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Researcharticles RESEARCH ARTICLES Quantum Spin Hall Insulator State in HgTe Quantum Wells Markus König,1 Steffen Wiedmann,1 Christoph Brüne,1 Andreas Roth,1 Hartmut Buhmann,1 Laurens W. Molenkamp,1* Xiao-Liang Qi,2 Shou-Cheng Zhang2 AUTHORS’ SUMMARY he discovery more than 25 Conductance theoretically that the electronic years ago of the quantum channel with structure of inverted HgTe quan- THall effect (1), in which the up-spin charge tum wells exhibits the properties “Hall,” or “transverse electrical” con- carriers that should enable an observation ductance of a material is quantized, of the quantum spin Hall insula- came as a total surprise to the physics tor state. Our experimental obser- community. This effect occurs in vations confirm this. layered metals at high magnetic These experiments only be- fields and results from the forma- came possible after the devel- tion of conducting one-dimensional opment of quantum wells of channels that develop at the edges sufficiently high carrier mobility, on April 6, 2015 of the sample. Each of these edge combined with the lithographic channels, in which the current moves techniques needed to pattern the only in one direction, exhibits a quan- sample. The patterning is espe- tized conductance that is character- Conductance cially difficult because of the very istic of one-dimensional transport. The channel with high volatility of Hg. Moreover, number of edge channels in the sam- Quantum down-spin we have developed a special low– ple is directly related to the value of well charge carriers deposition temperature Si-O-N the quantum Hall conductance. More- Schematic of the spin-polarized edge channels in a quantum spin Hall gate insulator (7), which allows over, the charge carriers in these chan- insulator. us to control the Fermi level (the www.sciencemag.org nels are very resistant to scattering. energy level up to which all Not only can the quantum Hall effect be observed in macroscopic samples electronics states are filled) in the quantum well from the conduction band, for this reason, but within the channels, charge carriers can be transported through the insulating gap, and into the valence band. Using both electron without energy dissipation. Therefore, quantum Hall edge channels may be beam and optical lithography, we have fabricated simple rectangular useful for applications in integrated circuit technology, where power dis- structures in various sizes from quantum wells of varying width and sipation is becoming more and more of a problem as devices become smaller. measured the conductance as a function of gate voltage. Of course, there are some formidable obstacles to overcome—the quantum We observe that samples made from narrow quantum wells with a Hall effect only occurs at low temperatures and high magnetic fields. “normal” electronic structure basically show zero conductance when the Downloaded from In the past few years, theoretical physicists have suggested that Fermi level is inside the gap. Quantum wells with an inverted electronic edge channel transport of current might be possible in the absence of a structure, by contrast, show a conductance close to what is expected for the magnetic field. They predicted (2–4) that in insulators with suitable edge channel transport in a quantum spin Hall insulator. This interpretation electronic structure, edge states would develop where—and this is is further corroborated by magnetoresistance data. For example, high– different from the quantum Hall effect—the carriers with opposite magnetic field data on samples with an inverted electronic structure show a spins move in opposite directions on a given edge, as shown sche- very unusual insulator-metal-insulator transition as a function of field, matically in the figure. This is the quantum spin Hall effect, and its which we demonstrate is a direct consequence of the electronic structure. observation has been hotly pursued in the field. The spin-polarized character of the edge channels still needs to be Although there are many insulators in nature, most of them do not have unequivocably demonstrated. For applications of the effect in actual the right structural properties to allow the quantum spin Hall effect to be microelectronic technology, this low-temperature effect (we observe it observed. This is where HgTe comes in. Bulk HgTe is a II-VI semi- below 10 K) will have to be demonstrated at room temperature, which may conductor, but has a peculiar electronic structure: In most such materials, be possible in wells with wider gaps. the conduction band usually derives from s-states located on the group II atoms, and the valence band from p-states at the VI atoms. In HgTe this Summary References order is inverted, however (5). Using molecular beam epitaxy, we can 1. K. v. Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980). grow thin HgTe quantum wells, sandwiched between (Hg,Cd)Te barriers, 2. S. Murakami, N. Nagaosa, S.-C. Zhang, Phys. Rev. Lett. 93, 156804 (2004). Phys. Rev. Lett. 3. C. L. Kane, E. J. Mele, 95, 146802 (2005). SCIENCE that offer a unique way to tune the electronic structure of the material: When = 4. B. A. Bernevig, S.-C. Zhang, Phys. Rev. Lett. 96, 106802 (2006). the quantum well is wide, the electronic structure in the well remains 5. A. Novik et al., Phys. Rev. B 72, 035321 (2005). “ ” BICKEL inverted. However, for narrow wells, it is possible to obtain a normal 6. B. A. Bernevig, T. L. Hughes, S.-C. Zhang, Science 314, 1757 (2006). : alignment of the quantum well states. Recently, Bernevig et al.(6) predicted 7. J. Hinz et al., Semicond. Sci. Technol. 21, 501 (2006). CREDIT: C 766 2 NOVEMBER 2007 VOL 318 SCIENCE www.sciencemag.org RESEARCH ARTICLES quantum phase transition has also been inves- FULL-LENGTH ARTICLE tigated in more realistic models beyond the simple four-band model presented here, reach- Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of ing the same conclusion (11). matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. The QSH phase occurs in the inverted re- We fabricated such sample structures with low density and high mobility in which we could tune, gime where M < 0, i.e., when d > dc. The through an external gate voltage, the carrier conduction from n-type to p-type, passing through an sample edge can be viewed as a domain wall insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime of the mass parameter M, separating the topo- showed the conventional behavior of vanishingly small conductance at low temperature. However, logically nontrivial phase with M < 0 from for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a the topologically trivial phase with M >0, plateau of residual conductance close to 2e2/h, where e is the electron charge and h is Planck’s which is adiabatically connected to the vac- constant. The residual conductance was independent of the sample width, indicating that it is caused uum (12). Massless helical states are confined by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic on the sample edge. The sample has a finite field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also conductance even when the Fermi level lies independently determined from the magnetic field–induced insulator-to-metal transition. These inside the bulk insulating gap. Therefore, as observations provide experimental evidence of the quantum spin Hall effect. suggested in (6), the QSH state can be ex- perimentally detected by measuring a residual he theoretical prediction of the intrinsic alization of the quantum spin Hall effect (6). conductance plateau as one varies the gate spin Hall effect in metals and insulators In zincblende-type semiconductor QWs, there voltage in the nominally insulating regime. T(1–3) has generated great interest in the are four relevant bands close to the Fermi Furthermore, because the current is carried by field of spintronics, because this effect allows level. The E1 band consists of the two spin the edge states, the conductance should be direct electric manipulation of the spin de- states of the s orbital, whereas the HH1 band independent of sample width. Protected by grees of freedom without a magnetic field, consists of the |px + ipy, ↑〉 and | −(px − ipy), ↓〉 the time-reversal symmetry, nonmagnetic im- and the resulting spin current can flow with- orbitals. The effective Hamiltonian near the G purities or any other time-reversal invariant out dissipation. These properties could lead to point, the center of the Brillouin zone, is local perturbations cannot cause elastic back- promising spintronic devices with low power given by scattering of the helical edge states, which war- dissipation. rants the topological robustness of the edge state However, beyond the potential technolog- ð HðkÞ 0 Þ conductance. However, the presence of a mag- H ðk ,k Þ¼ ∗ , ical applications, the intrinsic spin Hall effect eff x y 0 H ð−kÞ netic field breaks time-reversal symmetry and has guided us in the search for new and topo- therefore can open up a gap in the energy spec- H ¼ eðkÞþd ðkÞs ð1Þ logically nontrivial states of matter. The quan- i i trum of the edge states and remove the residual tum Hall state is the first, and so far the only conductance due to the edge states. example, of a topologically nontrivial state of where si are the Pauli matrices, and Experimental details. We set out to test these theoretical predictions by measuring matter, where the quantization of the Hall con- þ ¼ ð þ Þ ≡ ductance is protected by a topological invar- d1 id2 A kx iky Akþ the transport properties of HgTe/(Hg,Cd)Te iant.
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