Quantized charge & Fractional charge: Few facts, findings and new ideas | Adamas University

Physics

# Quantized charge & Fractional charge: Few facts, findings and new ideas

The physical world around us is made up of different atoms and molecules which are the building blocks of the Universe. Molecules are the collection of atoms and atoms are consisting of neutral neutrons, negatively charged electrons, and an equal number of positively charged protons. Atoms are effectively charged neutral. However, any system possessing an unequal number of electrons and protons is referred to as the ionic system.

What is charge?

It is one of the most fundamental questions of nature. Like mass, charge is also a physical property. If we place an object in the gravitational field, due to “mass” it will experience force. In the same way, a charged particle experiences force in the electromagnetic field due to the presence of “charge” in it.

How to measure it?

Unlike mass, charge is known to be quantized. In the year 1909 Robert A. Millikan and Harvey Fletcher of Chicago University performed a simple but elegant experiment, which demonstrated that charge is quantized. This experiment is popularly known as the “Oil Drop Experiment” [1], which brought the Nobel Prize in Physics to Millikan in the year 1923. Since then it is believed that any amount of charge is nothing but the integer multiple of small units of charge, called the elementary charge, e, which is equal to  Coulomb (SI unit of charge). Eventually, particles like electron and proton possess that amount of charge. During the last two decades Stanford Linear Accelerator Centre (SLAC), Stanford University, USA, has conducted various computer-automated experiments in search of fractionally charged particles, but no evidence of fractional charge has been detected yet. Thus, it’s well accepted that e is the smallest available independent charge in the physical world. However, the composite particles like neutrons and protons are made up of some elementary particles called ‘quarks’ having smaller charges, multiple of e/3. But isolated quarks have not been observed yet, they are only found within the composite particles such as neutron, proton, mesons, etc. Counter-intuitive theories related to independent fractional charges were also persisted. Laughlin had given such a proposal.

Figure 1: Millikan’s setup for the oil drop experiment, in the Ryerson Physical Laboratory at the University of Chicago.

The proposal:

In the year of 1982, Robert Laughlin [2] made a bold proposal about the existence of quasi-particles having fractional charge of e/3 inside tiny semiconductor devices to explain the phenomenon of Fractional Quantum Hall effect.

The evidence:

The proposal was counter-intuitive. There was no experimental evidence during that time in support of fractional charges. During one and a half-decade after Laughlin’s proposal various aspects of the theory had been experimentally verified but direct evidence of the quasi-particle with fractional charges was elusive. Finally, in September 1997, two groups [3,4] independently published two articles claiming the experimental observation of fractional charges in support of Laughlin’s theory. One of the groups, from Israel, published their article in Nature and the other one from France published it in Physical Review Letters. In the experiments, they have considered two-dimensional electron gas at the interface of two semiconductors to estimate the charge of the particles (quasiparticles). Interestingly, the technique resembles the process of predicting the size of the hailstones by listening to their hitting sounds on the tin or asbestos roof during a hailstorm. Just imagine, during a hailstorm, we are in a house having a tin or asbestos roof. Merely listening to the hitting sounds of the hailstones on the roof we can easily identify the size, e.g. comparatively larger stones will create louder crashes whereas small hailstones will generate soft pitter-patter, hard to identify in the continuous background noise. Likewise, the charge of the particles was estimated by monitoring the fluctuations of the current flowing through the circuit. Technically this method is known as “shot-noise theory”. The charge of the particles was estimated from the ratio of the mean square fluctuation in current to average current through the circuit. Moreover, they concluded that the particles flowing through the circuit are not electrons but particles (quasiparticles) with fractional charges nearly equal to e/3.

Conclusion:

Presently, the fractional charge is not a widely accepted fact. Direct evidence of such observation for other experiments is scanty. It may be due to our hindrance to pursuing such experimental arrangements. But, let us ignore the limitations of the fact, rather we may think at least in a phenomenological way that the sub-atomic particles can have fractional charges. Considering the fact, we can acquire some interesting concepts. For instance, we may think about continuously varying nuclear charges (Z) of atomic systems. However, we are accustomed to the integer values of the nuclear charges according to which the elements of the periodic table have been arranged e.g. for Z=1 it corresponds to a Hydrogen atom (1H1) or any one-electron ion, for Z=2 it’s a Helium (2He4) or any two-electron ion and so on. If we gradually reduce the nuclear charge of Helium, then there should be a Z value for which the nucleus will no longer be able to hold the electrons! That amount of nuclear charge is referred to as Critical Nuclear Charge (Zc). Applying Quantum Mechanics and considering Z as a real continuous variable one can estimate the Zc value form a multi-electron system. For instance, the corresponding Zc value for a two-electron system is 0.911 028 224 077 255 73, which was published in the year 2014 by a group in the journal Physical Review Letters and this is known to be the most accurate value of it till date [5]. Knowing the Zc values for a many-electron system, is very useful to predict the stability of any multi-electron ionic systems. For example, Zc is less than 1.0 for a two-electron system therefore, Z=1 is sufficient to hold two electrons to form a stable bound system and that’s why Hion exists in nature. Whereas, for three electron system Zc =2.08, consequently He ion doesn’t exist in nature, but there are some controversies about the fact. Many other applications of this concept are there but they are beyond the scope of this article.

Despite the experimental condition nowadays, we hope this concept would soon be observed in the laboratories.

References:

[1] Milliken, R. A., The Electron: Its Isolation and Measurement and the Determination of Some of its Properties, Chicago: Univ. of Chicago Press. (1917).

[2] Laughlin, R. B., Phys. Rev. Lett. 50, 1395 (1982).

[3] de-Picciotto, R. et. al. Nature 389, 162–164 (1997).

[4] Saminadayar, L., Glattli, D. C., Jin, Y. & Etienne, B. Phys. Rev. Lett. 79, 2526 (1997).

[5] C. S. Estienne et. al. Phys. Rev. Lett. 112, 039902 (2014).

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