Quantum Hall Effect Trivia Quiz

Explanation
Edwin Hall is the correct answer for the question "Who discovered the Hall effect?" The Hall effect is a phenomenon in physics that was discovered by Edwin Hall in 1879. He observed that when a magnetic field is applied perpendicular to the flow of an electric current in a conductor, a voltage difference is created across the conductor. This voltage difference is known as the Hall voltage and is proportional to the strength of the magnetic field and the current flowing through the conductor. Edwin Hall's discovery of this effect has been significant in understanding the behavior of electrons in materials and has led to various applications in fields like electronics and solid-state physics.

Explanation
The symbol σ represents Hall Conductance. Hall Conductance is a fundamental property in condensed matter physics that describes the relationship between the electric current and the applied magnetic field in a conducting material. It is a measure of the ease with which electric current flows perpendicular to the magnetic field.

Explanation
The correct answer is 2 because the Quantum Hall Effect is observed in a two-dimensional electron system. In this phenomenon, when a magnetic field is applied perpendicular to the plane of the system, the electrons experience a Lorentz force that causes them to move to one side of the system, creating a voltage difference across the material. This effect is only observed in systems with two dimensions, such as a thin semiconductor layer or a graphene sheet. In three-dimensional systems, the electrons are free to move in all directions, and the Hall effect is not as pronounced.

Explanation
The symbol "e" in this formula represents the elementary charge. The elementary charge is the electric charge carried by a single electron or proton. It is a fundamental constant in physics and is denoted by the symbol "e".

Explanation
The given value, 6.62607015×10−34, represents the Planck constant, denoted by "h".

Explanation
The pre-factor value is what determines whether the Quantum Hall effect is IQHE (Integer Quantum Hall Effect) or FQHE (Fractional Quantum Hall Effect). In the IQHE, the pre-factor value is an integer, while in the FQHE, the pre-factor value is a fraction. This distinction is crucial in understanding the behavior of electrons in the Quantum Hall effect and the formation of quantized energy levels.

Explanation
FQHE, or Fractional Quantum Hall Effect, majorly depends on electron-electron interaction. This phenomenon occurs in a two-dimensional electron gas subjected to a strong magnetic field and low temperatures. The interaction between electrons plays a crucial role in FQHE, leading to the formation of fractional charge and fractional statistics. This effect is observed as a series of plateaus in the Hall resistance, known as the Hall Plateau, which is a characteristic feature of FQHE. Planck's constant is a fundamental constant in quantum mechanics but is not directly related to FQHE.

Explanation
Klaus Von Klitzing discovered that Hall conductivity was quantized. This discovery, known as the Quantum Hall Effect, earned him the Nobel Prize in Physics in 1985. Von Klitzing's work showed that at low temperatures and strong magnetic fields, the Hall conductivity of a two-dimensional electron gas becomes quantized, meaning it can only take on discrete values. This groundbreaking finding opened up new avenues for studying the behavior of electrons in condensed matter physics and has important implications for the field of quantum mechanics.

Explanation
Gallium arsenide is widely used in IQH (integer quantum Hall) experiments. It is a compound semiconductor that exhibits high electron mobility and a large energy gap, making it suitable for studying quantum phenomena. Its unique properties allow researchers to observe the quantum Hall effect, which occurs when a two-dimensional electron gas is subjected to a strong magnetic field and exhibits quantized resistance values. Gallium arsenide's popularity in IQH experiments is due to its excellent electronic properties and its ability to provide a controlled environment for studying quantum effects.