Multiple Quantum Phases in Graphene with Enhanced Spin-Orbit Coupling: From the Quantum Spin Hall Regime to the Spin Hall Effect and a Robust Metallic State

Abstract

We report an intriguing transition from the quantum spin Hall phase to the spin Hall effect upon segregation of thallium adatoms adsorbed onto a graphene surface. Landauer-Büttiker and Kubo-Greenwood simulations are used to access both edge and bulk transport physics in disordered thallium-functionalized graphene systems of realistic sizes. Our findings not only quantify the detrimental effects of adatom clustering in the formation of the topological state, but also provide evidence for the emergence of spin accumulation at opposite sample edges driven by spin-dependent scattering induced by thallium islands, which eventually results in a minimum bulk conductivity ∼4e 2 =h, insensitive to localization effects. Introduction.-In 2005, Kane and Mele predicted the existence of the quantum spin Hall effect (QSHE) in graphene due to intrinsic spin-orbit coupling (SOC) [1,2]. Within the QSHE, the presence of spin-orbit coupling, which can be understood as a momentum-dependent magnetic field coupling to the spin of the electron, results in the formation of chiral edge channels for spin up and spin down electron populations. The observation of the QSHE is, however, prohibited in clean graphene owing to vanishingly small intrinsic spin-orbit coupling on the order of μeV [3], but demonstrated in strong SOC materials (such as CdTe/ HgTe/CdTe quantum wells or bismuth selenide and telluride alloys), giving rise to the new exciting field of topological insulators [4][5][6][7]. Recent proposals to induce a topological phase in graphene include functionalization with heavy adatoms [8,9], covalent functionalization of the edges [10], proximity effect with topological insulators [11][12][13], or intercalation and functionalization with 5d transition metals [14,15]. In particular, the seminal theoretical study [8] by Weeks and co-workers has revealed that graphene endowed with a modest coverage of heavy adatoms (such as indium and thallium) could exhibit a substantial band gap and QSH fingerprints (detectable in transport or spectroscopic measurements). For instance, one signature of such a topological state would be a robust quantized two-terminal conductance (2e 2 =h), with an adatom density-dependent conductance plateau extending inside the bulk gap induced by SOC [8,16,17]. To date, such a prediction lacks experimental confirmation [18], despite some recent results on indiumfunctionalized graphene that have shown a surprising reduction of the Dirac point resistance with increasing indium density [19]. On the other hand, it is known that adatoms deposited on two-dimensional materials inevitably

Weak localization of bismuth cluster-decorated graphene and its spin–orbit interaction

“…In theories and experiments regarding adatoms on the graphene, the size of adsorbed heavy metal nanoclusters or the coverage of adatoms is often considered [7,22,41,42]. After the first Bi-cluster deposition, the cluster coverage is low, as indicated by the 4.2% change in the resistance at room temperature.…”

“…Several approaches have been suggested, such as utilizing the proximity effect in graphene/strong SOC material heterostructures [2][3][4], the hydrogenation and fluorination of graphene [5,6], and depositing certain heavy adatoms on graphene [7][8][9][10]. Experimentally, angle-resolved photoemission spectroscopy did not reveal an SOC gap in epitaxial Bi 2 Te 2 Se on chemical vapor deposition (CVD)- grown graphene [11].…”

Spin Hall Effect and Origins of Nonlocal Resistance in Adatom-Decorated Graphene

“…Moreover, while Kubo formula [29] offers fully quantum-mechanical treatment that can in principle capture all relevant effects, its standard analytical evaluation neglects [30] terms in the perturbative expansion in disorder strength which can become crucial for clusters of adatoms (such as those corresponding to skew-scattering from pairs of closely spaced impurities [31]). Finally the impact of unavoidable adatom clustering [32] onto graphene surface on θ sH is an open and important question, since adatom segregation has been shown to strongly affect spin transport properties [33,34].…”

Electrical control of intervalley scattering in graphene via the charge state of defects

“…Therefore, this effect is particularly relevant in materials promising for valleytronics, such as graphene and TMDs. Furthermore, we would like to point out that it also provides important insight into another topic in which adatoms have been proposed to engineer the properties of graphene, such as spin-orbit coupling [32][33][34][35][36] and magnetism [37][38][39][40]. Despite many theoretical proposals, transport studies have shown that Au, Mg and In adatoms on graphene generate only long-range Coulomb impurity scattering, while neither spin-orbit scattering nor magnetic scattering has been introduced [41][42][43][44].…”