Adiabatic Edge Channel Transport in a Nanowire ... - ACS Publications

Letter pubs.acs.org/NanoLett

Adiabatic Edge Channel Transport in a Nanowire Quantum Point Contact Register S. Heedt,*,† A. Manolescu,‡ G. A. Nemnes,¶,§ W. Prost,∥ J. Schubert,† D. Grützmacher,† and Th. Schap̈ ers*,† †

Peter Grünberg Institut (PGI-9) and JARA-Fundamentals of Future Information Technology, Forschungszentrum Jülich, 52425 Jülich, Germany ‡ School of Science and Engineering, Reykjavik University, IS-101 Reykjavik, Iceland ¶ Faculty of Physics, MDEO Research Center, University of Bucharest, 077125 Magurele-Ilfov, Romania § Horia Hulubei National Institute of Physics and Nuclear Engineering, 077126 Magurele-Ilfov, Romania ∥ Solid State Electronics Department, University of Duisburg-Essen, 47057 Duisburg, Germany S Supporting Information *

ABSTRACT: We report on a prototype device geometry where a number of quantum point contacts are connected in series in a single quasi-ballistic InAs nanowire. At finite magnetic field the backscattering length is increased up to the micron-scale and the quantum point contacts are connected adiabatically. Hence, several input gates can control the outcome of a ballistic logic operation. The absence of backscattering is explained in terms of selective population of spatially separated edge channels. Evidence is provided by regular Aharonov−Bohm-type conductance oscillations in transverse magnetic fields, in agreement with magnetoconductance calculations. The observation of the Shubnikov−de Haas effect at large magnetic fields corroborates the existence of spatially separated edge channels and provides a new means for nanowire characterization. KEYWORDS: Adiabatic transport, quantum point contacts, InAs nanowire, edge channels, Shubnikov−de Haas effect

A

sample, respectively. There, the 2D−1D scattering length between the two-dimensional contact area and the quantum wire was found to determine the emissivity into the 1D channel. That configuration is far from being an ideal ohmic contact to a 1D system, which would rather require an adiabatic funnel between the discrete 1D spectrum and the 2D continuum in the density of states. Whereas in a twodimensional system the coupling to a QPC can be nonideal due to an abrupt transition in the density of states from 2D to 1D, in the case of a nanowire-based QPC the transition might be intrinsically more smooth, so that the density of states is transformed adiabatically from segment to segment.7 Kouwenhoven et al.8 have created a device with two QPCs connected in series in a high-mobility 2DEG. The part between the two QPCs can be regarded as a reservoir where the momentum gets randomized, so that the total resistance is given by the series resistance of the two QPCs, provided the QPC separation is sufficient.9 However, at finite out-of-plane magnetic field, the current between the two QPCs is carried by edge channels, with the consequence that electron transport is determined by the QPC with the lowest transmission. The underlying process

quantum point contact (QPC) is a constriction between two extended regions of a conductor, which has a lateral dimension of the order of the Fermi wavelength of an electron. It behaves as a highly nonlinear mesoscopic circuit element and has been employed to reveal profound physical phenomena, e.g., related to electron−electron interaction effects.1,2 In this study, we explore QPCs, which are created in an altogether different system than the conventional two-dimensional electron gases (2DEGs). Multiple quantum point contacts connected in series along a quasi-one-dimensional InAs nanowire are investigated. In a previous report,3 we have demonstrated ballistic transport in the same nanowire device, where at zero magnetic field quantized conductance plateaus emerge at integer multiples of 2e2/h. The elastic scattering length is found to be ∼250 nm. In this work, we demonstrate that by applying a magnetic field, the large backscattering length is further enhanced up to the micron-scale. At finite magnetic field two QPCs in the few-mode regime are connected adiabatically via a multimode nanowire segment, i.e., the subband index is conserved upon electron propagation. The impact of dimensional changeover on conductance quantization is critical. De Picciotto et al.4,5 and Dwir et al.6 have investigated a series connection of one-dimensional (1D) quantum wires formed by means of epitaxial overgrowth of the cleaved edge of a high-mobility 2DEG and in a V-groove © 2016 American Chemical Society

Received: May 5, 2016 Revised: June 8, 2016 Published: June 27, 2016 4569

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cally coupled. Thus, when operating multiple QPCs in series, we ensure that they are separated by at least one grounded top gate. Utilizing this register of QPCs, we can explore the adiabatic propagation of electrons along the nanowire in the few-mode regime. To account for nonballistic segments of the wire as well as contact resistances due to the nanowire/metal interfaces, a series resistance of the order of 20 to 35 kΩ is subtracted (depending on the applied magnetic field) in order to retrieve the equidistant separation of conductance plateaus according to the Landauer formula.19 The transmission probabilities of all subbands are close to one. The measurements shown in this work are two-terminal characterizations, and except for the electron interference measurements, dc conductance is presented throughout this Letter. The finite dcbias voltages applied to source and drain ensure that Fabry− Pérot interference does not compromise the conductance quantization.3 Transition to the Adiabatic Transport Regime. The experimental configuration resembles the setup used to investigate adiabatic transport in GaAs/AlGaAs two-dimensional electron gases.8,9,20,21 In Figure 2 our device is illustrated

is the selective occupation and the adiabatic transmission of edge channels. In our study, we replace the 2D reservoir with a quasi-1D nanowire segment. For moderate out-of-plane magnetic fields we find that the magnetic confinement dominates over the intrinsic lateral confinement leading to the formation of Landau levels.3 In this study, we explain several magnetoconductance phenomena in the context of these adiabatic edge states, also known as snaking orbits,10,11 which extend along the interior side of the nanowire sidewall. The magnetic field leads to a depopulation of the 1D subbands in the QPCs and in the nanowire as a whole. The latter is reflected in the emergence of Shubnikov−de Haas oscillations in the magnetoresistance. We make use of local potential barriers to close the edge states. In the phase-coherent transport regime the 1D edge states interfere and constitute coherent closed-loop states that pick up a magnetic flux in a transverse magnetic field giving rise to regular magnetoconductance oscillations. These flux-periodic oscillations can be harnessed to extract the enclosed channel area.7 Experimentally, van Wees et al.12 have observed these Aharonov−Bohm-type oscillations in a disk-shaped enclosed 2D cavity formed between two QPCs, while Staring et al.13 have identified a shallow potential basin to host the coherent quantum state in an open 2DEG region. Magnetoconductance oscillations in quasi-ballistic nanowires subject to an axial magnetic field have been discussed by Tserkovnyak and Halperin.14 Such regular oscillations have been experimentally observed by Gül et al.15 and attributed to coherent closed-loop states along the tubular surface of a core−shell nanowire. In our work, the coherent closed-loop quantum states are elongated and not found along the nanowire circumference but along the edges of a segment coupled to the rest of the nanowire via local electrostatic barriers. Experimental Methods. The InAs nanowires are grown via gold-catalyzed metal−organic vapor phase epitaxy.16,17 The nanowire with a diameter of 100 nm is mechanically transferred to a thermally oxidized Si substrate, which provides back-gate functionality in order to change the global Fermi level in the nanowire. A patch of high-k dielectric (LaLuO3) is deposited onto the nanowire via pulsed laser deposition18 and liftoff technique. Seven closely spaced Ω-shaped top-gate electrodes are evaporated onto the dielectric. Each gate has a width of 180 nm and the pitch is 30 nm (see Figure 1). Hence, neighboring gates are so close that the created electrostatic confinement potentials overlap and that the resulting QPCs are electrostati-

Figure 2. Subband filtering at B = 10 T and at a dc-bias voltage of Vdc = 3 mV (T = 250 mK). The blue curves in (a−c) depict quantized conductance in single QPCs for (a) QPC-V, (b) QPC-III, and (c) QPC-II. For the orange curves in (b) and (c) QPC-V voltage is fixed at −390 mV [orange circle in (a)], in order to selectively populate only the lowest Landau level. The two QPCs are separated by (b) 420 nm and (c) 630 nm (center to center). The transmitted current remains nearly unaffected when driving the second top gate to the single subband regime.

in conjunction with top-gate characteristics for three different QPCs. At a magnetic field of B = 10 T each top-gate sweep features conductance plateaus at half-integer multiples of 2e2/h, reflecting transport through Zeeman-split nondegenerate subbands. The voltage drop across the QPCs is much smaller than the applied dc-voltage of Vdc = 3 mV due to the large series resistance of the 2.94 μm-long nanowire. The blue curves in Figures 2a−c represent the overall conductance of the device upon variation of a single top-gate voltage. In order to demonstrate adiabatic transport, we fix one of the QPCs to

Figure 1. Scanning electron micrograph of the nanowire device with Ti/Au source and drain electrodes. The device consists of seven topgate electrodes placed on top of a LaLuO3 high-k dielectric, between a pair of source and drain electrodes. These gates create and control a set of seven independent quantum point contacts designated QPC-I to QPC-VII from the source end to the drain end, as shown. 4570

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Nano Letters selectively block out certain subbands and inject the current exclusively into those subbands transmitted by this QPC. To this end, QPC-V voltage is fixed at −390 mV, i.e., in the regime where only a single subband is transmitted (cf. orange circle in Figure 2a). Subsequently, top gate III and top gate II are operated, as shown in the orange curves in Figures 2b,c, respectively. These two gates are separated by 420 and 630 nm from top gate V. The second conductance plateau has completely vanished, leaving only the plateau at G = e2/h, corresponding to transport through the subband lowest in energy with spin-up polarized electrons. The fact that the series conductance nearly equals the conductance of a single QPC clearly illustrates the nonadditivity of the QPC resistances in series.22 This can be understood via the notion of edge channel transport. In ballistic nanowires, the momentum randomization between QPCs is expected to be less pronounced than in a 2DEG cavity since the angular dispersion of the momentum is intrinsically reduced. As a consequence, the presented device exhibits adiabatic transport already at a few tesla in spite of the small edge channel separation and a significantly smaller mobility in comparison to a conventional two-dimensional electron gas. In 2DEGs the collimation behind a QPC can be rather weak, and a branched current flow23 emerges into a continuum of 2D states, making it difficult for an electron to reach the next QPC constriction in the absence of Landau edge states. The robustness of the adiabatic transport features in our nanowire device is an indication for well-separated edge channels between the two QPCs. Hence, on the one hand, the nanowire geometry is prone to backscattering through the QPC constriction at zero magnetic field.24 On the other hand, at finite magnetic field adiabatic transport between multiple QPCs in series might benefit from the waveguide properties of the nanowire.25 In Figure 3a adiabatic transport is demonstrated for a different combination of QPCs, i.e., for QPC-II and QPC-IV, at B = 9.5 T. Since the measurements are carried out much later (see below) than those in Figure 2, the pinch-off voltage is changed, so that another energetically higher subband with two spin-split plateaus becomes visible. The fact that the overall conductance is not reduced when electrons are transmitted across two potential barriers in series indicates that the electrons are neither backscattered nor scattered into adjacent subbands in the nanowire segment connecting the two QPCs. The underlying mechanism giving rise to the observed nonohmic conductance is the selective population of edge channels in conjunction with the absence of scattering between edge channels in the intermediate nanowire segment.21 In Figure 3a a small reduction in conductance is observed just when the next higher subband is about to be transmitted by one of the QPCs. This effect can likely be explained by intersubband scattering at the constriction. In contrast to 2DEGs the intrinsic nanowire confinement leads to considerable subband separation already in the quasi-one-dimensional segments between the QPCs. For 2DEGs a field of B ≈ 2 T is required in order to achieve adiabatic transport 21 by suppressing intersubband scattering among adjacent edge channels at the same boundary. In the nanowire, however, the subband spacing is much larger, and as a consequence intrasubband scattering between opposite boundaries might be more detrimental. We attribute the robustness of adiabatic transport at finite out-of-plane magnetic fields to the formation of snaking edge channels.10,11 Electrons in these modes propagate on snaking orbits extended along opposite sides of the nanowire, where the radial magnetic field component

Figure 3. (a) Quantized conductance plateaus at B = 9.5 T and Vdc = 3.5 mV as a function of QPC-IV voltage with QPC-II voltage as a parameter (T = 150 mK). Both QPCs can individually control the number of transmitted nondegenerate Zeeman-split subbands between zero and four. Hence, only the QPC with the lowest transmission determines the overall conductance. (b,c) Conductance as a function of QPC-III voltage versus QPC-V voltage (Vdc = 5 mV) at (b) 4 T and (c) 10 T, respectively. These measurements are taken at T = 250 mK.

vanishes. The formation of edge states is relevant already when the magnetic length lm = ℏ/eB becomes comparable in magnitude to the nanowire radius,10 which occurs at fields higher than 260 mT. Hence, the spatial separation of counterpropagating states efficiently suppresses backscattering. Figures 3b,c shows another series connection of two QPCs (QPC-III and QPC-V) at B = 4 T and at B = 10 T, respectively. The former proves that the transition to the adiabatic transport regime is already possible at significantly smaller magnetic fields. By assigning the plateau regimes of the individual QPCs to particular logic states the overall conductance of QPCs connected in series is given by the total number of adiabatically transmitted edge channels and hence yields the smallest input state as the output.26 Thus, a register of nanowire QPCs can be exploited for ballistic logic operations. Shubnikov−de Haas Oscillations. We have demonstrated adiabatic transport between two QPCs in series. The question arises whether we can also find signatures for edge channel transport when all top gates are grounded. Remarkably, at finite magnetic field, the investigated device demonstrates at least partially adiabatic transport along the entire length of the nanowire of L = 2.94 μm (source-drain contact separation). In Figure 4a peaks emerge in the nanowire resistance, reflecting the resonant backscattering into counter-propagating edge channels of the same Landau level index when the Landau levels in the nanowire align with the Fermi energy. Since the 4571

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To substantiate our findings, the back-gate voltage is varied in an interval, where intrinsic QPC formation does not play a role.3 Still, we expect a distinct decrease in the electron concentration by changing the global gate from 1 to −0.92 V. Indeed, the decrease in n goes along with an increase in the Shubnikov−de Haas oscillation period in Figure 4c and confirms the origin of the resistance resonances. According to the model in eq 1, n decreases from 1.34 to 1.18 × 1017 cm−3 within the gate voltage interval. Aharonov−Bohm Interference of One-Dimensional Edge Channels. In the previous sections we have demonstrated that the QPCs can selectively populate magnetoelectric subbands and that in the high-field regime intra-Landau-level scattering inside the nanowire segment between the QPCs can be very weak due to the spatial separation of edge channels. To corroborate this notion we selectively form coherent closedloop quantum states by bringing together the edge states using local potential barriers that are created by the top gates forming the QPCs. The 1D interferometer configuration we seek to establish is illustrated in Figure 5a. Two potential barrier configurations have been numerically simulated in Figures 5b,c.27 The depicted space charge distribution along the center of the nanowire directly reflects the potential landscape, with 180 and 390 nm half-maximum potential barrier separation, respectively. The temperature is low enough (80 mK) to ensure phase-coherent transport, in particular due to the large scattering length. Differential conductance measurements (ac excitation voltage Vac= 100 μVrms) are performed with a small dc-bias of Vdc = 500 μV. When only one potential barrier is employed, irregular universal conductance fluctuations are observed in an out-of-plane magnetic field. When two potential barriers enclose a nanowire segment regular oscillations appear (cf. Supporting Information). This can be seen in the magnetoconductance measurements depicted in Figure 5d, where two QPCs (i.e., QPC-III and QPC-V) both operate close to pinch-off, yet still in the regime of strong coupling (G ≲ 2e2/ h) between the enclosed nanowire segment and the rest of the nanowire. By increasing the QPC separation, the oscillation frequency is enhanced (see Figure 5e). With regard to Figure 5g, one potential barrier is fixed, and the second potential barrier is raised until it dominates and finally quenches the overall conductance. We examine experimental configurations with different QPC separations, and we verify the expected variation of the oscillation period experimentally and via numerical modeling. The observed regular oscillations can be explained in the framework of snaking edge channels along opposite sides of the nanowire that can form closed-loop trajectories enclosing a magnetic flux.11,28,29 Manolescu et al.29 demonstrated a transition from resonant peaks to flux-periodic oscillations upon lowering the potential barrier height. Here, we are still in the low-barrier regime with strong coupling, where the measured regular conductance oscillations in Figures 5d,e,g are attributed to the interference between counter-propagating edge channels, which are transmitted and reflected at the constrictions. In order to support our experimental findings, we carried out magnetoconductance simulations making use of the R-matrix method,30 which allows for strong coupling between the leads (i.e., the nanowire segments to the left and to the right of the region enclosed by the two QPCs) and the segment between the two QPCs. By introducing potential barriers, the coupling between this segment and the leads can be controlled. When

Figure 4. Shubnikov−de Haas oscillations at T = 80 mK and Vdc = 4 mV. (a) Resistance R versus reciprocal magnetic field 1/B exhibits resonant peaks associated with spin-split Landau levels being aligned with the Fermi energy. The periodicity of the filling factor ν yields an electron density n ≈ 0.78 × 1017 cm−3. (b) Evolution of the carrier concentration n over the time scale of 14 months. (c) The back-gate induced change in electron concentration over the back-gate voltage interval VBG = −0.92 to 1.0 V is reflected in the changing oscillation period of the resistance R (time t = 12 months). The curves have been offset for clarity. The dashed lines are guides to the eye.

measurements are two-terminal characterizations, the background resistance increases with the depopulation of edge states. The resonances can be associated with particular Zeeman-split Landau levels (see Supporting Information), and the period Δ(1/B) of the filling factor ν can be evaluated and related to the electron concentration n. The model we use was derived for a two-dimensional electron gas, but corrections to the Landau level eigenenergies related to confinement due to the nanowire geometry are rather weak for B > 5 T.3 This is corroborated by the fact that the simple 2D model 2e 2 n3D = 1 πr hΔ

(B)

(1)

yields an electron concentration of the order of 1.0 × 10 cm−3 in very good agreement with field-effect transistor characterization using the top gates and the back gate, respectively.3 Thus, we retrospectively validate the viability of the dual-gate evaluation method demonstrated earlier.27 It turns out that n has increased over the time scale of 14 months by nearly 70% from 0.78 to 1.31 × 1017 cm−3 (cf. Figure 4b). We attribute this effect to presumable detrapping of charges bound at states localized in the LaLuO3 oxide layer. 17

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Figure 5. (a) Setup of the 1D electron interferometer, where the edge channels and the QPCs enclose an area A penetrated by a flux Φ = A|B⃗ |. (b,c) Numerically calculated induced space charge ΔQ along the nanowire axis at the center of the nanowire. In (b) top gates III and V are fixed at −1 V, while the other top gates are grounded. The potential barrier separation at half-maximum is 180 nm. In (c) top gate II instead of top gate III is used and the potential barrier separation is 390 nm. (d,e) Variation of the differential conductance at T = 80 mK as a function of magnetic field for an excitation voltage of Vac = 100 μVrms and Vdc = 500 μV. In (d) top gate III and top gate V are close to pinch-off, corresponding to the configuration in (b). (e) Top gate II and top gate V are close to pinch-off, corresponding to the configuration in (c). (f) Magnetic field values of the conductance oscillation peaks in (d) and (e). (g) Measured and (h) calculated magnetoconductance oscillations for the top-gate configuration in (b). In (g) QPCV voltage is fixed at VTG−V = −0.45 V, and top gate III is employed to raise the second potential barrier. In (h) a cylindrical surface conductor with a diameter of 70 nm and a half-maximum potential barrier separation of 180 nm was assumed. One potential barrier height is fixed at ΦTG−V = 7 meV, while the other (ΦTG−III) is varied as the parameter. The Fermi energy is EF = 6.2 meV. (i) Conductance oscillations calculated for a potential barrier separation of 180 nm. The height of the potential barriers is fixed at 7 meV. In (j) the potential barrier separation is increased to 390 nm. In (d,e,g,h) a magnetoconductance background has been subtracted.

length of the nanowire was 500 and 600 nm, respectively, and the results were tested for nanowire lengths up to 1 μm. The computed conductances are shown in Figures 5h−j. We evaluate the experimental data in the context of interference of coherent snaking orbits. In high transverse magnetic fields (B ≳ 3 T) regular flux-periodic oscillations emerge. For smaller magnetic fields the periodicity is larger and the frequency starts to increase (as depicted in Figures 5d,e). This is a manifestation of the fact that the edge channels are

the coupling is increased by lowering the barriers, regular magnetoconductance oscillations are obtained, which confirm our experimental observations. The origin of these flux-periodic oscillations is the relative phase difference between pairs of snaking states at opposite edges of the nanowire. For direct comparison with the experimental data the nanowire is modeled as a cylindrical surface conductor with a diameter of 70 nm (see below) and a separation of the half-maximum potential barriers of 180 and 390 nm, respectively. The total 4573

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Nano Letters gradually formed when a magnetic field is applied. When two QPCs are both tuned to the regime just before pinch-off, these edge channels enclose a well-defined area. The fast Fourier transform of the magnetoconductance is presented in the Supporting Information. As depicted in Figure 5f for QPC-III and QPC-V the oscillation period is found to be 0.322 T. For QPC-II and QPC-V the oscillation period is 0.146 T. Hence, in agreement with Aharonov−Bohm-type oscillations we find that the periodicity scales with the area between the QPCs. Both measurements in Figures 5d,e yield nearly identical results for the edge channel separation of 71 and 73 nm, respectively. The fact that the periodicity at small magnetic fields appears significantly larger (corresponding to a channel separation of ∼40 nm) substantiates the notion that, at least for small magnetic fields, electronic transport in InAs nanowires is not as surface-dominated as one might predict based on the bulk InAs properties.27 The channels are located in close proximity to the surface only at large magnetic fields. This might indicate the limitations of our theoretical model assuming ideal surface conduction.29 However, the experimental magnetoconductance pattern in Figure 5g agrees surprisingly well with the calculated data in Figure 5h. The second potential barrier (top gate III) starts to dominate for VTG−III < −0.415 V. There, a phase change occurs, and as VTG−III is made more negative the overall conductance decreases and the oscillation pattern is subject to a monotonic phase shift. This continues until VTG−III reaches the pinch-off voltage. Similarly, the magnetoconductance calculations in Figure 5h also predict an increasing phase shift upon raising the second potential barrier. This is attributed to the variation of the electrostatic potential profile between the QPCs. For B > 1 T the calculated oscillation period is about 0.4 T, which is in reasonable agreement with the magnetic flux picked up inside the snaking edge channels. Nevertheless, the snaking edge channels can extend to some degree along the nanowire cylinder surface, effectively reducing the enclosed magnetic flux. Magnetoconductance line cuts are depicted in Figures 5i,j in analogy to the measurements in Figures 5d,e, respectively. In agreement with our measurements the enhanced QPC separation is reflected in an increased oscillation frequency. Hence, in Figures 5i,j the oscillation period can be associated with an edge channel separation of about 60 nm. The observation that electronic transport takes place in spatially separated edge channels at large magnetic field justifies the choice of a 2D model to describe the Shubnikov−de Haas effect in a nanowire, thus projecting the mobile carriers on the cross-section plane along the nanowire axis. Summary. To conclude, we report on adiabatic transport between nanowire QPCs connected in series, which is reflected in the nonadditivity of the QPC resistances. Due to the adiabatic nature of transport, electrons can be selectively injected into a one-dimensional subband of the nanowire and propagate over a distance up to the micron-scale at large magnetic fields with conservation of subband index. Thus, we demonstrate a viable prototype setup for nanowire-based ballistic logic devices. The large adiabatic backscattering length opens the door for ballistic logic gate operations that are highly efficient for minimum number finding tasks.26 We attribute the robustness of the observed adiabatic transport to the spatial separation of counter-propagating electrons in Landau edge channels. The presence of coherent closed-loop edge channels in a magnetic field is revealed by regular Aharonov−Bohm oscillations, which bear information on the channel dimensions.

The observation of the Shubnikov−de Haas effect in the semiconductor nanowire indicates that edge channel transport at large magnetic fields is at least partially adiabatic even along the entire nanowire length. Also, it validates our previous dualgate field-effect transistor study of the electron concentration27 and offers a novel tool for nanowire characterization. We predict that by raising the mean free path beyond the current value of 250 nm, the viability of nanowire-based ballistic logic applications can be extended to the zero-field regime and to higher temperatures.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b01840. Landé g factor calculated from the Shubnikov−de Haas peaks, Aharonov−Bohm oscillations in a transverse magnetic field, fast Fourier transform of the magnetoconductance oscillations as a function of potential barrier separation, and a comparison between the irregular universal conductance fluctuations and the quasi-periodic oscillations resulting from the coherent closed-loop states (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

We are grateful to St. Trellenkamp for performing electron beam lithography and H. Kertz for support during the measurements.

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DOI: 10.1021/acs.nanolett.6b01840 Nano Lett. 2016, 16, 4569−4575