of 19
Competing correlated states around the zero field Wigner crystallization transition of
electrons in two-dimensions
J. Falson,
1, 2, 3,
I. Sodemann,
4, 5
B. Skinner,
6
D. Tabrea,
1
Y. Kozuka,
7, 8
A. Tsukazaki,
9
M. Kawasaki,
10, 11
K. von Klitzing,
1
and J. H. Smet
1
1
Max-Planck-Institute for Solid State Research, D-70569 Stuttgart, Germany
2
Department of Applied Physics and Materials Science,
California Institute of Technology, Pasadena, California 91125, USA.
3
Institute for Quantum Information and Matter,
California Institute of Technology, Pasadena, California 91125, USA
4
Max-Planck-Institute for the Physics of Complex Systems, 01187 Dresden, Germany
5
Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
6
Department of Physics, Ohio State University, Columbus, Ohio 43210, USA
7
Research Center for Magnetic and Spintronic Materials,
National Institute for Materials Science, Tsukuba 305-0047, Japan
8
JST, PRESTO, Kawaguchi, Saitama, 332-0012, Japan
9
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
10
Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan
11
RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
The competition between kinetic energy and Coulomb interactions in electronic systems can lead
to complex many-body ground states with competing superconducting, charge density wave, and
magnetic orders. Here we study the low temperature phases of a strongly interacting zinc-oxide-
based high mobility two dimensional electron system that displays a tunable metal-insulator transi-
tion. Through a comprehensive analysis of the dependence of electronic transport on temperature,
carrier density, in-plane and perpendicular magnetic fields, and voltage bias, we provide evidence
for the existence of competing correlated metallic and insulating states with varying degrees of spin
polarization. Our system features an unprecedented level of agreement with the state-of-the-art
Quantum Monte Carlo phase diagram of the ideal jellium model, including a Wigner crystalliza-
tion transition at a value of the interaction parameter
r
s
30 and the absence of a pure Stoner
transition. In-plane field dependence of transport reveals a new low temperature state with partial
spin polarization separating the spin unpolarized metal and the Wigner crystal, which we exam-
ine against possible theoretical scenarios such as an anti-ferromagnetic crystal, Coulomb induced
micro-emulsions, and disorder driven puddle formation.
Dilute interacting electrons harbor competing ground
states when their Coulomb repulsion greatly exceeds
their kinetic energy. In a parabolically dispersing two
dimensional electron system (2DES) the ratio of inter-
action to kinetic energy scales is parameterized by the
dimensionless parameter
r
s
, given by
r
s
=
1
(
πn
)
1
/
2
a
B
.
(1)
Here,
a
B
= 4
π
~
2
/m
e
2
is the effective Bohr radius of
carriers and
n
is the electron concentration. As the den-
sity is lowered, the electron system undergoes a Wigner
crystallization transition, which Quantum Monte Carlo
(QMC) studies predict to occur at around
r
s
30 [1–7].
In spite of decades of research efforts,
8–12
many aspects of
the phase diagram of a strongly interacting 2DES in the
limit of zero temperature and zero magnetic field remain
clouded in the range of 25
< r
s
<
40, where QMC cal-
culations predict a breakdown of the Fermi liquid (FL)
state. One of the main obstacles has been the trade-
off of interaction and disorder strengths in these plat-
forms; namely, the cleanest systems, such as electron-
doped GaAs, are also typically the ones that are rela-
tively weakly interacting, while those with stronger inter-
actions tend to be more disordered. Thus, systematic ex-
perimental studies in the high
r
s
regime (
r
s
20) remain
few.
13–15
The advent of ZnO heterostructures, however,
offers a new platform that is sufficiently strongly inter-
acting and clean. This combination is evidenced by its
display of some of the most fragile correlated states of the
fractional quantum Hall regime, such as the 5/2 and 7/2
incompressible states, bubbles and stripes,
16,17
while still
remaining strongly interacting at zero magnetic field, as
we demonstrate in this study.
The
enhanced
electronic
interactions
in
MgZnO/ZnO heterostructures stem primarily from
the relatively heavy band mass (
m
b
= 0
.
3
m
0
) and small
dielectric constant (

= 8
.
5

0
). Moreover, the occupation
of a single electron pocket at Γ combined with weak
non-parabolicity and spin-orbit interaction ensure that
the system is very close to the ideal jellium model
studied in QMC. The bands are highly spin degener-
ate, and the band
g
b
-factor (
2) is isotropic.
18
The
quasi-Hall bar device under study is rendered in Fig.1
a
.
The epitaxial MgZnO/ZnO heterostructure confines a
2DES approximately 500 nm beneath the wafer surface
with
n
tuned
in-situ
via a capacitively coupled gate
electrode on the back-side of the wafer. The field-effect
transfer characteristics are displayed in Fig.1
b
. Here,
n
is determined from the period of quantum oscillations
arXiv:2103.16586v1 [cond-mat.str-el] 30 Mar 2021