Dielectric Screening by 2D Substrates

Two-dimensional (2D) materials are increasingly being used as active components in nanoscale devices. Many interesting properties of 2D materials stem from the reduced and highly non-local electronic screening in two dimensions. While electronic screening within 2D materials has been studied extensively, the question still remains of how 2D substrates screen charge perturbations or electronic excitations adjacent to them. Thickness-dependent dielectric screening properties have recently been studied using electrostatic force microscopy (EFM) experiments. However, it was suggested that some of the thickness-dependent trends were due to extrinsic effects. Similarly, Kelvin probe measurements (KPM) indicate that charge fluctuations are reduced when BN slabs are placed on SiO$_2$, but it is unclear if this effect is due to intrinsic screening from BN. In this work, we use first principles calculations to study the fully non-local dielectric screening properties of 2D material substrates. Our simulations give results in good qualitative agreement with those from EFM experiments, for hexagonal boron nitride (BN), graphene and MoS$_2$, indicating that the experimentally observed thickness-dependent screening effects are intrinsic to the 2D materials. We further investigate explicitly the role of BN in lowering charge potential fluctuations arising from charge impurities on an underlying SiO$_2$ substrate, as observed in the KPM experiments. 2D material substrates can also dramatically change the HOMO-LUMO gaps of adsorbates, especially for small molecules, such as benzene. We propose a reliable and very quick method to predict the HOMO-LUMO gap of small physisorbed molecules on 2D and 3D substrates, using only the band gap of the substrate and the gas phase gap of the molecule.Comment: 24 pages, 5 figures, Supplementary Informatio

Giant edge state splitting at atomically precise zigzag edges

Zigzag edges of graphene nanostructures host localized electronic states that are predicted to be spin-polarized. However, these edge states are highly susceptible to edge roughness and interaction with a supporting substrate, complicating the study of their intrinsic electronic and magnetic structure. Here, we focus on atomically precise graphene nanoribbons whose two short zigzag edges host exactly one localized electron each. Using the tip of a scanning tunneling microscope, the graphene nanoribbons are transferred from the metallic growth substrate onto insulating islands of NaCl in order to decouple their electronic structure from the metal. The absence of charge transfer and hybridization with the substrate is confirmed by scanning tunneling spectroscopy (STS), which reveals a pair of occupied / unoccupied edge states. Their large energy splitting of 1.9 eV is in accordance with ab initio many-body perturbation theory calculations and reflects the dominant role of electron-electron interactions in these localized states.Comment: 14 pages, 4 figure

Strain and Electric Field Modulation of the Electronic Structure of Bilayer Graphene

We study how the electronic structure of the bilayer graphene (BLG) is changed by electric field and strain from {\it ab initio} density-functional calculations using the LMTO and the LAPW methods. Both hexagonal and Bernal stacked structures are considered. The BLG is a zero-gap semiconductor like the isolated layer of graphene. We find that while strain alone does not produce a gap in the BLG, an electric field does so in the Bernal structure but not in the hexagonal structure. The topology of the bands leads to Dirac circles with linear dispersion in the case of the hexagonally stacked BLG due to the interpenetration of the Dirac cones, while for the Bernal stacking, the dispersion is quadratic. The size of the Dirac circle increases with the applied electric field, leading to an interesting way of controlling the Fermi surface. The external electric field is screened due to polarization charges between the layers, leading to a reduced size of the band gap and the Dirac circle. The screening is substantial in both cases and diverges for the Bernal structure for small fields as has been noted by earlier authors. As a biproduct of this work, we present the tight-binding parameters for the free-standing single layer graphene as obtained by fitting to the density-functional bands, both with and without the slope constraint for the Dirac cone.Comment: 7 pages, 7 figure

Low-energy effective interactions beyond the constrained random-phase approximation by the functional renormalization group

In the derivation of low-energy effective models for solids targeting the bands near the Fermi level, the constrained random phase approximation (cRPA) has become an appreciated tool to compute the effective interactions. The Wick-ordered constrained functional renormalization group (cfRG) generalizes the cRPA approach by including all interaction channels in an unbiased way. Here we present applications of the cfRG to two simple multi-band systems and compare the resulting effective interactions to the cRPA. First we consider a multiband model for monolayer graphene, where we integrate out the $\sigma$-bands to get an effective theory for $\pi$-bands. It turns out that terms beyond cRPA are strongly suppressed by the different $xy$-plane reflection symmetry of the bands. In our model the cfRG-corrections to cRPA become visible when one disturbs this symmetry difference slightly, however without qualitative changes. This study shows that the embedding or layering of two-dimensional electronic systems can alter the effective interaction parameters beyond what is expected from screening considerations. The second example is a one-dimensional model for a diatomic system reminiscent of a CuO chain, where we consider an effective theory for Cu 3d-like orbitals. Here the fRG data shows relevant and qualitative corrections compared to the cRPA results. We argue that the new interaction terms affect the magnetic properties of the low-energy model.Comment: 17 pages, 14 figure

Phase diagram for the ν=0\nu=0 quantum Hall state in monolayer graphene

The $\nu=0$ quantum Hall state in a defect-free graphene sample is studied within the framework of quantum Hall ferromagnetism. We perform a systematic analysis of the pseudospin anisotropies, which arise from the valley and sublattice asymmetric short-range electron-electron (e-e) and electron-phonon (e-ph) interactions. The phase diagram, obtained in the presence of generic pseudospin anisotropy and the Zeeman effect, consists of four phases characterized by the following orders: spin-polarized ferromagnetic, canted antiferromagnetic, charge density wave, and Kekul\'{e} distortion. We take into account the Landau level mixing effects and show that they result in the key renormalizations of parameters. First, the absolute values of the anisotropy energies become greatly enhanced and can significantly exceed the Zeeman energy. Second, the signs of the anisotropy energies due to e-e interactions can change upon renormalization. A crucial consequence of the latter is that the short-range e-e interactions alone could favor any state on the phase diagram, depending on the details of interactions at the lattice scale. On the other hand, the leading e-ph interactions always favor the Kekul\'{e} distortion order. The possibility of inducing phase transitions by tilting the magnetic field is discussed.Comment: 25 pages, 19 figs; v2: nearly identical to the published version, some stylistic improvements, Tables I-IV added, anisotropy energies redefined as u -> u/2 for aesthetic reaso

An orbitally derived single-atom magnetic memory

A single magnetic atom on a surface epitomizes the scaling limit for magnetic information storage. Indeed, recent work has shown that individual atomic spins can exhibit magnetic remanence and be read out with spin-based methods, demonstrating the fundamental requirements for magnetic memory. However, atomic spin memory has been only realized on thin insulating surfaces to date, removing potential tunability via electronic gating or distance-dependent exchange-driven magnetic coupling. Here, we show a novel mechanism for single-atom magnetic information storage based on bistability in the orbital population, or so-called valency, of an individual Co atom on semiconducting black phosphorus (BP). Distance-dependent screening from the BP surface stabilizes the two distinct valencies and enables us to electronically manipulate the relative orbital population, total magnetic moment and spatial charge density of an individual magnetic atom without a spin-dependent readout mechanism. Furthermore, we show that the strongly anisotropic wavefunction can be used to locally tailor the switching dynamics between the two valencies. This orbital memory derives stability from the energetic barrier to atomic relaxation and demonstrates the potential for high-temperature single-atom information storage

Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene

Two monolayers of graphene twisted by a small `magic' angle exhibit nearly flat bands leading to correlated electronic states and superconductivity, whose precise nature including possible broken symmetries, remain under debate. Here we theoretically study a related but different system with reduced symmetry - twisted {\em double} bilayer graphene (TDBLG), consisting of {\em two} Bernal stacked bilayer graphene sheets, twisted with respect to one another. Unlike the monolayer case, we show that isolated flat bands only appear on application of a vertical displacement field $D$. We construct a phase diagram as a function of twist angle and $D$, incorporating interactions via a Hartree-Fock approximation. At half filling, ferromagnetic insulators are stabilized, typically with valley Chern number $C_v=2$. Ferromagnetic fluctuations in the metallic state are argued to lead to spin triplet superconductivity from pairing between electrons in opposite valleys. Response of these states to a magnetic field applied either perpendicular or parallel to the graphene sheets is obtained, and found to compare favorably with a recent experiment. We highlight a novel orbital effect arising from in-plane fields that can exceed the Zeeman effect and plays an important role in interpreting experiments.Comment: main 15 pages, appendix 11 page