Fractional quantum hall effect

Definition

The fractional quantum hall effect is a quantum phenomenon observed in two-dimensional electron systems under low temperatures and strong magnetic fields, where the Hall conductance takes on quantized values that are fractional multiples of fundamental constants. This effect reveals the existence of anyonic excitations and has profound implications for understanding strongly correlated many-body systems, particularly in the context of topological order.

5 Must Know Facts For Your Next Test

1. The fractional quantum hall effect was first observed in 1982 by physicist Robert Laughlin, who proposed a theoretical framework explaining the phenomenon through the concept of anyonic excitations.
2. In this effect, the Hall conductance can be expressed as \( u \frac{e^2}{h} \), where \( u \) represents a fractional filling factor, indicating that the system's properties depend on the electron interactions.
3. This phenomenon occurs at specific magnetic field strengths and electron densities, leading to various fractional states such as \( \frac{1}{3} \), \( \frac{5}{2} \), and higher fractions.
4. The fractional quantum hall effect is closely tied to condensed matter physics and has inspired advancements in quantum computing due to its topological characteristics.
5. It provides experimental evidence for theoretical predictions regarding non-abelian statistics, which have potential applications in fault-tolerant quantum computation.

Review Questions

• How does the fractional quantum hall effect differ from the integer quantum hall effect in terms of Hall conductance?
  • The main difference between the fractional quantum hall effect and the integer quantum hall effect lies in the quantization of Hall conductance. In the integer case, the conductance is quantized at integer multiples of \( \frac{e^2}{h} \), whereas in the fractional case, it is quantized at fractional values represented by \( u \frac{e^2}{h} \). This distinction indicates that the underlying physical mechanisms are different, with strong electron correlations playing a crucial role in the fractional regime.
• Discuss the significance of anyons in understanding the fractional quantum hall effect and their potential applications.
  • Anyons are crucial for understanding the fractional quantum hall effect because they provide a framework for describing the unique excitations that emerge in these systems. Unlike traditional fermions or bosons, anyons exhibit fractional statistics, which can lead to exotic behaviors and correlations. This has significant implications for potential applications in quantum computing, particularly in developing topological quantum computers that utilize anyonic braiding as a method for error correction.
• Evaluate how the discovery of the fractional quantum hall effect has influenced advancements in condensed matter physics and quantum technologies.
  • The discovery of the fractional quantum hall effect has significantly advanced our understanding of many-body systems and contributed to new theories in condensed matter physics. By revealing complex interactions among electrons and leading to concepts like topological order, it has opened avenues for exploring new states of matter. Furthermore, these insights have driven innovations in quantum technologies, particularly in quantum computation where harnessing non-abelian statistics from anyons offers promising routes for robust, fault-tolerant qubits, thus bridging theoretical physics with practical applications.

Related terms

Quantum Hall Effect: A phenomenon where the Hall conductance of a two-dimensional electron gas exhibits quantization at integer multiples of fundamental constants, occurring under strong magnetic fields and low temperatures.

Topological Order: A form of order in many-body systems that is not characterized by local order parameters, often associated with robust ground states and anyonic excitations.

Anyons: Exotic quasiparticles that arise in two-dimensional systems and can exhibit statistics that are neither fermionic nor bosonic, crucial for understanding the fractional quantum hall effect.