Quantum Interference Effects

• Quantum interference effects are physical phenomena where coherent superpositions of quantum amplitudes cause observable changes in transport and scattering properties.
• They underpin phenomena such as universal conductance fluctuations, magnetic field correlations, and enhanced transport via Andreev reflection in mesoscopic conductors.
• These effects critically influence the design of quantum devices by enabling precise control over phase coherence in superconducting and semiconductor hybrid systems.

Quantum interference effects constitute a class of physical phenomena in which coherent superposition of quantum amplitudes for different trajectories, pathways, or histories leads to observable consequences in transport, scattering, and response properties of quantum systems. These effects are fundamentally rooted in the phase coherence of quantum mechanical wavefunctions and manifest in a broad range of condensed matter, mesoscopic, optical, and atomic systems. A paradigmatic context is phase-coherent electron transport in mesoscopic conductors, where quantum interference yields phenomena such as universal conductance fluctuations (UCF), conductance quantization, and Andreev-reflection-induced modifications in hybrid superconducting structures.

1. Universal Conductance Fluctuations in Mesoscopic Systems

In weakly disordered, phase-coherent one-dimensional conductors, such as InAs semiconductor nanowires, quantum interference generates aperiodic but reproducible fluctuations in the conductance as a function of external parameters—magnetic field $B$, gate voltage $V_g$, and bias voltage $V$. These UCF arise from the interference of partial electron waves traversing different disordered paths between contacts. For a nanowire segmented into $N_\phi = L / L_\phi$ uncorrelated phase-coherent regions (with $L$ the length and $L_\phi$ the phase coherence length), the root-mean-square amplitude of the conductance fluctuations is given by

$$\mathrm{rms}[G] \sim \frac{e^2}{h} \left(\frac{L_\phi}{L}\right)^{3/2}. \tag{1}$$

This scaling captures the reduction of coherence-induced fluctuations as the conductor length increases relative to $L_\phi$ and agrees quantitatively with experiments in nanowires strongly coupled to superconducting electrodes, confirming the identification of UCF as a key quantum interference haLLMark (0712.4298).

2. Magnetic Field Correlations and Phase Coherence Length Extraction

A central tool for analyzing UCF is the autocorrelation function

$$F(\Delta B) = \langle G(B) G(B+\Delta B) \rangle - \langle G(B) \rangle^2, \tag{2}$$

for lag $\Delta B$ in magnetic field. The correlation field $B_c$, defined by the half-width at half-maximum of $F(\Delta B)$, is linked to microscopic sample parameters: $B_c \simeq 0.42 \frac{\Phi_0}{w L_\phi}, \tag{3}$ where $\Phi_0 = h/e$ is the flux quantum and $w$ the nanowire width. Experimentally, $w \approx 80\,\text{nm}$ and $B_c \approx 0.2\,\text{T}$ give $L_\phi \approx 100\,\text{nm}$, matching theoretical expectations for mesoscopic InAs nanowires. This approach allows precise determination of intrinsic phase-breaking scales, crucial for understanding decoherence and electron-electron interaction effects in low-dimensional conductors (0712.4298).

3. Dependence on Gate Voltage, Bias, and Superconducting Proximity

Quantum interference patterns are sensitive to external gate voltage $V_g$, which modulates the chemical potential and locally alters electron trajectories and impurity configurations, resulting in a new realization of interference-induced conductance fluctuations. Increasing the source-drain bias suppresses the amplitude of the fluctuations: $$\mathrm{rms}[\delta G(V)] = \langle |\delta G(V)| \rangle,$$ with a pronounced drop in amplitude when $V$ exceeds the superconducting energy gap $V_\mathrm{gap} = 2\Delta/e$. This suppression signals the crossover from coherent Andreev-enhanced transport to normal quasi-particle-dominated conduction as phase coherence is lost for electrons with energies beyond the superconducting gap (0712.4298).

4. Andreev Reflection and Enhancement of Interference Amplitudes

When the nanowire is contacted by superconducting electrodes, Andreev reflection—where an electron is retro-reflected as a phase-coherent hole—effectively doubles the charge transport per coherent event, enhancing interference phenomena. For a single phase-coherent segment at the interface, the enhancement factor is $\alpha \simeq 2.08$. For $N_\phi$ uncorrelated segments, the overall enhancement of the fluctuation amplitude is

$$\gamma = \sqrt{1 + \frac{2(\alpha - 1)}{N_\phi}}, \tag{5}$$

which for the studied nanowires gives $\gamma \approx 1.59$, closely matching the measured value ($\approx 1.6$) for biases below $V_\mathrm{gap}$. This is unambiguous experimental evidence for the direct role of phase-coherent Andreev processes in boosting mesoscopic quantum interference effects (0712.4298).

5. Temperature, Dephasing, and Quantum-Coherent to Classical Crossover

Thermal fluctuations act as dephasing mechanisms, diminishing phase coherence and thus UCF. The characteristic scale is the Thouless temperature $T_\mathrm{Th}$, related by $E_c = \hbar D / (2\pi L^2)$, where $D$ is the diffusion constant. For temperatures $T \gg T_\mathrm{Th}$ (e.g., $T = 4.2\,\text{K}$ and $T_\mathrm{Th} \sim 1.2\,\text{K}$ in these nanowires), quantum interference contributions are suppressed, and conductance becomes smooth with respect to $B$ and $V_g$ (0712.4298).

Remarkably, in this thermally decohered regime, anomalous conductance quantization emerges with steps of $e^2/h$ (rather than the common $2e^2/h$ from spin-degenerate conductance channels), evidencing a transition to quantum point contact-like transport possibly reflecting lifted spin degeneracy or spontaneous spin polarization in quasi-one-dimensional confinement.

Temperature	UCF Amplitude	Conductance Behavior
$T < T_\mathrm{Th}$	Large ($\sim e^2/h$)	Fluctuations (UCF)
$T \gg T_\mathrm{Th}$, $4.2\,\text{K}$	Suppressed/vanishing	Quantization ($e^2/h$ steps)

6. Theoretical and Experimental Convergence

Quantitative agreement between theory and experiment is observed on several fronts:

• UCF amplitude magnitude and scaling with $L_\phi/L$ as in Eq. (1).
• Extraction of $L_\phi$ from the autocorrelation function and its agreement with direct measurements.
• Suppression of UCF amplitude with increased bias/temperature and its abrupt drop at the superconducting gap.
• Enhancement of UCF amplitude in the superconducting state by a factor consistent with Andreev reflection theory.
• Emergence of unconventional $e^2/h$ conductance quantization at high temperature, indicative of a new transport regime (0712.4298).

7. Implications and Context

These findings in InAs nanowires bridge fundamental mesoscopic physics and potential quantum device applications. The ability to control and characterize quantum interference via magnetic field, electrostatic gating, temperature, and superconductivity is central to the development of coherent quantum electronics. The demonstrated agreement between advanced theories of quantum coherence, such as those for UCF and Andreev reflection in one-dimensional disordered conductors, and experimental results in hybrid superconductor–semiconductor devices highlights the feasibility of engineering phase-coherent quantum functionalities at the nanoscale, with implications ranging from quantum information processing to the realization of Majorana modes in proximitized nanowires.

In summary, quantum interference effects in InAs nanowires coupled to superconducting electrodes manifest as UCF, bias and temperature-dependent fluctuation amplitudes, Andreev-enhanced coherent transport, and conductance quantization, with all features in precise agreement with theoretical predictions for weakly disordered one-dimensional mesoscopic systems (0712.4298).