^{1}, S. Estévez Hernández

^{1}, C. Blömers

^{1}, T. Stoica

^{1}, R. Calarco

^{1}and Th. Schäpers

^{1,a)}

### Abstract

The low-temperature quantum transport of InN nanowires grown by plasma-assisted molecular beam epitaxy is investigated. Two sets of nanowires with diameters of 100 and 45 nm originating from two different growth runs are studied. Magnetic-field-dependent as well as gate-dependent measurements of universal conductance fluctuations are performed to gain information on the phase-coherence in the electron transport. By analyzing the correlation field and the average fluctuation amplitude a phase-coherence length of several hundred nanometers is extracted for both sets of nanowires at temperatures below 1 K. Conductance fluctuations are also observed when the Fermi wavelength is varied by applying a bias voltage to a back-gate. The results on the electron phase-coherence obtained from the gate-dependent measurements are consistent with the findings from the magnetic field dependent measurements. A considerable damping of the fluctuation amplitude by ensemble averaging is achieved by connecting nanowires in parallel. The suppression of the fluctuation amplitude is studied systematically by measuring samples with different numbers of nanowires. By utilizing the damping of the conductance fluctuations by connecting nanowires in parallel in combination with an averaging over the gate voltage, weak localizationeffects are resolved. For both sets of nanowires a clear evidence of the weak antilocalization is found, which indicates the presence of spin-orbit coupling. For the spin-orbit scattering length values in the order of 100 nm are extracted.

We are grateful to D. Grützmacher for fruitful discussions and comments to the manuscript. We thank K.-H. Deussen and H. Kertz for the support during the wire growth and during the measurements.

I. INTRODUCTION

II. EXPERIMENTAL

III. RESULTS AND DISCUSSION

A. Conductance fluctuations: Magnetic field

B. Conductance fluctuations: gate voltage

C. Localization effects

IV. CONCLUSIONS

### Key Topics

- Nanowires
- 46.0
- Magnetic fields
- 30.0
- Localization effects
- 16.0
- Magnetic field measurements
- 16.0
- Electric measurements
- 10.0

## Figures

(a) Scanning electron beam micrograph of sample B-6 with six InN wires connected in parallel and (b) detail of a contacted InN nanowire. (c) Schematic illustration of a contacted nanowire. The Si substrate used as a back-gate electrode is isolated from the nanowire by a 100 nm thick layer.

(a) Scanning electron beam micrograph of sample B-6 with six InN wires connected in parallel and (b) detail of a contacted InN nanowire. (c) Schematic illustration of a contacted nanowire. The Si substrate used as a back-gate electrode is isolated from the nanowire by a 100 nm thick layer.

(a) Conductance fluctuations in units of for a single wire (sample A-1) at various temperatures in the range from 0.8 to 30 K. (b) Corresponding measurements for a sample with eight wires connected in parallel (sample A-8). (c) Comparison of the conductance fluctuations of samples A-1 and A-8 at 0.8 K. The curve of sample A-8 was shifted by 0.03.

(a) Conductance fluctuations in units of for a single wire (sample A-1) at various temperatures in the range from 0.8 to 30 K. (b) Corresponding measurements for a sample with eight wires connected in parallel (sample A-8). (c) Comparison of the conductance fluctuations of samples A-1 and A-8 at 0.8 K. The curve of sample A-8 was shifted by 0.03.

(a) Normalized average amplitude of the conductance fluctuations as a function of temperature for sample A-1 (green dots) and sample A-8 (red triangle), respectively. Also shown are the average fluctuation amplitude calculated using Eq. (2) (open symbols), with determined from the correlation field. The full lines show the fitted exponential decrease in . (b) Correlation field as a function of temperature of sample A-1 and A-8, respectively. (c) Phase-coherence length extracted from . The dashed line corresponds to the thermal length .

(a) Normalized average amplitude of the conductance fluctuations as a function of temperature for sample A-1 (green dots) and sample A-8 (red triangle), respectively. Also shown are the average fluctuation amplitude calculated using Eq. (2) (open symbols), with determined from the correlation field. The full lines show the fitted exponential decrease in . (b) Correlation field as a function of temperature of sample A-1 and A-8, respectively. (c) Phase-coherence length extracted from . The dashed line corresponds to the thermal length .

Conductance fluctuations normalized to at various temperatures of 0.4, 3, 10, and 30 K for samples with different numbers of wires connected in parallel: (a) sample B-1, (b) B-6, (c) B-10, and (d) B-12. Color scale plot of the conductance fluctuations of sample B-10 as function of magnetic field and temperature. was determined by subtracting the slowly varying background conductance.

Conductance fluctuations normalized to at various temperatures of 0.4, 3, 10, and 30 K for samples with different numbers of wires connected in parallel: (a) sample B-1, (b) B-6, (c) B-10, and (d) B-12. Color scale plot of the conductance fluctuations of sample B-10 as function of magnetic field and temperature. was determined by subtracting the slowly varying background conductance.

(a) as a function of temperature for a single wire (sample B-1) as well as for six, ten, and 12 wires (samples B-6, B-10, and B-12) connected in parallel. The open symbols represent the calculated values for B-6 and B-10 using Eq. (2). The full lines show the fitted exponential decrease in . (b) as a function of for samples B-1, B-6, B-10, and B-12. The dashed line represents the thermal length . The inset shows the decrease in with increasing number of wires for below 1 K.

(a) as a function of temperature for a single wire (sample B-1) as well as for six, ten, and 12 wires (samples B-6, B-10, and B-12) connected in parallel. The open symbols represent the calculated values for B-6 and B-10 using Eq. (2). The full lines show the fitted exponential decrease in . (b) as a function of for samples B-1, B-6, B-10, and B-12. The dashed line represents the thermal length . The inset shows the decrease in with increasing number of wires for below 1 K.

Conductance of sample B-12 as a function of gate voltage for various temperatures.

Conductance of sample B-12 as a function of gate voltage for various temperatures.

(a) Normalized conductance fluctuations averaged over as a function of temperature for a single wire (sample B-1) as well as for six, ten, and 12 wires (samples B-6, B-10, and B-12) connected in parallel. The open symbols represent the calculations using Eq. (2). The full lines show the exponential decrease of . (b) Respective phase-coherence length as a function of temperature. The dashed line represents the thermal length .

(a) Normalized conductance fluctuations averaged over as a function of temperature for a single wire (sample B-1) as well as for six, ten, and 12 wires (samples B-6, B-10, and B-12) connected in parallel. The open symbols represent the calculations using Eq. (2). The full lines show the exponential decrease of . (b) Respective phase-coherence length as a function of temperature. The dashed line represents the thermal length .

(a) Magnetoconductance of sample A-8 at 0.8 K at a gate voltage of 0, 2, 4, 6, and 8 V, respectively. (b) Correction of the magnetoconductance of sample A-8 averaged over different gate voltages at 0.8 K, 1.0 K and 4.0 K, respectively. Here, the zero field conductance was subtracted from the total conductance.

(a) Magnetoconductance of sample A-8 at 0.8 K at a gate voltage of 0, 2, 4, 6, and 8 V, respectively. (b) Correction of the magnetoconductance of sample A-8 averaged over different gate voltages at 0.8 K, 1.0 K and 4.0 K, respectively. Here, the zero field conductance was subtracted from the total conductance.

(a) and (b) Magnetoconductance of samples B-6, B-10, and B-12 after subtracting the zero field conductance at a temperature of 2 K and at 30 K, respectively. (c) vs of sample B-6 after averaging over different gate voltages. The full line shows the fit to the experimental data. (d) in units of of the gate voltage dependent fluctuations as a function of .

(a) and (b) Magnetoconductance of samples B-6, B-10, and B-12 after subtracting the zero field conductance at a temperature of 2 K and at 30 K, respectively. (c) vs of sample B-6 after averaging over different gate voltages. The full line shows the fit to the experimental data. (d) in units of of the gate voltage dependent fluctuations as a function of .

## Tables

Sample dimensions and characteristic parameters: growth run, number of wires connected in parallel, average wire length , average wire diameter , total resistance at 1 K including the contact resistance.

Sample dimensions and characteristic parameters: growth run, number of wires connected in parallel, average wire length , average wire diameter , total resistance at 1 K including the contact resistance.

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