Interplay between Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations in phase-pure GaAs/InAs core/shell nanowires of different lengths

Technical Summary: Interplay between Aharonov–Bohm and Altshuler–Aronov–Spivak oscillations in phase-pure GaAs/InAs core/shell nanowires of different lengths

Problem Statement
Semiconductor nanowires with tubular conducting shells, specifically GaAs/InAs core/shell structures, offer a promising platform for superconducting quantum devices due to their ability to confine charge carriers in a tubular geometry. These systems exhibit quantum interference phenomena under axial magnetic fields, manifesting as Aharonov–Bohm (AB) oscillations ($h/e$-periodic) and Altshuler–Aronov–Spivak (AAS) oscillations ($h/2e$-periodic). While AB oscillations arise from the interference of non-time-reversed paths (angular momentum states encircling the insulating core), AAS oscillations result from the interference of time-reversed paths.

A critical challenge in utilizing these systems is understanding how sample dimensions and the transport regime influence the interplay between these effects. Previous studies have established that averaging effects, dependent on sample size and disorder, govern the visibility of these oscillations. While higher harmonic oscillations ($h/3e$, $h/4e$) have been observed in planar rings and topological insulator nanowires due to long phase coherence lengths, their occurrence and phase rigidity in tubular semiconductor nanowires, particularly in the quasi-ballistic regime with few scattering centers, remained unexplored. The specific mechanism governing the phase rigidity of higher harmonics in this geometry was also unclear.

Methodology
The authors conducted a systematic experimental and theoretical study on phase-pure zinc-blende GaAs/InAs core/shell nanowires grown via molecular beam epitaxy (MBE).

• Sample Fabrication: Nanowires with an average GaAs core radius of 65 nm and an InAs shell thickness of 30 nm were transferred onto global backgate substrates. Devices were fabricated with varying inner contact separation lengths ($L_c$) ranging from 300 nm to 2 µm.
• Experimental Measurements: Magnetoconductance measurements were performed at a base temperature of 1.3 K under axial magnetic fields ($\pm 2$ T). The conductance was measured as a function of magnetic field and gate voltage ($V_g$) to probe the phase coherence and averaging effects.
• Data Analysis: The researchers analyzed the oscillations using Fast Fourier Transform (FFT) to identify periodicities ($h/e$, $h/2e$, $h/3e$, $h/4e$). They quantified "phase rigidity" by calculating the average oscillation amplitude and its standard deviation over the gate voltage range. A rigid phase is indicated by a stable amplitude and low standard deviation, whereas a non-rigid phase shows random shifts and high standard deviation.
• Simulations: Tight-binding quantum transport simulations were performed using the KWANT software package. The models simulated nanowires of lengths 0.6, 2, and 4 µm with Gaussian disorder, Rashba spin-orbit coupling, and Zeeman splitting, varying the chemical potential to mimic gate voltage changes.

Key Results

1. Length-Dependent Averaging: As the contact separation length ($L_c$) increased, the amplitude of $h/e$-periodic AB oscillations decreased due to averaging effects over non-phase-rigid segments. Conversely, the relative contribution of phase-rigid AAS oscillations ($h/2e$) increased with length.
2. Phase Rigidity of AAS Oscillations: The $h/2e$-periodic oscillations exhibited phase rigidity (stable amplitude and maximum at $B=0$) within a specific magnetic field range ($\approx \pm 0.4$ T). This rigidity was more pronounced in longer nanowires (2 µm) compared to shorter ones (600 nm), confirming that AAS effects are robust against ensemble averaging in these quasi-ballistic systems.
3. Observation of Higher Harmonics: The study reported the first observation of $h/3e$- and $h/4e$-periodic oscillations in tubular GaAs/InAs nanowires.
   • $h/3e$ Oscillations: These exhibited unexpected phase rigidity. The authors attribute this not to a distinct physical interference mechanism for $h/3e$, but to the "propagation" of phase rigidity from the underlying $h/2e$ AAS oscillations.
   • $h/4e$ Oscillations: These showed a robust phase-rigid region approximately half the width of the $h/2e$ region. This is interpreted as the second harmonic of the phase-rigid AAS effect, where time-reversed paths circumvent the tube twice, effectively encircling the flux four times.
4. Simulation Confirmation: Tight-binding simulations on wires with few scattering centers reproduced the experimental trends. They confirmed the reduction of AB amplitude with length, the enhancement of AAS contribution, and the emergence of phase rigidity in higher harmonics ($h/3e$, $h/4e$) for longer wires, supporting the hypothesis of quasi-ballistic transport.

Significance and Claims
The paper claims to provide a systematic understanding of how sample dimensions dictate the crossover between AB and AAS interference regimes in phase-pure GaAs/InAs nanowires. The primary significance lies in demonstrating that:

• Quasi-ballistic transport in these nanowires supports persistent AB oscillations and phase-rigid AAS oscillations despite the presence of only a few scattering centers.
• Higher harmonics ($h/3e$, $h/4e$) can be observed in tubular semiconductor nanowires, a phenomenon previously unreported for this specific geometry.
• Phase rigidity in higher harmonics (specifically $h/3e$) is not an independent effect but is derived from the phase rigidity of the fundamental AAS ($h/2e$) oscillations.

The authors conclude that these findings validate the potential of GaAs/InAs core/shell nanowires for future quantum information devices, as the observed interference effects remain robust and tunable via gate voltage and device geometry, even in the presence of limited disorder.