Ballistic Transport and Exchange Interaction in InAs Nanowire

Letter pubs.acs.org/NanoLett

Ballistic Transport and Exchange Interaction in InAs Nanowire Quantum Point Contacts S. Heedt,*,† 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 ‡ Solid State Electronics Department, University of Duisburg-Essen, 47057 Duisburg, Germany S Supporting Information *

ABSTRACT: One-dimensional ballistic transport is demonstrated for a high-mobility InAs nanowire device. Unlike conventional quantum point contacts (QPCs) created in a two-dimensional electron gas, the nanowire QPCs represent one-dimensional constrictions formed inside a quasi-onedimensional conductor. For each QPC, the local subband occupation can be controlled individually between zero and up to six degenerate modes. At large out-of-plane magnetic fields Landau quantization and Zeeman splitting emerge and comprehensive voltage bias spectroscopy is performed. Confinement-induced quenching of the orbital motion gives rise to significantly modified subband-dependent Landé g factors. A pronounced g factor enhancement related to Coulomb exchange interaction is reported. Many-body effects of that kind also manifest in the observation of the 0.7·2e2/h conductance anomaly, commonly found in planar devices. KEYWORDS: Ballistic transport, InAs nanowire, quantum point contacts, g factors, 0.7·2e2/h anomaly, exchange interaction

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is the one-dimensional nature of transport and the control of subband occupation. We have created one-dimensional constrictions inside an InAs nanowire where the number of spin-degenerate electronic modes can be controlled between zero and six at zero magnetic field. In doing so, we take up the work accomplished by van Weperen et al.,11 who observed conductance quantization in back-gated InSb nanowires at finite magnetic fields. In our work, we introduce precise control over the location where the constriction forms. Given the large nanowire length, numerous QPCs with similar properties can be created along the nanowire axis. By evaluating the subband separations as a function of the magnetic field, the effect of Landau quantization and Zeeman spin-splitting is analyzed. Particular emphasis is devoted to the influence of the unconventional confinement potential of the nanowire QPCs compared with 2DEG-based channels. In the low electron density regime of the nanowire QPCs, the effect of electron−electron interaction on the Landé g factors is investigated. The prominent role of strong interactions on one-dimensional transport in our device is emphasized by the observation of a conductance feature that is attributed to the 0.7 G0 anomaly. Experimental Methods. InAs nanowires were grown via gold-catalyzed metal−organic vapor phase epitaxy on GaAs (111)B substrates. The nanowires feature a zinc blende crystal

uantum point contacts formed in ultraclean twodimensional electron gases (2DEGs) are among the most widely studied systems illustrating the wave nature of electrons1,2 and offer a natural environment to study electron many-body effects.3−5 Commonly, electrostatic gates separate two reservoirs of a high-mobility 2DEG typically formed inside group III−V semiconductors, leaving open only a small channel of tunable width.6 As the constriction is narrowed, the conductance between the reservoirs drops in steps of G0 = 2e2/h given by two universal quantities, the electronic charge e and Planck’s constant h. Each step corresponds to the depopulation of a one-dimensional mode inside the constriction. Ballistic electron transport in those devices typically exceeds several micrometers. Signatures of ballistic transport have also been observed in carbon nanotubes7 and semiconductor nanowires before.8−11 This Letter, however, reports on the formation of quantum point contacts (QPCs) in a nanowire by local gating. High-mobility group III−V nanowires12−15 are compelling building blocks for spintronic devices due to their strong spin−orbit coupling and due to the excellent electrical tunability of spin and charge transport. It has been investigated theoretically16,17 and experimentally18,19 how onedimensional semiconductors with strong spin−orbit coupling, such as InAs and InSb nanowires, can be tailored to serve as hosts for Majorana bound states and therefore can be highly attractive for topological quantum computing.20 Apart from the implementation of spinless p-wave superconductivity inside the nanowire, another essential, yet largely unexplored prerequisite © XXXX American Chemical Society

Received: January 30, 2016 Revised: April 10, 2016

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DOI: 10.1021/acs.nanolett.6b00414 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters structure with periodic rotational twinnings.22 In previous studies on similar nanowires field-effect mobilities were found to exceed 104 cm2/(V s).23 After growth, the wires are transferred onto a Si substrate with a 200 nm-thick thermal oxide layer. Regions of LaLuO3 dielectric24 are defined on the nanowires via pulsed laser deposition at room temperature and using liftoff technique. The employed high-k dielectric ensures excellent top-gate control. It is 100 nm thick, and the relative permittivity εr is measured to be 26.9. In a second step, Ti/Au top-gate electrodes of 180 nm width and 30 nm spacing are fabricated, denoted as QPC-I to QPC-VII. The electrostatic coupling to the gates is very strong due to the Ω-shaped topgate geometry and the employed high-k dielectric. The nanowire is contacted using in situ Ar+ sputtering and deposition of 120 nm-thick Ti/Au electrodes. The nanowire under investigation shown in Figure 1a exhibits minor tapering and an average diameter of 100 nm. The source and drain contact spacing of L = 2.94 μm is much larger than the electronic mean free path. Electronic transport measurements are performed at temperatures between 20 mK and 25 K. A dc-bias voltage is applied symmetrically with respect to ground from source to drain, and

the current is measured concurrently on either side of the nanowire, in order to be susceptible to possible leakage currents to the gates. Results. Field-effect transistor (FET) measurements using the global back gate and a single top gate (see Figure 1b) are performed in order to determine the electron mobility and concentration. Only one gate is operated at a time, while all other gates are grounded. Finite element method calculations of the capacitive coupling for the actual device geometry yield a back-gate capacitance of C = 90 aF, whereas the capacitance of a single top gate amounts to 110 aF. The numerical simulation is particularly useful in accounting for the actual dielectric surroundings of the nanowire, for the semiconducting nature of the channel and for the finite density of surface states, which lead to moderate electron accumulation at the nanowire surface.21 Utilizing the information on the gate coupling, the electron concentration can be determined from the pinch-off voltage Vth. In order to fit the current-gate voltage (I−VG) traces in Figure 1b, we utilize an expression15 for the I−VG relation:

I=

Vdc LLG* μC(VG − Vth)

+ Rs

(1)

with the field-effect mobility μ, the dc-bias voltage Vdc, and the series resistance Rs of the unmodulated nanowire segments. Here, LG* corresponds to the effective gate length correcting the geometric gate length for electrostatic (screening) effects. Fitting eq 1 to both transfer characteristics in Figure 1b yields identical results for the mobility. We obtain μ = 25000 cm2/(V s) for the top-gate as well as for the back-gate FET characterization. Using the pinch-off voltages, the average electron concentration is derived15 to be n3D ≈ 1 × 1017 cm−3, which corresponds to an estimate for the Fermi energy of EF ≈ 35 meV. Accordingly, the elastic mean free path is le = vFτe ≈ 250 nm, with the scattering time τe and the Fermi velocity vF. In another study, Hansen et al.25 estimated an elastic scattering length for InAs nanowires of 60−100 nm comparable in magnitude to the nanowire diameter. Chuang et al.10 reported a mean free path of about 150 nm for 30 nm-wide InAs nanowires. Hence, the device investigated here exhibits a mean free path that is nearly twice as large. Quantization of Conductance. All of the QPCs demonstrate quantized conductance even down to zero magnetic field. This can be seen in Figure 2a, in agreement with the Landauer formula for the conductance of a point contact:

G=N

2e 2 h

(2)

for an integer number of subbands N. Equation 2 also holds for quantum wires which are not restricted to two dimensions as long as the transverse width is of the order of the Fermi wavelength λF. A series resistance in the order of 20 kΩ is subtracted to match the consecutive conductance plateaus with the quantized values, in agreement with eq 2. This is required, since only a fraction of the nanowire is actually modulated by the gate. The onset of transport through the one-dimensional subbands is linked with the risers between the quantized conductance plateaus. Hence, the lines of the transconductance maxima in Figure 2b can be associated with the subband edges. Degeneracy of two angular eigenstates of the nanowire, which was discussed by Ford et al.,9 was not observed, likely due to the asymmetry introduced by the gates. By applying an out-of-

Figure 1. (a) Scanning electron micrograph of the InAs nanowire investigated in this study (diameter 100 nm). It is partially covered with 100 nm of the high-k dielectric LaLuO3 (εr = 26.9). Hence, each top-gate electrode is coupled stronger to the nanowire than the back gate. The seven top gates (QPC-I to QPC-VII) each have a width of 180 nm, and the gate pitch is 30 nm. The back gate and each top gate can be used to pinch-off the channel completely and control the number of subbands contributing to transport. (b) Back-gate and single top-gate (QPC-I) pinch-off traces for a dc-bias voltage of Vdc = 15 mV, while keeping the other gate and the remaining top gates grounded. Inset: Calculated space charge distribution21 along the axial nanowire cross-section (with the electron concentration increasing from red to blue) and the approximately Gaussian top-gate potential shape. B


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Figure 2. (a) Conductance traces using QPC-III at 90 mK for the magnetic field values indicated by the arrows in panel (b) plotted with offsets for clarity. The dc-voltage applied to the entire nanowire is 4 mV. The voltage drop across the QPC itself is much smaller. Hence, the Zeeman-split halfinteger plateaus can clearly be resolved at large magnetic fields. Due to the finite dc-bias Fabry-Pérot interference fringes do not compromise the conductance quantization (cf. below). (b) Onset of transport through nanowire subbands represented by maxima in the transconductance dG/dVTG, which correspond to risers between quantized conductance plateaus in panel (a). Magnetic depopulation of the subbands occurs in a perpendicular magnetic field between 0 and 12 T due to the additional magnetic confinement.

plane magnetic field B, half-integer conductance plateaus appear in Figure 2a at multiples of e2/h, corresponding to Zeeman-split subbands of lifted spin-degeneracy. This is reflected in Figure 2b in the splitting of the high-transconductance lines at large magnetic fields. We also observe a magnetic depopulation of the one-dimensional subbands with increasing magnetic field, which is a hallmark of Landau quantization (see Figure 2b). At finite dc-bias, the QPC conductance exhibits secondary features of one-dimensional transport, i.e., diamond-like structures in the nonlinear conductance that represent the bias-dependent quantized conductance plateaus and which are most apparent in the transconductance dG/dVTG. Two exemplary source-drain biasing measurements for QPC-IV are shown in Figure 3a,b. Because the QPC constitutes only a fraction of the nanowire, the applied bias voltages are corrected for the voltage drop across the series resistance to obtain the actual voltage drop across the QPC. When source and drain chemical potential, μs and μd, respectively, are detuned (see Figure 3c), the conductance plateaus decrease in size in terms of the top-gate voltage VTG. As the detuning reaches a certain subband separation, the associated plateau vanishes. Hence, the dc-bias voltage width of the diamond-shaped conductance plateaus (cf. blue arrow in Figure 3a) is an immediate measure for the energy separation between neighboring subbands or Zeeman-split levels. In Figure 3d, the subband separation E↑2 − E↓1 is depicted. In contrast to QPCs conventionally formed inside 2DEGs, the nanowire constriction is comprised of two orthogonal confinement axes in both the vertical and the horizontal direction with comparable impact on the properties of the QPC (see Figure 3d, inset). Whereas the eigenenergies at B = 0 T are given by the confinement, which is intrinsic or induced by the gate, they converge toward Landau levels at higher magnetic fields. The out-of-plane magnetic field couples to the lateral orbital motion of the electrons, which adds to the geometrical and electrostatic QPC confinement. However, the magnetic confinement is much weaker than expected based on the cyclotron energy ℏeB/m* ≈ B·4.5 meV/T, with the effective mass m*. The unconventional confinement potential V(x,y) might couple the orthogonal directions, which would

Figure 3. Transconductance dG/dVTG for QPC-IV at (a) B = 5 T and (b) B = 8 T. The data have been symmetrized with respect to Vdc = 0 mV. The numbers in the diamond-shaped plateau regions denote the corresponding conductance in units of G0. At small dc-bias voltage Fabry-Pérot resonances emerge. (c) Energy-momentum dispersion of the one-dimensional subbands in a magnetic field. μs and μd denote the source and drain chemical potential, respectively. (d) Level separation E↑2 −E↓1 averaged for QPC-I to QPC-V as a function of the magnetic field determined from source-drain biasing studies as depicted in panels (a) and (b). The orange line represents a fit accounting for confinement, Landau quantization, and Zeeman splitting. The blue shaded region designates the error bars. In the inset, the confinement geometry of the nanowire cross-section is depicted with two orthogonal axes of comparable confinement strength.

prevent the separation of V(x,y) into the harmonic potentials of two independent harmonic oscillators and may explain the C


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Figure 4. (a) Characteristic checkerboard pattern in the differential conductance as a function of the dc-bias and the top-gate voltage resulting from Fabry-Pérot resonances in QPC-V at B = 12 T. (b) Differential conductance oscillations in the linear regime (Vdc = 0 mV). The boxed region corresponds to the gate voltage regime in (a).

single top gate. Reflections of electron partial waves occur where the potential changes on both sides of the QPC constriction. Similar observations have been made by van Wees et al.,31 who have drawn an analogy to the reflections that occur at an open-ended waveguide. Lande ́ g Factors. The formation of half-integer conductance plateaus reflects the lifting of the spin-degeneracy of the 1D subbands. The Landé g factor is a measure for the energy scale of the Zeeman level splitting ΔEZ = gμBB, with the Bohr magneton μB. In the following, we investigate the impact of confinement on the Landé g factor. To this end, voltage bias spectroscopy is performed for QPC-I to QPC-V. The variation of the diamond-shaped conductance plateaus with respect to the applied magnetic field (e.g., in Figure 3a,b) yields the g factors for the subbands lowest in energy. The method developed by Patel et al.,32 which is commonly employed in the literature33,34 is not utilized here, in order to prevent variations in the gate lever arm to compromise the resulting g factors. Also, the zero bias voltage regime is not accessible at low temperatures due to Fabry−Pérot interferences. Instead, the Zeeman splitting is measured for each magnetic field and each subband individually from the bias voltage width of the transconductance diamonds, in the same way the subband separations are determined.35,36 The dc-bias width of the halfinteger plateaus increases linearly with the magnetic field (as can be seen in Figure 5a for QPC-V) and with the slope d(ΔEZ,n)/dB, the effective g factors are given by

smaller diamagnetic shift of the energy levels. A relatively weak coupling of the magnetic field to the orbital motion has also been observed for InSb nanowires.11 The quantization of conductance at zero magnetic field breaks down for temperatures above 25 K owing to temperature averaging. The broadening of the Fermi−Dirac distribution ΔE ≈ 4kBT = 8.6 meV for this temperature is in excellent agreement with the level separations determined via voltage bias spectroscopy (cf. Figure 3d). The exceptional robustness of the conductance plateaus at finite out-of-plane magnetic fields could possibly be attributed to the formation of snaking orbits extending at opposite sides along the nanowire,26 whereas localized cyclotron states can only form at the top and bottom of the nanowire. This way, the counter-propagating states are spatially separated and thus backscattering is efficiently suppressed. Fabry−Peŕ ot Interference. In the phase-coherent transport regime deviations from the quantized conductance plateaus can be observed. At low temperatures, resonances emerge for small bias voltage due to the interference of reflected and transmitted electron partial waves, which leads to a checkerboard pattern that is characteristic of Fabry−Pérot interferences (see Figure 4a).27,28 It is noteworthy that the Fabry−Pérot oscillations in the differential conductance at zero bias voltage can give information on the number of one-dimensional subbands contributing to transport in the channel (cf. Kretinin et al.29). By measuring at a high magnetic field of 12 T, only two nondegenerate subbands are involved for QPC-V. The periodicity ΔVG of the Fabry−Pérot oscillations in Figure 4b can be estimated to be 3.3 mV using a fast Fourier transform. The Fabry−Pérot period can be utilized to derive the onedimensional resonator length L. A variation ΔVG of the electrostatic potential induces a change in the electron density of the one-dimensional channel of δn = CLG ΔVG/e = 2δkF/π, where CLG denotes the capacitance per unit length. Within a single Fabry−Pérot period the Fermi wavenumber is changed by δkF = π/L. Hence, ΔVG is associated with a resonator length of L = 2e/ΔVGCLG ≈ 210 nm. We have numerically calculated the electrostatic gate length to be about 240 nm, which matches L almost perfectly. Such a configuration is similar to the regime reported by Amasha et al.,30 which in our case is controlled by a

|gn*| =

1 d(ΔEZ,n) μB dB

(3)

for each subband index n. For the n = 1 subband, we find that the g factor of |g*1 | = 7.0 averaged over all QPCs falls within the regime previously reported for InAs quantum dots.37 On the one hand, the reduced orbital degree of freedom in the QPC lowers the substantial contribution of spin−orbit coupling to the g factor, which quenches the large effective bulk g factor of InAs. On the other hand, close to pinch-off, the stronger confinement gives rise to an enhanced overlap of electron wave functions and causes an increase in |g*| by virtue of exchange interaction. For the n > 1 subbands, the g factor drops below D


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4.0, indicating the decreasing impact of exchange interaction for the higher subbands33 (see Figure 5b). Many-body effects are expected to be particularly prominent in our nanowire QPCs, since the confinement is intrinsically much larger than for most conventional QPCs formed in heterostructure 2DEGs. The Landé g factors commonly found for quantum dots formed in InAs nanowires via gating are in the range of |g*| = 7−9,38 but depending on the degree of confinement quantum dots formed via crystallographic confinement exhibit |g*| down to 2.3.37 Hence, the reduced dimensionality leads to a significantly diminished g factor compared to the bulk value of about 14.7. It has been described theoretically39 and observed experimentally in nanowire double quantum dots38 that the electron g factor is smaller perpendicular to the nanowire axis in comparison to the g factor for magnetic fields applied along the wire axis. Csonka et al.40 derived very large fluctuations of the g factor of adjacent InAs nanowire quantum dot states between 2 and 18. In the present nanowire device, a local QPC can also be implemented via a different gate configuration, by using the

Figure 5. (a) Zeeman energy ΔEZ,n = E↓n −E↑n measured in QPC-V as a function of the perpendicular magnetic field for different subband indices n. The linear fit through the origin yields the effective Landé factors |gn*| for the three subbands lowest in energy. (b) |gn*| as a function of one-dimensional subband index for five different local QPCs. The dashed line is a guide to the eye along the weighted average. The green shaded region designates the standard deviations of the g factors.

Figure 6. (a) Differential conductance characteristics of QPC-III and QPC-IV (offset in VTG) for an excitation voltage of Vac = 80 μVrms at B = 0 T. The temperature of 9 K ensures the absence of Fabry−Pérot oscillations such that the zero dc-bias regime becomes accessible. (b) Conductance for QPC-IV at Vdc = 3 mV and B = 0 T as a function of temperature. Below 5 K, Fabry−Pérot oscillations begin to emerge, whereas the 0.7 G0 plateau strengthens with increasing temperature. (c) Bias-corrected differential conductance as a function of QPC-IV gate voltage and for an excitation voltage of Vac = 50 μVrms at B = 0 T and T = 120 mK. From top to bottom, the traces are taken at fixed top-gate voltages from −0.5 V to −1.05 V. The data have been symmetrized with respect to Vdc = 0 mV to remove instrument-related background artifacts.42 Inset: Quantized conductance with signatures of the 0.7 G0 anomaly corresponding to the extra plateau in the subopen regime (G < G0) in the main panel at the bias voltages indicated by the arrows. The curves are offset for clarity. E


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dimensional density of states owing to the strong confinement.49,50 Also considerable indications for spontaneous spin polarization below the first integer plateau have been brought up.51,52 It has been shown that the observability of the 0.7 G0 anomaly depends on the length of the QPC region,47 since it would affect the parity of the number of emergent localized states. Actually, in the present work, the lithographic gate width is comparable to the device dimensions of Iqbal et al.47 Manybody effects might give rise to localized electrons inside the QPC, and we indeed observe Coulomb blockade as a function of top-gate voltage in the pinch-off regime. However, maybe due to the predominance of Fabry−Pérot resonances close to zero bias, we could not find signatures of the Kondo effect at low temperatures. Nevertheless, it has been shown previously53 that Kondo-like zero bias anomalies can coexist with the 0.7 G0 feature without being causally linked. Summary. In conclusion, we have presented fundamentally new results on conductance quantization in an InAs nanowire. We have introduced a register of local gates, which is utilized to demonstrate quantization of conductance with high accuracy by creating well-controlled constrictions in the electrostatic potential landscape. A crucial aspect of this achievement is the coverage of the nanowire with a high-k dielectric. Thus, we provide a protection of the surface against adsorbents, which would otherwise deteriorate the ballistic device performance. It is possible to accurately control the number of one-dimensional subbands that contribute to transport between zero and six. We extracted a mean free path from the FET mobility at zero magnetic field of le = 250 nm, which is significantly larger than previously reported for InAs nanowires25 and comparable to the mean free path found in high-mobility InSb nanowires.11,15 The series connection of QPCs formed by the top-gate register can be regarded as a prototype for ballistic nanowire logic applications.54 Voltage bias spectroscopy provided valuable information on subband-dependent g factors. The confinement strongly suppresses the effective |g*| factors compared to the bulk value, which is large due to the pronounced spin−orbit coupling in InAs. When the channel is increasingly confined by the top gates, an enhancement of the g factor is observed due to exchange interaction, doubling in size to a value of 7.0 for the first subband. This is attributed to pronounced wave function overlap in the low-density regime. Despite the fact that in our case the confinement in the channel cross-section is comparable along both axes, the enhanced g factors are in good agreement with 2DEG-based QPCs33,43,51,55 comprising a significantly more asymmetric confinement. The important role of electron−electron interaction is substantiated by the observation of key features of the 0.7 G0 conductance anomaly. These observations provide a qualitatively new aspect in the ongoing debate of this effect by being linked to an unconventional nonplanar QPC geometry. Our findings are supported by the recent observation of strong exchange interaction in InAs nanowires,56 providing further incentive to study Luttinger liquid physics in confined InAs nanowires. Given that the effect of spin−orbit coupling can be tuned via electric gating (e.g., via the back gate), the presented device offers the desired properties essential for creating and investigating Majorana bound states owing to the large g factor of the lowest subband and the accurate control of local subband occupation.

back gate to tune the Fermi level. As depicted in the Supporting Information, the back gate can electrostatically control the energy levels of a local QPC created by a single top gate. However, the back gate can additionally induce a second local QPC at another location in the nanowire, which we hence term an intrinsic QPC. The formation mechanism is presumably related to surface potential variations, which also give rise to intrinsic quantum dots.41 However, in the present case, the electrostatic shape of the back-gate-induced QPC is probably elongated in comparison to the top-gate-defined QPCs. Remarkably, the common conductance quantization and Zeeman-splitting is found for finite out-of-plane magnetic fields, demonstrating the efficiency of the mechanism that prevents backscattering.11 We conjecture that the spatial separation of edge modes in the form of snaking edge channels26 is a potential mechanism. We find that, in agreement with the top-gate-induced QPCs, the second subband exhibits a relatively small g factor of the order of |g*2 | = 4.0. The value of |g1*| for the lowest subband is also significantly enhanced for the global gate QPC in agreement with the value given above for the top-gate QPCs. However, the exact value for |g*1 | is difficult to quantify since the series resistance that determines the actual voltage drop across the QPC is strongly affected by the backgate voltage. While, in the top-gate geometry, the Coulomb interactions between the electrons at the constriction could still be affected by residual screening, the back-gate QPC might resemble much more an ideal one-dimensional wire. The 0.7 G0 Conductance Anomaly. At elevated temperatures the Fabry−Pérot resonances disappear due to the reduced phase coherence. At zero dc-bias (and zero magnetic field) differential conductance measurements then exhibit an additional step-like feature below 2e2/h (cf. Figure 6a). This feature is reminiscent of the 0.7 G0 conductance anomaly, a subinteger step in conductance around the value of 0.7·2e2/h. Our data exhibit the characteristic temperature behavior revealed in the initial report by Thomas et al.43 As depicted in Figure 6b, the subinteger conductance step does not disappear due to thermal broadening but strengthens with rising temperature. In Figure 6c, the dense accumulations of traces in the bias-dependent differential conductance correspond to the conductance plateaus at B = 0 T. Half-integer plateaus at high Vdc arise when the number of subbands below the source and the drain chemical potential differ by one. An extra plateau is observed in the subopen regime (G < G0). The feature bears remarkable similarities to the data by Cronenwett et al.44 where the “0.7 G0” structure also rises in conductance with increasing dc-bias. Previously, Lu et al.8 reported on first signatures of the feature in a hole gas formed inside a Ge/Si core−shell nanowire. It has been observed in various material systems, however, in all other cases the investigated devices have been two-dimensional.4,34,42−46 Here, we report on the observation of the 0.7 G0 conductance anomaly in a nanowire representing a quasi-one-dimensional conductor, drawing attention to the generic nature of this phenomenon in onedimensional transport. The aspect of dimensionality appears to be key in understanding and finally settling the origin of this effect. Fully conclusive explanations have long been elusive. In recent years several comprehensive studies have been carried out to pin down an explanation for the 0.7 G0 structure, all invoking the crucial role of exchange interaction. These studies have advocated either for the formation of emergent bound states inside the QPC constriction47,48 or the amplification of interaction effects due to an enhancement of the oneF


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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.6b00414. Measurements of the quantized conductance as a function of back-gate voltage and magnetic field, conductance measurements as a function of back-gate voltage and QPC-IV top-gate voltage at 10 T, and a device proposal for a quantum dot charge readout using a local QPC (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 We are grateful to St. Trellenkamp for performing electron beam lithography and H. Kertz for support during the measurements. The authors acknowledge A. Manolescu and T. Ö . Rosdahl for fruitful discussions.

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REFERENCES

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