Instrumentation & Measurement Magazine 23-3 - 16

the electron gas. While the discovery of the quantum Hall effect was made using silicon field-effect transistors, where a
potential on the gate forced the electrons in a narrow 2d channel, most metrological applications used Gallium-Arsenide/
Gallium-Aluminum-Arsenide heterostructures. Here, the
electrical band structure is engineered such that the electrons
are confined at a 10 nm thin interface layer between the two
materials.
The research activity in the metrological application of the
quantum Hall effect received a large impetus in 2004 with the
discovery of graphene [17]. Graphene is a naturally 2D material and shows a much sparser set of submultiples of RK, which
helps the quantized resistance to be maintained at higher temperatures. In recent years, the research in graphene devices for
resistance realization has made significant strides. Initially,
the devices were made from exfoliated graphene. This tedious
process involved carefully isolating a single layer from natural
crystals of graphite and allowed only for small devices capable of handling tiny currents. These days, epitaxial graphene
layers grown on Silicon-Carbide substrates are widely used to
fabricate devices.
The graphene-based quantum Hall devices operate at
lower magnetic fields, higher currents, and larger temperatures than the GaAs devices. Hence, the graphene devices are
more practical and less costly to operate than the early conventional devices. For example, a graphene device can operate at a
temperature of 4 K, and a magnetic flux density of 5 T, while a
conventional GaAs might require 1.2 K and 9 T. While the differences in the respective operating parameters are small, the
technical benefits are enormous: the graphene device can be
operated in a closed-cycle cryostat, and this overall decrease
in complexity and cost enables primary laboratories to acquire and operate their own quantum Hall standard. In fact,
at NIST, a table-top graphene quantum Hall device has been
used as part of the calibration services in resistance metrology since 2017.
There are two exciting developments in this research field
that we can look forward to in 2020: pn-junctions and topological insulators [18]. While the order of magnitude of RK/2
is practical, the numerical value 12.906 kΩ, is far away from
the decadal sequence of standard resistors. An interesting
solution to this problem is an array device that combines parallel and/or serial connection of quantum Hall devices. With
gated graphene devices, researchers can control the density
and even the polarity of charge carriers. For example, by applying an electric potential to gates electrically insulated from
graphene, charge carrier density in the graphene can be adjusted (Fig. 6). With large enough electric potential difference
on gates in different regions of the graphene, pn-junctions are
created. Such junctions allow either multiples or fractions of
RK. Hence, by changing the voltages on the various top gates
the total resistance of the device can be programmed. Clearly,
a programmable quantum Hall effect will have a huge benefit
for the realization of the ohm.
Broadly speaking, the quantum Hall effect falls in the category of topological quantum effects. In another class of
16	

Fig. 6. An example of a complex pn-junction graphene device the potential
of the top gates can be changed to externally program various values of
resistance (image courtesy of Albert Rigosi, NIST).

materials, called topological insulators, electrical conduction
occurs strictly along the surface and not in the bulk of the material. In the quantum Hall devices, the current travels along
the edge of the device, in a so-called edge state, because the
strong magnetic field restricts where current flow can occur.
Interestingly, some new composite materials such as Cr-doped
(Bi,Sb)2Te3 are topological insulators and can maintain similar
edge effects without external magnetic fields. Several reports
on observing the quantum Hall effect in such materials have
been published in the literature. Currently, the required temperatures to achieve the quantum anomalous Hall effect in
topological insulators are very low, tens of mK [9]. A focus of
research is to find material systems that are topological insulators at higher temperature without an external magnetic field,
which would substantially simplify the realization and dissemination chain of the unit of resistance.
So far, we discussed the application of the quantum Hall
effect in direct current applications. What about applications
in alternating current circuits? The dc unit of resistance can be
transferred to ac by using calculable resistors [20]. These devices can be calibrated at dc values, and the calibration value
can be extended to low frequencies because the frequency dependence of the resistor can be calculated from first principle.
Once an ac value of a resistance is known, it can be transferred
to capacitors and inductors using quadrature bridges. A second way to realize the farad is via the calculable capacitor, also
known as the Thompson-Lampard capacitor [21]. In this capacitor the capacitance per unit length is given by
	

C 0
= ln 2,	(17)
L π

where ϵ0 is the electric constant. The Thompson-Lampard
capacitor is an electro-mechanical device that is similarly complex as the Kibble balance. In theory, both the Kibble balance
and the Thompson-Lampard capacitor seem simple, but most
of the complexity of each experiment lies in managing the
small imperfections that the real apparatus has in contrast to
the idealized geometry on paper. Hence, using the quantum

IEEE Instrumentation & Measurement Magazine	

May 2020



Instrumentation & Measurement Magazine 23-3

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