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Electric and Magnetic Field Control of Tunneling Between Coupled Nanowires: A Theoretical and Experimental Study


Core Concepts
The application of electric and magnetic fields can be used to precisely control and manipulate the tunneling behavior of electrons between coupled nanowires, leading to distinct conductance features and potential applications in quantum simulation and nanoelectronics.
Abstract

Bibliographic Information

Anand, S., Ramachandran, R., Eom, K., Lee, K., Yang, D., Yu, M., Biswas, S., Nethwewala, A., Eom, C., Carlson, E.W., Irvin, P., & Levy, J. (2024). Electric and Magnetic Field-dependent Tunneling between Coupled Nanowires. arXiv. https://arxiv.org/abs/2410.01936v1

Research Objective

This study investigates the impact of electric and magnetic fields on the tunneling behavior of electrons between coupled nanowires, both theoretically and experimentally.

Methodology

The researchers developed a theoretical model based on the Wentzel–Kramers–Brillouin (WKB) approximation to calculate the tunneling rate between two coupled nanowires subject to a transverse electric field and an out-of-plane magnetic field. They then compared their theoretical predictions with experimental measurements conducted on coupled nanowires fabricated on a LaAlO3/SrTiO3 (LAO/STO) interface.

Key Findings

  • A critical voltage threshold exists, dependent on the applied magnetic field, above which significant electron tunneling occurs between the nanowires.
  • The interplay of electric and magnetic fields sculpts the interwire potential barrier, leading to characteristic peaks and valleys in the transverse differential conductance.
  • A local minimum in conductance is observed at zero magnetic field, consistent with experimental observations.
  • Increasing the potential barrier height leads to the emergence of an insulating region in the conductance map at low electric fields.
  • The model predicts sharp changes in conductance corresponding to magnetic depopulation events when energy subbands within the nanowires cross the chemical potential.

Main Conclusions

The study demonstrates the ability to precisely control electron tunneling between coupled nanowires using external electric and magnetic fields. The theoretical model successfully captures key experimental trends, highlighting the crucial role of the field-dependent interwire potential barrier in governing transport properties.

Significance

This research provides valuable insights into the fundamental physics of coupled low-dimensional electron systems. The ability to manipulate electron tunneling in nanowires has significant implications for the development of novel nanoelectronic devices, including quantum simulators and advanced transistors.

Limitations and Future Research

The current study focuses on a simplified two-wire system. Future research could explore the complex interplay of electron-electron interactions and disorder effects in larger nanowire arrays. Additionally, investigating the impact of varying temperature and different material systems could further enrich our understanding of these systems.

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Deeper Inquiries

How would the presence of strong electron-electron interactions or disorder within the nanowires affect the observed tunneling behavior and conductance features?

The presence of strong electron-electron interactions or disorder within the nanowires can significantly alter the observed tunneling behavior and conductance features compared to the non-interacting, clean limit considered in the paper. Here's how: Strong Electron-Electron Interactions: Luttinger Liquid Behavior: In one-dimensional systems like nanowires, strong electron-electron interactions can lead to the emergence of Luttinger liquid behavior. Unlike Fermi liquids, where electrons behave independently, Luttinger liquids exhibit collective excitations. This can result in: Suppression of tunneling: Tunneling into a Luttinger liquid is suppressed at low energies due to the formation of a "Coulomb blockade" effect. Power-law dependencies: Conductance as a function of temperature, voltage, or magnetic field can exhibit power-law dependencies instead of the step-like features predicted by the non-interacting model. Formation of exotic phases: Strong interactions can give rise to exotic phases like the Wigner crystal, where electrons arrange themselves in a periodic lattice to minimize their electrostatic energy. Such phases can dramatically impact the tunneling behavior. Disorder: Localization: Disorder can lead to Anderson localization, where electron wave functions become spatially localized, inhibiting their ability to tunnel. This can result in: Increased resistance: The overall resistance of the nanowires will increase, and the conductance will be suppressed. Variable range hopping: At low temperatures, transport might be dominated by variable range hopping, where electrons tunnel between localized states with different energies. Modification of conductance features: The sharp features in the conductance maps, such as those arising from magnetic depopulation, can be smeared out or even disappear entirely due to disorder-induced broadening of energy levels. Combined Effects: The interplay of strong electron-electron interactions and disorder can lead to even richer physics, such as the formation of a Bose glass phase, where localized Cooper pairs can exhibit superfluidity. In summary, the presence of strong electron-electron interactions or disorder can significantly modify the tunneling behavior and conductance features in coupled nanowires. Understanding these effects is crucial for accurately interpreting experimental results and harnessing the potential of these systems for quantum technologies.

Could the manipulation of tunneling in coupled nanowires using electric and magnetic fields be exploited for the development of novel logic gates or memory elements in future quantum computers?

Yes, the manipulation of tunneling in coupled nanowires using electric and magnetic fields holds significant potential for developing novel logic gates and memory elements in future quantum computers. Here are some possibilities: Logic Gates: Quantum Dot Qubits: Coupled nanowires can be used to define quantum dots, which can serve as qubits – the basic unit of information in a quantum computer. By controlling the tunneling between adjacent dots using electric and magnetic fields, one can implement single-qubit and two-qubit gates, essential for quantum computation. Tunneling-based Coupling: The strength of the inter-wire tunneling can be tuned to control the interaction between qubits. This allows for the implementation of entangling gates, crucial for generating entangled states that underpin the power of quantum computing. Topological Protection: Certain materials, like topological insulators, can host edge states that are robust against disorder. Combining coupled nanowires with topological materials could lead to topologically protected qubits, which are less susceptible to errors. Memory Elements: Charge Qubits: The presence or absence of an extra electron on a nanowire segment can represent a bit of information. By controlling the tunneling barriers, one can trap or release electrons, effectively writing and reading information. Spin Qubits: The spin of an electron confined in a quantum dot can also serve as a qubit. Magnetic fields can be used to manipulate the spin state, enabling the storage and retrieval of quantum information. Advantages of Coupled Nanowires: Scalability: Nanowires offer a promising platform for building scalable quantum devices due to their small size and potential for integration with existing semiconductor technologies. Tunability: The ability to precisely control tunneling using electric and magnetic fields provides a high degree of tunability, essential for building robust and controllable qubits. Versatility: Coupled nanowires can be fabricated from a variety of materials, allowing for the exploration of different qubit platforms and functionalities. Challenges: Coherence: Maintaining the coherence of qubits is crucial for quantum computation. This requires minimizing the effects of noise and decoherence, which can arise from interactions with the environment. Control Fidelity: Implementing high-fidelity control over tunneling and qubit states is essential for accurate quantum operations. In conclusion, the manipulation of tunneling in coupled nanowires using electric and magnetic fields offers a promising avenue for developing novel logic gates and memory elements for future quantum computers. While challenges remain in terms of coherence and control fidelity, the scalability, tunability, and versatility of nanowire-based platforms make them attractive candidates for advancing quantum technologies.

If we consider the coupled nanowires as a single unit, how might its behavior resemble that of a single electron transistor, and what new possibilities for control and manipulation might this analogy offer?

Considering the coupled nanowires as a single unit reveals intriguing similarities to a single-electron transistor (SET), opening up new possibilities for control and manipulation. Analogies with a Single-Electron Transistor: Source and Drain: The two nanowires act as the source and drain of the SET, with electrons tunneling between them. Island: The region between the nanowires, where the interwire potential barrier is located, serves as the "island" of the SET. Gate Electrode: The transverse voltage (VT) applied between the nanowires acts as the gate voltage in an SET, modulating the potential barrier height and controlling the tunneling current. SET-like Behavior: Coulomb Blockade: At low temperatures and for small VT, the tunneling of electrons between the nanowires can be suppressed due to the Coulomb blockade effect. This occurs when the electrostatic energy required to add an extra electron to the "island" (interwire region) is larger than the thermal energy. Conductance Oscillations: As VT is increased, the conductance through the coupled nanowires can exhibit periodic oscillations, similar to the Coulomb oscillations observed in SETs. These oscillations arise from the discrete nature of charge and the quantized energy levels in the "island." New Possibilities for Control and Manipulation: Sensitive Charge Detection: The coupled nanowire system, operating in the Coulomb blockade regime, can be extremely sensitive to changes in the local electric field. This sensitivity can be exploited for charge sensing applications, such as detecting single electrons or measuring weak electrical signals. Quantum Information Processing: The analogy with SETs suggests that coupled nanowires could be used for more complex quantum information processing tasks. For example, by coupling multiple nanowire pairs, one could create quantum circuits with multiple "islands" and implement more sophisticated quantum operations. Exploring Novel Quantum States: The tunability of the coupled nanowire system allows for exploring novel quantum states of matter that emerge in low-dimensional systems. By controlling the electron density, interwire coupling, and magnetic field, one can potentially access exotic phases like Luttinger liquids or Wigner crystals. Challenges and Opportunities: Fabrication: Creating coupled nanowire systems with the required precision and control over interwire coupling remains a challenge. Coherence: Maintaining coherence in these systems, especially at low temperatures, is crucial for exploiting their quantum properties. In conclusion, viewing coupled nanowires through the lens of a single-electron transistor provides valuable insights into their behavior and opens up exciting possibilities for control and manipulation. This analogy could pave the way for developing novel quantum devices for sensing, information processing, and exploring fundamental physics in low-dimensional systems.
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