The talk summarizes the application of the

quantum Hall effect in metrology with the focus on the replacement of the kilogram with a fixed value for the Planck constant.

Physicists call this the fractional

quantum hall regime.

The discovery was made by studying the results of two

quantum hall experiments.

In [32, 33] we pointed out that the behavior of black hole entropy in LQG suggests a connection between the physics of a black hole horizon and that of the

quantum hall effect.

These Floquet edge states are topologically protected and responsible for a quantized Hall conductance in the absence of a magnetic field [16-18], a remarkable realization of the so-called "

quantum Hall systems without Landau levels" originally proposed by Haldane [19].

Mende et al., "Epitaxial graphene homogeneity and

quantum Hall effect in millimeter-scale devices," Carbon, vol.

Another 17 articles review the current status of such condensed matters as

quantum Hall effects: discovery and application, extreme mechanics: self-folding origami, glass and jamming transitions: from exact results to finite-dimensional descriptions, diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods, and Andreev reflections in superfluid 3He: a probe for quantum turbulence.

10) who studied <<the integer

quantum Hall effect>> opened in 1980 by Klaus von Klitzing (born in 1943) at <<helium>> temperatures (till 1 K) and strong static magnetic fields (at magnetic flux density till 30 T) in the silicon field effect transistor and the award of the Nobel Prize in physics for 1985 [4, 18], using a two-dimensional ultra-pure gallium arsenide films at lower temperatures (below 1 K) and stronger permanent magnetic fields (for the magnetic flux density over 30 T) opened new <<fractional

quantum Hall effect>> [18-20].

In 1983, Thouless explained the mysterious

quantum Hall effect.

Nevertheless, as we describe below, the demonstration of the fractional charge in the fractional

quantum Hall regime in the noise (6,7) is widely appreciated.

Its unique band structure has led to many interesting phenomena such as tunable charge carriers densities [3], anomalous integer

quantum Hall effect [1, 4], and ultrahigh mobilities at room temperature [5].