Results for "Graphene"
Physics Encyclopedia Entry 1777204819
** This entry is about the **Quantum Hall Effect**, a fundamental phenomenon in condensed matter physics that has far-reaching implications for our understanding of the behavior of electrons in solids. ## Overview The Quantum Hall Effect (QHE) is a fascinating phenomenon in condensed matter physics that has revolutionized our understanding of the behavior of electrons in solids. Discovered in 1980 by Klaus von Klitzing, the QHE is a manifestation of the intricate dance between electrons and the lattice structure of solids. At its core, the QHE is a manifestation of the **quantization of the Hall conductivity**, where the conductivity of a two-dimensional electron gas exhibits discrete plateaus as a function of the applied magnetic field. This phenomenon has been observed in various materials, including **GaAs** and **Si**. The QHE has far-reaching implications for our understanding of the behavior of electrons in solids, particularly in the context of **mesoscopic physics**. It has been extensively studied in various systems, including **quantum wells**, **superlattices**, and **graphene**. The QHE has also been used as a tool to study the properties of **topological insulators**, **superconductors**, and **ferromagnets**. ## History/Background The discovery of the QHE is attributed to Klaus von Klitzing, a German physicist who was working at the **Max Planck Institute** in Stuttgart, Germany. Von Klitzing was studying the behavior of electrons in a **GaAs** heterojunction, and he observed a peculiar behavior in the Hall conductivity as a function of the applied magnetic field. He reported his findings in a paper published in the journal **Physical Review Letters** in 1980. The QHE was initially met with skepticism by the scientific community, but it was later confirmed by numerous experiments. The QHE was recognized as a fundamental phenomenon in condensed matter physics, and it was awarded the **Nobel Prize in Physics** in 1985 to Klaus von Klitzing. ## Key Information The QHE is characterized by the following key features: * **Quantization of the Hall conductivity**: The Hall conductivity exhibits discrete plateaus as a function of the applied magnetic field. * **Plateau structure**: The plateaus are separated by **critical magnetic fields**, which are determined by the **Landau level** filling factor. * **Integer quantum Hall effect**: The QHE is characterized by the presence of **integer plateaus**, where the Hall conductivity is quantized to integer values. * **Fractional quantum Hall effect**: The QHE can also exhibit **fractional plateaus**, where the Hall conductivity is quantized to fractional values. The QHE has been extensively studied in various systems, including: * **GaAs**: The QHE was first observed in GaAs heterojunctions. * **Si**: The QHE has also been observed in silicon-based systems. * **Graphene**: The QHE has been observed in graphene, a two-dimensional material with unique electronic properties. * **Topological insulators**: The QHE has been used to study the properties of topological insulators. ## Significance The QHE has far-reaching implications for our understanding of the behavior of electrons in solids. It has been used to study the properties of various materials, including topological insulators, superconductors, and ferromagnets. The QHE has also been used as a tool to study the behavior of electrons in mesoscopic systems, where the electronic properties are influenced by the lattice structure of the material. The QHE has also led to the development of new technologies, including: * **Quantum computing**: The QHE has been used to develop new quantum computing architectures. * **Spintronics**: The QHE has been used to develop new spintronic devices. * **Graphene-based electronics**: The QHE has been used to develop new graphene-based electronic devices. ## InfoBox: - **Name:** Quantum Hall Effect - **Type:** Condensed matter phenomenon - **Date:** 1980 (discovery) - **Location:** Max Planck Institute, Stuttgart, Germany - **Known For:** Quantization of the Hall conductivity in two-dimensional electron gases ## Tags: Condensed matter physics, Quantum Hall Effect, Quantization of Hall conductivity, Landau levels, Topological insulators, Superconductors, Ferromagnets, Mesoscopic physics, Graphene, Spintronics, Quantum computing.
SciencePhysics Encyclopedia Entry 1780320725
** **Quantum Hall Effect** is a phenomenon in **Condensed Matter Physics** where the Hall conductivity of a two-dimensional electron gas exhibits quantized plateaus as a function of the magnetic field strength. ## Overview The **Quantum Hall Effect** (QHE) is a fundamental concept in **Condensed Matter Physics**, describing the behavior of electrons in a two-dimensional electron gas (2DEG) subjected to a strong magnetic field. This phenomenon was first observed in 1980 by Klaus von Klitzing, who discovered that the Hall conductivity of a 2DEG exhibits quantized plateaus as a function of the magnetic field strength. The QHE has since become a cornerstone of modern condensed matter physics, with far-reaching implications for our understanding of quantum mechanics and the behavior of electrons in solids. In a 2DEG, the electrons are confined to a plane, and their motion is restricted to two dimensions. When a strong magnetic field is applied perpendicular to the plane, the electrons experience a force that causes them to move in a circular orbit. The Hall conductivity, which is the ratio of the Hall voltage to the magnetic field strength, is a measure of the electron's response to this force. In the QHE, the Hall conductivity exhibits a series of quantized plateaus, where the conductivity is precisely quantized in units of the fundamental constant e^2/h, where e is the elementary charge and h is the Planck constant. ## History/Background The QHE was first observed in 1980 by Klaus von Klitzing, a German physicist who was working at the Max Planck Institute for Solid State Research in Stuttgart, Germany. Von Klitzing's discovery was a major breakthrough in condensed matter physics, and it led to a fundamental shift in our understanding of the behavior of electrons in solids. The QHE was initially thought to be a rare phenomenon, but subsequent experiments have shown that it is a ubiquitous feature of 2DEGs, occurring in a wide range of materials and systems. ## Key Information The QHE is characterized by a series of quantized plateaus in the Hall conductivity, which occur at specific values of the magnetic field strength. These plateaus are separated by gaps, and the conductivity is precisely quantized in units of e^2/h. The QHE is a result of the interplay between the electron's kinetic energy and the magnetic field, which causes the electrons to form a series of Landau levels. The Landau levels are quantized energy levels that arise from the electron's motion in the magnetic field, and they play a crucial role in the QHE. The QHE has been observed in a wide range of materials and systems, including semiconductor heterostructures, graphene, and topological insulators. The QHE has also been used to study the behavior of electrons in solids, including their spin, charge, and orbital degrees of freedom. The QHE has far-reaching implications for our understanding of quantum mechanics and the behavior of electrons in solids, and it has led to a fundamental shift in our understanding of condensed matter physics. ## Significance The QHE has had a profound impact on our understanding of condensed matter physics, and it has led to a fundamental shift in our understanding of the behavior of electrons in solids. The QHE has also had significant technological implications, including the development of high-precision resistors and the creation of new types of electronic devices. The QHE has also been used to study the behavior of electrons in solids, including their spin, charge, and orbital degrees of freedom. INFOBOX: - **Name:** Quantum Hall Effect - **Type:** Condensed Matter Physics - **Date:** 1980 - **Location:** Max Planck Institute for Solid State Research, Stuttgart, Germany - **Known For:** Discovery of quantized plateaus in the Hall conductivity of a 2DEG TAGS: Quantum Hall Effect, Condensed Matter Physics, Quantum Mechanics, Hall Conductivity, Landau Levels, Two-Dimensional Electron Gas, Graphene, Topological Insulators, Solid-State Physics.
SciencePhysics Encyclopedia Entry 1779956839
** This encyclopedia entry is about the **Quantum Hall Effect**, a phenomenon in which the Hall conductivity of a two-dimensional electron gas exhibits plateaus at specific rational values of the inverse magnetic field. ## Overview The Quantum Hall Effect is a fundamental concept in condensed matter physics that has far-reaching implications for our understanding of the behavior of electrons in solids. It was first observed in 1980 by Klaus von Klitzing, a German physicist, while working at the Max Planck Institute in Stuttgart, Germany. The Quantum Hall Effect is a manifestation of the interplay between the quantization of energy levels and the behavior of electrons in a magnetic field. In a two-dimensional electron gas, the electrons are confined to a plane and are subjected to a magnetic field perpendicular to the plane. As the magnetic field is increased, the electrons begin to occupy specific energy levels, known as Landau levels. The Quantum Hall Effect occurs when the electrons in these Landau levels exhibit a quantized Hall conductivity, meaning that the conductivity of the electron gas is precisely quantized at specific rational values of the inverse magnetic field. ## History/Background The discovery of the Quantum Hall Effect is attributed to Klaus von Klitzing, who was working on a project to study the behavior of electrons in a magnetic field. On October 30, 1980, von Klitzing observed a plateau in the Hall conductivity of a two-dimensional electron gas at a magnetic field of approximately 10 Tesla. This observation was a major breakthrough, as it provided evidence for the quantization of the Hall conductivity. The Quantum Hall Effect was initially met with skepticism by the scientific community, as it seemed to defy the conventional understanding of the behavior of electrons in solids. However, further experiments and theoretical work confirmed the existence of the Quantum Hall Effect, and it was soon recognized as a fundamental phenomenon in condensed matter physics. ## Key Information The Quantum Hall Effect is characterized by the following key features: * **Quantization of Hall conductivity**: The Hall conductivity of a two-dimensional electron gas is precisely quantized at specific rational values of the inverse magnetic field. * **Plateaus in Hall conductivity**: The Hall conductivity exhibits plateaus at specific rational values of the inverse magnetic field, indicating a quantized behavior. * **Landau levels**: The electrons in the two-dimensional electron gas occupy specific energy levels, known as Landau levels, which are quantized due to the magnetic field. * **Fermi energy**: The Fermi energy, which is the energy level at which the electrons are filled, plays a crucial role in the Quantum Hall Effect. The Quantum Hall Effect has been observed in a variety of systems, including: * **GaAs/AlGaAs heterostructures**: These systems are commonly used to study the Quantum Hall Effect due to their high mobility and well-defined electron gas. * **Graphene**: Graphene, a two-dimensional material made of carbon atoms, has been shown to exhibit the Quantum Hall Effect at high magnetic fields. * **Topological insulators**: Topological insulators, which are materials that have a non-trivial topological structure, have been shown to exhibit the Quantum Hall Effect. ## Significance The Quantum Hall Effect has far-reaching implications for our understanding of the behavior of electrons in solids. It has led to a deeper understanding of the behavior of electrons in magnetic fields and has provided insights into the behavior of electrons in two-dimensional systems. The Quantum Hall Effect has also led to the development of new technologies, including: * **Quantum Hall devices**: These devices utilize the Quantum Hall Effect to measure the Hall conductivity of a two-dimensional electron gas. * **Magnetic field sensors**: These sensors utilize the Quantum Hall Effect to measure the magnetic field. * **Quantum computing**: The Quantum Hall Effect has been proposed as a potential platform for quantum computing. INFOBOX: - **Name:** Quantum Hall Effect - **Type:** Phenomenon in condensed matter physics - **Date:** 1980 - **Location:** Max Planck Institute, Stuttgart, Germany - **Known For:** Quantization of Hall conductivity in a two-dimensional electron gas TAGS: Quantum Hall Effect, Condensed Matter Physics, Landau Levels, Fermi Energy, GaAs/AlGaAs Heterostructures, Graphene, Topological Insulators, Quantum Computing, Magnetic Field Sensors.