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Register a new userEvidence for a quantum-spin-Hall phase in graphene decorated with Bi2Te3 nanoparticles
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Realization of the quantum-spin-Hall effect in graphene devices has remained an outstanding challenge dating back to the inception of the field of topological insulators. Graphenes exceptionally weak spin-orbit coupling -stemming from carbons low mass- poses the primary obstacle. We experimentally and theoretically study artificially enhanced spin-orbit coupling in graphene via random decoration with dilute Bi2Te3 nanoparticles. Remarkably, multi-terminal resistance measurements suggest the presence of helical edge states characteristic of a quantum-spin-Hall phase; the magnetic-field and temperature dependence of the resistance peaks, X-ray photoelectron spectra, scanning tunneling spectroscopy, and first-principles calculations further support this scenario. These observations highlight a pathway to spintronics and quantum-information applications in graphene-based quantum-spin-Hall platforms.
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The introduction of spin-orbit interactions (SOIs) and the subsequent appearance of a two-dimensional (2D) topological phase are crucial for voltage-controlled and zero-emission energy spintronic devices. In contrast, graphene basically lacks SOIs due to the small mass of the carbon atom, and appropriate experimental reports for SOIs are rare. Here, we control small-amount (cover ratios < 8%) random decoration of heavy nanoparticles [platinum (Pt) or bismuth telluride (Bi2Te3)] onto mono-layer graphene by developing an original nanoneedle method. X-ray photoelectron spectra support low-damage and low-contamination decoration of the nanoparticles, suggesting the presence of Bi-C and Te-C coupling orbitals. In the samples, we find particle-density-dependent non-local resistance (RNL) peaks, which are attributed to the (inverse) spin Hall effect (SHE) arising from SOI with energies as large as about 30 meV. This is a larger value than in previous reports and supported by scanning tunneling spectroscopy. The present observation should lead to topological phases of graphene, which can be introduced by random decoration with controlled small amounts of heavy nanoparticles, and their applications.
Theoretical predictions and recent experimental results suggest one can engineer spin Hall effect in graphene by enhancing the spin-orbit coupling in the vicinity of an impurity. We use a Chebyshev expansion of the Kubo-Bastin formula to compute the spin conductivity tensor for a tight-binding model of graphene with randomly distributed impurities absorbed on top of carbon atoms. We model the impurity-induced spin-orbit coupling with a graphene-only Hamiltonian that takes into account three different contributions~cite{Gmitra2013} and show how the spin Hall and longitudinal conductivities depend on the strength of each spin-orbit coupling and the concentration of impurities. Additionally, we calculate the real-space projection of the density of states in the vicinity of the Dirac point for single and multiple impurities and correlate these results with the conductivity calculations.
We investigate integer and half-integer filling states (uniform and unidimensional stripe states respectively) for graphene using the Hartree-Fock approximation. For fixed filling factor, the ratio between the scales of the Coulomb interaction and Landau level spacing $g=(e^2/epsilon ell)/(hbar v_F/ell)$, with $ell$ the magnetic length, is a field-independent constant. However, when $B$ decreases, the number of filled negative Landau levels increases, which surprisingly turns out to decrease the amount of Landau level mixing. The resulting states at fixed filling factor $ u$ (for $ u$ not too big) have very little Landau level mixing even at arbitrarily weak magnetic fields. Thus in the density-field phase diagram, many different phases may persist down to the origin, in contrast to the more standard two dimensional electron gas, in which the origin is surrounded by Wigner crystal states. We demonstrate that the stripe amplitudes scale roughly as $B$, so that the density waves ``evaporate continuously as $Bto 0$. Tight-binding calculations give the same scaling for stripe amplitude and demonstrate that the effect is not an artifact of the cutoff procedure used in the continuum calculations.
The most celebrated property of the quantum spin Hall effect is the presence of spin-polarized counter-propagating edge states. This novel edge state configuration has also been predicted to occur in graphene when spin-split electron- and hole-like Landau levels are forced to cross at the edge of the sample. In particular, a quantum spin Hall analogue has been predicted at { u}=0 in bilayer graphene if the ground state is a spin ferromagnet. Previous studies have demonstrated that the bilayer { u}=0 state is an insulator in a perpendicular magnetic field, though the exact nature of this state has not been identified. Here we present measurements of the { u}=0 state in a dual-gated bilayer graphene device in tilted magnetic field. The application of an in-plane magnetic field and perpendicular electric field allows us to map out a full phase diagram of the { u}=0 state as a function of experimentally tunable parameters. At large in-plane magnetic field we observe a quantum phase transition to a metallic state with conductance of order 4e^2/h, consistent with predictions for the ferromagnet.
The naturally weak spin-orbit coupling in Graphene can be largely enhanced by adatom deposition (e.g. Weeks et al. Phys. Rev. X 1, 021001 (2011)). However, the dynamics of the adatoms also induces a coupling between phonons and the electron spin. Using group theory and a tight-binding model, we systematically investigate the coupling between the low-energy in-plane phonons and the electron spin in single-layer graphene uniformly decorated with heavy adatoms. Our results provide the foundation for future investigations of spin transport and superconductivity in this system. In order to quantify the effect of the coupling to the lattice on the electronic spin dynamics, we compute the spin-flip rate of electrons and holes. We show that the latter exhibits a strong dependence on the quasi-particle energy and system temperature.
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