# Physics: Quantum Classical Expretation Of IQHE)

Great Essays
Table of content

Introduction Two dimensional electron system Hall geometry Classical interpretation of IQHE Quantum mechanical interpretation of IQHE Significance of IQHE References

Introduction
The integral quantum hall effect (IQHE) was first discovered by Klaus von Klitzing and coworkers in 1980. It was demonstrated by two dimensional electron system in a device called metal oxide semiconductor field effect transistor (MOSFET), under low temperature and large magnetic field. They discovered that the transverse conductance dropped to zero at some values of magnetic field, and concurrently the longitudinal resistance didn’t change its value and hence showing plateaus on figure 1 [1980]. It was a definitely remarkable discovery featured by a wonderful equation R_H=h/ie^2 saying that the hall resistance is quantized where i is an integer. This equation relates physical quantity to fundamental physical constants, and thus can be served as a standard of physical quantities like resistance [].
This essay will explain how the hall resistance is quantized and its contributions to physics world.

Two
So, before looking at IQHE in details, we can gain some insights from the simple Hall effect. Let’s look at the simple theory of Hall effect. Consider a rectangular metal with height h, width w and length l. Suppose the current I_x=Aj_x is flowing inside along x direction and we apply magnetic field B in z-direction. The magnetic force pushes the electrons to the negative y-direction and a transverse electric field is built up. In equilibrium, the electric force and magnetic force on electrons balance each other or mathematically E_y=vB, where v is the drift velocity of electrons. Then the Hall voltage is measured in y-direction, V_H=wE_y. In term of volume density of electron in the metal, the current density can be written as j_x=nev. The Hall resistance is

## Related Documents

• Great Essays

In the chapter Kinematics of Particles, we studied about various relations among time, position, velocity and acceleration of a particle. When we have a relation between any two parameters, we can calculate remaining parameters. In Kinetics of Particles, we applied Newton’s second law of motion ƩF = ma. The fundamental concept is when external forces acting on a particle are balanced (zero resultant), the particle will be in equilibrium. But when external forces acting on a particle are not balanced, the particle will move in the direction of the resultant with magnitude ma.…

• 1828 Words
• 8 Pages
Great Essays
• Improved Essays

Electric current is measured in amperes (A). Voltage: The difference in electric potential energy of charged particles between two points within the electric field is called voltage. The free electrons at the higher potential have more electrical potential energy whereas the free electrons at lower potential have less electrical potential energy. Voltage is measured in volts (V). Resistance: Resistance is the opposite force that resists the flow of electrons.…

• 946 Words
• 4 Pages
Improved Essays
• Superior Essays

This problem is important because when new elements and compounds are discovered, scientists can figure out their characteristics They do this using KMT (Kinetic Molecular Theory). KMT states that in the substance as a gas behaves like hard, spherical objects that are always in constant motion with no attraction. The stated information is the staple of multiple gaseous theories. Some examples are frequency of the collisions, the distance between the particles in the container and the gas’s volume, and the temperature of said gas. The behavior of these particles affects their properties.…

• 1765 Words
• 8 Pages
Superior Essays
• Superior Essays

The ratio of the number of attosecond-gated electrons respect to the total number of electrons of the original electron pulse represent the attosecond optical gating efficiency which depends on the original electron pulse duration. It is calculated by dividing the integration of the coupling part of the spectrum by the integration of all spectrum. This relation is illustrated in Fig. 4D. Thus, the attosecond optical gating of short (few tens femtosecond) electron pulse will allow the generation of the attosecond electron pulses with the sufficient strength to capture the electron motion in the act, which opens the way for attaining the attosecond resolution in electron microscopy and establishing the…

• 1722 Words
• 7 Pages
Superior Essays
• Improved Essays

If the paramagnetism is cooled below the curie point it could create ferromagnetism, antiferromagnetism or ferrimagnetism. The ferromagnetism is when uncharged metals are attracted to others. Lodestone and iron produce magnetic fields by the alignment of their atoms. When their atoms spin in the same direction they reinforce each other magnetic fields. They have saturation Jupiter Ed https://login.jupitered.com/0/staff.php?sz=a2cd251f&user=619716 2 of 4 12/4/2017, 10:18 PM in the entire object that it will composes a single domain.…

• 973 Words
• 4 Pages
Improved Essays
• Improved Essays

He found that particles would always move towards the positively charged side. By using a Cathode Ray Tube, Thompson was able to conclude that some particles are negatively charged; therefore, discovering electrons. Thompson 's Plum Pudding Model showed that electrons were distributed throughout the atom and that the rest of the atom would be positively…

• 1041 Words
• 5 Pages
Improved Essays
• Improved Essays

Results An initial resistance versus magnetic field measurement on NdMo16O44 reveals a pronounced magnetic hysteresis effect when a magnetic field is applied perpendicular to the current, but with unknown orientation with respect to the crystal axes, as shown in Fig. 2a for temperatures from 12K to 30K (at temperature below 12K, the overall resistance is too high to produce low-noise measurements with resolvable magnetoresistance features). The individual plots are offset to better show the effect. A sharp drop in the magneto-resistance on the order of 30% of the zero-field resistance appears at a temperature of 12K, with local extrema at fields of approximately +0.38T and +0.55T (-0.38T and -0.55T, respectively) when the field is swept from…

• 1234 Words
• 5 Pages
Improved Essays
• Superior Essays

(6) The remaining contribution to the net Coulomb energy comes from the self-interaction of each charge with its own image, which is the so-called “dielectric solvation energy” ()()aaaaHRaaarVrrdrVˆ02ρ∫+=. (7) In above expressions, ()()2rraaℜ=ρ is the electron or hole density, and a = e, h; ()herrW,ˆ is a spherically symmetric component of the point charges direct Coulomb interaction operator, is a spherically symmetric component of the polarization energy operator, and ( herrU,ˆ ()rVˆ is the dielectric solvation energy operator. To obtain the explicit form of these operators we solve analytically the Poisson equation for a potential due to a point charge in the core/shell structure with the standard boundary conditions that account for discontinuity of the dielectric constant at hetero-interfaces.3 As a result, we obtain the following solutions: 3 ()()()()()()[](hecescheheherrqRrRrrRrRrrW,max2,ˆ2εεεθθθθ−+−+−−−= (8) ()()()()()(HRqRqrRrRrrUsesecscehehe+−−−−−−=εεεεεεθθ11,ˆ22 (9) where cε , sε and eε are the dielectric constants of the core, the shell, and the environment, respectively, and ()xθ is the Heaviside step function. The expression for the dielectric solvation energy is more complex and can be represented as a sum of two…

• 970 Words
• 4 Pages
Superior Essays
• Improved Essays

Thomson measured the amount of magnetic force needed to exactly counterbalance the deflection of a strong beam of electrons projected between charged plates. He used this to find the ratio of charge to mass of an electron: -1.76x1011 C/kg. Thomson re-concluded the fact that atoms are divisible and explained their overall neutral charge by proposing that the electrons were embedded in a sea…

• 2086 Words
• 9 Pages
Improved Essays
• Improved Essays

To address the physics behind observed anomalous behavior of Hc2 (T), Gurevich, and Gloubov and Koshelov theory was developed. The unique benefit of this approach is that the details of complex Fermi surface of MgB2 is not necessary to calculate Hc2 [132]. The impurity scattering is accounted by the nature of normal state electronic diffusivities and which are controlled by their respective intraband scattering rates in the and π bands, and interband scattering rates , , and…

• 889 Words
• 4 Pages
Improved Essays