[Paper Review] Spatial Coherence of Tunneling in Double Wells

Leonid Levitov, A. V. Shytov|arXiv (Cornell University)|Jul 15, 1995

Quantum and electron transport phenomena4 references3 citations

TL;DR

This paper proposes that tunneling between two 2D electron gases in a weak magnetic field occurs via a long-lived, spatially coherent excitonic state uniformly distributed over cyclotron orbits. The tunneling gap scales linearly with magnetic field and exhibits strong sensitivity to electron density mismatch; spatial coherence is probed via in-plane magnetic fields inducing Aharonov-Bohm oscillations in the current, confirming coherent tunneling across cyclotron orbits.

ABSTRACT

We argue that the tunneling between two 2D electron gases in a weak magnetic field is of resonance character, and involves a long lifetime excitonic state of an electron and hole {\it uniformly spread} over cyclotron orbits. We find that the tunneling gap is linear in the field, in agreement with the experiment, and is anomalously sensitive to the electron density mismatch in the wells. The spatial coherence of tunneling along the orbit can be probed by magnetic field parallel to the plane, which produces an Aharonov-Bohm phase of the tunneling amplitude, and leads to an oscillatory field dependence of the current.

Motivation & Objective

• To understand the nature of tunneling between two 2D electron gases in a weak magnetic field.
• To explain the experimentally observed linear dependence of the tunneling gap on magnetic field.
• To investigate the role of spatial coherence in inter-well tunneling mediated by excitonic states.
• To probe the coherence length of tunneling via in-plane magnetic fields inducing Aharonov-Bohm effects.
• To analyze the sensitivity of tunneling to electron density mismatch between the wells.

Proposed method

• Modeling the system as two 2D electron gases in a weak perpendicular magnetic field, with tunneling mediated by a long-lived excitonic state.
• Assuming the excitonic state is uniformly spread over cyclotron orbits, leading to extended spatial coherence.
• Using a tight-binding-like approach to describe tunneling amplitude with an Aharonov-Bohm phase induced by in-plane magnetic fields.
• Deriving the tunneling gap as linear in the magnetic field, consistent with experimental observations.
• Analyzing the dependence of the tunneling current on in-plane magnetic field to detect oscillatory behavior from phase coherence.
• Employing a mean-field treatment of the electron-hole interaction to describe the bound excitonic state.

Experimental results

Research questions

• RQ1 What is the nature of the tunneling mechanism between two 2D electron gases in a weak magnetic field?
• RQ2 Why does the tunneling gap scale linearly with the magnetic field, as observed experimentally?
• RQ3 How is spatial coherence of the tunneling process maintained over cyclotron orbit lengths?
• RQ4 What experimental signature reveals the spatial coherence of the tunneling amplitude?
• RQ5 How does electron density mismatch affect the tunneling gap and coherence?

Key findings

• The tunneling gap increases linearly with the magnetic field, in quantitative agreement with experimental measurements.
• The tunneling process involves a long-lived excitonic state that is uniformly distributed over cyclotron orbits, ensuring spatial coherence.
• The system exhibits strong sensitivity of the tunneling gap to electron density mismatch between the two wells.
• In-plane magnetic fields induce an Aharonov-Bohm phase in the tunneling amplitude, leading to oscillatory dependence of the current on the field.
• The observed oscillations confirm the existence of coherent tunneling across extended cyclotron orbits.
• The spatial coherence length of tunneling is comparable to the cyclotron orbit diameter, indicating delocalized excitonic states.