Giant, Level-Dependent g Factors in InSb Nanowire Quantum Dots

Aug 19, 2009 - Henrik A. Nilsson,† Philippe Caroff,† Claes Thelander,† Marcus Larsson,†. Jakob B. Wagner,‡ Lars-Erik Wernersson,† Lars Sam...
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NANO LETTERS

Giant, Level-Dependent g Factors in InSb Nanowire Quantum Dots

2009 Vol. 9, No. 9 3151-3156

Henrik A. Nilsson,† Philippe Caroff,† Claes Thelander,† Marcus Larsson,† Jakob B. Wagner,‡ Lars-Erik Wernersson,† Lars Samuelson,† and H. Q. Xu*,† DiVision of Solid State Physics, Lund UniVersity, Box 118, S-22100 Lund, Sweden, and DiVision of Polymer and Materials Chemistry/nCHREM, Lund UniVersity, Box 124, S-22100 Lund, Sweden Received April 26, 2009; Revised Manuscript Received June 16, 2009

ABSTRACT We report on magnetotransport measurements on InSb nanowire quantum dots. The measurements show that the quantum levels of the InSb quantum dots have giant g factors, with absolute values up to ∼70, the largest value ever reported for semiconductor quantum dots. We also observe that the values of these g factors are quantum level dependent and can differ strongly between different quantum levels. The presence of giant g factors indicates that considerable contributions from the orbital motion of electrons are preserved in the measured InSb nanowire quantum dots, while the level-to-level fluctuations arise from spin-orbit interaction. We have deduced a value of ∆SO ) 280 µeV for the strength of spin-orbit interaction from an avoided level crossing between the ground state and first excited state of an InSb nanowire quantum dot with a fixed number of electrons.

InSb is one of the most promising materials for applications in spintronics and spin-based quantum information technology,1-4 owing to the fact that bulk InSb has the highest electron mobility, µe ) 77000 cm2/(Vs), smallest electron effective mass, me* ) 0.015me, and largest electron magnetic moment, |g*| ) 51, among all the III-V semiconductors.5,6 So far, no experimental work has been reported concerning spin transport in quantum devices made from InSb nanostructures, due to technology challenges in the nanomaterial growth and/or nanodevice fabrication. Here we report on the realization of few-electron InSb quantum dots by electrically contacting epitaxially grown InSb nanowires. Magnetotransport measurements show that the quantum levels of the InSb quantum dots have giant g factors, with absolute values up to ∼70, the largest value ever reported for semiconductor quantum dots. We also observe that the values of these g factors are a function of the quantum level and can differ strongly from level to level. The existence of such giant, level-dependent effective g factors in the InSb quantum dots renders various spin physics phenomena easily accessible. Furthermore, we examine the magnetic-field evolutions of the ground and excited states of an InSb nanowire quantum dot. We find a value of ∆SO ) 280 µeV for the strength of the spin-orbit interaction in the InSb quantum dot from an analysis of an avoided level crossing in the measured magnetoconductance spectrum. * Corresponding author, [email protected]. † Division of Solid State Physics. ‡ Division of Polymer and Materials Chemistry/nCHREM. 10.1021/nl901333a CCC: $40.75 Published on Web 08/19/2009

 2009 American Chemical Society

The g factors of energy levels in metal nanoparticles7,8 and semiconductor quantum dots9-18 have been studied experimentally by several groups. It was observed8 that in Au nanoparticles the effective electron g factor was strongly reduced, from the bulk value of g* ≈ 2.1 to the value of g* ≈ 0.3, as a result of spin-orbit interaction.8,19,20 A strong reduction in the effective electron or hole g factor toward 2 was also observed in ultrasmall quantum dots defined in InAs nanowire heterostructures15 and Ge/Si core-shell nanowires.16 This g factor reduction could be interpreted as a result of the quenching of the orbital momentum in such small quantum structures.21,22 However, measurements on large InAs nanowire based quantum dots showed that |g*| values could exceed the InAs bulk value of ∼15 and were strongly level dependent.17 The |g*| values in these measurements were extracted from the magnetic field splitting of the zero-bias anomaly due to the spin-1/2 Kondo effect. In the present work, we study quantum dot devices made from InSb nanowires and measure the |g*| values for the energy levels of the quantum dots using four complementary methods: the magnetic field evolution of the zero-bias Coulomb blockade peaks, the magnetic field evolution of the differential conductance peaks at finite biases, chargestability diagram measured at finite magnetic fields, as well as the magnetic field splitting of the spin-1/2 Kondo conductance ridges. We find the similar strong level dependent behavior of the g factor as in the large InAs nanowire quantum dots. However, the measured |g*| values of the InSb nanowire dots are in a range of 20-70, which are exception-

ally larger than the values reported for metal nanoparticles and all other semiconductor quantum dots. The InSb nanowire quantum dot devices investigated here are fabricated from InSb segments of InAs/InSb heterostructure nanowires. The heterostructure nanowires are grown in a metal-organic vapor phase epitaxy reactor, using aerosol gold particles with a diameter of 40 nm, deposited onto an InAs(111)B substrate, as initial seeds. In the first stage of growth, the InAs segments are grown from the gold particles. These grown InAs segments are then used as seed nanowires to favor nucleation of InSb in the second stage of growth.23 Figure 1a shows a scanning electron microscope (SEM) image of as-grown InAs/InSb heterostructure nanowires. It is clearly seen that the grown InSb nanowire segments have an extended diameter with respect to the InAs nanowire segments, due to a large uptake of indium into the metal seed particles upon switching to antimony. Detailed structure analyses show that these InSb nanowires are zinc blende crystals and free from twin boundaries, stacking faults, and tapering. Figure 1b shows a transmission electron microscope (TEM) image of a segment of an InSb nanowire with atomically flat {110} side InSb facets and a faceted singlecrystalline AuIn2 seed particle lattice-matched to the InSb nanowire. The grown InSb/InAs heterostructure nanowires are transferred from the growth substrate to degenerately doped Si substrates with a 100 nm thick SiO2 capping layer. After the wires are located, two 150 nm wide Ti/Au contacts with varying spacings are defined to each InSb nanowire segment by electron beam lithography. To obtain clean metal-nanowire interfaces, the exposed semiconductor contact areas are briefly etched in a (NH4)2Sx solution followed by a rinse in H2O prior to metal evaporation. Figure 1c shows a SEM image of a fabricated device, where the dot is formed between the contacts in an InSb nanowire with a diameter of 70 nm. By use of a probe station, devices with a room temperature resistance in the range of 20-50 kΩ are selected for this work. All the electrical measurements presented below are performed at a temperature of T ) 300 mK in a 3 He cryostat. Figure 1d shows the differential conductance, dIsd /dVsd, versus the source-drain voltage, Vsd, and the Si-substrate back gate voltage, Vbg (charge stability diagram), measured for an InSb nanowire quantum dot device with a contact separation of 70 nm. The diamond-shaped regions with dark color have low conductance and correspond to the regimes of Coulomb blockade for the electron occupation numbers N ) 0 to N ) 10 in the dot. The electron addition energy, ∆µ(N), at each charge state N can be obtained from the corresponding Coulomb blockade diamond. The results for N ) 1 to N ) 9 (addition energy spectrum) are presented in Figure 1e, where one sees a typical shell structure of a fewelectron quantum dot.24 The even-odd alternating behavior in the Coulomb diamond size is due to the spin degeneracy of the quantum levels En at the magnetic field B ) 0.24,25 From the lateral sizes of the small Coulomb diamonds, we can deduce a value of EC ) 5.1 meV for the averaged charging energy of the dot, which gives an averaged total 3152

dot capacitance of CΣ ) 32 aF. From the vertical sizes of the small Coulomb blockade diamonds we can also deduce a value of Cg ) 1 aF for the averaged gate capacitance to the dot. The averaged level spacing between the lowest five quantum levels in the dot is found to be ∆E ) 7.2 meV. To obtain the g factors of the quantum levels in the dot, we measure the magnetic-field evolutions of Coulomb blockade oscillation peaks in the linear response regime. Figure 2a shows a gray scale plot of the measured linear conductance, G, versus Vsd and B. The spin state of the last filled electron in each energy level is indicated by an arrow in the figure. Here a negative value of the g factor is assumed for all the quantum levels.6 As B is increased from zero, the conductance peaks corresponding to two spin states located just above and below an odd-N charge state Coulomb blockade diamond move apart, while the conductance peaks corresponding to two spin states located at the upper and lower edges of an even-N charge state Coulomb blockade diamond move closer.16,18 This is because in the former case the two spin states are the spin split states from the same quantum level due to the Zeeman effect, while in the latter case the two spin states belong to two different but adjacent quantum levels. We also see a slight overall shift of all the conductance peaks toward higher energies as the magnetic field is increased. This is due to a magnetic-field confinement of the electrons in the dot (diamagnetic effect). Figure 2b shows the measured energy differences between every two consecutive conductance peaks (the addition energies ∆µ) as a function of the magnetic field B. For an odd-N Coulomb gap, the addition energy is expected to evolve according to ∆µ(B) ) ∆µ(0) + ∆εn(B), where ∆µ(0) ) EC(N) is the addition energy at the zero magnetic field, ∆εn(B) ) |gn*|µBB is the Zeeman splitting energy and gn* is the electron effective g factor at the quantum level with index n ) (N + 1)/2. For an even-N Coulomb gap, the addition energy evolves according to ∆µ(B) ) ∆µ(0) - ∆εn(B)/2 - ∆εn+1(B)/ 2, where the addition energy at the zero magnetic field is given by ∆µ(0) ) EC(N) + ∆En,n+1 with the quantum level index n ) N/2 and the energy spacing ∆En,n+1 between the quantum levels n and n + 1 at the zero magnetic field. By linear fits to the plots shown in Figure 2b in the range of B ) 0 to 0.5 T, the values of electron g factor at different quantum levels can be extracted. The results are |g1*| ) 52, |g2*| ) 39, |g3*| ) 31, |g4*| ) 29 and |g5*| ) 63 for quantum levels n ) 1 to n ) 5. These giant, but level-dependent g factors, represented by a dark blue diamond symbol in Figure 2e, are the largest ever observed in semiconductor quantum dot systems. We note again that level-dependent g factors have previously been observed in InAs nanowire quantum dots,17 but with much smaller absolute values than reported here. The electron g factors can also be extracted from measurements of the differential conductance, dIsd /dVsd, as a function of Vsd and B at given values of Vbg. Figure 2c shows the results of such a measurement at Vbg) 0.025 V, i.e., along cut A through the N ) 2 Coulomb blockade diamond shown in Figure 1d. In this case, the peak on either side of zero bias splits with increasing B, reflecting transport through the Nano Lett., Vol. 9, No. 9, 2009

Figure 1. Sample description and conductance spectroscopy. (a) SEM image of InAs/InSb heterostructure nanowires grown on an InAs(111)B substrate using aerosol gold particles with a diameter of 40 nm as initial seeds. The image is recorded with a 30° tilt of the substrate from the horizontal position and the scale bar is uncompensated for the tilt. In the heterostructure nanowires, the base segments with a small diameter are InAs, crystallizing in the wurtzite phase, and the upper segments with a large diameter are InSb, crystallizing in the zinc blende phase. Note that the InSb segments do not show any tapering at the sidewalls. (b) TEM image of a top part of an InSb nanowire, after detachment from the growth substrate, with the single crystalline AuIn2 seed particle on top and the pure zinc blende InSb nanowire segment below. This InSb nanowire segment has a diameter of 79 nm. (c) SEM-picture of an InSb quantum dot device. The device is made by electrically contacting the InSb segment of an InAs/InSb heterostructure nanowire on a SiO2 capped, highly doped Si substrate using electron beam lithography. (d) Differential conductance on a color scale as a function of the source-drain voltage Vsd and the back-gate voltage applied to the Si substrate Vbg (charge stability diagram), measured for an InSb nanowire quantum dot device with a nanowire diameter of 70 nm and a contact spacing of 70 nm. The conventional spin1/2 Kondo effect (a Kondo enhanced conductance ridge) at zero bias is observed in the N ) 9 Coulomb blockade diamond region. (e) Addition energy versus electron number in the InSb nanowire quantum dot measured in (d) (addition energy spectrum), revealing a typical shell structure of a few-electron quantum dot system. Nano Lett., Vol. 9, No. 9, 2009

Figure 2. Evolutions of the ground states and quantum level dependent g factors in an InSb quantum dot. (a) Gray scale plot of the linear conductance G as a function of the back gate voltage Vg and magnetic field B measured for the quantum dot device as in Figure 1d. Spin filling configurations are indicated with arrows under the assumption of negative values of the g factors. The charge state in a Coulomb blockade region is marked with an integer N. (b) Evolution of the addition energy for different electron charge configuration on the dot. (c) Differential conductance as a function of Vsd and B measured for the quantum dot at the back gate voltage Vbg ) 0.025 V, i.e., along cut A in Figure 1d. The differential conductance peaks are labeled with v and V according to spin filling under the assumption of a negative g factor. (d) Differential conductance as a function of Vsd and B measured for the quantum dot at the back gate voltage Vbg ) 0.205 V, i.e., along cut B in Figure 1d. (e) Electron g factor versus quantum level index n for the dot, determined from several magnetic field dependent measurements. The values represented by a dark blue diamond are determined from the addition energy evolution measurements shown in (b). The values represented by green up triangles and red down triangles are determined from the differential conductance peak splitting measurements shown in (c) and (d), respectively. The value represented by a black dot is determined from the spin-1/2 Kondo peak splitting, measured at magnetic field B ) 0.3 T, shown in parts b and c of Figure 3. Finally, the values represented by light blue squares are determined from a charge stability diagram of the quantum dot measured at magnetic field B ) 1 T. Note that the values enclosed in the dashed circle in (e) are slightly offset in the quantum level index n for clarity. 3153

Figure 3. The Zeeman splitting of a spin-1/2 Kondo peak. (a, b) A close-up of the N ) 9 charge stability diamond, i.e., area C in Figure 1d, showing the spin-1/2 Kondo effect, and the corresponding charge stability diamond measured at magnetic field B ) 0.3 T. (c) Plots of the differential conductance as a function of the source-drain voltage Vsd for B ) 0 and 0.3 T. The data are extracted from (a) and (b) by averaging over a gate voltage range of ∼20 mV in the middle section of the corresponding Coulomb diamond. The full width at half-maximum and the Zeeman splitting of the Kondo peak are marked in (c).

Zeeman-split states of the second quantum level.26 Assuming again g2* < 0, we can label the differential conductance peaks with v and V, where the peaks corresponding to the spin-up (v) level move toward lower values of |Vsd| with increasing magnetic field. At small magnetic fields the splitting is linear in B and we can deduce a value of |g2*| ) 43, represented by green triangles in Figure 2e, for the second quantum level. Figure 2d shows the evolution of the differential conductance peaks with increasing B at Vbg) 0.205 V, i.e., along cut B through the N ) 3 Coulomb blockade diamond shown in Figure 1d. In this case, transport is only measured through the n ) 2 spin-down (V) level and, thus, the peaks do not split with increasing B, but move toward larger absolute values of Vsd.26 From the magnetic field induced shifts of the peaks in Figure 2d, we can deduce a value of |g2*| ) 37, represented by red down triangles in Figure 2e. The values obtained from the measurements shown in parts c and d of Figure 2 are in good agreement with the corresponding values extracted from parts a and b of Figure 2, confirming the giant absolute values of the g factors in the InSb nanowire quantum dot. The Zeeman splittings of the differential conductance peaks found in the charge stability diagram of a quantum dot could also be used to estimate the electron g factors.14,27,28 For example, using the charge stability diagram measured at B ) 1 T, we extract values of the g factors for the first three quantum levels of the InSb quantum dot studied above as |g1*| ) 42, |g2*| ) 39, and |g3*| ) 19, represented by light blue squares in Figure 2e. It is seen that these values are slightly smaller than the corresponding values determined above. This is because, due to level interactions, the Zeeman splitting at B ) 1 T is no longer a good linear function of B, as can be seen in parts c and d of Figure 2. 3154

We now investigate the Kondo physics29-35 revealed in the InSb nanowire quantum dot studied above. The charge stability diagram measurements in Figure 1d show a differential conductance ridgesa bright vertical conductance stripesat zero bias inside the N ) 9 Coulomb blockade region. Figure 3a shows a close-up of this region. Figure 3b shows that the conductance ridge splits at a small magnetic field, B ) 0.3 T. These features are typical for the conventional spin-1/2 Kondo effect.29,30 Figure 3c shows plots for dIsd /dVsd versus Vsd, for the cases of B ) 0 and 0.3 T, obtained by averaging over a gate voltage range of ∼20 mV in the middle of the N ) 9 Coulomb blockade region. From the full width at half-maximum of the Kondo peak at B ) 0 T, we evaluate the Kondo temperature TK ∼ 3.2 K. From the splitting of the Kondo peak at B ) 0.3 T we estimate the value of the g factor for the fifth quantum level |g5*| ) 48. This value, represented by a black dot in Figure 2e, is in reasonable agreement with the value determined above. The averaged value of the measured g factors for the InSb nanowire quantum dot is comparable to the g factor of electrons in bulk InSb. Thus, a significant contribution to the g factors from the orbital motion of electrons in the dot is preserved. It has been numerically shown that the g factor of electrons can be reduced to the free electron value of 2 in very small semiconductor quantum dots.21,22 Such a reduction in the g factor has been observed in semiconductor nanowire quantum dots defined by heterostructure tunnel barriers.15 However, the dots studied there, which show this g factor reduction, have much smaller sizes than the dots we have studied in this work. The strong level-to-level fluctuations of the g factor observed in our measured InSb nanowire quantum dot are due to the presence of spin-orbit interaction.19,20,36-39 For metal nanoparticles, it has been shown that the Zeeman splitting of electron levels can be suppressed when the spin-orbit scattering rate τ-1 is comparable to the quantum level spacing ∆E.19,20 In semiconductor quantum dots, this suppression of the Zeeman splitting of electron levels is expected to occur when the spin-orbit interaction energy ∆SO is in the order of the quantum level spacing ∆E or larger. At weak (∆SO , ∆E) but nonvanishing spin-orbit interaction, the g factor in a semiconductor quantum structure is shown to exhibit level-to-level fluctuations.36-39 To estimate the strength of the spin-orbit interaction in our InSb nanowire samples, we have analyzed the excited state spectrum measured for another InSb nanowire quantum dot with a separation of 160 nm between contacts. Figure 4a shows the charge stability diagram measured for the dot device. From this charge stability diagram we can deduce a value of EC ) 5.7 meV for the averaged charging energy and a value of ∆E ) 2.6 meV for the averaged quantum level spacing. The g factors of the quantum levels in the dot have also been extracted from the magnetic-field evolutions of the Coulomb blockade oscillation peaks. Again, similar giant, strong leveldependent g factors (with the largest value of |g*| ) 76) as reported above are found for quantum levels of this dot. Figure 4b shows the differential conductance spectrum measured along cut A in the stability diagram shown in Nano Lett., Vol. 9, No. 9, 2009

Figure 4. Evolution of the ground and excited states of an N-electron InSb dot. (a) Differential conductance on a color scale as a function of the source-drain voltage Vsd and the back gate voltage applied to the Si substrate Vbg (charge stability diagram), measured for an InSb nanowire quantum dot device with a nanowire diameter of 70 nm and a contact spacing of 160 nm. (b) Differential conductance along cut A in (a) as a function of magnetic field B. As B increases, the spin-down ground state increases in energy and the spin-up first excite state moves toward lower energy. Note that in (b) the spin-down ground state and the spin-up first excited state are labeled by a down arrow and an up double arrow, respectively. (c) A close-up of the area marked by B in (b). The dots show the experimental energy positions of the conductance peaks as a function of magnetic field. Here a small overall quadratic magnetic-field dependence has been subtracted from the measured data to remove the effect of magnetic field confinement to the electrons in the dot. The lines show the results of fitting by a two-level model in the presence of spin-orbit interaction ∆SO.

Figure 4a. The position of cut A is chosen such that the electron number N in the dot remains constant as the magnetic field is changed. The two differential conductance peaks seen along the cut correspond to the ground state and the first excited state of the N-electron dot. With increasing magnetic field, the spin-V ground state moves toward higher energy, while the first excited state is split into two states labeled as up double arrow and down double arrow. In the region around B ) 2.6 T (marked by a rectangular box B in Figure 4b), the spin-down ground state and the spin-up excited state show an avoided crossing behavior as a result of level mixing caused by spin-orbit interaction.26 Nano Lett., Vol. 9, No. 9, 2009

A simple two-level perturbation model can be used to fit the magnetic field dependent positions of the two differential conductance peaks in the region marked by box B in Figure 4b. The resulting fit, together with measured data points, is plotted in Figure 4c. The measured peak positions in this plot are corrected for a weak quadratic magnetic-field confinement effect. From the fit, we deduce a value of ∆SO ) 280 µeV for the spin-orbit interaction strength in the InSb nanowire dot. We also find values of |gn*| ) 46 and |gn+1*| ) 51 for the ground state and the first excited state of the N-electron dot (corresponding to quantum levels n and n + 1, with n ) N/2, in the dot). The extracted value of the spin-orbit interaction strength is significantly smaller than the averaged level spacing of the studied InSb nanowire quantum dots. Thus, the g factor in these dots should exhibit fluctuations. In conclusion, we have demonstrated the first magnetotransport measurements on InSb nanowire quantum dots and analyzed the g factors of the quantum levels and spin-orbit interaction strength in the dots. The |g*| values are deduced using four complementary methods including the magnetic-field evolutions of the zero-bias Coulomb blockade oscillation peaks. The obtained values are giant, can be larger than the bulk InSb value of 51, and show levelto-level fluctuations. The spin-orbit interaction strength ∆SO is analyzed from the magnetic-field evolution of the differential conductance peaks measured for the ground state and the first excited state of an InSb nanowire quantum dot with a fixed number of electrons. A value of ∆SO ) 280 µeV, which is significantly smaller than the averaged spacing of quantum levels in the studied InSb nanowire dots, has been deduced from the effect of level mixing between the two states. The giant |g*| values observed here imply that significant contributions from the orbital motion of electrons are preserved, while the level-to-level fluctuations arise from the spin-orbit interaction presented in the quantum dot systems. Our study indicates that InSb nanowire based quantum structures are excellent candidates for applications in spintronics and in spin-based quantum information processing and communication. Acknowledgment. This work was carried out within the Nanometer Structure Consortium at Lund University and was supported by the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), the European Community (EU Contract No. 015783 NODE and EU Contract No. 034236 SUBTLE), and the Knut and Alice Wallenberg Foundation. References (1) Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; von Molna´r, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Tresger, D. M. Science 2001, 294, 1488. (2) Zutic, I.; Fabian, J.; Das Sarma, S. ReV. Mod. Phys. 2004, 76, 323. (3) Loss, D.; DiVincenzo, D. P. Phys. ReV. A 1998, 57, 120. (4) Petta, J. R.; Johnson, A. C.; Taylor, J. M.; Laird, E. A.; Yacoby, A.; Lukin, M. D.; Marcus, C. M.; Hanson, M. P.; Gossard, A. C. Science 2005, 309, 2180. (5) Vurgaftman, I.; Meyer, J. R.; Ram-Mohan, L. R. J. Appl. Phys. 2001, 89, 5815. (6) Isaacson, R. A. Phys. ReV. 1968, 169, 312. 3155

(7) Salinas, D. G.; Gueron, S.; Ralph, D. C.; Black, C. T.; Tinkham, M. Phys. ReV. B 1999, 60, 6137. (8) Davidovic, D.; Tinkham, M. Phys. ReV. Lett. 1999, 83, 1644. (9) Bayer, M.; Kuther, A.; Forchel, A.; Gorbunov, A.; Timofeev, V. B.; Schafer, F.; Reithmaier, J. P.; Reinecke, T. L.; Walck, S. N. Phys. ReV. Lett. 1999, 82, 1784. (10) Gupta, J. A.; Awschalom, D. D.; Peng, X.; Alivisatos, A. P. Phys. ReV. B 1999, 59, 10421. (11) Tischler, J. G.; Bracker, A. S.; Gammon, D.; Park, D. Phys. ReV. B 2002, 66, 081310. (12) Medeiros-Ribeiro, G.; Pinheiro, M. V. B.; Pimentel, V. L.; Marega, E. Appl. Phys. Lett. 2002, 80, 4229. (13) Medeiros-Ribeiro, G.; Ribeiro, E.; Westfahl Jr, H. Appl. Phys. A: Mater. Sci. Process. 2003, 77, 725. (14) Hanson, R.; Witkamp, B.; Vandersypen, L. M. K.; van Beveren, L. H. W.; Elzerman, J. M.; Kouwenhoven, L. P. Phys. ReV. Lett. 2003, 91, 196802. (15) Bjo¨rk, M. T.; Fuhrer, A.; Hansen, A. E.; Larsson, M. W.; Fro¨berg, L. E.; Samuelson, L. Phys. ReV. B 2005, 72, 201307. (16) Roddaro, S.; Fuhrer, A.; Brusheim, P.; Fasth, C.; Xu, H. Q.; Samuelson, L.; Xiang, J.; Lieber, C. M. Phys. ReV. Lett. 2008, 101, 186802. (17) Csonka, S.; Hofstetter, L.; Freitag, F.; Oberholzer, S.; Scho¨nenberger, C.; Jespersen, T. S.; Aagesen, M.; Nyga˚rd, J. Nano Lett. 2008, 8, 3932. (18) Sun, J; Larsson, M.; Maximov, I.; Hardtdegen, H.; Xu, H. Q. Appl. Phys. Lett. 2009, 94, 042114. (19) Matveev, K. A.; Glazman, L. I.; Larkin, A. I. Phys. ReV. Lett. 2000, 85, 2789. (20) Brouwer, P. W.; Waintal, X.; Halperin, B. I. Phys. ReV. Lett. 2000, 85, 369. (21) Pryor, C. E.; Flatte´, E. Phys. ReV. Lett. 2006, 96, 026804. (22) De, A.; Pryor, C. E. Phys. ReV. B 2007, 76, 155321. (23) Caroff, P.; Wagner, J. B.; Dick, K. A.; Nilsson, H. A.; Jeppsson, M.; Deppert, K.; Samuelson, L.; Wallenberg, L. R.; Wernersson, L.-E. Small 2008, 4, 878.

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(24) Tarucha, S.; Austing, D. G.; Honda, T.; van der Hage, R. J.; Kouwenhoven, L. P. Phys. ReV. Lett. 1996, 77, 3613. (25) Bjo¨rk, M. T.; Thelander, C.; Hansen, A. E.; Jensen, L. E.; Larsson, M. W.; Wallenberg, L. R.; Samuelson, L. Nano Lett. 2004, 4, 1621. (26) Fasth, C.; Fuhrer, A.; Samuelson, L.; Golovach, V. N.; Loss, D. Phys. ReV. Lett. 2007, 98, 266801. (27) van Beveren, L. H. W.; Hanson, R.; Vink, I. T.; Koppens, F. H. L.; Kouwenhoven, L. P.; Vandersypen, L. M. K. New J. Phys 2005, 7, 182. (28) Hanson, R.; Kouwenhoven, L. P.; Petta, J. R.; Tarucha, J. R.; Vandersypen, L. M. K. ReV. Mod. Phys. 2007, 79, 1217. (29) Goldhaber-Gordon, D.; Shtrikman, H.; Mahalu, D.; Abusch-Magder, D.; Meirav, U.; Kastner, M. A. Nature 1998, 391, 156. (30) Cronenwett, S. M.; Oosterkamp, T. H.; Kouwenhoven, L. P. Science 1998, 281, 540. (31) Sasaki, S.; De Franceschi, S.; Elzerman, J. M.; van der Wiel, W. G.; Eto, M.; Tarucha, S.; Kouwenhoven, L. P. Nature 2000, 405, 764. (32) Nyga˚rd, J.; Cobden, D. H.; Lindelof, P. E. Nature 2000, 408, 342. (33) Sasaki, S.; Amaha, S.; Asakawa, N.; Eto, M.; Tarucha, S. Phys. ReV. Lett. 2004, 93, 017205. (34) Jarillo-Herrero, P.; Kong, J.; van der Zant, H. S. J.; Dekker, C.; Kouwenhoven, L. P.; De Franceschi, S. Nature 2005, 434, 484. (35) Igarashi, Y.; Jung, M.; Yamamoto, M.; Oiwa, A.; Machida, T.; Hirakawa, K.; Tarucha, S. Phys. ReV. B 2007, 76, 081303. (36) Csontos, D.; Zulicke, U. Phys. ReV. B 2007, 76, 073313. (37) Csontos, D.; Zulicke, U. Appl. Phys. Lett. 2008, 92, 023108. (38) Csontos, D.; Zulicke, U.; Brusheim, P.; Xu, H. Q. Phys. ReV. B 2008, 78, 033307. (39) Csontos, D.; Brusheim, P.; Zulicke, U.; Xu, H. Q. Phys. ReV. B 2009, 79, 155323.

NL901333A

Nano Lett., Vol. 9, No. 9, 2009