Abstract: Chiral p-wave superconductors in applied magnetic field can exhibit more complex topological defects than just conventional superconducting vortices, due to the two-component order parameter (OP) and the broken time-reversal symmetry. We investigate the electronic properties of those exotic states, some of which contain clusters of one-component vortices in chiral components of the OP and/or exhibit skyrmionic character in the relative OP space, all obtained as a self-consistent solution of the microscopic Bogoliubov-de Gennes equations. We reveal the link between the local density of states (LDOS) of the novel topological states and the behavior of the chiral domain wall between the OP components, enabling direct identification of those states in scanning tunneling microscopy. For example, a skyrmion always contains a closed chiral domain wall, which is found to be mapped exactly by zero-bias peaks in LDOS. Moreover, the LDOS exhibits electron-hole asymmetry, which is different from the LDOS of conventional vortex states with same vorticity. Finally, we present the magnetic field and temperature dependence of the properties of a skyrmion, indicating that this topological defect can be surprisingly large in size, and can be pinned by an artificially indented nonsuperconducting closed path in the sample. These features are expected to facilitate the experimental observation of skyrmionic states, thereby enabling experimental verification of chirality in emerging superconducting materials.

Abstract: The Tomasch effect (TE) is due to quasiparticle interference (QPI) as induced by a nonuniform superconducting order parameter, which results in oscillations in the density of states (DOS) at energies above the superconducting gap. Quantum confinement in nanoscale superconductors leads to an inhomogenerous distribution of the Cooperpair condensate, which, as we found, triggers the manifestation of a new TE. We investigate the electronic structure of nanoscale superconductors by solving the Bogoliubov-de Gennes (BdG) equations self-consistently and describe the TE determined by two types of processes, involving two-or three-subband QPIs. Both types of QPIs result in additional BCS-like Bogoliubov-quasiparticles and BCS-like energy gaps leading to oscillations in the DOS and modulated wave patterns in the local density of states. These effects are strongly related to the symmetries of the system. A reduced 4 x 4 inter-subband BdG Hamiltonian is established in order to describe analytically the TE of two-subband QPIs. Our study is relevant to nanoscale superconductors, either nanowires or thin films, Bose-Einsten condensates, and confined systems such as two-dimensional electron gas interface superconductivity.

Abstract: Vortex matter in mesoscopic superconductors is known to be strongly affected by the geometry of the sample. Here we show that in nanoscale superconductors with coherence length comparable to the Fermi wavelength the shape resonances of the order parameter results in an additional contribution to the quantum topological confinement-leading to unconventional vortex configurations. Our Bogoliubov-de Gennes calculations in a square geometry reveal a plethora of asymmetric, giant multivortex, and vortex-antivortex structures, stable over a wide range of parameters and which are very different from those predicted by the Ginzburg-Landau theory. These unconventional states are relevant for high-T-c nanograins, confined Bose-Einstein condensates, and graphene flakes with proximity-induced superconductivity.

Abstract: <script type='text/javascript'>document.write(unpmarked('Spin-triplet chiral p-wave superconductivity is typically described by a two-component order parameter, and as such is prone to unique emergent effects when compared to the standard single-component superconductors. Here we present the equilibrium phase diagram for small mesoscopic chiral p-wave superconducting disks in the presence of magnetic field, obtained by solving the microscopic Bogoliubov-de Gennes equations self-consistently. In the ultrasmall limit, the cylindrically symmetric giant-vortex states form the ground state of the system. However, with increasing sample size, the cylindrical symmetry is broken as the two components of the order parameter segregate into domains, and the number of fragmented domain walls between them characterizes the resulting states. Such domain walls are topological defects unique for the p-wave order, and constitute a dominant phase in the mesoscopic regime. Moreover, we find two possible types of domain walls, identified by their chirality-dependent interaction with the edge states.'));

Abstract: We numerically investigate the spin-orbit (SO) coupling effect on the magnetic flux evolution of energy and supercurrent in mesoscopic d-wave superconducting loops by solving the spin-generalized Bogoliubov-de Gennes equations self-consistently. It is found that the energy spectrum splits when the SO interaction is involved and the Majorana zero mode can be realized in the [100] edges of square systems for an appropriate SO coupling strength. Superconducting phase transitions appear when the energy gap closes, accompanied by energy jumps between different energy parabolas in the ground state, which provides a possible mechanism to support fractional flux periodicity of supercurrent. Moreover, in the case of rectangular loops with SO coupling, the jumps of the ground-state energy gradually disappear by increasing the ratio of length to height of the sample, and a paramagnetic response with opposite direction of the screening current around zero flux value can occur in such systems.

Abstract: The Majorana zero modes and persistent spin current in mesoscopic d-wave-superconducting loops with spin-orbit (SO) interaction are investigated by numerically solving the spin-generalized Bogoliubov-de Gennes equations self-consistently. For some appropriate strength of the SO coupling, Majorana zero-energy states and sharp jumps of the spin-polarized currents can be observed when the highest energy levels cross the Fermi energy in the spectrum, leading to spin currents with opposite chirality flowing near the inner and outer edges of the sample. When the threaded magnetic flux turns on, four flux-dependent patterns of the persistent spin current with step-like features show up, accompanied by Majorana edge modes at flux values where the energy gap closes. Moreover, the Majorana zero mode is highly influenced by the direction of the Zeeman field. A finite in-plane field can lead to the gap opening since the inversion symmetry is broken. Remarkably, multiple Majorana zero-energy states occur in the presence of an out-of-plane field h(z), and the number of steps in the spin current evolution can be effectively tuned by the field strength due to the shift of Majorana zero modes. Finally, when the loop sample contains surface indentation defects, zero-energy modes can always show up in the presence of an appropriate h(z). Interestingly, multiple Majorana states may be present in the system with a corner defect even if h(z) = 0.

Abstract: We report the formation of nanobubbles on graphene with a radius of the order of 1 nm, using ultralow energy implantation of noble gas ions (He, Ne, Ar) into graphene grown on a Pt(111) surface. We show that the universal scaling of the aspect ratio, which has previously been established for larger bubbles, breaks down when the bubble radius approaches 1 nm, resulting in much larger aspect ratios. Moreover, we observe that the bubble stability and aspect ratio depend on the substrate onto which the graphene is grown (bubbles are stable for Pt but not for Cu) and trapped element. We interpret these dependencies in terms of the atomic compressibility of the noble gas as well as of the adhesion energies between graphene, the substrate, and trapped atoms.

Abstract: The flexoelectric and electronic properties of zig-zag graphene nanoribbons are explored under mechanical bending using state of the art first principles calculations. A linear dependence of the bending induced out of plane polarization on the applied strain gradient is found. The inferior flexoelectric properties of graphene nanoribbons can be improved by more than two orders of magnitude by hydrogen and fluorine functionalization (CH and CF nanoribbons). A large out of plane flexoelectric effect is predicted for CF nanoribbons. The origin of this enhancement lies in the electro-negativity difference between carbon and fluorine atoms, which breaks the out of plane charge symmetry even for a small strain gradient. The flexoelectric effect can be further improved by co-functionalization with hydrogen and fluorine (CHF Janus-type nanoribbon), where a spontaneous out of plane dipole moment is formed even for flat nanoribbons. We also find that bending can control the charge localization of valence band maxima and therefore enables the tuning of the hole effective masses and band gaps. These results present an important advance towards the understanding of flexoelectric and electronic properties of hydrogen and fluorine functionalized graphene nanoribbons, which can have important implications for flexible electronic applications. (C) 2020 Elsevier Ltd. All rights reserved.

Abstract: The electronic properties of a triaxially strained hexagonal graphene flake with either armchair or zigzag edges are investigated using molecular dynamics simulations and tight-binding calculations. We found that (i) the pseudomagnetic field in strained graphene flakes is not uniform neither in the center nor at the edge of zigzag terminated flakes, (ii) the pseudomagnetic field is almost zero in the center of armchair terminated flakes but increases dramatically near the edges, (iii) the pseudomagnetic field increases linearly with strain, for strains lower than 15% but increases nonlinearly beyond it, (iv) the local density of states in the center of the zigzag hexagon exhibits pseudo-Landau levels with broken sublattice symmetry in the zeroth pseudo-Landau level, and in addition there is a shift in the Dirac cone due to strain induced scalar potentials, and (v) there is size effect in pseudomagnetic field. This study provides a realistic model of the electronic properties of inhomogeneously strained graphene where the relaxation of the atomic positions is correctly included together with strain induced modifications of the hopping terms up to next-nearest neighbors.

Abstract: The ground-state properties of a paramagnetic Mott insulator at half-filling are investigated in the presence of an external electric field using the inhomogeneous Gutzwiller approximation for a single-band Hubbard model in a slab geometry. We find that the metal-insulator transition is shifted toward higher Hubbard repulsions by applying an electric field perpendicular to the slab. The main reason is the accumulation of charges near the surface. The spatial distribution of site-dependent quasiparticle weight shows that it is maximal in a few layers beneath the surface, while the central sites where the field is screened have a very low quasiparticle weight. Our results show that above a critical-field value, states near the surface will be metallic, while the bulk quasiparticle weight is extremely suppressed but never vanishing, even for large Hubbard repulsions above the bulk zero-field critical value. Below the critical-field value, our results hint toward an insulating state in which the electric field is totally screened and the slab is again at half-filling.

Abstract: Using a numerical tight-binding approach based on the Chebyshev–Bogoliubov–de Gennes method we describe Josephson junctions made of multilayer graphene contacted by top superconducting gates. Both Bernal (ABA) and rhombohedral (ABC) stacking are considered and we find that the type of stacking has a strong effect on the proximity effect and the supercurrent flow. For both cases the pair amplitude shows a polarization between dimer and nondimer atoms, being more pronounced for rhombohedral stacking. Even though the proximity effect in nondimer sites is enhanced when compared to single-layer graphene, we find that the supercurrent is suppressed. The spatial distribution of the supercurrent shows that for Bernal stacking the current flows only in the topmost layers while for rhombohedral stacking the current flows throughout the whole structure.

Abstract: Using highly efficient GPU-based simulations of the tight-binding Bogoliubov-de Gennes equations we solve self-consistently for the pair correlation in rhombohedral (ABC) and Bernal (ABA) multilayer graphene by considering a finite intrinsic s-wave pairing potential. We find that the two different stacking configurations have opposite bulk/surface behavior for the order parameter. Surface superconductivity is robust for ABC stacked multilayer graphene even at very low pairing potentials for which the bulk order parameter vanishes, in agreement with a recent analytical approach. In contrast, for Bernal stacked multilayer graphene, we find that the order parameter is always suppressed at the surface and that there exists a critical value for the pairing potential below which no superconducting order is achieved. We considered different doping scenarios and find that homogeneous doping strongly suppresses surface superconductivity while nonhomogeneous field-induced doping has a much weaker effect on the superconducting order parameter. For multilayer structures with hybrid stacking (ABC and ABA) we find that when the thickness of each region is small (few layers), high-temperature surface superconductivity survives throughout the bulk due to the proximity effect between ABC/ABA interfaces where the order parameter is enhanced. DOI: 10.1103/PhysRevB.87.134509

Abstract: Electrons in graphene, in addition to their spin, have two pseudospin degrees of freedom: sublattice and valley pseudospin. Valleytronics uses the valley degree of freedom as a carrier of information similarly to the way spintronics uses electron spin. We show how a double-barrier structure consisting of electric and vector potentials can be used to filter massive Dirac electrons based on their valley index. We study the resonant transmission through a finite number of barriers and we obtain the energy spectrum of a superlattice consisting of electric and vector potentials. When a mass term is included, the energy bands and energy gaps at the K and K′ points are different and they can be tuned by changing the potential.

Abstract: The strain fields of periodically buckled graphene induce a periodic pseudomagnetic field (PMF) that modifies the electronic band structure. From the geometry, amplitude, and period of the periodic pseudomagnetic field, we determine the necessary conditions to access the regime of correlated phases by examining the band flattening. As compared to twisted bilayer graphene the proposed system has the advantages that (1) only a single layer of graphene is needed, (2) one is not limited to hexagonal superlattices, and (3) narrower flat bandwidth and larger separation between flat bands can be induced. We, therefore, propose that periodically strained graphene single layers can become a platform for the exploration of exotic many-body phases.

Abstract: Two-dimensional atomic crystals can radically change their properties in response to external influences, such as substrate orientation or strain, forming materials with novel electronic structure(1-5). An example is the creation of weakly dispersive, 'flat' bands in bilayer graphene for certain 'magic' angles of twist between the orientations of the two layers(6). The quenched kinetic energy in these flat bands promotes electron-electron interactions and facilitates the emergence of strongly correlated phases, such as superconductivity and correlated insulators. However, the very accurate fine-tuning required to obtain the magic angle in twisted-bilayer graphene poses challenges to fabrication and scalability. Here we present an alternative route to creating flat bands that does not involve fine-tuning. Using scanning tunnelling microscopy and spectroscopy, together with numerical simulations, we demonstrate that graphene monolayers placed on an atomically flat substrate can be forced to undergo a buckling transition(7-9), resulting in a periodically modulated pseudo-magnetic field(10-14), which in turn creates a 'post-graphene' material with flat electronic bands. When we introduce the Fermi level into these flat bands using electrostatic doping, we observe a pseudogap-like depletion in the density of states, which signals the emergence of a correlated state(15-17). This buckling of two-dimensional crystals offers a strategy for creating other superlattice systems and, in particular, for exploring interaction phenomena characteristic of flat bands. Buckled monolayer graphene superlattices are found to provide an alternative to twisted bilayer graphene for the study of flat bands and correlated states in a carbon-based material.