Topological Flat Bands in Strained Graphene: Substrate Engineering and Optical Control.

The discovery of correlated phases in twisted moiré superlattices accelerated the search for low-dimensional materials with exotic properties. A promising approach uses engineered substrates to strain the material. However, designing substrates for tailored properties is hindered by the incomplete understanding of the relationship between the substrate's shapes and the electronic properties of the deposited materials. By analyzing effective models of graphene under periodic deformations with generic crystalline profiles, we identify strong C2z symmetry breaking as the critical substrate geometric feature for emerging energy gaps and quasi-flat bands. We find continuous strain profiles producing connected pseudomagnetic field landscapes are important for band topology. We show that the resultant electronic and topological properties from a substrate can be controlled with circularly polarized light, which also offers unique signatures for identifying the band topology imprinted by strain. Our results can guide experiments on strain engineering for exploring interesting transport and topological phenomena.

Tuning the Pseudospin Polarization of Graphene by a Pseudomagnetic Field.

One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudomagnetic field as a result of mechanical deformation. In the case of graphene, the Landau quantization resulting from this pseudomagnetic field has been measured using scanning tunneling microscopy. Here we show that a signature of the pseudomagnetic field is a local sublattice symmetry breaking observable as a redistribution of the local density of states. This can be interpreted as a polarization of graphene's pseudospin due to a strain induced pseudomagnetic field, in analogy to the alignment of a real spin in a magnetic field. We reveal this sublattice symmetry breaking by tunably straining graphene using the tip of a scanning tunneling microscope. The tip locally lifts the graphene membrane from a SiO2 support, as visible by an increased slope of the I(z) curves. The amount of lifting is consistent with molecular dynamics calculations, which reveal a deformed graphene area under the tip in the shape of a Gaussian. The pseudomagnetic field induced by the deformation becomes visible as a sublattice symmetry breaking which scales with the lifting height of the strained deformation and therefore with the pseudomagnetic field strength. Its magnitude is quantitatively reproduced by analytic and tight-binding models, revealing fields of 1000 T. These results might be the starting point for an effective THz valley filter, as a basic element of valleytronics.

Enhancement of the Kondo effect through Rashba spin-orbit interactions.

We study a one-orbital Anderson impurity in a two-dimensional electron bath with Rashba spin-orbit interactions in the Kondo regime. The spin SU(2) symmetry-breaking term couples the impurity to a two-band electron gas. A Schrieffer-Wolff transformation shows the existence of the Dzyaloshinsky-Moriya interaction away from the particle-hole symmetric impurity state. A renormalization group analysis reveals a two-channel Kondo model with ferro- and antiferromagnetic couplings. The parity-breaking Dzyaloshinsky-Moriya term renormalizes the antiferromagnetic Kondo coupling with an exponential enhancement of the Kondo temperature.

Tunable pseudogap Kondo effect and quantum phase transitions in Aharonov-Bohm interferometers.

We study two quantum dots embedded in the arms of an Aharonov-Bohm ring threaded by a magnetic flux. This system can be described by an effective one-impurity Anderson model with an energy- and flux-dependent density of states. For specific values of the flux, this density of states vanishes at the Fermi energy, yielding a controlled realization of the pseudogap Kondo effect. The conductance and transmission phase shifts reflect a nontrivial interplay between wave interference and interactions, providing clear signatures of quantum phase transitions between Kondo and non-Kondo ground states.

Unscreened Coulomb interactions and the quantum spin Hall phase in neutral zigzag graphene ribbons.

A study of the effect of unscreened Coulomb interactions on the quantum spin Hall phase of finite-width neutral zigzag graphene ribbons is presented. By solving a tight-binding Hamiltonian that includes the intrinsic spin-orbit (ISO) interaction, exact expressions for band structures and edge-state wave functions are obtained. These analytic results, supported by tight-binding calculations, show that chiral spin-filtered edge states are composed of localized and damped oscillatory wave functions, reminiscent of the ones obtained in armchair ribbons. The addition of long-range Coulomb interactions opens a gap in the charge sector with a gapless spin sector. In contrast to armchair terminations, the charge gap vanishes exponentially with the ribbon width and its amplitude and decay length are strongly dependent on the ISO coupling. Comparison with reported ab initio calculations are presented.

Electron-electron and spin-orbit interactions in armchair graphene ribbons.

The effects of intrinsic spin-orbit and Coulomb interactions on low-energy properties of finite width graphene armchair ribbons are studied by means of a Dirac Hamiltonian. It is shown that metallic states subsist in the presence of intrinsic spin-orbit interactions as spin-filtered edge states, in contrast with the insulating behavior predicted for graphene planes. A charge-gap opens due to Coulomb interactions in neutral ribbons, that vanishes as Delta approximately 1/W, with a gapless spin sector. Weak intrinsic spin-orbit interactions do not change the insulating behavior. Explicit expressions for the width-dependent gap and various correlation functions are presented.

Zero-field kondo splitting and quantum-critical transition in double quantum dots.

Double quantum dots offer unique possibilities for the study of many-body correlations. A system containing one Kondo dot and one effectively noninteracting dot maps onto a single-impurity Anderson model with a structured (nonconstant) density of states. Numerical renormalization-group calculations show that, while band filtering through the resonant dot splits the Kondo resonance, the singlet ground state is robust. The system can also be continuously tuned to create a pseudogapped density of states and access a quantum-critical point separating Kondo and non-Kondo phases.

Scanning tunneling microscopy and surface simulation of zinc-blende GaN(001) intrinsic 4x reconstruction: linear gallium tetramers?

Scanning tunneling microscopy images confirm electron diffraction studies that the zinc-blende GaN(001)-4x reconstruction consists of rows aligned along [110] with a spacing along [110] of 4a. Dual-bias imaging shows a 180 degree shift of the corrugation maximum position between the profiles of empty and occupied states, in agreement with surface simulations based on the 4 x 1 linear tetramer model of Neugebauer et al. [Phys. Rev. Lett. 80, 3097 (1998)]. Electronic structure calculations predict a surface band gap of 1.1 eV, close to the measured value of 1.14 eV and the previously predicted value (1.2 eV). Despite the successes of this model, high-resolution images reveal an unexpected 3x periodicity (not seen in diffraction) along the [110] row direction, indicating the need for a 4 x 3 model, and putting into question the existence of linear Ga tetramers.