Transport through quantum spin Hall insulator/metal junctions in graphene ribbons

Prada, Elsa; Metalidis, G.

doi:10.1007/s10825-012-0427-6

Cited by 15 publications

(13 citation statements)

References 61 publications

(76 reference statements)

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“…We note that dotted horizontal line in Figs. 2(c) and 2(d) plots T el (E) = 2 within a wider range of energies E F ∈ [−0.4 eV, 0.4 eV] for a uniform ZGNR + heavyadatoms, which is inherited from the underlying subband structure of GNRs with zigzag edges (ZGNRs) [21]. However, once nanopores and/or edge disorder are introduced the quantized T el (E) = 2 in Figs.…”

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“…2(a) increases as one moves away from the Dirac point (DP) at E F = 0, so that when states from opposite edges start to overlap a minigap is created thereby removing the crossing point in the inset of Fig. 1(a) and protection by TRS [21]. Although no symmetry prevents inelastic backscattering off phonons, quantized transmission is expected to be insensitive to such inelastic mechanisms to leading order [23].…”

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Giant Thermoelectric Effect in Graphene-Based Topological Insulators with Heavy Adatoms and Nanopores

et al. 2014

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Designing thermoelectric materials with high figure of merit ZT = S 2 GT /κ requires fulfilling three often irreconcilable conditions, i.e., the high electrical conductance G, small thermal conductance κ and high Seebeck coefficient S. Nanostructuring is one of the promising ways to achieve this goal as it can substantially suppress lattice contribution to κ. However, it may also unfavorably influence the electronic transport in an uncontrollable way. Here we theoretically demonstrate that this issue can be ideally solved by fabricating graphene nanoribbons with heavy adatoms and nanopores. These systems, acting as a two-dimensional topological insulator with robust helical edge states carrying electrical current, yield a highly optimized power factor S 2 G per helical conducting channel. Concurrently, their array of nanopores impedes the lattice thermal conduction through the bulk. Using quantum transport simulations coupled with first-principles electronic and phononic band structure calculations, the thermoelectric figure of merit is found to reach its maximum ZT 3 at T 40 K. This paves a way to design high-ZT materials by exploiting the nontrivial topology of electronic states through nanostructuring.PACS numbers: 73.50. Lw, 03.65.Vf, 85.80.Fi Thermoelectrics [1-3] transform temperature gradients into electric voltage and vice versa. Although a plethora of thermoelectric energy harvesting and cooling applications has been envisioned, their usage is presently limited by their small efficiency. This is due to the fact that increasing thermoelectric figure of meritrequires careful trade-off between electrical conductance G, the Seebeck coefficient S, and the thermal conductance κ el + κ ph . The total thermal conductance has contributions from both electrons κ el and phonons (i.e., lattice vibrations) κ ph . ZT quantifies the maximum efficiency of a thermoelectric cycle conversion in the linearresponse regime where a small voltage ∆V = −S∆T exactly cancels the current induced by the small temperature difference ∆T = T H − T C at average operating temperature T = (T H + T C )/2. The values approaching ZT → ∞ would ensure Carnot efficiency as the theoretical limit for a heat engine operating between a hot T H and a cold T C temperature. However, ZT of realistic devices is limited by irreversible energy losses via Joule heat and thermal conduction, so that a pragmatic goal is to achieve ZT 3 with low parasitic losses and stability over a broad temperature range [2, 3]. The major directions to increase ZT have been focused on either materials with high power factor S 2 G, such as doped narrow-gap semiconductors; or on minimizing κ ph by enhanced phonon scattering in different frequency ranges, such as through nanostructuring [1,2]. Although nanostructuring has progressed rapidly over the past decade [1,2], it typically affects bulk electronic states of conventional materials in unfavorable way for thermoelectricity. Thus, the recently discovered topological insulator (TI) materials [4,5] are of particular intere...

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Giant Thermoelectric Effect in Graphene-Based Topological Insulators with Heavy Adatoms and Nanopores

et al. 2014

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“…We observe that the electrons injected from the source (x > 50 nm) are rapidly and completely deviated along the top edge for spin down, see Fig.3(a), and along the lower edge for spin up, see Fig.3(b). The width of the polarized edge channels in armchair ribbons does not depend on the energy but only on the SOC [40] as aγ/(2 √ 3λ eff ) ≈13.5 nm, where a is the carbon interatomic distance. The separation between the right-to-left and left-to-right moving channels, which is opposite for different spin polarizations, is at the origin of the QSHE.…”

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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

et al. 2014

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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

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“…It is worth mentioning that even in systems with nonzero topological invariants in the bulk band structure, such as the Chern number  in quantum Hall and quantum anomalous Hall insulators, which counts the number of metallic edge states [32] (note that  º 0 in the case of G/hBN [32]), zigzag edges of the honeycomb lattice play a special role due to their ability to modify the energy-momentum dispersion and the corresponding conductance carried by edge states [47]. They also shrink the spatial extent of edge states [45,47,48]. Nevertheless, the presence of nonzero  guarantees that the quantized conductance ´e h 2 2 will survive disorder [47], while no such topological protection exists in the case of G/hBN wires whose two-terminal conductance is nonquantized  e h 2 2 in the presence of edge disorder ( figure 3(b)).…”

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Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents

et al. 2018

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The recent observation (Gorbachev et al 2014 Science 346 448) of nonlocal resistance R NL near the Dirac point (DP) of multiterminal graphene on aligned hexagonal-boron nitride (G/hBN) has been interpreted as the consequence of topological valley Hall currents carried by the Fermi sea states just beneath the bulk gap E g induced by inversion symmetry breaking. However, the corresponding valley Hall conductivity s xy v , quantized inside E g , is not directly measurable. Conversely, the Landauer-Büttiker formula, as a numerically exact approach to observable nonlocal transport quantities, yields R NL ≡ 0 for the same simplistic Hamiltonian of gapped graphene that generates s ¹ 0 xy v OPEN ACCESS RECEIVED

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Transport through quantum spin Hall insulator/metal junctions in graphene ribbons

Cited by 15 publications

References 61 publications

Giant Thermoelectric Effect in Graphene-Based Topological Insulators with Heavy Adatoms and Nanopores

Giant Thermoelectric Effect in Graphene-Based Topological Insulators with Heavy Adatoms and Nanopores

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

Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents

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