We present a simple, general purpose, quantum Monte Carlo algorithm for out-of-equilibrium interacting nanoelectronic systems. It allows one to systematically compute the expansion of any physical observable (such as current or density) in powers of the electron-electron interaction coupling constant $U$. It is based on the out-of-equilibrium Keldysh Green's function formalism in real-time and corresponds to evaluating all the Feynman diagrams to a given order $U^n$ (up to $n=15$ in the present work). A key idea is to explicitly sum over the Keldysh indices in order to enforce the unitarity of the time evolution. The coefficients of the expansion can easily be obtained for long-time, stationary regimes, even at zero temperature. We then illustrate our approach with an application to the Anderson model, an archetype interacting mesoscopic system. We recover various results of the literature such as the spin susceptibility or the “Kondo ridge” in the current-voltage characteristics. In this case, we found the Monte Carlo free of the sign problem even at zero temperature, in the stationary regime and in absence of a particle-hole symmetry. The main limitation of the method is the lack of convergence of the expansion in $U$ for large $U$, i.e., a mathematical property of the model rather than a limitation of the Monte Carlo algorithm. Standard extrapolation methods of divergent series can be used to evaluate the series in the strong correlation regime.

We study the reliability of the constrained random-phase approximation (cRPA) method for the calculation of low-energy effective Hamiltonians by considering multiorbital lattice models with one strongly correlated “target” band and two weakly correlated “screening” bands. The full multiorbital system and the effective model are solved within dynamical mean-field theory (DMFT) in a consistent way. By comparing the quasiparticle weights for the correlated bands, we examine how accurately the effective model describes the low-energy properties of the multiband system. We show that the violation of the Pauli principle in the cRPA method leads to overscreening effects when the interorbital interaction is small. This problem can be overcome by using a variant of the cRPA method which restores the Pauli principle.

It has recently been found that Dirac and Weyl metals are characterized by an unusual weak-field longitudinal magnetoresistance: large, negative, and quadratic in the magnetic field. This has been shown to arise from the chiral anomaly, i.e., nonconservation of the chiral charge in the presence of external electric and magnetic fields, oriented collinearly. In this paper we report on a theory of this effect in both Dirac and Weyl metals. We demonstrate that this phenomenon contains two important ingredients. One is the magnetic-field-induced coupling between the chiral and the total (or vector, in relativistic field theory terminology) charge densities. This arises from the Berry curvature and is present in principle whenever the Berry curvature is nonzero, i.e., is nonspecific to Dirac and Weyl metals. This coupling, however, leads to a large negative quadratic magnetoresistance only when the second ingredient is present, namely when the chiral charge density is a nearly conserved quantity with a long relaxation time. This property is specific to Dirac and Weyl metals and is realized only when the Fermi energy is close to Dirac or Weyl nodes, expressing an important low-energy property of these materials, emergent chiral symmetry.

Carbon substrates such as graphite or epitaxial graphene can be employed to support metal nanoparticles for applications in diverse areas of surface science. In this paper, we address the computational modeling of such systems by means of semiempirical potentials, and in particular the possible role of long-range London dispersion forces. Following the Grimme (D2) strategy often used in combination with density-functional theory calculations, we propose some analytical extensions taking into account the crystalline and semi-infinite natures of the substrate and, in the case of epitaxial graphene, the possible screening of the van der Waals interaction by the bulk underlying metal. These ideas are tested in the specific case of platinum nanoparticles deposited on graphene, graphite, and graphene epitaxially grown on Pt(111) modeled using a many-body Brenner-type potential, and validated against available electronic-structure calculations. Systematic optimizations carried out at zero temperature indicate the relative stability of various nanoparticle shapes on their support, for adsorbates containing several thousand atoms. Using molecular dynamics simulations, we shed light on the thermal behavior and emphasize the key role of dispersion forces on the stabilization of the adsorbates at finite temperature. The vibrational properties of graphene layers in contact with a Pt nanoparticle or epitaxially grown on Pt(111) also reveal some clear sensitivity on temperature and strain.

The atomic structure and mechanical properties of the carbyne (monatomic linear chains), containing from 2 to 21 carbon atoms, are theoretically investigated by ab-initio methods. We demonstrate the existence of a stable cumulene structure in the inner part of chains with the number of atoms $N\ge 10$. We present a general stress-strain diagram of chains until the moment when they break, which enables to determine their strength, elasticity, and fragility. These diagrams can be utilized to calibrate empirical potentials, especially for large deviations of the atoms from the equilibrium positions. For chains with $N\ge 4$, the relationship between the strength of the chain and the binding energy of the edge atom in the chain is established. The existence of scale-effect and “even-odd” effect for such properties as strength, elasticity, and fragility is observed. We demonstrate that the five-atom carbon chains show the maximum strength value.

We study the RKKY interaction mediated by the helical edge states of a quantum spin Hall insulator in the presence of the Rashba spin-orbital coupling induced by an external electric field and the electron-electron interaction. We show that in the presence of the Rashba coupling, the RKKY interaction induced by the helical edge states contains not only the Heisenberg-like and the Dzyaloshinskii-Moria terms, but also the nematic-type term that is not present in the absence of the Rashba coupling. Moreover, the range functions depend on the strength of the Rashba coupling. We also show that the electron-electron interaction changes the strength of the RKKY interaction by modifying the power of the $1/\left|x\right|$ dependence of the range functions. In particular, by varying the strength of the interaction or the Rashba coupling, there is an (impurity) quantum phase transition involving the sign change of the RKKY interaction at the value of the Luttinger liquid parameter $K=1/2$. Since both the strength of the Rashba coupling and the chemical potential of the helical edge states are electrically controllable by external gate voltages, our results not only shed light on the nature of magnetic impurity correlations in the edge of a two-dimensional topological insulator, but also pave a way to manipulate the qubits in quantum computing.

We consider hardcore bosons in two coupled chains of one dimensional lattices at half filling with repulsive intrachain interaction and interchain attraction. This can be mapped onto a coupled chain of spin-1/2 $XXZ$ model with interchain ferromagnetic coupling. We investigate various phases of hardcore bosons (and related spin model) at zero temperature by a density matrix renormalization group method. Apart from the usual superfluid and density wave phases, pairing of interchain bosons leads to the formation of phases like pair superfluid and density wave of strongly bound pairs. We discuss the possible experimental realization of such correlated phases in the context of cold dipolar gas.

A recent report that sulfur hydride under pressure is an electron-phonon superconductor with a $T_c$ of 190 K has been met with much excitement although it is yet to be confirmed. Based on several electron-phonon spectral density functions already available from density functional theory, we find that the electron-phonon spectrum is near optimum for $T_c$ with a particularly large value of its characteristic phonon energy ${\omega }_{\ln }$ which is due to the small hydrogen mass. We find that the thermodynamic universal BCS ratios are near those for Pb and ${\mathrm{Nb}}_3\mathrm{Sn}$. We suggest that optical measurements could be a useful tool to establish the existence and nature of the superconductivity in this system. Conventional superconductors are in the impurity-dominated dirty limit. By contrast sulfur hydride will be in the clean limit because of its large energy gap scale. The ac optical conductivity will display distinct and separate signatures of the superconducting gap in the low-energy impurity-dominated range of the optical spectrum and additional phonon structures at higher energies where the clean limit applies.

We conducted a systematic study of the disorder dependence of the termination of superconductivity, at high magnetic fields $\left(B\right)$, of amorphous indium oxide films. Our lower disorder films show conventional behavior where superconductivity is terminated with a transition to a metallic state at a well-defined critical field, $B_{\mathrm{c}2}$. Our higher-disorder samples undergo a $B$-induced transition into a strongly insulating state, which terminates at higher $B$'s forming an insulating peak. We demonstrate that the $B$ terminating this peak coincides with $B_{\mathrm{c}2}$ of the lower disorder samples. Additionally, we show that, beyond this field, these samples enter a different insulating state in which the magnetic field dependence of the resistance is weak. These results provide crucial evidence for the importance of Cooper-pairing in the insulating peak regime.

The pairing symmetry is examined in highly electron-doped $\mathrm{Ba}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}\right)}_2$ and $A_y{\mathrm{Fe}}_2{\mathrm{Se}}_2$ (with $A=\text{K}$, Cs) compounds, with similar crystallographic and electronic band structures. Starting from a phenomenological two-orbital model, we consider nearest-neighbor and next-nearest-neighbor intraorbital pairing interactions on the Fe square lattice. In this model, we find a unified description of the evolution from $s_{\pm }$-wave pairing $\left(2.0<n\lesssim 2.4\right)$ to $d$-wave pairing $\left(2.4\lesssim n\lesssim 2.5\right)$ as a function of electron filling. In the crossover region, a time-reversal symmetry breaking $s_{\pm }+id$ pairing state emerges. This minimal model offers an overall picture of the evolution of superconductivity with electron doping for both $s_{\pm }$-wave and $d$-wave pairings, as long as the dopants only play the role of a charge reservoir. However, the situation is more complicated for $\mathrm{Ba}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}\right)}_2$. A real-space study further shows that when the impurity scattering effects of Co dopants are taken into account, the superconductivity is completely suppressed for $n>2.4$. This preempts any observation of $d$-wave pairing in this compound, in contrast to $A_y{\mathrm{Fe}}_2{\mathrm{Se}}_2$ with $0.8<y<1.0$.

We theoretically study the superconducting proximity effect between a topological insulator (TI) and a high-temperature $d$-wave superconductor (dSC). When the TI-dSC heterostructure violates ${90}^{\circ }$ rotation and certain reflection symmetries, we show that a sizable $s$-wave pairing, coexisting with a $d$-wave one, emerges in the proximity-induced superconductivity in the TI's top surface states. Weak disorder further suppresses $d$-wave pairing (but not $s$-wave pairing) in the TI's surface states. More importantly, the pairing gap in the surface states is found to be nodeless and nearly isotropic when the Fermi pocket of surface states is relatively small. Our theoretical results qualitatively explain recent experimental evidences of a nearly-isotropic pairing gap on surface states of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ induced by proximity to high-$T_c$ cuprate ${\mathrm{Bi}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$. We also demonstrate convincing evidence of Majorana zero modes in a magnetic $hc/2e$ vortex core which may be detectable in future experiments.

We employ resonant soft x-ray diffraction to individually study the magnetic ordering of the Mn and the Tm sublattices in single-crystalline films of orthorhombic $\left(o\text{−}\right)\mathrm{TmMn}{\mathrm{O}}_3$. The same magnetic ordering wave vector of $\left(0q0\right)$ with $q\approx 0.46$ is found for both ionic species, suggesting that the familiar antiferromagnetic order of the Mn ions induces a magnetic order on the Tm unpaired $4f$ electrons. Indeed, intensity variations of magnetic reflections with temperature corroborate this scenario. Calculated magnetic fields at the Tm sites are used as a model magnetic structure for the Tm, which correctly predicts intensity variations at the Tm resonance upon azimuthal rotation of the sample. The model allows ruling out a $bc$-cycloid modulation of the Mn ions as the cause for the incommensurate ordering, as found in $\mathrm{TbMn}{\mathrm{O}}_3$. The structural distortion, which occurs in the ferroelectric phase below $T_C$, was followed through nonresonant diffraction of structural reflections forbidden by the high-temperature crystal symmetry. The $\left(0q0\right)$ magnetic reflection appears at the Mn resonance well above $T_C$, indicating that this reflection is sensitive also to the intermediate sinusoidal magnetic phase. The model presented suggests that the Tm $4f$ electrons are polarized well above the ferroelectric transition and are possibly not affected by the transition at $T_C$. The successful description of the induced order observed at the Tm resonance is a promising example for future element-selective studies in which “spectator” ions may allow access to previously unobtainable information about other constituent ions.

We present a systematic method for developing a five-band Hamiltonian for the metal $d$ orbitals that can be used to study the effect of electric and magnetic fields on multilayer $M{X}_2$ ($M=\mathrm{Mo}$,W and $X=\mathrm{S}$,Se) systems. On a hexagonal lattice of $d$ orbitals, the broken inversion symmetry of the monolayers is incorporated via fictitious $s$ orbitals at the chalcogenide sites. A tight-binding Hamiltonian is constructed and then downfolded to get effective $d$-orbital overlap parameters using quasidegenerate perturbation theory. The steps to incorporate the effects of multiple layers, external electric and magnetic fields, are also detailed. We find that an electric field produces a linear-$k$ Rashba splitting around the $\mathrm{\Gamma }$ point, while a magnetic field removes the valley pseudospin degeneracy at the $\pm K$ points. Our model provides a simple tool to understand the recent experiments on electric and magnetic control of valley pseudospin in monolayer dichalcogendies.

We study theoretically the properties of buckled graphenelike materials, such as silicene and germanene, in a strong perpendicular magnetic field and a periodic potential. We analyze how the spin-orbit interaction and the perpendicular electric field influence the energy spectra of these systems. When the magnetic flux through a unit cell of the periodic potential measured in the magnetic flux quantum is a rational number, $\alpha =p/q$, then in each Landau level the energy spectra have a band structure, which is characterized by the corresponding gaps. We study the dependence of those gaps on the parameters of the buckled graphenelike materials. Although some gaps have weak dependence on the magnitude of the spin-orbit coupling and the external electric field, there are gaps that show strong nonmonotonic dependence on these parameters. For $\alpha =1/2$, the spin-orbit interaction also opens up a gap at one of the Landau levels. The magnitude of the gap increases with spin-orbit coupling and decreases with the applied electric field.

In order to design clusters with desired properties, we have implemented a suite of genetic algorithms tailored to optimize for low total energy, high vertical electron affinity (VEA), and low vertical ionization potential (VIP). Applied to ${\left(\mathrm{Ti}{\mathrm{O}}_2\right)}_n$ clusters, the property-based optimization reveals the underlying structure-property relations and the structural features that may serve as active sites for catalysis. High VEA and low VIP are correlated with the presence of several dangling-O atoms and their proximity, respectively. We show that the electronic properties of ${\left(\mathrm{Ti}{\mathrm{O}}_2\right)}_n$ up to $n=20$ correlate more strongly with the presence of these structural features than with size.

We study the single-band Hubbard model in the presence of a large spatially uniform electric field out of equilibrium. Using the Keldysh nonequilibrium formalism, we solve the problem using perturbation theory in the Coulomb interaction $U$. We present numerical results for the charge current, the total energy of the system, and the double occupancy on an infinite-dimensional hypercubic lattice with nearest-neighbor hopping. The system is isolated from an external bath and is in the paramagnetic state. We show that an electric field pulse can drive the system to a steady nonequilibrium state, which does not evolve into a thermal state. We compare results obtained within second-order perturbation theory (SOPT), self-consistent SOPT, and iterated perturbation theory (IPT). We also discuss the importance of initial conditions for a system which is not coupled to an external bath.

Single-walled carbon nanotube (SWCNT)-fullerene (${\mathrm{C}}_{60}$) bilayers represent an attractive “donor-acceptor” binary system for solar photoconversion, where the kinetics of photoinduced processes depend critically on the properties of the interface between the two materials. Using photoconductivity measurements we identify the kinetic scheme that describes the free carrier kinetics in such bilayers where the dominant SWCNT species is the (7,5) semiconducting nanotube. Following charge separation, the carrier kinetics, covering up to four orders of magnitude in volumetric hole density, are described by a recombination process that is limited by capture and emission at traps or states at the SWCNT-${\mathrm{C}}_{60}$ interface. The high-frequency mobility of holes in the (7,5) SWCNT phase is lower than in multichiral films, potentially due to differences in SWCNT defect density for nanotubes that have been purified more aggressively. The results obtained here provide fundamental insights into the transport and recombination of both charges and excitons within SWCNT thin films and bilayers, and point to several potential ways to improve SWCNT-${\mathrm{C}}_{60}$ photovoltaic devices.

Two-dimensional (2D) mobile carriers are a wellspring of quantum phenomena. Among various 2D-carrier systems, such as field effect transistors and heterostructures, polar materials hold a unique potential; the spontaneous electric polarization in the bulk could generate positive and negative 2D carriers at the surface. Although several experiments have shown ambipolar carriers at the surface of a polar semiconductor BiTeI, their origin is yet to be specified. Here we provide compelling experimental evidences that the ambipolar 2D carriers at the surface of BiTeI are induced by the spontaneous electric polarization. By imaging electron standing waves with spectroscopic imaging scanning tunneling microscopy, we find that positive or negative carriers with Rashba-type spin splitting emerge at the surface corresponding to the polar directions in the bulk. The electron densities at the surface are constant independently of those in the bulk, corroborating that the 2D carriers are induced by the spontaneous electric polarization. We also successfully image that lateral $p-n$ junctions are formed along the boundaries of submicron-scale domains with opposite polar directions. Our study presents a means to endow nonvolatile, spin-polarized, and ambipolar 2D carriers as well as, without elaborate fabrication, lateral $p-n$ junctions of those carriers at atomically sharp interfaces.