Physics: Conductance quantum

Condensed Matter Quantum Mechanics Thermodynamics

Conductance quantum G₀ = 7.748×10⁻⁵ S The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values R x y = V Hall I channel = h e 2 ν , {\displaystyle R_{xy}={\frac {V_{\text{Hall}}}{I_{\text{channel}}}}={\frac {h}{e^{2}\nu }},} where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is the Planck constant.

Commentary

Conductance quantum Symbol: G₀ = 7.748×10⁻⁵ S The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values R x y = V Hall I channel = h e 2 ν , {\displaystyle R_{xy}={\frac {V_{\text{Hall}}}{I_{\text{channel}}}}={\frac {h}{e^{2}\nu }},} where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is the Planck constant. Why G₀ matters This constant appears everywhere in physics equations. It defines a fundamental limit or relationship in nature that holds true everywhere in the universe. R x y = V Hall I channel = h e 2 ν , {\displaystyle R_{xy}={\frac {V_{\text{Hall}}}{I_{\text{channel}}}}={\frac {h}{e^{2}\nu }},} Understanding G₀ G₀ = 7.748×10⁻⁵ S The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values R x y = V Hall I channel = h e 2 ν , {\displaystyle R_{xy}={\frac {V_{\text{Hall}}}{I_{\text{channel}}}}={\frac {h}{e^{2}\nu }},} where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is the Planck constant. The divisor ν can take on either integer (ν = 1, 2, 3,...) or fractional (ν = ⁠1/3⁠, ⁠2/5⁠, ⁠3/7⁠, ⁠2/3⁠, ⁠3/5⁠, ⁠1/5⁠, ⁠2/9⁠, ⁠3/13⁠, ⁠5/2⁠, ⁠12/5⁠,...) values. Here, ν is roughly but not exactly equal to the filling factor of Landau levels. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction, respectively. The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density is varied. Since the electron density remains constant when the Fermi level is in a clean spectral gap, this situation corresponds to one where the Fermi level is an energy with a finite density of states, though these states are localized (see Anderson localization). The fractional quantum Hall effect is a more complicated state whose existence relies fundamentally on electron–electron interactions. In 1988, it was proposed that there was a quantum Hall effect without Landau levels. This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents.

Sources: Wikipedia