Modulation of Kekul\'e adatom ordering due to strain in graphene

Intervalley scattering of carriers in graphene at `top' adatoms may give rise to a hidden Kekul\'e ordering pattern in the adatom positions. This ordering is the result of a rapid modulation in the electron-mediated interaction between adatoms at the wavevector $K- K'$, which has been shown experimentally and theoretically to dominate their spatial distribution. Here we show that the adatom interaction is extremely sensitive to strain in the supporting graphene, which leads to a characteristic spatial modulation of the Kekul\'e order as a function of adatom distance. Our results suggest that the spatial distributions of adatoms could provide a way to measure the type and magnitude of strain in graphene and the associated pseudogauge field with high accuracy.Comment: 9 pages, 7 figure

Band topology and quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin orbit coupling, to assess its behavior as a topological insulator. The first Chern number $n$ for the energy bands of single and bilayer graphene is computed and compared. It is shown that for a given valley and spin, $n$ in a bilayer is doubled with respect to the monolayer. This implies that bilayer graphene will have twice as many edge states as single layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We also assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. Finally, we consider an intermediate situation in which only one of the two layers has spin orbit coupling, and find that although individual valleys have non-trivial Chern numbers, the spectrum as a whole is not gapped, so that the system is not a topological insulator.Comment: 9 pages. 9 figures include

Electron-induced rippling in graphene

We show that the interaction between flexural phonons, when corrected by the exchange of electron-hole excitations, may place the graphene sheet very close to a quantum critical point characterized by the strong suppression of the bending rigidity of the membrane. Ripples arise then due to spontaneous symmetry breaking, following a mechanism similar to that responsible for the condensation of the Higgs field in relativistic field theories. In the presence of membrane tensions, ripple condensation may be reinforced or suppressed depending on the sign of the tension, following a zero-temperature buckling transition in which the order parameter is given essentially by the square of the gradient of the flexural phonon field.Comment: 4 pages, 3 figure

Non-hermitian topology as a unifying framework for the Andreev versus Majorana states controversy

Zero-energy Andreev levels in hybrid semiconductor-superconductor nanowires mimic all expected Majorana phenomenology, including 2 e2∕ h conductance quantisation, even where band topology predicts trivial phases. This surprising fact has been used to challenge the interpretation of various transport experiments in terms of Majorana zero modes. Here we show that the Andreev versus Majorana controversy is clarified when framed in the language of non-Hermitian topology, the natural description for quantum systems open to the environment. This change of paradigm allows one to understand topological transitions and the emergence of zero modes in more general systems than can be described by band topology. This is achieved by studying exceptional point bifurcations in the complex spectrum of the system’s non-Hermitian Hamiltonian. Within this broader topological classification, Majoranas from both conventional band topology and a large subset of Andreev levels at zero energy are in fact topologically equivalent, which explains why they cannot be distinguishedWe thank J. Cayao for useful discussions in the early stages of this work. Research supported by the Spanish Ministry of Science, Innovation and Universities through Grants PGC2018-097018-B-I00, FIS2015-65706-P, FIS2015-64654-P, FIS2016-80434-P (AEI/FEDER, EU), the FPI programme BES-2016-078122, the Ramón y Cajal programme Grants RYC-2011-09345, RYC-2013-14645, the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0377), and the European Union’s Horizon 2020 research and innovation programme under the FETOPEN Grant Agreement No. 828948. We also acknowledge support from CSIC Research Platform on Quantum Technologies PTI-00

Zero Landau level in folded graphene nanoribbons

Graphene nanoribbons can be folded into a double layer system keeping the two layers decoupled. In the Quantum Hall regime folds behave as a new type of Hall bar edge. We show that the symmetry properties of the zero Landau level in metallic nanoribbons dictate that the zero energy edge states traversing a fold are perfectly transmitted onto the opposite layer. This result is valid irrespective of fold geometry, magnetic field strength and crystallographic orientation of the nanoribbon. Backscattering suppression on the N=0 Hall plateau is ultimately due to the orthogonality of forward and backward channels, much like in the Klein paradox.Comment: Final published version, with supplementary material appendi

Strain-induced bound states in transition-metal dichalcogenide bubbles

This is an author-created, un-copyedited version of an article published in 2D Materials. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/2053-1583/ab0113We theoretically study the formation of single-particle bound states confined by strain at the center of bubbles in monolayers of transition-metal dichalcogenides (TMDs). Bubbles ubiquitously form in two-dimensional crystals on top of a substrate by the competition between van der Waals forces and the hydrostatic pressure exerted by trapped fluid. This leads to strong strain at the center of the bubble that reduces the bangap locally, creating potential wells for the electrons that confine states inside. We simulate the spectrum versus the bubble radius for the four semiconducting group VI TMDs, MoS2, WSe2, WS2 and MoSe2, and find an overall Fock-Darwin spectrum of bubble bound states, characterised by small deviations compatible with Berry curvature effects. We analyse the density of states, the state degeneracies, orbital structure and optical transition rules. Our results show that elastic bubbles in these materials are remarkably efficient at confining photocarriersWe acknowledge funding from the Graphene Flagship, contract CNECTICT-604391, from the Comunidad de Madrid through Grant MAD2D-CM, S2013/MIT-3007, from the Spanish Ministry of Economy and Competitiveness through Grants No. RYC-2011-09345, RYC-2016-20663, FIS2015-65706-P, FIS2016-80434-P (AEI/FEDER, EU) and the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0377

Geometric phases in semiconductor spin qubits: Manipulations and decoherence

We describe the effect of geometric phases induced by either classical or quantum electric fields acting on single electron spins in quantum dots in the presence of spin-orbit coupling. On one hand, applied electric fields can be used to control the geometric phases, which allows performing quantum coherent spin manipulations without using high-frequency magnetic fields. On the other hand, fluctuating fields induce random geometric phases that lead to spin relaxation and dephasing, thus limiting the use of such spins as qubits. We estimate the decay rates due to piezoelectric phonons and conduction electrons in the circuit, both representing dominant electric noise sources with characteristically differing power spectra.Comment: 17 pages, 8 figures, published versio

Disorder-induced pseudodiffusive transport in graphene nanoribbons.

We study the transition from ballistic to diffusive and localized transport in graphene nanoribbons in the presence of binary disorder, which can be generated by chemical adsorbates or substitutional doping. We show that the interplay between the induced average doping (arising from the nonzero average of the disorder) and impurity scattering modifies the traditional picture of phase-coherent transport. Close to the Dirac point, intrinsic evanescent modes produced by the impurities dominate transport at short lengths giving rise to a regime analogous to pseudodiffusive transport in clean graphene, but without the requirement of heavily doped contacts. This intrinsic pseudodiffusive regime precedes the traditional ballistic, diffusive, and localized regimes. The last two regimes exhibit a strongly modified effective number of propagating modes and a mean free path which becomes anomalously large close to the Dirac point

Majorana Zero Modes in Graphene

A clear demonstration of topological superconductivity (TS) and Majorana zero modes remains one of the major pending goal in the field of topological materials. One common strategy to generate TS is through the coupling of an s-wave superconductor to a helical half-metallic system. Numerous proposals for the latter have been put forward in the literature, most of them based on semiconductors or topological insulators with strong spin-orbit coupling. Here we demonstrate an alternative approach for the creation of TS in graphene/superconductor junctions without the need of spin-orbit coupling. Our prediction stems from the helicity of graphene's zero Landau level edge states in the presence of interactions, and on the possibility, experimentally demonstrated, to tune their magnetic properties with in-plane magnetic fields. We show how canted antiferromagnetic ordering in the graphene bulk close to neutrality induces TS along the junction, and gives rise to isolated, topologically protected Majorana bound states at either end. We also discuss possible strategies to detect their presence in graphene Josephson junctions through Fraunhofer pattern anomalies and Andreev spectroscopy. The latter in particular exhibits strong unambiguous signatures of the presence of the Majorana states in the form of universal zero bias anomalies. Remarkable progress has recently been reported in the fabrication of the proposed type of junctions, which offers a promising outlook for Majorana physics in graphene systems.Comment: 14 pages, 8 figures. Included simulations of Andreev spectroscopy and mor

Stacking boundaries and transport in bilayer graphene

Pristine bilayer graphene behaves in some instances as an insulator with a transport gap of a few meV. This behaviour has been interpreted as the result of an intrinsic electronic instability induced by many-body correlations. Intriguingly, however, some samples of similar mobility exhibit good metallic properties, with a minimal conductivity of the order of $2e^2/h$. Here we propose an explanation for this dichotomy, which is unrelated to electron interactions and based instead on the reversible formation of boundaries between stacking domains (`solitons'). We argue, using a numerical analysis, that the hallmark features of the previously inferred many-body insulating state can be explained by scattering on boundaries between domains with different stacking order (AB and BA). We furthermore present experimental evidence, reinforcing our interpretation, of reversible switching between a metallic and an insulating regime in suspended bilayers when subjected to thermal cycling or high current annealing.Comment: 13 pages, 15 figures. Published version (Nano Letters