arXiv:cond-mat/0106375v1 [cond-mat.mes-hall] 19 Jun 2001
Evidence for a Quantum Hall Insulator in an InGaAs/InP Heterostructure
D.T.N. de Lang, L. A. Ponomarenko, A. de Visser
Van der Waals-Zeeman Instituut, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands
C. Possanzini, S.M. Olsthoorn
High Field Magnet Laboratory, University of Nijmegen, 6525 ED Nijmegen, The Netherlands
A.M.M. Pruisken
Institute for Theoretical Physics, University of Amsterdam, 1018 XE Amsterdam, The Netherlands
(October 25, 2018)
We study the quantum critical behavior of the plateau-insulator (PI) transition in a low mobility
In0.53Ga0.47 As/InP heterostructure. By reversing the direction of the magnetic field (B) we find an
averaged Hall resistance ρxy which remains quantized at the plateau value h/e2 throughout the PI
transition. We extract a critical exponent κ′ = 0.57 ± 0.02 for the PI transition which is slightly
different from (and possibly more accurate than) the established value 0.42 ± 0.04 as previously
obtained from the plateau-plateau (PP) transitions.
One of the fundamental issues in the field of two di-
mensional electron gases is the nature of the transitions
between adjacent quantum Hall plateaus. By measuring
the resistance tensor of low mobility In0.53Ga0.47As/InP
heterostructures, Wei et al. [1,2] demonstrated that the
quantum Hall steps become infinitely sharp as T → 0,
indicating that the transitions between adjacent quan-
tum Hall plateaus (PP transitions) represent a sequence
of quantum phase transitions (QPT). Both the max-
imum slope in the Hall resistance with varying B,
(∂ρxy/∂B)max, and the inverse of the half-width of the
longitudinal resistance between two adjacent quantum
Hall plateaus, (∆B)−1, have been shown to follow the
power law T −κ as T approaches absolute zero, indepen-
dent of Landau level index. Here, κ = p/2ν where p
denotes the exponent of the phase breaking length ℓϕ at
finite T (i.e. ℓϕ ∼ T −p/2) and ν is the critical index for
the localization length ξ which is defined at zero T .
In order to probe the QPT, it is essential to carry
out experiments on samples where the dominant scatter-
ing mechanism is provided by short ranged random po-
tential fluctuations [3]. Like in In0.53Ga0.47As/InP, this
produces the widest range in T where quantum critical-
ity is accessible experimentally. At the same time, little
is known about the effects of macroscopic sample inho-
mogeneities which generally complicate experiments on
the QPT. The problem of sample inhomogeneities was
recently addressed by van Schaijk et al. [4] who inves-
tigated the plateau-insulator (PI) transition in the low-
est Landau level. The data were taken from the same
In0.53Ga0.47As/InP heterostructure which was previously
used in the study of the PP transitions [2].
Following the analysis by van Schaijk et al. one can
extract different exponents κ and κ′ from the transport
data on the PI transition, dependent on the specific quan-
tity one considers. For example, the longitudinal resis-
tance ρxx was shown to follow the exponential law [5]
ρxx(ν, T ) ∝ exp(−∆ν/ν0(T )). Here, ∆ν = ν − νc rep-
resents the filling fraction ν of the lowest Landau level
relative to the critical value νc ≈ 1
2 and ν0(T ) ∝ T κ′
with an experimental value κ′ = 0.55 ± 0.05.
The numerical value of the exponent κ′ differs by more
than the experimental error from the established “univer-
sal” value 0