Related Experiment Video
Updated: Aug 3, 2025
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
9.7K
Quantum transports in two-dimensions with long range hopping
Si-Si Wang1,2,3, Kangkang Li4, Yi-Ming Dai1
1School of Physics and Materials Science, Guangzhou University, Guangzhou, 510006, China.
Scientific Reports
|April 8, 2023
Summary
Disorder in 2D systems with long-range hopping creates conducting channels. As disorder increases, quantum transport exhibits a hybrid phase, showing both localization and delocalization.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Materials Science
Background:
- Quantum transport in disordered systems is crucial for understanding material properties.
- Long-range hopping introduces unique quantum phenomena not seen in short-range models.
- Disorder effects can lead to metal-insulator transitions.
Purpose of the Study:
- To investigate the impact of disorder and shielding on quantum transport in 2D systems with all-to-all long-range hopping.
- To analyze the emergence of conducting channels and the nature of wave function localization.
- To characterize the phase transitions and transport properties under varying disorder strengths.
Main Methods:
- Theoretical investigation of a two-dimensional system with all-to-all long-range hopping.
- Analysis of quantum transport phenomena under varying degrees of disorder.
- Examination of wave function properties, including localization centers and fractal dimensions.
- Study of size scaling and conductance behavior to identify phase transitions.
Main Results:
- Weak disorder leads to perfect conducting channels, masking long-range hopping effects.
- Increased disorder breaks shielding, enhancing conductance fluctuations and enabling long-range hopping.
- Wave functions exhibit hybrid localization-delocalization, with multiple centers and fractal dimensions between 0 and 2.
- A marginal phase is identified, characterized by saturated conductance and a scaling function between metallic and insulating behaviors.
- An isolated, disorder-robust extended state emerges due to all-to-all coupling, showing efficient transport via quantum short-circuiting.
Conclusions:
- Disorder and shielding interplay significantly in 2D systems with long-range hopping.
- A novel marginal phase of quantum transport exists, distinct from typical metallic or insulating states.
- The unique properties of long-range hopping can lead to robust quantum transport phenomena, even in the presence of disorder.
More Related Videos
Related Concept Videos
03:06The Pauli Exclusion Principle
41.8K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
41.8K
01:18First Law: Particles in Two-dimensional Equilibrium
5.1K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
Newton's first law tells us about...
5.1K
02:45The Quantum-Mechanical Model of an Atom
42.6K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
42.6K
02:32The de Broglie Wavelength
26.0K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
26.0K
01:27¹H NMR: Long-Range Coupling
1.9K
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
1.9K
01:10First Law: Particles in One-dimensional Equilibrium
7.0K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
7.0K