Quantum spin Hall phase in multilayer graphene

The so-called quantum spin Hall phase is a topologically nontrivial insulating phase that is predicted to appear in graphene and graphenelike systems. In this paper we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four-orbital tight-binding model that includes full atomic spin-orbit coupling and we calculate the Z2 topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all possible stackings, only those with an odd number of layers host gapless edge states while those with an even number of layers are trivial insulators. For heterostructures where graphene is encapsulated by trivial insulators, it turns out that interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.

On the forbidden gap of finite graphene nanoribbons

The electronic structure of isolated finite graphene nanoribbons is investigated by solving, at the Hartree-Fock (HF) level, the Pariser, Parr and Pople (PPP) many-body Hamiltonian. The study is mainly focused on 7-AGNR and 13-AGNR (Armchair Graphene Nano-Ribbons), whose electronic structures have been recently experimentally investigated. Only paramagnetic solutions are considered. The characteristics of the forbidden gap are studied as a function of the ribbon length. For a 7-AGNR, the gap monotonically decreases from a maximum value of ~6.5 eV for short nanoribbons to a very small value of ~0.12 eV for the longer calculated systems. Gap edges are defined by molecular orbitals that are spatially localized near the nanoribbon extremes, that is, near both zig-zag edges. On the other hand, two delocalized orbitals define a much larger gap of about 5 eV. Conductance measurements report a somewhat smaller gap of ~3 eV. The small real gap lies in the middle of the one given by extended states and has been observed by STM and reproduced by DFT calculations. On the other hand, the length dependence of the gap is not monotonous for a 13-AGNR. It decreases initially but sharply increases for lengths beyond 30 Å remaining almost constant thereafter at a value of ~2.1 eV. Two additional states localized at the nanoribbon extremes show up at energies 0.31 eV below the HOMO (Highest Occupied Molecular Orbital) and above the LUMO (Lowest Unoccupied Molecular Orbital). These numbers compare favorably with those recently obtained by means of STS for a 13-AGNR sustained by a gold surface, namely 1.4 eV for the energy gap and 0.4 eV for the position of localized band edges. We show that the important differences between 7- and 13-AGNR should be ascribed to the charge rearrangement near the zig-zag edges obtained in our calculations for ribbons longer than 30 Å, a feature that does not show up for a 7-AGNR no matter its length.

Fabrication and characterization of metallic nanowires

The shape of metallic constrictions of nanoscopic dimensions (necks) formed using a scanning tunneling microscope is shown to depend on the fabrication procedure. Submitting the neck to repeated plastic deformation cycles makes it possible to obtain long necks or nanowires. Point-contact spectroscopy results show that these long necks are quite crystalline, indicating that the repeated cycles of plastic deformation act as a “mechanical annealing” of the neck.

Quantum interference in atomic-sized point contacts

The conductance of atomic-sized metallic point contacts is shown to be strongly voltage dependent due to quantum interference with impurities even in samples with low impurity concentrations. Transmission through these small contacts depends not only on the local atomic structure at the contact but also on the distribution of impurities or defects within a coherence length of the contact. In contrast with other mesoscopic systems we show that transport through atomic contacts is coherent even at room temperature. The use of a scanning tunneling microscope (STM) makes it possible to fabricate one atom contacts of gold whose transmission can be controlled by manipulation of the contact allowing inelastic spectroscopy in such small contacts.

Calibration of the length of a chain of single gold atoms

Using a scanning tunnelling microscope or mechanically controllable break junction it has been shown that it is possible to control the formation of a wire made of single gold atoms. In these experiments an interatomic distance between atoms in the chain of ∼3.6 Å was reported which is not consistent with recent theoretical calculations. Here, using precise calibration procedures for both techniques, we measure the length of the atomic chains. Based on the distance between the peaks observed in the chain length histogram we find the mean value of the interatomic distance before chain rupture to be 2.5±0.2 Å. This value agrees with the theoretical calculations for the bond length. The discrepancy with the previous experimental measurements was due to the presence of He gas, that was used to promote the thermal contact, and which affects the value of the work function that is commonly used to calibrate distances in scanning tunnelling microscopy and mechanically controllable break junctions at low temperatures.

Magnetization reversal of ferromagnetic nanowires studied by magnetic force microscopy

The magnetization reversal of two-dimensional arrays of parallel ferromagnetic Fe nanowires embedded in nanoporous alumina templates has been studied. By combining bulk magnetization measurements (superconducting quantum interference device magnetometry) with field-dependent magnetic force microscopy (MFM), we have been able to decompose the macroscopic hysteresis loop in terms of the irreversible magnetic responses of individual nanowires. The latter are found to behave as monodomain ferromagnetic needles, with hysteresis loops displaced (asymmetric) as a consequence of the strong dipolar interactions between them. The application of field-dependent MFM provides a microscopic method to obtain the hysteresis curve of the array, by simply registering the fraction of up and down magnetized wires as a function of applied field. The observed deviations from the rectangular shape of the macroscopic hysteresis loop of the array can be ascribed to the spatial variation of the dipolar field through the inhomogeneously filled membrane. The system studied proves to be an excellent example of the two-dimensional classical Preisach model, well known from the field of hysteresis modeling and micromagnetism.

Absence of magnetically induced fractional quantization in atomic contacts

Using the mechanically controlled break junction technique at low temperatures and under cryogenic vacuum conditions we have studied atomic contacts of several magnetic (Fe, Co, and Ni) and nonmagnetic (Pt) metals, which recently were claimed to show fractional conductance quantization. In the case of pure metals we see no quantization of the conductance nor half quantization, even when high magnetic fields are applied. On the other hand, features in the conductance similar to (fractional) quantization are observed when the contact is exposed to gas molecules. Furthermore, the absence of fractional quantization when the contact is bridged by H2 indicates the current is never fully polarized for the metals studied here. Our results are in agreement with recent model calculations.

Stretching dependence of the vibration modes of a single-molecule Pt-H2-Pt bridge

A conducting bridge of a single hydrogen molecule between Pt electrodes is formed in a break junction experiment. It has a conductance near the quantum unit, G0=2e2∕h, carried by a single channel. Using point-contact spectroscopy three vibration modes are observed and their variation upon isotope substitution is obtained. The stretching dependence for each of the modes allows uniquely classifying them as longitudinal or transversal modes. The interpretation of the experiment in terms of a Pt-H2-Pt bridge is verified by density-functional theory calculations for the stability, vibrational modes, and conductance of the structure.

Transport in magnetically ordered Pt nanocontacts

Pt nanocontacts, like those formed in mechanically controlled break junctions, are shown to develop spontaneous local magnetic order. Our density functional calculations predict that a robust local magnetic order exists in the atoms presenting low coordination, i.e., those forming the atom-sized neck. We thus find that the electronic transport can be spin polarized, although the net value of the conductance still agrees with available experimental information. Experimental implications of the formation of this new type of nanomagnet are discussed.

Molecular signature of highly conductive metal-molecule-metal junctions

The simplicity of single-molecule junctions based on direct bonding of a small molecule between two metallic electrodes makes them an ideal system for the study of fundamental questions related to molecular electronics. Here we study the conductance properties of six different types of molecules by suspending individual molecules between Pt electrodes. All the molecular junctions show a typical conductance of about 1G0 which is ascribed to the dominant role of the Pt contacts. However, despite the metalliclike conductivity, the individual molecular signature is well expressed by the effect of molecular vibrations in the inelastic contribution to the conductance.

Analysis of the Kondo effect in ferromagnetic atomic-sized contacts

Atomic contacts made of ferromagnetic metals present zero-bias anomalies in the differential conductance due to the Kondo effect. These systems provide a unique opportunity to perform a statistical analysis of the Kondo parameters in nanostructures since a large number of contacts can be easily fabricated using break-junction techniques. The details of the atomic structure differ from one contact to another so a large number of different configurations can be statistically analyzed. Here we present such a statistical analysis of the Kondo effect in atomic contacts made from the ferromagnetic transition metals Ni, Co, and Fe. Our analysis shows clear differences between materials that can be understood by fundamental theoretical considerations. This combination of experiments and theory allows us to extract information about the origin and nature of the Kondo effect in these systems and to explore the influence of geometry and valence in the Kondo screening of atomic-sized nanostructures.

Nanocontacts: probing electronic structure under extreme uniaxial strains

Nanometer-sized metallic necks have the unique ability to sustain extreme uniaxial loads (about 20 times greater than the bulk material). We present an experimental and theoretical study of the electronic transport properties under such extreme conditions. Conductance measurements on gold and aluminum necks show a strikingly different behavior: While gold shows the expected conductance decrease with increasing elastic elongation of the neck, aluminum necks behave in the opposite way. We have performed first-principles electronic-structure calculations which reproduce this behavior, showing that it is an intrinsic property of the bulk band structure under high uniaxial strain.

Evolution of conducting channels in metallic atomic contacts under elastic deformation

We investigate both experimentally and theoretically the evolution of conductance in metallic one-atom contacts under elastic deformation. While simple metals like Au exhibit almost constant conductance plateaus, Al and Pb show inclined plateaus with positive and negative slopes. It is shown how these behaviors can be understood in terms of the orbital structure of the atoms forming the contact. This analysis provides further insight into the issue of conductance quantization in metallic contacts revealing important aspects of their atomic and electronic structures.

Common origin for surface reconstruction and the formation of chains of metal atoms

During the fracture of nanocontacts gold spontaneously forms freely suspended chains of atoms, which is not observed for the isoelectronic noble metals Ag and Cu. Au also differs from Ag and Cu in forming reconstructions at its low-index surfaces. Using mechanically controllable break junctions we show that all the 5d metals that show similar reconstructions (Ir, Pt, and Au) also form chains of atoms, while both properties are absent in the 4d neighbor elements (Rh, Pd, and Ag), indicating a common origin for these two phenomena. A competition between s and d bonding is proposed as an explanation.

Onset of energy dissipation in ballistic atomic wires

Electronic transport at finite voltages in free-standing gold atomic chains of up to seven atoms in length is studied at low temperatures using a scanning tunneling microscope. The conductance vs voltage curves show that transport in these single-mode ballistic atomic wires is nondissipative up to a finite voltage threshold of the order of several mV. The onset of dissipation and resistance within the wire corresponds to the excitation of the atomic vibrations by the electrons traversing the wire and is very sensitive to strain.