Identifying the two-dimensional (2D) topological insulating (TI) state in new materials and its control are crucial aspects towards the development of voltage-controlled spintronic devices with low power dissipation. Members of the 2D transition metal dichalcogenides (TMDCs) have been recently predicted and experimentally reported as a new class of 2D TI materials, but in most cases edge conduction seems fragile and limited to the monolayer phase fabricated on specified substrates. Here, we realize the controlled patterning of the 1T'-phase embedded into the 2H-phase of thin semiconducting molybdenum-disulfide (MoS2) by laser beam irradiation. Integer fractions of the quantum of resistance, the dependence on laser-irradiation conditions, magnetic field, and temperature, as well as the bulk gap observation by scanning tunneling spectroscopy and theoretical calculations indicate the presence of the quantum spin Hall phase in our patterned 1T' phases.Two-dimensional (2D) topological insulting (TI) states have been mainly investigated in HgTe/CdTe or InAs/GaSb quantum well systems (1-3). In the 2D TI state the quantum spin Hall (QSH) effect emerges thanks to the simultaneous presence of a bulk energy gap and gapless helical edge states protected by time-reversal symmetry, namely, opposite and counter-propagating spin states forming a Kramers doublet. Interestingly, 2D TI states were first theoretically predicted for graphene (4-6), but experimentally reported in only few related systems (7-9) such as low-coverage Bi2Te3 nanoparticle-decorated graphene (8). Moreover, control of the QSH phase in graphene-based systems remains a challenge.Recently, a family of atom-thin transition metal dichalcogenides (TMDCs) materials has also been predicted to exhibit the QSHE (10-12), having its origin in the natural band inversion of the 1T' phase (one of the phases of TMDC; see Supplementary Material (SM) 1) and the spin-orbit coupling (SOC)induced band-gap opening. Moreover, the TI state has been experimentally verified in the case of WTe 2 (13-15) thanks to the stability and high-quality of WTe 2 monolayers carefully formed on bilayer graphene/atom-thin hBN. Various signatures of the TI state have been demonstrated in this 2 material (13,15), including the latest observation of a half-integer quantum value of resistance (RQ/2 = h/2e 2 = 12.9 k, where h is Planck's constant and e is the charge on the electron) (14).However, the TI phenomenon in WTe2 is rather sensitive to the substrates, synthesis process, and the chemical environment, making its controlled use in practical applications challenging. Moreover, although the (metastable) 1T' phase can be found or induced in other TMDCs (23,25), nobody has demonstrated the existence of the QSHE in these other TMDCs. The conditions under which helical edge states can exist at the 1T'-2H interfaces is a crucial problem which should be mastered for both TI physics and its applications. Here, we pattern a metallic 1T'-phase (SM 1) embedded into the nontopological and semiconducting 2H p...
Features of electronic currents in solids are truly diverse depending on circumstances, e.g. non-equilibrium transport currents leading to dissipation and persistent currents flowing in equilibrium. Differences between these currents may be clear in many cases, while there are some where they are not. Results of theoretical studies on the latter cases will be introduced briefly focusing on the inter-band effects of magnetic fields in orbital magnetisms and Hall effects of Dirac electrons.
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