Hall state quantization in a rotating frame

Abstract

PACS. 73.40Hm-Quantum Hall effect (integer and fractional). PACS. 73.50−h -Electronic transport phenomena in thin films and low-dimensional structures.Abstract. -We derive electromagnetomotive force fields for charged particles moving in a rotating Hall sample, satisfying a twofold U(1) gauge invariance principle. It is then argued that the phase coherence property of quantization of the line integral of total collective particle momentum into multiples of Planck's quantum of action is solely responsible for quantization in the Hall state. As a consequence, the height of the Hall quantization steps should remain invariant in a rapidly rotating Hall probe. Quantum Hall particle conductivities do not depend on charge and mass of the electron, and are quantized in units of the inverse of Planck's action quantum.Modern molecular beam epitaxy enables the preparation of modulation-doped semiconductor heterostructures in which, at low enough temperatures, a high mobility two-dimensional electron gas is formed. This system is characterized by a long Thouless dephasing length l φ , the distance within which phase coherence of mobile electrons is maintained. In good samples, and at low enough temperatures, the length l φ reaches several micrometers, exceeding the magnetic length l B = h/eB for applied magnetic fields of order one Tesla. Under these conditions, it should be possible to detect noninertial effects due to rotation or acceleration of the sample as a result of the change of quantum interference conditions, since the gauge potentials of the electromagnetic and noninertial fields experienced by the electrons both appear in their collective phase. In what follows, we shall argue that quantum coherence under the influence of noninertial force fields is directly observable in the quantum Hall effect [1]. The quantum of Hall conductivity for particle transport is given by the inverse of Planck's quantum of action alone, and involves no properties specific to the electron. The arguments used to prove this result crucially rely on the existence of a collective particle momentum expressing quantum coherence. By including gauge fields other than the electromagnetic one, we promote the idea that Hall quantization is of necessity derivable from a topological quantum number related to this coherence. It will be shown that this prediction about the nature of the quantum Hall effect is verifiable within current technological means.The main quantity of interest to us is the total particle momentum p = mv + mΩ × r + qA .Typeset using EURO-T E X

Inertial-Hall effect: the influence of rotation on the Hall conductivity

“…Charged particles in a rotating Hall sample were already studied in Ref. [21], where it was pointed out that the quantization of the Hall conductivity is not affected by the rotation. However, as it will be shown here, the rotation breaks same degeneracy of the LLs and the counting of states fully occupied bellow the Fermi energy may change, altering the Hall quantization steps.…”

On an atom with a magnetic quadrupole moment in a rotating frame

“…Rotating effects have also been observed in the quantum Hall effect [16], spintronics [17][18][19], quantum rings [20][21][22], Bose-Einstein condensation [23] and in the presence of the Kratzer potential [24].…”

A geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot

“…Hence, studies of the behaviour of Majorana fermions in noninertial systems can be interesting in confinement to quantum dots [10,35,46], and the quantum Hall effect [60][61][62][63].…”