Low temperature transport and evidence for nuclear order in GaAs Quantum Wires

In this thesis we focus on low temperature transport through cleaved edge overgrowth
(CEO) quantum wires. This thesis is motivated by recent theoretical work on one hand
that predicts the formation of a nuclear helimagnet in presence of a Luttinger liquid
(LL) below a critical system temperature [1] and previous measurements on CEO wires
on the other hand that might indicate the onset of such a phase transition [2].
The first task for this thesis was to create suitable measurement conditions to approach
the theoretically predicted strongly correlated state of matter. More precisely,electron
sample temperatures much lower than the predicted ordering temperature of 75mK for
GaAs CEO wires have to be demonstrated. For this purpose, cryogenic microwave filters
with very low cut-off frequency and good thermalization properties were developed
and installed for all measurement cables. With that a minimum electron temperature
of 7.5mK was reached in metallic coulomb blockade thermometers [3],and furthermore,
for the first time in these devices, a deviation from pure electron-phonon cooling is
observed [4].
At low refrigerator temperatures T_R, the CEO (double) wires show pronounced and
completely reproducible conductance oscillations as a function of density. We show
that these oscillations, also present in the zero magnetic field tunneling current
between the parallel quantum wires, emerge as 1D Fabry Perot resonances in the ballistic
CEO wires [5]. We analyze the maximum transmission (T=1) through these wires, i.e
the oscillation maxima, in the single mode regime as a function of temperature. While
the quantum wires approach universal conductance quantization of 2e^2/h for a single
quantum wire only at quite large T_R>15K, we find that the conductance saturates
below T_R=75mK at 1e^2/h [6]. Furthermore, we give strong evidence that the
conductance saturation is not related to insuffcient thermalization, i.e.the CEO wires
cool far beyond the saturation temperature of 75mK. This seems to indicate lifting
of electron spin degeneracy at zero external magnetic field, consistent with the theo-
retically predicted low temperature limit for a clean LL in the ordered helicalstate [1].
We can further exclude other potential mechanisms (temperature dependent contact
resistance, freeze-out of weakly disordered LL, Wigner crystal formation/incoherent
LL), leaving only nuclear spins as candidates for the source of the (possibly) observed
lifted spin degeneracy as spin-orbit coupling is rather weak in GaAs, and the saturation
at 1e^2/h is observed in absence of an external magnetic field. This might resolve
the long-standing mystery of the temperature-dependent (non-universal) conductance
quantization in GaAs cleaved edge overgrowth quantum wires, and furthermore might
give first experimental evidence for a new, strongly correlated state of matter, namely
(helical) nuclear order induced by the strongly interacting electrons via hyperfine
coupling.
We also measure real-time tunneling in a GaAs few electron double quantum dot (DQD)
by means of an adjacent quantum dot as charge sensor. At low temperatures, in the
limit of negligible interdot tunneling and low tunnel rates to source and drain, we
observe metastable charge state switching. The metastability only occurs within diamond
shaped regions that are centered between associated triple points of the charge stability
diagram (CSD). We show that these charge fluctuations arise as an intrinsic property
in DQDs, and take place via fast intermediate states that include an electron exchange
with the leads [7]. Due to the geometrical shape of the diamond (in very good agreement
with our model of thermally activated electron exchange with the leads), its large
energy scale (>1.7K) and due to its visibility even at charge sensor bias voltages as
small as 5µV, we exclude extrinsic effects such as phonon or photon assisted tunneling.
Furthermore, the simultaneous observation of the diamond shaped region of metastable
charge state switching at various points in the CSD and its pinning to associated triple
points upon reshaping the DQD, make charge traps and other defects a very unlikely
explanation.