cylinder.

Graphene has been identified as a promising material with numerous applications, particularly in spintronics. In this paper we investigate the peculiar features of spin excitations of magnetic units deposited on graphene nanoribbons and how they can couple through a dynamical interaction mediated by spin currents. We examine in detail the spin lifetimes and identify a pattern caused by vanishing density of states sites in pristine ribbons with armchair borders. Impurities located on these sites become practically invisible to the interaction but can be made accessible by a gate voltage or doping. We also demonstrate that the coupling between impurities can be turned on or off using this characteristic, which may be used to control the transfer of information in transistorlike devices.

Order-disorder transition of the epitaxial surface alloy of bulk immiscible elements ${\mathrm{Au}}_{1-x}{\mathrm{Fe}}_x$ on Ru(0001) is studied using complementary experiments of scanning tunneling microscopy and grazing incidence x-ray diffraction. For $x\simeq 1/3$, we evidence an apparent continuous transition towards disorder with increasing temperature from 550 to 700 K. An ordered ${\mathrm{Au}}_2\mathrm{Fe}$ two-dimensional alloy is found to be composed of nanometer size domains of the three variants that switch to a two-dimensional solid solution with temperature. A two-levels model is developed to analyze those results which conducts to interpret this phase transition as the result of an order-disorder transition within two dimensional uncorrelated grains, or domains, with nearly fixed size. This system is a good candidate in order to study two-dimensional phase transitions of surface alloy, a largely unexplored domain but crucial to understanding thermal stability of bimetallic nanoparticles.

This paper is devoted to examining the effect of intrinsic spin-orbit interaction on the possible appearance of edge magnetic moments and spin-dependent transport in graphenelike nanoflakes. In the case of finite-size graphenelike nanostructures it is shown that, on one hand, energetically the most advantageous configuration corresponds to magnetic moments located at zigzag edges with the in-plane antiferromagnetic inter-edge coupling. On the other hand, the tunnel magnetoresistance and the shot noise also have thoroughly been tested both for the in-plane configuration as well as for the out-of-plane one (for comparison reasons). Transport properties are described in terms of the mean-field Kane-Mele-Hubbard model with spin mixing correlations, supplemented by additional terms describing external leads, charging energy, and lead-nanostructure tunneling. The results show that Coulomb blockade stability spectra of graphenelike nanoflakes with ferromagnetic contacts provide information on both the intrinsic spin-orbit interaction and the expected edge magnetism.

Electronic structure properties of nanowires (NWs) with diameters of 1.5 and 3 nm based on semimetallic $\alpha -\mathrm{Sn}$ are investigated by employing density functional theory and perturbative GW methods. We explore the dependence of electron affinity, band structure, and band-gap values with crystallographic orientation, NW cross-sectional size, and surface passivants of varying electronegativity. We consider four chemical terminations in our study: methyl $\left({\mathrm{CH}}_3\right)$, hydrogen $\left(\mathrm{H}\right)$, hydroxyl $\left(\mathrm{OH}\right)$, and fluorine $\left(\mathrm{F}\right)$. Results suggest a high degree of elasticity of Sn-Sn bonds within the Sn NWs' cores with no significant structural variations for nanowires with different surface passivants. Direct band gaps at Brillouin-zone centers are found for most studied structures with quasiparticle corrected band-gap magnitudes ranging from 0.25 to 3.54 eV in 1.5-nm-diameter structures, indicating an exceptional range of properties for semimetal NWs below the semimetal-to-semiconductor transition. Band-gap variations induced by changes in surface passivants indicate the possibility of realizing semimetal-semiconductor interfaces in NWs with constant cross-section and crystallographic orientation, allowing the design of novel dopant-free NW-based electronic devices.

Mn-doped GaAs exhibits a critical metal-insulator transition at the Mn concentration of $x_{\mathrm{crit}}\approx 1\%$. Our self-interaction corrected first principles calculation shows that for Mn concentrations $x\gtrsim 1\%$, hole carriers are delocalized in host valence states, and for $x\lesssim 1\%$, holes tend to be trapped in impurity-band-like states. We further show that for a finite range of concentrations around $x_{\mathrm{crit}}$ the system exhibits a nonadiabatic superposition of these states, i.e., a mixing of electronic and nuclear wave functions. This means that the phase transition is continuous, and its criticality is caused by quantum effects of the atomic nuclei. In other words, the apparently electronic phase transition from the insulator to metal state cannot be described by electronic effects alone.

Perovskite $R{\mathrm{AlO}}_3$ $(R=\mathrm{La},\text{Nd},\text{Sm},\text{and Gd})$ films have been deposited epitaxially on (001) ${\mathrm{TiO}}_2\text{-terminated}$ ${\mathrm{SrTiO}}_3$ substrates. It is observed that the two-dimensional transport characteristics at the $R{\mathrm{AlO}}_3/{\mathrm{SrTiO}}_3$ interfaces are very sensitive to the species of rare-earth element, that is to chemical strain. Although electron energy loss spectroscopy measurements show that electron transfer occurs in all the four polar/nonpolar heterostructures, the amount of electrons transferred across ${\mathrm{SmAlO}}_3/{\mathrm{SrTiO}}_3$ and ${\mathrm{GdAlO}}_3/{\mathrm{SrTiO}}_3$ interfaces are much less than those across ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ and ${\mathrm{NdAlO}}_3/{\mathrm{SrTiO}}_3$ interfaces. First-principles calculations reveal the competition between ionic polarization and electronic polarization in the polar layers in compensating the build-in polarization due to the polar discontinuity at the interface. In particular, a large ionic polarization is found in ${\mathrm{SmAlO}}_3/{\mathrm{SrTiO}}_3$ and ${\mathrm{GdAlO}}_3/{\mathrm{SrTiO}}_3$ systems (which experience the largest tensile epitaxial strain), hence reducing the amount of electrons transferred.

Solid-state spin arrays are being engineered in varied systems, including gated coupled quantum dots and interacting dopants in semiconductor structures. Beyond quantum computation, these arrays are useful integrated analog simulators for many-body models. As entanglement between individual spins is extremely short ranged in these models, one has to measure the entanglement entropy of a block in order to truly verify their many-body entangled nature. Remarkably, the characteristic scaling of entanglement entropy, predicted by conformal field theory, has yet to be measured. Here, we show that with as few as two replicas of a spin array, and capacitive double-dot singlet-triplet measurements on neighboring spin pairs, the above scaling of the entanglement entropy can be verified. This opens up the controlled simulation of quantum field theories, as we exemplify with uniform chains and Kondo-type impurity models, in engineered solid-state systems. Our procedure remains effective even in the presence of typical imperfections of realistic quantum devices and can be used for thermometry, and to bound entanglement and discord in mixed many-body states.

The chiral anomaly is based on a nonconserved chiral charge and can happen in Dirac fermion systems under the influence of external electromagnetic fields. In this case, the spectral flow leads to a transfer of right- to left-moving excitations or vice versa. The corresponding transfer of chiral particles happens in momentum space. Here we describe an intriguing way to introduce the chiral anomaly into real space. Our system consists of two quantum dots that are formed at the helical edges of a quantum spin Hall insulator by means of magnetic barriers. Such a setup gives rise to fractional charges which we show to be sharp quantum numbers for large barrier strengths. Interestingly, it is possible to map the system onto a quantum spin Hall ring in the presence of a flux pierced through the ring, where the relative angle between the magnetization directions takes the role of the flux. The chiral anomaly in this system is then directly related to the excess occupation of particles in the two quantum dots. This analogy allows us to predict an observable consequence of the chiral anomaly in real space, which is connected to the presence of fractional charges in the very same system.

We measure the full distribution of current fluctuations in a single-electron transistor with a controllable bistability. The conductance switches randomly between two levels due to the tunneling of single electrons in a separate single-electron box. The electrical fluctuations are detected over a wide range of time scales and excellent agreement with theoretical predictions is found. For long integration times, the distribution of the time-averaged current obeys the large-deviation principle. We formulate and verify a fluctuation relation for the bistable region of the current distribution.

We investigate theoretically the magnetoplasmon (cyclotron) resonance in a hybrid system consisting of spatially separated two-dimensional layers of electron and dipolar exciton gases coupled via Coulomb forces. We study the dynamics of this system under the action of a weak alternating external electromagnetic field in the presence of a uniform magnetic field, perpendicular to the layers. We reveal that the electromagnetic power absorption exhibits a double-resonance spectrum. We show that the first resonance is associated with the conventional well-studied magnetoplasmon excitations of the electron gas and it has a standard Lorentzian shape, whereas the second resonance is a peculiarity attributed to the Bose-condensed exciton gas. Further, we explicitly demonstrate that the spectrum of the system exhibits an asymmetric Fano-type profile, where the excitonic peak is extremely narrow in comparison with the magnetoplasmon one. We show that the shape of the resonance and the position of the peaks depend on the magnitude of the applied magnetic field, exciton-condensate density, and exciton-impurity scattering time. In particular, the Fano profile turns into a Lorentzian shape with decreasing exciton-impurity scattering time and the position of the plasmon-associated resonance is mainly sensitive and determined by the magnetic field strength, whereas the exciton-condensate peak position is determined by the exciton-condensate density. It opens the experimental possibility to determine the latter quantity in cyclotron resonance experiments.

The high-temperature superconducting state in cuprates appears if charge carriers are doped into a Mott-insulating parent compound. An unresolved puzzle is the unconventional nature of the normal state above the superconducting dome and its connection to the superconducting instability. At weak hole doping, a “pseudogap” metal state with signatures of time-reversal symmetry breaking is observed, which near-optimal doping changes into a “strange metal” with non-Fermi-liquid properties. Qualitatively similar phase diagrams are found in multiorbital systems, such as pnictides, where the unconventional metal states arise from a Hund-coupling-induced spin freezing. Here, we show that the relevant model for cuprates, the single-orbital Hubbard model on the square lattice, can be mapped onto an effective multiorbital problem with strong ferromagnetic Hund coupling. The spin-freezing physics of this multiorbital system explains the phenomenology of cuprates, including the pseudogap, the strange metal, and the $d$-wave superconducting instability. Our analysis suggests that spin/orbital freezing is the universal mechanism which controls the properties of unconventional superconductors.

In this work, we studied time-reversal-breaking topological phases as a result of the interplay between antiferromagnetism and inverted band structures in antiferromagnetic double perovskite transition-metal ${\mathrm{Sr}}_2{\mathrm{FeOsO}}_6$ films. By combining the first-principles calculations and analytical models, we demonstrate that the quantum anomalous Hall phase and chiral topological superconducting phase can be realized in this system. We find that to achieve time-reversal-breaking topological phases in antiferromagnetic materials, it is essential to break the combined symmetry of time reversal and inversion, which generally exists in antiferromagnetic structures. As a result, we can utilize an external electric gate voltage to induce the phase transition between topological phases and trivial phases, thus providing an electrically controllable topological platform for future transport experiments.

We extend the continuous-time interaction-expansion quantum Monte Carlo method with respect to measuring observables for fermion-boson lattice models. Using generating functionals, we express expectation values involving boson operators, which are not directly accessible because simulations are done in terms of a purely fermionic action, as integrals over fermionic correlation functions. We also demonstrate that certain observables can be inferred directly from the vertex distribution, and present efficient estimators for the total energy and the phonon propagator of the Holstein model. Furthermore, we generalize the covariance estimator of the fidelity susceptibility, an unbiased diagnostic for phase transitions, to the case of retarded interactions. The new estimators are applied to half-filled spinless and spinful Holstein models in one dimension. The observed renormalization of the phonon mode across the Peierls transition in the spinless model suggests a soft-mode transition in the adiabatic regime. The critical point is associated with a minimum in the phonon kinetic energy and a maximum in the fidelity susceptibility.