Effect of the Nuclear Hyperfine Field on the 2D Electron Conductivity in the Quantum Hall Regime Page: 4 of 9
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JETP Lett., Vol. 69, No. 1, 10 January 1999
served in bulk InSb.6,7 In a 2D electron system the effect of hyperfine interaction on
electron spin resonance (Overhauser effect) has been observed in A1GaAs/GaAs.9'9 In the
present study we demonstrate experimentally that the hyperfine interaction can produce
an observable change of the dc conductivity of a 2D electron system under quantum Hall
To predict the effect of the hyperfine field on the 2D conductivity we use the
conventional assumption that the energy of the excitations of the ground state in the QHE
near filling factor v=1 can be expressed as a sum of two terms:10,
A =Ao+gpAB(BO+B,,), (1)
where AO is the exchange energy due to e-e interaction and gpABo is the Zeeman term
due to the externally applied field BO. Through the hyperfine field the nuclei provide an
additional contribution gupB, to the 2D ground state excitation energy. Here g is the
Land6 g factor of the excitations and pa is the electron Bohr magneton. The local
hyperfine field B, is proportional to the nuclear spin polarization, B,=a(Iz),IZt where a
is the contact hyperfine coupling constant. At temperatures much greater than a few mK,
the thermal equilibrium hyperfine field Be can ordinarily be neglected. In the context of
electron spin resonance (ESR), B~ is known as the Overhauser shift.8,13,14 In the absence
of spin-orbit interaction, as in the conduction band of GaAs,""'5s neither the cyclotron
energy nor the electron-electron Coulomb interactions are affected by B~,, regardless of
its magnitude or sign, because the origin of B~ is the spin-spin coupling between the
electron and nucleus.
Under our experimental conditions, where T-2.5 K and BO= 5.35 T, the longitudi-
nal conductivity at v=1 obeys an Arrhenius law:
oxx= o-O exp(- A/2kT), (2)
where O is a constant. In the thermally activated regime the energy gap A can be
determined from the temperature dependence of o-xx. Consider the conductivity change
that would result from a change in the nuclear polarization: through the collective hyper-
fine interaction of the 2D electrons with the nuclei in the vicinity of the 2D electrons, the
local nuclear hyperfine field B, will be enhanced. For a small change in the hyperfine
field, SB,<BO, we will have from (1) and (2):
/-xxo-x x=-gpA B,,I2kT=aSB,/BO, (3)
where a= - g9p8BoI2kT is a constant. Experimentally we measured the dc conductivity
of the AIGaAs/GaAs multiquantum well samples by the standard four probe method in
magnetic fields up to BO= 6 T and temperatures T=1.7-4.2K. To obtain the 2D longi-
tudinal conductivity o-xx we measured the longitudinal resistivity pxx=3UxxI and the
Hall resistivity pxy= Uxy/I, where /3 is a geometric factor, I is the current through the
sample, and Uxx and Uxy are the longitudinal and Hall voltages. To calculate the 2D
conductivity we used the standard formula -xx=pxx/(psx+ py).
According to (3) the relative dc conductivity change is proportional to the change in
the nuclear hyperfine field B,,. To observe this dependence experimentally, we have
employed the method of dynamic nuclear polarization (DNP) by down-field swept ESR
to enhance the magnitude of (IZ).-'. The corresponding DNP-enhanced hyperfine field is
BDNP. The change in the Overhauser shift of the ESR line is given by 6B,=B
,., ., .. _ .. .. ... ........_ _ v r , .. .. Ot, __ ..._
Vitkalov et al. 65
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VITKALOV,S.A.; BOWERS,C.R.; SIMMONS,JERRY A. & RENO,JOHN L. Effect of the Nuclear Hyperfine Field on the 2D Electron Conductivity in the Quantum Hall Regime, article, July 13, 2000; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc706819/m1/4/: accessed April 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.