Fig. S1. Additional STEM-EELS elemental maps of integrated intensities of Ti L (red) edges showing asymmetrical roughness of the STO/LAO interfaces.

Fig. S2. Pseudo-dielectric functions for the three quantum well samples as a function of photon energy.
The oscillator models are shown in solid red, the experimental data in dashed green (real part) and dashed blue (imaginary part).
8.0
7.0
6.0
5.0
Model Fit
Exp <

1
>-E 60°
Model Fit
Exp <

2
>-E 60°
4.0
0.0
1.0
2.0
3.0
4.0
Photon Energy (eV)
5.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
7.0
7.0
6.5
6.0
5.5
5.0
4.5
4.0
0.0
1.0
Model Fit
Exp <

1
>-E 60°
Model Fit
Exp <

2
>-E 60°
2.0
3.0
4.0
Photon Energy (eV)
5.0
6.0
3.0
2.0
1.0
0.0
-1.0
7.0
7.0
6.5
6.0
5.5
5.0
4.5
4.0
0.0
1.0
Model Fit
Exp <

1
>-E 60°
Model Fit
Exp <

2
>-E 60°
2.0
3.0
Photon Energy (eV)
4.0
5.0
1.0
0.0
-1.0
6.0
4.0
3.0
2.0

Fig. S3. Valence band and core level spectra of LAO and STO substrates used for determining the valence band offset of the quantum well sample. (a) Valence band spectrum of STO substrate showing region used for linear extrapolation. The valence band top is located at an energy of 3.47 eV. (b) Valence band spectrum of LAO substrate showing region used for linear extrapolation. The valence band top is located at an energy of 3.19 eV. (c) Sr 3d spectrum of STO substrate. The Sr 3d
5/2
level has a binding energy of
134.11 eV with a width of 0.88 eV. (d) La 4d spectrum of LAO substrate. The strong component of La
4d
5/2
has a binding energy of 102.81 eV with a width of 1.46 eV.
12
140
10 8 6 4
Binding energy (eV)
2
138 136 134
Binding energy (eV)
132
0
0
50000
45000
40000
35000
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5000
70000
60000
50000
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130
0
14 12 10 8 6 4
Binding energy (eV)
2
112 110 108 106 104 102
Binding energy (eV)
100 98
0
50000
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40000
35000
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10000
5000
50000
45000
40000
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0
0

Fig. S4. Core level spectra of 5 uc quantum well sample. (a) Sr 3d spectrum. The Sr 3d
5/2
level is at an energy of 134.10 eV. (b) La 4d spectrum. The La 4d
5/2
level is at an energy of 103.14 eV. The core level separation in the 5 uc quantum well sample is 30.96 eV.
7000 14000
140 138 136 134 132 130
Binding energy (eV)
128
0
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112 110 108 106 104 102
Binding energy (eV)
100 98
0
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