Byrnes, T., Kim, N. Y., Kusudo, K. & Yamamoto, Y. Quantum simulation of Fermi-Hubbard models in semiconductor quantum-dot arrays. Phys. Rev. B 78, 075320 (2008). DOI: 10.1103/PhysRevB.78.075320
Jaksch, D. & Zoller, P. The cold atom hubbard toolbox. Ann. Phys. 315, 52–79 (2005). DOI: 10.1016/j.aop.2004.09.010
Annadi, A. et al. Quantized ballistic transport of electrons and electron pairs in LaAlO3/SrTiO3 nanowires. Nano Lett. 18, 4473–4481 (2018). DOI: 10.1021/acs.nanolett.8b01614
Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467 (1982). DOI: 10.1007/BF02650179
Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017). DOI: 10.1038/nature22362
Choi, J.-Y. et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016).
Porras, D. & Cirac, J. I. Effective quantum spin systems with trapped ions. Phys. Rev. Lett. 92, 207901 (2004). DOI: 10.1103/PhysRevLett.92.207901
Houck, A. A., Türeci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292–299 (2012). DOI: 10.1038/nphys2251
Politi, A., Matthews, J. C. F. & O’Brien, J. L. Shor’s quantum factoring algorithm on a photonic chip. Science 325, 1221 (2009). DOI: 10.1126/science.1173731
Singha, A. et al. Two-dimensional Mott–Hubbard electrons in an artificial honeycomb lattice. Science 332, 1176–1179 (2011). DOI: 10.1126/science.1204333
Slot, M. R. et al. Experimental realization and characterization of an electronic Lieb lattice. Nat. Phys. 13, 672–676 (2017). DOI: 10.1038/nphys4105
Drost, R., Ojanen, T., Harju, A. & Liljeroth, P. Topological states in engineered atomic lattices. Nat. Phys. 13, 668–671 (2017). DOI: 10.1038/nphys4080
Cen, C. et al. Nanoscale control of an interfacial metal–insulator transition at room temperature. Nat. Mater. 7, 298–302 (2008). DOI: 10.1038/nmat2136
Cen, C., Thiel, S., Mannhart, J. & Levy, J. Oxide nanoelectronics on demand. Science 323, 1026–1030 (2009). DOI: 10.1126/science.1168294
Kronig, R. D. L. & Penney, W. G. Quantum mechanics of electrons in crystal lattices. Proc. R. Soc. A 130, 499–513 (1931).
Pai, Y.-Y., Tylan-Tyler, A., Irvin, P. & Levy, J. Physics of SrTiO3-based heterostructures and nanostructures: a review. Rep. Prog. Phys. 81, 036503 (2018). DOI: 10.1088/1361-6633/aa892d
Cheng, G. et al. Electron pairing without superconductivity. Nature 521, 196–199 (2015).
Briggeman, M. et al. Pascal conductance series in ballistic one-dimensional LaAlO3/SrTiO3 channels. Science 367, 769–772 (2020). DOI: 10.1126/science.aat6467
Cheng, G. et al. Tunable electron-electron interactions in LaAlO3/SrTiO3 nanostructures. Phys. Rev. X 6, 041042 (2016).
Glazman, L. I. & Khaetskii, A. V. Nonlinear quantum conductance of a lateral microconstraint in a heterostructure. Europhys. Lett. 9, 263 (1989). DOI: 10.1209/0295-5075/9/3/013
Patel, N. K. et al. Ballistic transport in one dimension: additional quantisation produced by an electric field. J. Phys. Condens. Matter 2, 7247 (1990). DOI: 10.1088/0953-8984/2/34/018
Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559 (1982). DOI: 10.1103/PhysRevLett.48.1559
Thomas, K. J. et al. Possible spin polarization in a one-dimensional electron gas. Phys. Rev. Lett. 77, 135 (1996). DOI: 10.1103/PhysRevLett.77.135
van Wees, B. J. et al. Quantized conductance of point contacts in a two-dimensional electron gas. Phys. Rev. Lett. 60, 848 (1988). DOI: 10.1103/PhysRevLett.60.848
Wharam, D. A. et al. One-dimensional transport and the quantisation of the ballistic resistance. J. Phys. C 21, L209 (1988). DOI: 10.1088/0022-3719/21/8/002
Bauer, F. et al. Microscopic origin of the ‘0.7-anomaly’ in quantum point contacts. Nature 501, 73–78 (2013). DOI: 10.1038/nature12421
Gul, Y., Holmes, S. N., Myronov, M., Kumar, S. & Pepper, M. Self-organised fractional quantisation in a hole quantum wire. J. Phys. Condens. Matter 30, 09LT01 (2018). DOI: 10.1088/1361-648X/aaabab
Kumar, S. et al. Zero-magnetic field fractional quantum states. Phys. Rev. Lett. 122, 086803 (2019). DOI: 10.1103/PhysRevLett.122.086803
Oreg, Y., Sela, E. & Stern, A. Fractional helical liquids in quantum wires. Phys. Rev. B 89, 115402 (2014). DOI: 10.1103/PhysRevB.89.115402
Shavit, G. & Oreg, Y. Fractional conductance in strongly interacting 1D systems. Phys. Rev. Lett. 123, 036803 (2019). DOI: 10.1103/PhysRevLett.123.036803
Shavit, G. & Oreg, Y. Modulation induced transport signatures in correlated electron waveguides. SciPost Phys. 9, 51 (2020).
Briggeman, M. et al. Engineered spin-orbit interactions in LaAlO3/SrTiO3-based 1D serpentine electron waveguides. Sci. Adv. 6, eaba6337 (2020). DOI: 10.1126/sciadv.aba6337
Caviglia, A. D. et al. Tunable Rashba spin-orbit interaction at oxide interfaces. Phys. Rev. Lett. 104, 126803 (2010). DOI: 10.1103/PhysRevLett.104.126803
Ben Shalom, M., Sachs, M., Rakhmilevitch, D., Palevski, A. & Dagan, Y. Tuning spin-orbit coupling and superconductivity at the SrTiO3/LaAlO3 interface: a magnetotransport study. Phys. Rev. Lett. 104, 126802 (2010). DOI: 10.1103/PhysRevLett.104.126802
Kim, Y., Lutchyn, R. M. & Nayak, C. Origin and transport signatures of spin-orbit interactions in one- and two-dimensional SrTiO3-based heterostructures. Phys. Rev. B 87, 245121 (2013). DOI: 10.1103/PhysRevB.87.245121
Nethwewala, A. et al. Inhomogeneous energy landscape in LaAlO3/SrTiO3 nanostructures. Nanoscale Horiz. 4, 1194–1201 (2019). DOI: 10.1039/C9NH00188C
Cheng, G. et al. Sketched oxide single-electron transistor. Nat. Nanotechnol. 6, 343–347 (2011).
Briggeman, M. Replication data for: one-dimensional Kronig-Penney superlattices at the LAOSTO interface. Harvard Dataverse 10.7910/DVN/8IJ4QD (2021).
