# Large zero bias peaks and dips in a four-terminal thin InAs-Al nanowire
device

Huading Song  equal contribution State Key Laboratory of Low Dimensional
Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084,
China  Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
Zitong Zhang  equal contribution State Key Laboratory of Low Dimensional
Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084,
China  Dong Pan  equal contribution Beijing Academy of Quantum Information
Sciences, 100193 Beijing, China  State Key Laboratory of Superlattices and
Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.
O. Box 912, Beijing 100083, China  Donghao Liu  State Key Laboratory of Low
Dimensional Quantum Physics, Department of Physics, Tsinghua University,
Beijing 100084, China  Zhaoyu Wang  State Key Laboratory of Low Dimensional
Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084,
China  Zhan Cao  Beijing Academy of Quantum Information Sciences, 100193
Beijing, China  Lei Liu  State Key Laboratory of Superlattices and
Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.
O. Box 912, Beijing 100083, China  Lianjun Wen  State Key Laboratory of
Superlattices and Microstructures, Institute of Semiconductors, Chinese
Academy of Sciences, P. O. Box 912, Beijing 100083, China  Dunyuan Liao  State
Key Laboratory of Superlattices and Microstructures, Institute of
Semiconductors, Chinese Academy of Sciences, P. O. Box 912, Beijing 100083,
China  Ran Zhuo  State Key Laboratory of Superlattices and Microstructures,
Institute of Semiconductors, Chinese Academy of Sciences, P. O. Box 912,
Beijing 100083, China  Dong E Liu  State Key Laboratory of Low Dimensional
Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084,
China  Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
Frontier Science Center for Quantum Information, 100084 Beijing, China  Runan
Shang<EMAIL_ADDRESS>Beijing Academy of Quantum Information Sciences,
100193 Beijing, China  Jianhua Zhao<EMAIL_ADDRESS>Beijing Academy of
Quantum Information Sciences, 100193 Beijing, China  State Key Laboratory of
Superlattices and Microstructures, Institute of Semiconductors, Chinese
Academy of Sciences, P. O. Box 912, Beijing 100083, China  Hao Zhang
<EMAIL_ADDRESS>State Key Laboratory of Low Dimensional Quantum
Physics, Department of Physics, Tsinghua University, Beijing 100084, China
Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
Frontier Science Center for Quantum Information, 100084 Beijing, China

###### Abstract

We report electron transport studies of a thin InAs-Al hybrid semiconductor-
superconductor nanowire device using a four-terminal design. Compared to
previous works, thinner InAs nanowire (diameter less than 40 nm) is expected
to reach fewer sub-band regime. The four-terminal device design excludes
electrode contact resistance, an unknown value which has inevitably affected
previously reported device conductance. Using tunneling spectroscopy, we find
large zero-bias peaks (ZBPs) in differential conductance on the order of
$2e^{2}/h$. Investigating the ZBP evolution by sweeping various gate voltages
and magnetic field, we find a transition between a zero-bias peak and a zero-
bias dip while the zero-bias conductance sticks close to $2e^{2}/h$. We
discuss a topologically trivial interpretation involving disorder, smooth
potential variation and quasi-Majorana zero modes.

##  I Introduction

The decade-long hunting of Majorana zero modes (MZMs) [1, 2] in hybrid
semiconductor-superconductor nanowires is guided by a simple and elegant
theory in 2010 [3, 4]. This theory model requires four basic ingredients: a
one-dimensional electron system, strong spin-orbit interaction, s-wave
superconducting pairing and Zeeman energy. InAs and InSb semiconductor
nanowires coupled to a superconductor are the most exhaustively studied
material systems to engineer these four ingredients into a single device,
aiming for the realization of MZMs [5, 6]. Indeed, every single ingredient
could be directly or indirectly probed by electron transport experiments and
thus confirmed to be present in those devices. For example, (quasi-) one
dimensionality could be revealed by the observation of quantum point contact
(QPC)-like quantized conductance plateaus [7, 8], a hallmark of ballistic one
dimensional electron system; induced superconductivity could be probed by
tunneling conductance which resolves a hard induced superconducting gap [9,
10, 11, 12]; Zeeman energy is related to various estimations of effective
g-factors [13, 14]; spin-orbit coupling could be indirectly probed by anti-
crossings of Andreev levels as well as the anisotropic closing of the
superconducting gap for different magnetic field directions [14, 15]. Majorana
theory further predicts a quantized tunneling zero-bias conductance peak [16,
17, 18, 19]. Initial experiments have measured various zero-bias peaks (ZBPs)
in hybrid nanowires but with a small peak height [20, 21, 22, 23, 24]. These
first generation experiments have suffered from finite sub-gap tunneling
conductance, the soft gap problem. Theory later suggested that the soft gap is
due to disorder at the superconductor-semiconductor interface which leads to
spatially non-uniform couplings [25]. In the following years, much
experimental efforts have focused on the optimization of material growth and
device control, trying to minimize the disorder level at those interfaces
[26]. Indeed, epitaxial growth of superconductors on semiconductor nanowires
show a hard induced superconducting gap and cleaner ZBPs [27]. Later on, large
ZBPs with peak height reaching the order of $2e^{2}/h$ was also observed [28,
29, 30]. However, ZBPs with height robustly sticking to the quantized value by
varying both magnetic field and gate voltages, as predicted by MZM theory,
have not been demonstrated yet.

Meanwhile, new theory developments have introduced the concept of quasi-
Majorana zero modes (quasi-MZM) [31, 32], a type of zero-energy Andreev bound
states (ABS) [33, 34, 35, 36, 37] with a topologically trivial origin. The key
idea is that every ABS could be mathematically decomposed into two quasi-MZMs.
In some regimes with disorder or smooth potential variation [38, 39, 33], the
tunneling probe only couples to the first quasi-MZM. The second quasi-MZM,
while partially overlapping with the first one in space (thus topologically
trivial), has negligible coupling to the first one due to opposite spin.
Therefore, with only one quasi-MZM contributing to tunneling, ZBPs can be
quantized, mimicking topological MZMs.

On the device part, previous ZBP experiments used two-terminal device designs
where the electrode contact resistance remains unknown. This unknown
resistance introduces a systematic uncertainty, and if used as a fitting
parameter, non-quantized ZBPs could be fitted to the quantized value [40].
Improving device fabrication for lower contact resistance could reduce this
uncertainty to some extent. For example, one could estimate the upper bound of
this resistance based on QPC plateaus in ballistic devices, or properties of
the superconducting gap which should remain as a constant by varying the
tunnel barrier height [29]. If the contact resistance is under- or
overestimated, the gap size, extracted from bias voltage, would vary after
subtracting the bias drop shared by this inaccurate contact resistance. In
addition, if the contact resistance is not an unkown constant but depends on
bias, gate voltage or magentic field, the ZBP height and shape will be
affected in a more complex way. To solve these uncertainty problems, here we
use a four-terminal device design, the first time for ZBP experiments to the
best of our knowledge, aiming for quantized ZBPs.

Another improvement compared to previous works is the InAs nanowire diameter
which is $\sim$ 40 nm or below, much thinner than those commonly used in
literatures (typically $\sim$ 100 nm). The motivation is two-fold. First, the
simplest MZM model assumes a one-dimensional electron system, i.e. single sub-
band occupation. However, previous InAs/InSb devices likely have multiple sub-
bands occupied in the nanowire region underneath the superconductor. The top
sub-band, which hosts MZMs, usually has a much smaller coupling to the normal
probe than the lower sub-bands due to smooth barrier potential [41]. This
small tunnel coupling of MZM leads to a narrow ZBP whose quantized height (at
zero temperature) could easily be destroyed by thermal averaging [42].
Therefore, fewer or ultimately single sub-band occupation is preferred for
observing quantized ZBPs. To reach this regime, we reduce the wire diameter by
growth. Though occupation number can not be directly probed, a lower number of
occupied sub-bands is expected due to the small diameter which is already
comparable to InAs band bending size [43], and thus enhancing the sub-band
energy spacing. The second motivation is material quality. Thick InAs
nanowires (diameter larger than 50 nm) often exhibit randomly distributed twin
defects and stacking faults [44, 45, 46], uncontrolled sources of disorder.
Since disorder is currently the biggest obstacle in Majorana devices [47, 48,
49], thinner InAs nanowires with pure-phase crystal structure could suppress
this type of disorder. We do note that other disorder sources, e.g. InAs/Al
surface oxides and gate/dielectric imperfections, are still present which
remains as a future task.

##  II Experiment and Discussion

Fig. 1a shows a scanning electron micrograph (SEM) of the InAs-Al nanowire
device. Growth details can be found in Ref. [50]. N1, N2 and S1, S2 label the
four contact electrodes on the normal part of the nanowire and the
superconducting part, respectively. The upper side-gate is labeled as TG
(tunnel gate) for tunnel barrier tuning. The lower side-gate and global back
gate are labeled as SG and BG, respectively.

Figure 1: (a) False-color SEM of the device. Four normal electrodes (N1, N2,
S1 and S2) and two side gates (TG and SG) are Ti/Au (5/70 nm). The InAs
nanowire (gray) is partially covered by a thin Al shell (pink, thickness
$\sim$ 7 nm). Part of the Al shell was wet etched for contacts and tunnel
barrier. (b) Device and measurement circuit schematic, with dimensions (not in
scale) labeled. The substrate (brown) is p+ Si covered by 300 nm thick SiO2
(blue), acting as a global back gate (BG). (c) $dI/dV$ versus bias voltage $V$
and tunnel gate voltage $V_{TG}$ at zero magnetic field. $V_{BG}$ = -2.251 V.
(d, e) Vertical line-cut from (c) (black bar) in linear (d) and logarithmic
scale (e).  Figure 2: (a) $dI/dV$ versus $V$ and $B$ at fixed $V_{TG}$ and
$V_{BG}$ (see labeling). $B$ is aligned with the nanowire axis for all
measurements. (b) Extracted zero-bias (upper panel) and outside-gap
conductance $G_{N}$ (lower panel). Blue and red backgrounds in the lower panel
mark the $B$-ranges of zero-bias dip (ZBD) and ZBP. Blue and red lines in the
upper panel mark the $B$-range where the conductance is close to $2e^{2}/h$.
The full width at half maximums (FWHM) of ZBPs are shown as red crosses. (c)
$dI/dV$ line-cuts from 0.48 T to 1.06 T, resolving a transition from ZBD
(blue) to ZBP (red) near $2e^{2}/h$. (d) ZBP line-cuts (red) at 0.9, 1 and
1.24 T, together with Lorentzian line shapes (gray) assuming a thermal
broadening of 50 mK. Vertical red dashed lines mark the bias positions of
‘half maximum’. (e) Several $dI/dV$ line-cuts ($B$ labeled).

Fig. 1b shows the device schematic with dimensions labeled together with a
brief measurement circuit (see Supplement Fig. 1 for details). A DC bias
voltage and a small AC lock-in excitation are first summed and then applied
together to the N1 contact. The resulting current is drained from the S1
contact and measured through a pre-amplifier, as $I$ and $dI$. The voltage
drop between N2 and S2 is measured using a voltage meter and another lock-in
(synchronized with the first one) to get $V$ and $dV$. Therefore, the
differential conductance $dI/dV$ can be directly calculated without
subtracting any series resistance (e.g. fridge filters or contacts) as was
done before for two-terminal designs. In addition, the bias $V$ can also be
directly measured without subtracting the bias drop over series resistance as
in the two-terminal case.

Fig. 1c shows $dI/dV$ as a function of $V$ and $V_{TG}$, resolving a hard
induced superconducting gap in the tunneling regime (Fig. 1de) where the
outside-gap conductance is much smaller than $2e^{2}/h$. The gap size is
$\sim$ 0.27 meV. Fridge base temperature is $\sim$ 20 mK for all measurements.
The gap remains hard at finite magnetic field $B$ before its closing, see
SFig. 2 $B$-dependence and more gate scans. The super-gate (SG) is not well
functional (see SFig. 3 for details), thus fixed at 0 V for all measurements
unless specified. The hard gap resolved by tunneling conductance in the
gate-$B$ parameter space (where large ZBPs are observed) is an important
prerequisite for the search of quantized ZBPs: in soft gap devices [40],
Majorana ZBPs are not even expected to be quantized due to severe dissipation
broadening [51].

Next we apply $B$ along the nanowire axis, searching for possible MZM
signatures at different gate voltages (see SFig. 4 unsuccessful searches).
Fig. 2a shows such a $B$-scan example at a particular gate voltage setting
(labeled in the figure) with the zero-bias line-cut and $G_{N}$ shown in Fig.
2b. As $B$ increases, two broad levels detach from the gap edges and merge at
zero energy at $\sim$ 0.5 T. They first form a zero-bias dip (ZBD) which later
on evolves into a ZBP. The zero-bias conductance, during this dip-to-peak
transition (from 0.48 T to 1.06 T), sticks close to $2e^{2}/h$. The mean value
of the zero-bias conductance within this $B$-range of 0.58 T (blue and red
lines in Fig. 2b), is 0.98 with a standard deviation of 0.02, both in unit of
$2e^{2}/h$. All the $dI/dV$ line-cuts within this $B$-range are shown in Fig.
2c (blue for ZBDs and red for ZBPs). The smooth ZBD-ZBP crossover in $B$-scan
where the zero-bias conductance sticks close to $2e^{2}/h$ is a new
observation of this paper.

For $B$ higher than 1.06 T, the ZBP-height quickly decreases away from
$2e^{2}/h$, and finally the peak splits (line-cuts shown in SFig. 5). The
lower panel of Fig. 2b marks the full $B$-range of ZBP with a red background,
where its difference with the red line in the upper panel indicates the
$B$-range of ZBP whose height significantly decreases away from $2e^{2}/h$.
Fig. 2d shows three ZBP line-cuts with the full width at half maximum (FWHM)
indicated by the red dashed lines. FWHM is extracted by the bias $V$ where
$dI/dV$ is half of its zero-bias conductance. For some cases (e.g. 0.9 T in
Fig. 2d), the background conductance in the positive bias region is larger
than the ‘half maximum’. FWHM is then taken by doubling the $|V|$ found in the
negative bias region. If the background conductance is larger than the ‘half
maximum’ for the entire bias range, then no FWHM is extracted. The gray lines
are calculated Lorentzian line-shapes of $G_{0}/(1+(eV/\Gamma)^{2})$ after
assuming a thermal broadening of 50 mK, showing a rough match with the ZBPs.
$G_{0}$ is the zero-bias conductance while 2$\Gamma/e$ the extracted FWHM,
shown as red crosses in Fig. 2b.

The blue line in Fig. 2b indicates the $B$-range of ZBD with zero-bias
conductance sticking close to $2e^{2}/h$. We note that line-cuts at lower $B$
(e.g. 0 T) also have line-shapes of ‘ZBD’. This dip, a suppression by the
superconducting gap, is however different from the ZBDs we quoted in Fig. 2bc,
a result of two merging levels.

The outside-gap conductance $G_{N}$ shows a decreasing trend in Fig. 2b,
suggesting a $B$-dependent barrier height since $G_{N}$ is proportional to the
barrier transmission. However, our $G_{N}$ is extracted by averaging the
conductance for the most positive and negative bias voltages available from
the data. The available bias range (the color map edge in Fig. 2a) is not too
far away from the gap edge, leading to an overestimation of $G_{N}$,
especially at lower $B$. For a more accurate estimation, we use ZBP-width as
the indicator of barrier transmission in the $B$-range with no obvious peak
splitting. In Fig. 2bc, the FWHM decreases as increasing $B$ (from 0.86 T to
1.06 T), indicating that the barrier height (transmission) possibly increases
(decreases). Within this $B$-range, the ZBP-width varies by $\sim$ 50$\%$,
much larger than the variation of ZBP-height: $\sim$ 5$\%$ near $2e^{2}/h$.
The relative variation of ZBP-height near $2e^{2}/h$ being significantly
smaller than the relative variation of ZBP-width was used before to argue for
a quantized ZBP [29]. For higher $B$, the FWHM starts to increase while the
ZBP-height shows a continuous decrease. Both are likely due to peak splitting
which becomes visible where the splitting is large enough to be resolved, e.g.
see the 1.6 T line-cut in Fig. 2e.

Figure 3: Numercial simulation. (a) nanowire schematic (upper), potential
landscape (middle) and two quasi-MZM wavefunctions at $V_{z}$ = 1.3 meV
(lower). (b) Energy spectrum. (c) $dI/dV$ of the energy spectrum (middle),
zero-energy (bias) line-cut (lower), and $V_{z}$-dependent barrier height
$V_{b}$ (upper). (d) Line-cuts from (c), quantized ZBD-ZBP transition. Figure
4: (a) $dI/dV$ versus $V$ and $B$ at a different $V_{TG}$ and $V_{BG}$ (see
labeling) with the zero-bias line-cut, extracted $G_{N}$ and FWHM (red
crosses) shown in the lower panels. The right y-axis (red) is for FWHM in unit
of mV. (b) Line-cuts of ZBD and ZBP near $2e^{2}/h$ with the $B$-ranges
labeled. (c, d) and (e, f), same with (a, b) but different in gate voltage
settings (labeled). (g, h, i), Three more $B$-scans with maximum ZBP-heights
(g) close to, (h) above and (i) below $2e^{2}/h$ (gate voltages labeled).
Lower panels show zero-bias line-cuts. In (g), the ZBP first splits, then
merges back at $B\sim$ 2 T. Figure 5: (a) $dI/dV$ versus $V_{BG}$ and $B$
(left panel) with $V=0$, $V_{TG}$ = -3.544 V. Right panel: re-plot of the left
panel using three colors: white, cyan and red for conductance less than
0.9$\times 2e^{2}/h$, larger than 1.1$\times 2e^{2}/h$ and in between. (b)
Upper (lower) panel, two horizontal (vertical) line-cuts from (a), indicated
by the green (orange) dashed lines, see labeling for $V_{BG}$ ($B$). (c) Upper
panel, bias dependence of the black curve in the upper panel of (b). Middle
panel, zero-bias line-cut. Lower panel, vertical line-cuts at 0, 0.05, 0.1 and
0.15 T, respectively. (d) $dI/dV$ versus $V_{TG}$ and $B$ (left panel) with
$V=0$, $V_{BG}$ = -2.198 V. Right panel: three-color re-plot. (e) Upper
(lower) panel, two horizontal (vertical) line-cuts from (d), indicated by the
green (orange) dashed lines, see labeling $V_{TG}$ ($B$). (f) Horizontal line-
cut from (d) at $V_{TG}$ = -3.588 V. (g) $dI/dV$ line-cuts (from Fig. 6d, the
left most part) near the $V_{TG}$ setting of (f) at $B$ = 1 T. Figure 6: (a)
$dI/dV$ versus $V_{BG}$ and $V_{TG}$ at $V=0$. $B$ = 0 T. Lower panel,
horizontal line-cut at $V_{BG}$ = -2.198 V. (b) Same with (a) except that $B$
= 1 T. (c) Bias dependence of the line-cut in (a). Lower panel, zero-bias
line-cut. (d) Same with (b) except that $B$ = 1 T. (e) Several vertical line-
cuts from (c) (labeled with colored arrows) showing no obvious ZBPs. (f) Line-
cuts from (d) with $V_{TG}$-ranges labeled. For clarity, three panels and
colors are used.  Figure 7: (a) Three-color re-plot of Fig. 6b, highlighting
the conductance region near $2e^{2}/h$ (red) with $\pm 10\%$ variation. (b)
$V_{TG}$-scan at $B$ = 1 T, corresponding to the green dashed horizontal line-
cut in (a), outside the ‘red islands’. Lower panel, zero-bias line-cut. (c)
$V_{BG}$-scan at $B$ = 1 T, corresponding to the orange dashed vertical line-
cut in (a). Lower panel, zero-bias line-cut (black) from the upper panel
together with the vertical dashed line-cut from (a) (orange), matching
qualitatively. (d) $dI/dV$ line-cuts from (c) within the $V_{BG}$-range from
-2.225 V to -2.099 V. Split peaks ($V_{BG}$ labeled) and neighboring line-cuts
are shown in blue for clarity.  Figure 8: (a,b,c) $dI/dV$ at zero bias as a
function of $V_{BG}$ and $V_{TG}$ at $B$ = 0.95 T, 0.9 T and 0.8T,
respectively. Right panels, three-color re-plots. (d) $V_{BG}$-scan at 0.8 T
with $V_{TG}$ = -3.51 V, corresponding to the orange dashed line-cut in (c).
Lower panel, zero-bias line-cut. (e) $dI/dV$ line-cuts from (d), showing the
back-and-forth oscillations between ZBP and split peaks ($V_{BG}$ labeled).
(f) $V_{TG}$-scan at 0.8 T with $V_{BG}$ = -2.08 V, corresponding to the green
dashed line-cut in (c). Middle panel, zero-bias line-cut (red and blue for ZBP
and ZBD regions). Lower panel, $G_{N}$: the average of conductance at the most
positive and negative bias available in the data. Red and blue curves are two
vertical line-cuts from the upper panel (labeled by the corresponding color
bars), resolving a ZBP and a ZBD near $2e^{2}/h$ (horizontal ($V$) axis not
shown).  Figure 9: (a) $dI/dV$ versus $V_{BG}$ and $V_{TG}$ at $B$ = 0.85 T
with $V$ = 0. Right panel, three-color re-plot. (b) $dI/dV$ versus $V$ by
sweeping $V_{TG}$ and $V_{BG}$ simultaneously (following the blue dashed line
in (a)). Lower panel, zero-bias line-cut (black) and the blue dashed line-cut
(blue) from (a). (c) Line-cuts from (b) within the $V_{TG}$-range from -3.446
V to -2.963 V (see labeling). For clarity, only one third of the line-cuts are
plotted (one for every three neighboring curves).

MZM theory predicts a quantized zero-bias conductance at zero temperature.
Whether this resolves a ZBP or ZBD depends on the barrier height. For a high
barrier (therefore low transmission, tunneling regime), the sub-gap
conductance is suppressed and a quantized ZBP can be resolved. For a low
barrier with high total transmission (e.g. more than one sub-band occupation
in the barrier), the sub-gap conductance can be enhanced due to Andreev
reflection and exceeds $2e^{2}/h$. Meanwhile, the zero-bias conductance, due
to spin-filtering of MZMs, still stays at $2e^{2}/h$ and a quantized ZBD can
be resolved [19, 32, 52]. Theory has proposed using the quantized ZBP-ZBD
transition, enabled by lowering the barrier height, as an experimental tool to
exclude a case of quasi-MZMs from topological MZMs [32, 52]. In realistic
situations, exact MZM quantization is not expected due to finite temperature
and wire length. For a quantized ZBP with FWHM of 0.1 mV, thermal broadening
of 50 mK can already decrease the peak height by $\sim$ 2$\%$ of $2e^{2}/h$.
This height will decrease more for narrower ZBPs. To minimize temperature
effect, searching for quantized MZM peak requires a large peak width, thus
large barrier transmission (high $G_{N}$). In fact, $G_{N}$ of the ZBPs in
Fig. 2c is close to $2e^{2}/h$, suggesting that the barrier is in open regime
(instead of tunneling) with more than one spin-resolved sub-band occupied. In
this open regime, the sub-gap conductance is finite due to Andreev reflection
[53], resulting in a sizable background conductance for the ZBPs. This finite
(Andreev) sub-gap conductance, superficially similar to a soft gap, does not
‘hurt’ the quantized height of MZM peak [54], different from the true soft gap
case which destroys the quantization due to dissipation broadening [51]. To
confirm its ’hard gap’ nature, we tune $V_{TG}$ into tunneling regime where
$dI/dV$ indeed resolves a hard gap at zero $B$ (Fig. 1c) and finite $B$ (SFig.
2) for $V_{BG}$ = -2.251 V, same with the $V_{BG}$-value in Fig. 2. Overall,
our ZBP is large and different from the ZBPs with small net height [40]
because 1) the zero-bias conductance is close to $2e^{2}/h$, and 2) the ZBP’s
net height (above background) is also large and can exceed $e^{2}/h$. Another
non-negligible effect in realistic devices is the finite wire length. In fact,
our device has a relatively short length $\sim$ 658 nm for the superconducting
part (Fig. 2b). As a result, MZMs could easily overlap which can further
degrade the quantization quality [55].

The discussion above serves as a background introduction and by no means
suggests our observation as topological MZMs. In Fig. 3 we study an
alternative explanation involving quasi-MZMs, solely for a qualitative
illustration purpose rather than quantitative comparisons since many
experimental parameters are unknown. Considering the nanowire tapering, we
assume a tilted potential landscape shown in Fig. 3a (black curve). We note
this is not the only possible landscape, e.g. SFig. 6 shows another case
(triangle) which gives similar results. Fig. 3b shows the energy spectrum
where the zero-energy state at finite Zeeman energy $V_{z}$ is a pair of
quasi-MZMs. Fig. 3a plots the wavefunctions of these two quasi-MZMs (red
$\gamma_{1}$ and blue $\gamma_{2}$), located where the chemical potential
crosses the Zeeman split potential landscapes (red and blue lines). Though
$\gamma_{1}$ and $\gamma_{2}$ are spatially separated, they are not at the
wire ends, thus topologically trivial. Due to the separation, $\gamma_{1}$ has
a much stronger coupling ($\Gamma_{1}$) to the probe than $\gamma_{2}$
($\Gamma_{2}$, almost negligible), leading to quantized conductance as shown
in Fig. 3cd. For $dI/dV$ calculation, we assume a very narrow and high barrier
(vertical black line in Fig. 3a). We further assume that the barrier height is
$V_{z}$-dependent (Fig. 3c upper): slightly decreases first, then increases,
trying to capture the $B$-dependent FWHM of ZBPs and the gap shape at 0 T in
Fig. 2. The physics mechanism of this assumption is not fully clear and might
possibly be related to $B$-induced suppression of Andreev reflection or
shifting of dot levels, both affecting the barrier transmission. With this
barrier assumption, we find the numerical simulation (Fig. 3cd) qualitatively
consistent with our observation of dip-to-peak transition near $2e^{2}/h$.

We note the interpretation above is not exclusive, e.g. landscapes with
various disorder which have been extensively studied before [47] can not be
ruled out at this stage.

Fig. 4a-f show similar $B$-scans at three different gate voltage settings
where the zero-bias conductance stays close to $2e^{2}/h$, persisting over
sizable $B$-ranges: 0.54 T, 0.55 T and 0.56 T, respectively. The mean and
standard deviation of zero-bias conductance within these $B$-ranges are, 0.95
$\pm$ 0.02, 1.01 $\pm$ 0.04 and 1.02 $\pm$ 0.04, respectively (all in unit of
$2e^{2}/h$). The blue and red line-cuts indicate the large ZBDs and ZBPs close
to $2e^{2}/h$. The relative variation of ZBP-width for the red line-cuts in
Fig. 4df is significantly larger than the relative variation of ZBP-height
near $2e^{2}/h$, similar to Fig. 2 (Fig. 4b has too few data points to
conclude). For higher $B$, the ZBP height decreases away from $2e^{2}/h$,
accompanied by an increase of FWHM in roughly similar $B$-ranges (see Fig.
4ce), possibly due to peak splitting. See SFig. 5 line-cuts.

In Fig. 2 and Fig. 4a-f, we have shown smooth ZBD-ZBP transitions near
$2e^{2}/h$ with small fluctuations, forming ‘plateau-like’ features. Based on
measurements performed so far, we have not observed similar behavior at other
values significantly different from $2e^{2}/h$. This possibility, however,
could not be completely excluded since we did not (also can not) exhaust the
entire ($V$, $B$, $V_{TG}$, $V_{BG}$) multi-dimensional parameter space.

In Fig. 4g, h and i, we show three more $B$-scans where the maximum ZBP-
heights are (g) close to, (h) above and (i) below $2e^{2}/h$. We note that
there is no clear boundary between Fig. 4g-i and the ‘plateau-like’ features.
Instead, we expect a smooth crossover between these behaviors tuned by gate
voltages. For example, if the zero-bias conductance in Fig. 4i (Fig. 4c) was
higher and more (less) flat by tuning gate, it may evolve to Fig. 2 (Fig. 4h).
If the $B$-range in Fig. 4e was narrower, it may evolve to Fig. 4g. Though
this smooth transition may be expected in quasi-MZMs: tuning gate voltages or
$B$ may affect $\Gamma_{2}$ and $E_{M}$ (coupling between $\gamma_{1}$ and
$\gamma_{2}$) which cause deviations from $2e^{2}/h$, below or above, both
possible [32, 30]. The ZBPs exceeding $2e^{2}/h$ at many different gate
voltages also strongly suggest the presence of disorder [56] whose detailed
simulation is beyond the scope of this paper. For a full overview, we show ten
more $B$-scans in SFig. 7.

Next we study $B$-scans by fixing bias to zero, see Fig. 5ad the zero-bias
conductance map as a function of $B$ and $V_{BG}$ (Fig. 5a) or $V_{TG}$ (Fig.
5d). Right panels are re-plots using only three colors to highlight the
conductance regions (red) close to $2e^{2}/h$ within $\pm 10\%$ variation. We
note that this range of 10$\%$ is subjective: smaller variations surely lead
to smaller areas of ‘red islands’ in three-color re-plots. The red curves in
Fig. 5be are horizontal and vertical line-cuts across the ‘red islands’,
resolving ‘plateau-like’ features. The $B$-scan ‘plateaus’ have gate voltage
settings close to Fig. 4ae whose zero-bias line-cuts show similar match. The
$V_{BG}$-scan ‘plateau’ at 0.84 T (lower panel b) is resolved as large ZBPs in
further bias scan at a lower $B$ (0.8 T) and slightly different $V_{TG}$ (Fig.
8d). The $V_{TG}$-scan at 0.98 T (lower panel e) shows sizable fluctuations
near $2e^{2}/h$. Further bias dependence of this curve at similar $B$ (1 T)
also resolves large ZBPs (Fig. 6d). For comparisons, the black curves in Fig.
5be are line-cuts not passing through the ‘red islands’. See SFig. 8 more
line-cuts of Fig. 5ad.

The zero-bias maps only serve as a guidance in ZBP searching but does not
guarantee ‘it is a ZBP when sweeping bias’. For example, the two black curves
in Fig. 5b show a ‘peak’ above $2e^{2}/h$ in $B$\- and $V_{BG}$-scans,
corresponding to the cyan region in the lower left part of Fig. 5a (right
panel). This ‘peak’ turns out not being a ZBP in further bias scan as shown in
Fig. 5c. Another example is shown in Fig. 5f, a horizontal line-cut from Fig.
5d, resolving a ‘plateau’ feature in $B$-scan at a non-quantized value of
$\sim$ 0.3×$2e^{2}/h$. Further bias scan (Fig. 5g) on this ‘plateau’ reveals
split peaks instead of ZBPs (line-cuts taken from Fig. 6d).

Now we fix $B$ and study the gate dependence of the large ZBPs. Fig. 6a shows
the zero-bias conductance map as a function of $V_{BG}$ and $V_{TG}$ at $B$ =
0 T. We note the $V_{BG}$-values and $V_{TG}$-values for the $B$-scans of
ZBPs, i.e. Fig. 2, Fig, 4 and SFig. 7 (except for the two lower right panels),
are all within the scanned $V_{BG}$-range and $V_{TG}$-range as shown in Fig.
6ab. The several ‘red-line’ features are likely due to states of unintentional
quantum dots formed near the barrier. A horizontal line-cut (lower panel)
resolves these dot states or levels as peaks in $V_{TG}$-scan. Fig. 6c further
shows the bias dependence of this line-cut where these dot states do not
reveal clear and robust ZBPs (see line-cuts in Fig. 6e). At $B$ = 1 T, in
addition to the dot states as a background, continuous ‘red islands’ of
conductance near $2e^{2}/h$ are observed, see Fig. 6b whose $V_{BG}$-range and
$V_{TG}$-range are almost the same as Fig. 6a. Bias scan across this ‘island’
resolves large ZBPs whose height oscillates around $2e^{2}/h$ (Fig. 6d),
accompanied by peak-splittings. Line-cuts of the ZBPs and split peaks are
shown in Fig. 6f with corresponding $V_{TG}$-ranges labeled. We note that Fig.
6bd were measured under nominally the same gate voltage settings
($V_{TG}$-range slightly different) with Fig. 6ac but at 1 T. In addition, the
lower panels of Fig. 6abcd (zero-bias line-cuts) were measured at the same
$V_{BG}$-value. Therefore, comparing these four line-cuts allows to identify
the sharp ‘jump-like’ features and to what extent they can be reproduced upon
re-measuring. For example, most of the oscillating features near $2e^{2}/h$ in
the lower panel of Fig. 6d are reproducible based on the comparison with the
lower panel of Fig. 6b where matches can be found. These features, despite
being reminiscent of charge jumps, are reproducible sharp resonances (possibly
dot levels) tuned by gate voltages. The left most ‘jump’ in Fig. 6d ($V_{TG}$
$\sim$ -3.57 V) is a non-reproducible charge jump which is absent in Fig. 6b.

Fig. 7a shows the three-color re-plot of Fig. 6b, highlighting the ‘red
islands’ as regions close to $2e^{2}/h$. In Fig. 6d we have studied a
horizontal line-cut across the ‘red islands’, showing large ZBPs. For
comparison, Fig. 7b shows bias dependence of a horizontal line-cut outside the
‘red islands’ (green dashed line in Fig. 7a). No clear and robust ZBPs are
observed (occasionally there are non-robust ZBPs due to sharp level crossing
like SFig. 4bc). Next, in Fig. 7c, we study a vertical line-cut across the
‘red islands’ (orange dashed line in Fig. 7a) where the bias dependence also
resolves large ZBPs. These large ZBPs show a ‘plateau-like’ feature near
$2e^{2}/h$ in zero-bias conductance (lower panel) for $V_{BG}$ from -2.225 V
to -2.099 V. All the $dI/dV$ line-cuts within this quoted $V_{BG}$-range are
shown in Fig. 7d (split peaks and their neighboring line-cuts in blue for
clarity). The mean and standard deviation of the zero-bias conductance for
these line-cuts (including the split peaks) in Fig. 7d is 0.95 $\pm$ 0.07 in
unit of $2e^{2}/h$. The split peaks may be due to non-negligible coupling
($E_{M}$) between quasi-MZMs at that particular gate voltage setting. For
lower $V_{BG}$-values ($\sim$ -2.25 V), the ZBP-height significantly exceeds
$2e^{2}/h$ (maximally $\sim$ 1.2$\times 2e^{2}/h$), possibly due to non-
negligible coupling of the second quasi-MZM to the barrier ($\Gamma_{2}$)
enabled by smooth potential variation or purely a disorder effect [56]. See
SFig. 9 for more $V_{BG}$\- and $V_{TG}$\- scans of the large ZBPs at this
field of 1 T and SFig. 10 more line-cuts from Fig. 6b.

After the extensive gate scans at $B$ = 1 T, we now tune $B$ to other values
of 0.95 T, 0.9 T and 0.8 T, respectively, as shown in Fig. 8a-c. The right
panels are the three-color re-plots with ‘red islands’ highlighting regions
close to $2e^{2}/h$. Comparing Fig. 8a-c with Fig. 6b, we can find matches for
the main features (dot states or resonances) with minor overall gate voltage
drifts, possibly due to small charge jumps happened between those measurements
which reset/shift the overall gate voltage. Fig. 8d shows bias dependence for
a vertical line-cut across the ‘red islands’ in Fig. 8c (orange dashed line),
resolving large ZBPs and split peaks near $2e^{2}/h$. The zero-bias
conductance of these ZBPs and split peaks form a ‘plateau-like’ feature with
conductance fluctuating around $2e^{2}/h$ for $V_{BG}$ between -2.238 V and
-2.046 V. The mean and standard deviation of the zero-bias conductance within
this $V_{BG}$-range, including both ZBPs and split peaks, is 1.00 $\pm$ 0.08
in unit of $2e^{2}/h$. Fig. 8e shows several $dI/dV$ line-traces (with
$V_{BG}$-values labeled) from Fig. 8d, illustrating the back-and-forth
oscillating behavior for ZBPs vs splitting peaks.

Fig. 8f shows a $V_{TG}$-scan of the ZBPs, corresponding to a horizontal line-
cut from Fig. 8c (green dashed line). The red and blue colors indicate the
$B$-ranges for ZBPs and ZBDs, which alternate for a total $V_{TG}$-range from
-3.642 V to -3.342 V. Within this range, the mean and standard deviation of
zero-bias conductance is 1.06 $\pm$ 0.09 in unit of $2e^{2}/h$. The
transitions between ZBP and ZBD regions are accompanied by sharp and
reproducible resonances, possibly due to dot levels crossing zero energy.
These dot levels, tuned by gate voltages, can interact with quasi-MZMs when
approaching zero energy. Theory has suggested that the energy hybridization
between these dot levels and the zero-energy states can reveal asymmetric
couplings of the two quasi-MZM components to the normal probe [57, 58]. Fig.
8f further shows that this interaction could also interfere with the zero-bias
conductance, causing sizable deviations/fluctuations from/around $2e^{2}/h$.
All the $dI/dV$ line-cuts within the $V_{BG}$ and $V_{TG}$ ranges mentioned
above can be found in SFig. 11. The fluctuations of zero-bias conductance near
$2e^{2}/h$ and the alternating peak-split peak behavior shown in Fig. 8df
could possibly be related to an oscillatory couplings ($E_{M}$) between the
two quasi-MZMs and the coupling of the second quasi-MZM to the barrier
($\Gamma_{2}$), both tuned by gate voltages in a smooth or disordered
potential landscape. For more vertical and horizontal line-cuts at 0.8 T (Fig.
8c) as well as 1.0 T (Fig. 6b), see SFig. 10.

So far, we have presented several quantized ‘plateau-like’ features for the
zero-bias conductance in $B$-scan (Fig. 2, Fig. 4a-f) and gate voltage scans
(Fig. 7c, Fig. 8d), as well as several other non-plateau scans at different
$B$ and gate voltage settings. These ‘plateau-like’ features have noticeable
fluctuations: some smaller and some larger, but generally within $\pm$10$\%$
variation of the quantized value. Though perfect quantization of MZM is also
not expected in realistic devices with finite temperature and short wire
length as discussed before, we believe there is still much room for
improvement regarding the flatness and accuracy of plateaus based on our
current data quality. We further note that plateau-like features and non-
plateau features are not ‘black vs white’ with clear and sharp boundaries, as
was partially discussed before in Fig. 4. For example, our $V_{TG}$-scans
(Fig. 6d, Fig. 8f) in general show larger fluctuation amplitudes which
probably can not be identified as ‘plateau-like’. But they do show large ZBPs
oscillating around $2e^{2}/h$, different from those non-plateau features: Fig.
7b with no robust ZBPs and SFig. 4bc with small ZBPs due to sharp level
crossings (thus non-robust). Therefore, these $V_{TG}$-scans (Fig. 6d, Fig.
8f) can be treated as intermediate cases or transitions between plateau-like
and non-plateau features. With future device optimization, e.g. reducing
disorder, these features may develop into plateau-like or plateau features
[49].

Finally, we show a gate scan at $B$ = 0.85 T where we find ZBDs as the
dominating feature. Fig. 9a shows the zero-bias conductance map as a function
of $V_{BG}$ and $V_{TG}$. We notice a significant charge jump between the
measurement of Fig. 9 and the rest majority of the data (Fig. 2 to Fig. 8). As
a result, the main features (dot states) of the zero-bias map at different
fields (Fig. 6b and Fig. 8a-c) do not show clear match with Fig. 9a.
Therefore, the data set of Fig. 9 is isolated and can not be compared directly
with the rest (Fig. 2 to Fig.8). Nevertheless, we can still resolve ‘red
islands’ as shown in the right panel. The blue dashed line (tuning $V_{BG}$
and $V_{TG}$ simultaneously) marks a fine-tuned cut passing through the ‘red-
islands’ which resolves a ‘plateau-like’ feature around $2e^{2}/h$ for
$V_{TG}$ from -3.323 V to -2.963 V, as shown in Fig. 9b. The mean and standard
deviation of the zero-bias conductance within this gate range is 1.05 $\pm$
0.06 in unit of $2e^{2}/h$. $dI/dV$ line-cuts (Fig. 9c) within the ‘plateau-
like’ region resolve zero-bias dips (ZBD) with no clear and robust ZBPs. For
quantized ZBDs due to quasi-MZMs or MZMs, thermal averaging effect at finite
temperature tends to increase the zero-bias conductance above $2e^{2}/h$,
contrary to the case of quantized ZBPs. We further note the small quasi-
periodic oscillations for gate sweeps in Fig. 9b and Fig. 9a. Occasionally,
they resolve diamond-like shapes in bias vs gate scan as shown in Fig. 9b with
a diamond size of $\sim$ 0.2 mV or smaller, similar to Coulomb blockades.
These small quasi-periodic oscillations can also be found in Fig. 6ab and Fig.
8a-d. We do not know the origin of these oscillations but speculate that it
may be related to the short length of the nanowire (the superconducting part
$\sim$ 658 nm) which might be treated as an open and large quantum dot with a
small charging energy.

##  III Summary

To summarize, we have measured large zero-bias peaks on the order of
$2e^{2}/h$ in a thin InAs-Al hybrid nanowire device, using a four-terminal
device design. At particular gate voltage settings, we observe a smooth
transition between zero-bias peaks and zero-bias dips, driven by magnetic
field. The zero-bias conductance sticks close to $2e^{2}/h$ during this dip-
to-peak transition, forming a plateau-like feature. Further gate scans of
these zero-bias peaks at finite magnetic field reveal plateau-like features
(with fluctuations) around $2e^{2}/h$. We discuss our data with a possible
(not necessary exclusive) interpretation based on quasi-Majorana zero modes,
smooth potential variation and disorder. All the results in this paper are
from a single-device, and future devices could be aiming at longer and more
uniform (non-tapered) thin InAs-Al wires with better gate and dielectric
designs to minimize the level of disorder, which hopefully may lead to better
quantization: more flat and accurate plateaus.

###### Acknowledgements.

We thank Leo Kouwenhoven, Sankar Das Sarma, Önder Gül and Guanzhong Wang for
valuable comments and a critical reading of the manuscript. Raw data and
processing codes within this paper are available at
http://doi.org/10.5281/zenodo.5111639. This work is supported by Tsinghua
University Initiative Scientific Research Program, National Natural Science
Foundation of China (Grant Nos. 92065106 $\&$ 61974138), Beijing Natural
Science Foundation (Grant No. 1192017). H. S. acknowledges China Postdoctoral
Science Foundation (2020M670173 $\&$ 2020T130058), D. P. also acknowledges the
support from Youth Innovation Promotion Association, Chinese Academy of
Sciences (No. 2017156).

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001–003

# Colour-Magnitude Diagrams of candidate age-gap filling LMC clusters

Eduardo Balbinot1 Basílio X. Santiago1 Leandro Kerber2 Beatriz Barbuy2 Bruno
M. S. Dias2 1 Departamento de Astronomia, Universidade Federal do Rio Grande
do Sul
Porto Alegre, RS, Brazil
email: (balbinot<EMAIL_ADDRESS>
2 IAG, Universidade de Sao Paulo
Sao Paulo, SP, Brazil

(2008)

###### Abstract

The LMC has a rich star cluster system spanning a wide range of ages and
masses. One striking feature of the LMC cluster system is the existence of an
age gap between 3-10 Gyrs. Four LMC clusters whose integrated colours are
consistent with those of intermediate age simple stellar populations have been
imaged with the Optical Imager (SOI) at the Southern Telescope for
Astrophysical Research (SOAR). Their colour-magnitude diagrams (CMDs) reach V
$\sim$ 24\. Isochrone fits, based on Padova evolutionary models, were carried
out to these CMDs, after subtraction of field contamination. The preliminary
results are as follows: KMK88-38 has an age of about 1.3 Gyr, assuming typical
LMC metallicity and distance modulus, and a very low redenning. For OGLE-
LMC0531, the best eye fits to isochrones yield an age $\sim$ 1.6 Gyr and
E(B-V)=0.03. BSDL917 is younger, $\sim$ 150 Myrs, and subjected to larger
extinction (E(B-V)=0.08). The remaining cluster is currently under analysis.
Therefore, we conclude that these clusers are unlikely to fill in the LMC
cluster age gap, even when fitting uncertainties in the parameters are
considered.

###### keywords:

(galaxies:) Magellanic Clouds, galaxies: star clusters, (stars:) Hertzsprung-
Russell diagram

††volume: 256††journal: The Magellanic System: Stars, Gas, and
Galaxies††editors: Jacco Th. van Loon & Joana M. Oliveira, eds.

##  1 Introduction

The LMC has a rich star cluster system spanning a wide range of ages and
masses. One striking feature of the LMC cluster system is the existence of an
age gap between 3-10 Gyrs. Four LMC clusters whose integrated colours are
consistent with those of intermediate age simple stellar populations have been
imaged with the Optical Imager (SOI) at the Southern Telescope for
Astrophysical Research (SOAR).

##  2 Data

We have imaged 3 out of the 5 LMC clusters listed by Hunter et al (2003) as
belonging to the age gap. Two of them have been fully reduced.

The images were taken in 2007 with SOAR/SOI telescope in the B, V, and I
filters. A slow readout was used in order to minimise detector noise. A 2x2
pixel binning was adopted, yielding a spatial scale of 0.154 arcsec/pixel.
Seeing was always around 0.8 arcsec.

The exposures were flatfielded, bias subtracted, mosaiched and latter
combined. The photometry was carried out with standard point spread function
(PSF) fitting. The DAOPHOT package (Stetson 1994) was used to detect sources
(4 $\sigma$ above sky background) and measure magnitudes. The PSF was modelled
as a Moffat function with $\beta=1.5$. Photometric calibration was obtained
from the standard fields in the Northeast arm of the SMC (Sharpee et al.
2002). A typical SOAR/SOI image section is shown in Figure 1.

Figure 1: A 2.6’ x 3.6’ image section of the field around the cluster
KMK88-38, where two other known clusters are included. Their positions in the
image are indicated.

CMDs for the fields of the two age gap candidates already reduced are shown in
Figure 2. Their colour-magnitude diagrams (CMDs) reach $V\sim 23$. From left
to right, we show the full SOI field CMD, the CMD in the cluster region and
the field subtracted cluster CMD. Padova isochrones from Girardi et al. (2002)
are superposed to these latter. Field subtraction was performed statistically,
applying the method described in detail by Kerber et al. (2002).

Figure 2: V,(V-I) (top) and V,(B-V) (bottom) CMDs for the fields around
KMK88-38 (left) and LMC0531 (right) clusters. The panels from left to right
show: the entire SOI field, the region around the cluster, the result of field
subtraction. Padova isochrones are overlaid to the latter panels. Ages are
shown as $log(\tau_{max}(yrs))$, $log(\tau_{min})$, $\Delta log\tau$. The
adopted metallicity is also shown.

Besides the age gap candidates, the SOI images also covered other LMC clusters
listed in the catalogue by Bica et al. (2008). Figure 3 shows the field
subtracted CMDs for them, again with isochrones overlaid.

Figure 3: Field subtracted CMDs for the remaining clusters found in our
SOAR/SOI images. The symbols are the same as in the corresponding panels of
Figure 2.

Visual matching of the observed CMDs to the isochrone set has allowed us to
estimate age, metallicity, distance modulus and reddening for each cluster.
The resulting parameters are shown in Table 1.

##  3 Results and conclusions

The original targets, KMK88-38 and LMC0531, turn out to be the relatively old,
as expected, with ages $\sim 1-2$ Gyrs. However, they are still younger than
the lower age limit of the LMC gap. Interestingly, KMK88-39, LMC0214 and
LMC0523, which lie in the same SOI fields (5.5arcmin x 5.5 arcmin in size),
are much younger. LMC0523 final V,(B-V) CMD has 3 stars in the Red Clump
region. Even though they survived field subtraction, these stars have
relatively low probabilities of actually belonging to the cluster, and they
are, in fact, absent from the V,(V-I) CMD. For LMC0214 we have only B and V
images. The ages for this latter, as well as for KMK88-39 are upper limits, as
their upper main sequence is close to the saturation limit. Finally, NGC 1878
is a richer and denser cluster. Field subtraction was not as efficient in this
case, especially in V,(B-V). We attribute that to crowding effects, which make
photometric errors larger in the cluster region than in the field,
jeopardising the statistical field subtraction. Still, its V,(V-I) CMD
indicates that NGC 1878 is also younger than 0.5 Gyr.

$Name$ | $log(Age)$ | $Z$ | $E(B-V)$ | $(m-M)_{V}$
---|---|---|---|---
OGLE-LMC0214 | $8.4\pm 0.3$ | $0.013$ | $0.10$ | $18.50$
OGLE-LMC0523 | $7.8\pm 0.3$ | $0.013$ | $0.20$ | $18.40$
OGLE-LMC0531 | $9.2\pm 0.2$ | $0.014$ | $0.09$ | $18.50$
KMK88-38 | $9.2\pm 0.2$ | $0.006$ | $0.01$ | $18.65$
KMK88-39 | $8.5\pm 0.3$ | $0.011$ | $0.02$ | $18.50$
NGC1878 | $8.4\pm 0.3$ | $0.014$ | $0.17$ | $18.50$
Table 1: The parameters found for our sample.

We thus conclude that the sample analysed so far does not contain any cluster
located in the LMC age gap. We are currently reducing the field images of
another age gap candidate: LMC0169. We are also reducing lower exposure time
images of all clusters and perfecting the field subtraction algorithm; both
are important steps towards improving our age and metallicity constraints on
the clusters.

## References

  * [Bica et al. (2008)] Bica E. et al., 2008, MNRAS, in press (arXiv:0806.3049)
  * [Girardi et al.2002] Girardi L. et al., 2002, A&AS, 391, 195
  * [Hunter et al.2003] Hunter D. et al., 2003, AJ, 126, 1836
  * [Kerber et al.2002] Kerber, L.O. et al., 2002, A&A, 390, 121
  * [Sharpee et al.2002] Sharpee, B. et al., 2002, AJ, 123, 3216
  * [Stetson (1994)] Stetson, P.B., 1994, PASP, 106, 205