InAs Core

Letter pubs.acs.org/NanoLett

Electron Interference in Hall Effect Measurements on GaAs/InAs Core/Shell Nanowires Fabian Haas,*,†,‡ Patrick Zellekens,†,‡ Mihail Lepsa,†,‡ Torsten Rieger,†,‡ Detlev Grützmacher,†,‡ Hans Lüth,†,‡ and Thomas Schap̈ ers*,†,‡ †

Peter Grünberg Institute 9, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany Jülich Aachen Research Alliance, Fundamentals of Future Information Technology (JARA-FIT), 52425 Jülich, Germany

‡

ABSTRACT: We present low-temperature magnetotransport measurements on GaAs/InAs core/shell nanowires contacted by regular source−drain leads as well as laterally attached Hall contacts, which only touch parts of the nanowire sidewalls. Low-temperature measurements between source and drain contacts show typical phase coherent effects, such as universal conductance fluctuations in a magnetic field aligned perpendicularly to the nanowire axis as well as Aharonov− Bohm-type oscillations in a parallel aligned magnetic field. However, the signal between the Hall contacts shows a Hall voltage buildup, when the magnetic field is turned perpendicular to the nanowire axis while current is driven through the wire using the source−drain contacts. At low temperatures, the phase coherent effects measured between source and drain leads are superimposed on the Hall voltage, which can be explained by nonlocal probing of large segments of the nanowire. In addition, the Aharonov−Bohm-type oscillations are also observed in the magnetoconductance at magnetic fields aligned parallel to the nanowire axis, using the laterally contacted leads. This measurement geometry hereby directly corresponds to classical Aharonov−Bohm experiments using planar quantum rings. In addition, the Hall voltage is used to characterize the nanowires in terms of charge carrier concentration and mobility, using temperature- and gate-dependent measurements as well as measurements in tilted magnetic fields. The GaAs/InAs core/shell nanowire used in combination with laterally attached contacts is therefore the ideal system to three-dimensionally combine quantum ring experiments using the cross-sectional plane and Hall experiments using the axial nanowire plane. KEYWORDS: Hall effect, GaAs/InAs core/shell nanowires, Aharonov−Bohm effect, quantum transport, electron interference

T

core/shell nanowire at low temperatures. However, differences in the Hall signal are found for different Hall contact geometries, which allows to draw conclusions concerning the impact of phase coherence. In addition, using the Hall effect, we will investigate the change of the carrier concentration at different temperatures and at varying electrical field strengths from an external backgate. We demonstrate that this is a suitable alternative to field-effect measurements used to characterize the electronic properties of the nanowire.5,6 The first Hall effect measurements on nanowires were presented in 2012 by Blömers et al. and Storm et al., who used high precision electron beam lithography to fabricate the contacts.7,8 They measured the Hall effect at room temperature on homogeneous InAs and on InP p-type/n-type core/shell nanowires, respectively, and could both deduce the electron carrier concentration of the nanowires.7,8 Further measurements on these InP core/shell nanowires using Hall measurements followed shortly after,9,10 but so far no low-temperature Hall measurements on nanowires were presented in the

he Hall effect is one of the most commonly used physical effect to determine semiconductor properties like carrier concentration and electron or hole mobility. It is based on the Lorentz force, which is deflecting the charge carriers as they propagate through the structure in an external magnetic field, aligned perpendicular to the flow direction of the carriers. The charge carriers are separated by their electrical charge, resulting in a potential difference which builds up between the borders of the sample. This so-called Hall voltage can be measured via laterally attached voltage probes called Hall contacts and is generally used to determine the charge carrier concentration and mobility of the sample. Such a measurement geometry is difficult to realize using semiconductor nanowires, as Hall voltage probes need to be fabricated on the outermost sidewalls without touching each other, which is very challenging due to the nanoscale size of the wires and their three-dimensional morphology.1 The focus of the present paper is to study quantum transport at low temperature in a Hall effect contact geometry. So far, electron interference effects in GaAs/InAs core/shell nanowires were only measured between source and drain contacts attached at opposite ends of the nanowires.2−4 Here, we will show that the Hall effect can also be measured on a GaAs/InAs © XXXX American Chemical Society

Received: August 31, 2016 Revised: November 17, 2016

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DOI: 10.1021/acs.nanolett.6b03611 Nano Lett. XXXX, XXX, XXX−XXX

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Ar+ ion milling, before a Ti/Au bilayer was evaporated onto the sample and removed by liftoff. We study two samples labeled nanowires A and B. Figures 1a,b show a scanning electron micrograph of sample A in two

literature known to the authors. Such measurements are relevant not only to allow low-temperature characterization of semiconductor nanowires but also to investigate the influence of phase coherent quantum interference effects which are common in such small nanometer sized objects like nanowires.11−13 The GaAs/InAs core/shell nanowire heterostructure is favorable for low-temperature Hall effect measurements, as the structure forms a type I straddling gap band alignment.14−16 Here, the InAs bandgap energetically aligns itself centrally next to the larger bandgap of the GaAs core, effectively forming a radial quantum well in the InAs shell between the GaAs/InAs interface and the InAs surface.17−19 Because of the existence of donor-type surface states at the InAs surface, electrons accumulate within the InAs shell, forming a conductive nanotube.20,21 The shell is hence filled with intrinsic charge carriers even at lowest temperatures.2,22 Concerning quantum transport, the ringlike nanotube geometry allows the observation of quantum interference effects in terms of Aharonov−Bohm-type magnetoconductance oscillations with h/e flux periodicity.2,3,23,24 These oscillations are caused by magnetic flux enclosure of electrons encircling the GaAs core, when the core/shell nanowire is subjected to an external magnetic field aligned parallel to the nanowire axis.25−27 Measurements across the nanowire, using laterally attached Hall contacts, as well as along the wire, using the axially attached source and drain contacts, can hence be used to study the electron propagation along different directions in the nanowire. Experimental Details. We used GaAs/InAs core/shell nanowires grown by a two step self-catalyzed growth method using molecular beam epitaxy.15 In the first growth step, GaAs nanowires were grown from Ga droplets formed in tiny pinholes of a thin layer of silicon oxide on GaAs (111)B or Si (111) substrates. In the second step an InAs shell was grown on the sidewall facets of the GaAs core nanowire. The GaAs core nanowires had a hexagonal morphology and mainly formed a zinc blende crystal structure, which was adopted by the InAs shell. The crystal structure was not purely zinc blende but contained stacking faults and rotational twins along the ⟨111⟩ growth direction. Furthermore, misfit dislocations formed at the heterostructure interface between GaAs in InAs. The core diameter 2rC and shell thickness tS could be determined by scanning electron microscopy (SEM) as a small segment at the top of the GaAs core having the wurzite crystal structure always remained uncovered by InAs. More details on the nanowires used can be found in refs 15, 16, and 28. For preparation of Hall contacts onto the core/shell nanowires, an electron beam lithography process with very accurate marker definitions was used.7,29 For this purpose, the grown core/shell nanowires were transferred to a prepatterned, degenerately n-doped Si (100) substrate with thick SiO2 coverage, which was used as a gate dielectric for backgate measurements. To allow the precise positioning of the contacts, the nanowires were deposited onto a 100 μm × 100 μm marker field with 5 μm pitched Ti/Au markers. Three large markers for alignment were positioned about 1 mm away from the central marker field. High-resolution SEM images were taken from the deposited nanowires and contacts were defined using CAD software while accounting for proximity effects and nanowire misalignment. After electron beam lithography, the contact areas to the wire were cleaned using O2 dry etching and in situ

Figure 1. (a, b) SEM images of sample A. (c, d) SEM images of sample B. The small, visible connections in (b) and (d) are caused by metallic sidewall formation and are not electrically conductive. (e) Schematic of the relevant dimensions.

different perspectives. The nanowire is contacted at top and bottom by a source and a drain lead, separated LA = 2.2 μm apart. In the center the nanowire is contacted by two laterally attached contacts (so-called Hall contacts), each about WAH = 120 nm wide and separated by a dAH = 60 nm gap. Figure 1b shows that these Hall contacts only bind to two of the six sidewall facets of the nanowire, leaving the top and the three facets at the bottom side uncovered. From the upper part of the nanowire, which is not covered with InAs, we determined a GaAs core diameter of 2rAC = 150 nm and an InAs shell thickness of tAS = 30 nm. Sample B was taken from a different MBE growth run and consisted of a GaAs core of 2rBC = 170 nm diameter and an InAs shell of thickness tBS = 40 nm. The sample is shown in Figure 1c. The nanowire used was much shorter than sample A, so that the source−drain contact separation was only LB = 640 nm, which should increase the influence of the leads on the Hall contacts. The Hall contacts were also positioned centrally on the nanowire and had a width of WBH = 180 nm and a separation of dBH = 55 nm shown in Figure 1d. From the close-up in Figure 1d, we can see that the Hall contacts are located almost completely on the two inclined sidewall facets and not on the top facet. A schematic of the relevant dimensions for the Hall contact alignment is given in Figure 1e. The measurements were performed on rotatable and heatable sample holders in a He-3 cryostat and a pumped He-4 cryostat with a variable temperature insert (VTI). Temperatures from 300 mK up to 100 K could be achieved, and magnetic fields up to 16 T were available. Sample B could be rotated in the cryostat between an alignment of the magnetic field parallel and perpendicular to the nanowire axis. We label the angle between nanowire axis and magnetic field direction γ. Because of a small misalignment of the nanowire axis on the sample holder, the smallest angle between the axis of sample B and the magnetic field achievable was γ = 5°. As we have shown recently,4 such a small misalignment is tolerable for the B


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Figure 2. (a) Longitudinal resistance RL of the nanowire measured by the voltage drop VL between source and drain contact for varying magnetic fields B, aligned perpendicular to the nanowire axis, and gate voltages VG. (b) Analogous measurement of the transversal resistance, deduced from the voltage drop over the laterally attached Hall contacts. The curves in (a) and (b) are not artificially offset. The thicker lines show the measurement at VG = 0 V. (c) Conductivity σ3d and Hall slope dRH/dB for varying gate voltages, showing the correlation between the two variables over the carrier concentration. The errors in dRH/dB are determined from the mean deviations of the measured signal from an ideal line. The errors in σ3d are propagated from the assumed errors in RL. (d, e) Deduced carrier concentration nH and carrier mobility μ for varying conductivity and hence gate voltage.

source−drain current ISD. It is to note that no current flowed off via the Hall contacts as was controlled by the I/V converter at the drain lead. Hence, we here use the term RT only to relate the measured voltage drop VT directly to VL across the source− drain leads. For the longitudinal resistance RL, the influence of the gate voltage is clearly visible as change of the nanowire resistance over nearly 1 order of magnitude between VG = −10 and 22 V. At negative gate voltages, a small parabolic resistance increase is observed, which is suppressed for larger magnetic fields and positive gate voltage. We attribute this feature to a classical magnetoresistance of a Drude free electron gas as it is also seen at higher temperatures and will not consider it further.30 Figure 2c shows the conductivity σ3d = L/ASRL of the nanowire for the varying gate voltages determined from the RL(B = 0 T) resistance, where AS = 3√3/2·((rC + tS)2 − rC2) is the crosssectional area of the shell and L the contact separation. The increase in conductivity with increasing gate voltage is clearly visible, indicating that the transport is predominantly carried by electrons. Saturation effects are observed at the highest and lowest gate voltages applied, which are common for nanowire field-effect measurements.5,6 More importantly, we observe a clear asymmetrical transversal resistance RT = VT/ISD around B = 0 T, which we attribute to the buildup of a Hall voltage VH between the Hall contacts laterally attached to the nanowire. Here, the charge carriers are separated by the Lorentz force and accumulate at the Hall contacts. It is to note that the measured transversal

interpretation of the results. The angle of rotation was controlled via an external Hall sensor, and it allowed angledependent measurements with 2° accuracy. The magnetotransport measurements were carried out either by driving current or voltage across the contacts. When driving voltage, a small bias voltage of a few microvolts was applied between two of the four contacts and the current flow was detected by a low noise I/V converter, while the remaining two contacts were floating. When driving current, several nanoamperes were applied via the source and drain leads while the differential voltage drop over the Hall contacts VT as well as over the source−drain leads VL was recorded. A low noise I/V converter was used at the drain lead to control the current flow ISD in this setup, to detect current leaks. Measurements were performed either via dc excitation or using a standard lock-in technique. Results. Figures 2a and 2b show results of a measurement on sample A in a magnetic field, which is aligned perpendicular to the nanowire axis, for varying backgate voltages. The nanowire was current biased with ISD = 100 nA over the source−drain contacts, and the measurement temperature was T = 40 K, so that phase coherent effects were effectively suppressed.12,13,22 Figure 2a shows the measured resistance RL = VL/ISD of the nanowire, measured via the voltage drop longitudinal to the nanowire over the source and drain leads. Correspondingly, Figure 2b shows the measured transversal resistance RT = VT/ISD of the nanowire, deduced from the voltage drop VT over the lateral Hall contacts related to the C


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Figure 3. (a, b) and (c, d): Longitudinal and transversal magnetoresistance of sample A and sample B at varying temperatures and zero gate voltage in a perpendicularly aligned magnetic field. The inset in (b) shows the Hall slope determined from the measured Hall voltage for different temperatures. For both samples, signatures of UCF are observed for lowest temperatures, both in the longitudinal and in the transversal signal. The curves are not artificially offset. (e) Deduced carrier concentration nH of sample A for different temperatures, based on eq 3. (f) Asymmetric component of the transversal resistance of sample B. For elevated temperatures, a purely linear Hall voltage is found, which is modulated by UCF for lower temperatures. The inset shows the Hall slope as determined from linear fitting of the asymmetric component. It increases for lower temperatures due to the reduction in the carrier concentration for low temperatures, as shown in (g).

voltage VT is offset by a few microvolts from zero, which is attributed to the nonideal contact geometry of the Hall contacts on the nanowire, namely that the Hall contacts are wider than they are separated apart WH > dH. The offset has to be attributed to some remaining longitudinal contributions, which can also be seen by the decrease of RT for increasing gate voltage, as shown in Figure 2a.1 The Hall voltage VH must therefore be calculated from the transversal voltage drop VT by forming the asymmetrical component of the signal VH(B) ≡ VTAsym(B) =

1 (VT(B) − VT( −B)) 2

nH =

(3)

In Figures 2d and 2e the determined charge carrier concentration nH and the charge mobility μ = σ3d/nHe are plotted. The carrier concentration clearly depends on the gate voltage and is of order ∼5 × 1017 cm−3, which is slightly lower than found in previous publications using field-effect measurements at room temperature.2,3 As the carrier concentration only slightly depends on the temperature due to the strong electron accumulation caused by the surface states (see below), we attribute the discrepancy to the known overestimations of the field-effect measurements due to the charging of interface trap states, as was shown in earlier publications on the field effect and the Hall effect.5,7 It is however still uncertain how top and bottom parts of the nanowire are affected by the asymmetrically coupled backgate in this measurement configuration. The calculated carrier concentration must therefore be considered as a mean value for the whole nanowire. For the mobility, we find values of order ∼2000 cm2/(V s), which is higher than found previously in room-temperature experiments and can be explained by the reduction in scattering processes at these low temperatures. Figure 3 shows magnetoresistance traces at different temperatures of the longitudinal and the transversal resistance

(1)

By linear fitting of VH the Hall slope dR H 1 dVH = dB ISD dB

dH 2 1 dB 3 3 tS 2 + 2rCtS e dRH

(2)

can be determined, which is plotted in Figure 2c for varying gate voltage, next to the nanowire conductivity σ3d. Here, the opposite correlation is obvious, namely that the increase in the nanowire conductivity is accompanied by a decrease in the Hall slope. This is a consequence of the inverse relation between the charge carrier concentration nH and the Hall slope, which we calculate based on the model of Blömers et al.7 D


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Figure 4. (a, b) Asymmetrical components of the transversal magnetoresistance of sample B, measured for different angles γ between nanowire axis and magnetic field direction for an elevated temperature and for lowest temperature, respectively. At high temperature, the signal is nearly linear while at lowest temperatures, the influence of UCF is clearly visible. The insets show the determined Hall slopes from linear fitting of the asymmetrical components. Their course can be well described by the sinusoidal dependence given in eq 4, which is fitted as black solid line onto the data.

for both samples in a perpendicularly aligned magnetic field. Here, the longitudinal resistances shown in Figures 3a and 3c are clearly symmetric around B = 0 T, fulfilling the Onsager relation for a two-point measurement. For both samples a parabolic background is observed, which is modulated by reproducible fluctuations appearing at lower temperatures. These universal conductance fluctuations (UCF) are a wellknown effect found in nanowires in low-temperature magnetotransport measurements. They are more pronounced for sample B due to the smaller separation of the contacts as compared to sample A.4,13,31 They are caused by electron interference in loops with randomly varying area, which are formed by the electrons when they phase coherently diffuse through the nanowire and elastically scatter at defect sites between source and drain contact.11,12 Within these loops, magnetic flux is enclosed which modulates the electron interference and results in the observed fluctuation pattern.4 In addition, both signals show signatures of weak localization, namely a largely increased resistance around zero magnetic field. It disappears for increasing magnetic field due to breaking of the time-reversal symmetry of the electrons localized in scattering loops. We did not observe signatures of weak antilocalization, which we attribute to an insufficient radial electrical field in the InAs shell.2 For the transversal resistance shown in Figures 3b and 3d, again a clear asymmetry around B = 0 T is found for both samples, which we attribute to a voltage buildup caused by the Hall effect. For sample A, only minor changes in the signal are observed for lower temperatures, but the Hall slope increases slightly, as seen in the inset of Figure 3b. This can be related to a small reduction in the charge carrier concentration nH at lower temperatures, as seen in Figure 3e. For sample B, the change in the transversal resistance RT is more drastic at different temperatures. At elevated temperatures, the transversal resistance is asymmetric around B = 0 T and consists of a combination of a parabolic component, such

as for the longitudinal direction shown in Figure 3c, and of a linear component caused by the Hall voltage buildup. The latter can be seen by forming the asymmetric component VH(B) = VAsym (B) based on eq 1. It is plotted in Figure 3f and clearly T shows the linear Hall voltage over the full magnetic field range. For low temperatures, sample B shows strong UCF both in the longitudinal and in the transversal direction, which modulate the magnetoresistance. The UCF are superimposed on the linear Hall voltage, as can be seen in the asymmetric component of the signal shown in Figure 3f, which is nearly linear over the full magnetic field range but fluctuates around a mean value. This complicates the linear fit to determine the Hall slope, as it becomes dependent on the magnetic field range used for fitting. Here, we have always considered the maximum field range available and accounted for the fluctuation by a larger error. The results of the fits are shown in the inset of Figure 3f and clearly show the increase in the Hall slope for lower temperatures, which allows the calculation of the carrier concentration of sample B, plotted in Figure 3g. It is slightly lower than for sample A, but of same order, showing the consistency of this method to characterize the nanowires. The most obvious difference between the measurements of sample A with the long contact separation and sample B with the short contact separation is the different correlation between the transversal resistance RT and the longitudinal resistance RL. For sample A a mostly classical behavior is found, namely that UCF features are observed on top of a parabolic background for RL while a nearly linear Hall voltage is measured for RT. For sample B, however, there is strong correlation between RL and RT, namely that the UCF features found in the transversal resistance are partially correlated to the UCF features found in the longitudinal direction. Here, larger minima and maxima of the fluctuation pattern are found for both signals at the same position in magnetic field. This occurrence is a strong indication that the Hall contacts effectively probe the nanowire in the longitudinal direction in terms of a nonlocal measureE


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Figure 5. (a) Magnetoconductance oscillations with h/e periodicity of sample B measured over the source−drain contacts in a magnetic field aligned parallel to the nanowire axis (see illustration). (b) Corresponding Fourier transformation of the oscillations. The two black lines mark the two extremal frequencies, if the electrons would orbit around the innermost or outermost perimeter of the InAs shell. (c) Analogous magnetoconductance measurement as in (a), this time measured across the Hall contacts while the source−drain leads were left floating (see illustration). Again, an h/e periodic oscillations can be observed. (d) Corresponding Fourier transformation of (c), showing the same mean frequency as in (b), only slightly shifted to higher frequencies.

ment.32−34 As the contacts cover nearly a third of the distance between source and drain lead and are 3 times as wide as they are separated from another WH/dH = 3, they probe larger segments of the nanowire compared to an ideal Hall contact in a Hall bar geometry, which should be ideally point-like. The phase coherence length in nanowires at lowest temperatures is typically several tens of nanometers long, which means that the scattering loops next to and between the Hall contacts are also contributing to the signal.3,13,31 As they are also responsible for the UCF in the longitudinal direction, this explains the correlation of the main UCF features between the two signals. As a final characterization method and further proof that the asymmetry measured in the transversal resistance is the Hall effect, we have measured sample B at different angles between nanowire axis and magnetic field direction. Figures 4a and 4b show the asymmetrical component of the transversal resistance of sample B, measured at magnetic field directions nearly parallel to the nanowire axis to fully perpendicular, recorded at an elevated temperature of 50 K as well as at lowest temperature of 600 mK. In Figure 4a, the measurement at an elevated temperature is shown, where the influence of the UCF is suppressed by the high temperature. The asymmetrical component is clearly linear, with some modulation by electrical noise, and changes its slope for the different magnetic field alignments. For nearly parallel orientation γ < 10°, the slope is almost zero as here the electrons propagate parallel to the magnetic field and the Lorentz force does not separate the charge. The slope is maximal for the perpendicular field orientation, as expected for the Hall effect. The Hall slopes determined from linear fitting of the data are plotted versus tilt angle γ in the inset of Figure 4a. Their course of progression can be fitted by the equation

d R H (γ ) dH 2 1 = sin(γ ) 2 dB 3 3 tS + 2rCtS en

(4)

which accounts for the misalignment between magnetic field and direction of propagation of the charge carriers. As can be seen by the fit drawn as solid black line, the Hall slopes at varying tilt angle are described well by eq 4. From the fit, the charge carrier concentration can be extracted and is found to be n = 5.2(10) × 1017 cm−3, which is in excellent agreement with the value found with the temperature measurement shown in Figure 3g, proving the consistency of the experiment. It must be noted that eqs 3 and 4 consider the charge separation only on the upper part of the nanowire, while the inclined sidewalls are at equipotential due to the Hall contacts. It is however possible that compensating currents can flow on the bottom side of the nanowire, in which case dH in eqs 3 and 4 needs to be replaced by an effective separation given by deff = 5dH(rC + tS)/(dH + 3(rC + tS)) .7 If these currents are considered here, the charge carrier concentration would by about 40% higher. For the lower temperature shown in Figure 4b, the UCF complicate the linear fitting to determine the Hall slope. It is plotted in the inset of the figure and also shows an increase for larger tilt angles, but with a larger spread in values. The UCF amplitudes become maximal at perpendicular field orientation as a maximum of magnetic flux is enclosed within the scattering loops formed by the electrons while propagating through the InAs shell.4 The data can still be fitted by eq 4, as shown by the black solid line in the figure. Here, we deduce a carrier concentration of n = 3.0(12) × 1017 cm−3 from the sine fit, in agreement with the earlier measurement shown in Figure 3g. Finally, we present measurements of flux periodic magnetoconductance oscillations of Aharonov−Bohm type, measured on the GaAs/InAs core/shell nanowire of sample B.23 These oscillations have a period in magnetic field ΔB, which is related F


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Nano Letters to the magnetic flux quantum Φ0 ≡ h/e = ΔBANW, when a magnetic field aligned in parallel with the nanowire axis is penetrating the nanowire cross section ANW. We have presented measurements of this effect in recent publications, but so far only between contacts at separated positions along the nanowire.2−4,22 The oscillations are a consequence of the formation of angular momentum states, which are the solution of the Schrödinger equation for electrons in the InAs shell.26,27 Here, we make use of the laterally aligned Hall contacts, which only cover two of the six sidewalls of the InAs shell and hence resemble a typical measurement geometry of a planar ring, often used to analyze the Aharonov−Bohm effect.24 The difference to former measurements is that here it is possible that the electron wave function leaks into the contacts before a full orbit around the GaAs core has been accomplished, which would effectively open up the ring and suppress the Aharonov− Bohm effect. In Figure 5a, a magnetoconductance measurement of the Aharonov−Bohm-type oscillations of sample B at low temperature is shown, where only the source and the drain lead were contacted while the Hall contacts were left floating. The nanowire was biased with a voltage of VSD = 25 μV, and the drain current was recorded by an I/V converter. We observe typical h/e periodic oscillations, which mean frequency agrees well with the expected frequencies for an electron enclosing the magnetic flux while either orbiting on the innermost or outermost perimeter of the InAs shell, as shown by the black solid lines in the Fourier transformation in Figure 5b. In Figure 5c, we present the analogous magnetoconductance measurement, this time measured across the Hall contacts while the source−drain leads where left floating. Again, we observe a flux periodic oscillation with h/e periodicity. From the Fourier transformation of the measurement shown in Figure 5d, we find that the oscillations are well described by an electron orbiting around the GaAs core in the InAs shell. However, the frequency distribution is slightly shifted to higher frequencies compared to the measurement across the source−drain leads. Peak analysis showed that for the common setup using source− drain leads the oscillation frequency was f SD = 7.6 ± 2.0 T−1 (± labeling the 1σ range), whereas f Hall = 8.2 ± 4.2 T−1 was found for the measurement over the Hall leads. This can be translated to an orbit at slightly larger radius and might be related to the electron wave function partially leaking into the Hall contacts, therefore effectively increasing the ring size. However, additional measurements are necessary to confirm this assumption. In conclusion, we have shown that Hall effect measurements are possible on semiconductor nanowires, even at lowest temperatures. The effects of temperature, gate voltage, and varying tilt angle between magnetic field and nanowire axis on the Hall voltage buildup are clearly resolvable and allow a precise characterization of the nanowire in terms of carrier concentration as well as carrier mobility. However, it was found that phase coherent effects such as UCF modulate the signal at low temperatures due to the large phase coherence lengths in the nanowire and the nonideal Hall contact dimensions, which are still relatively large compared to the nanowire dimensions. Phase coherence affects the otherwise classical Hall effect, as segments of the nanowire next to the Hall contacts contribute to the signal measured at low temperature. In addition, it was shown that the magnetic flux enclosure in the GaAs/InAs core/ shell nanowire, showing Aharonov−Bohm-type oscillations with h/e periodicity, can be measured via different contact pairs located on the nanowire. This proves that the observation

of Aharonov−Bohm-type oscillations in a doubly connected system such as a nanotube are nearly independent of the contact geometry. GaAs/InAs core/shell nanowires are hence directly comparable to planar quantum ring structures analyzed so far.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (F.H.). *E-mail: [email protected] (T.S.). ORCID

Fabian Haas: 0000-0003-1726-5921 Author Contributions

F.H. and P.Z. contributed equally to this work. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Stefan Trellenkamp for electron beam writing, Christoph Krause for nanowire growth, Herbert Kertz for technical assistance with the cryostats, and Holger Neuhauß for support with the electronics.

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REFERENCES

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