Narasimha et al. (ACS Nano, 2025) demonstrated semi-autonomous construction of an artificial graphene lattice by reinforcement-learning-driven manipulation of CO molecules on Cu(111), with a spectroscopically confirmed Dirac point. The work is explicit that the overarching goal remains open: fully autonomous, closed-loop fabrication in which a target electronic structure is inverse-designed into an adsorbate placement pattern and then built and spectroscopically verified without human intervention. The unresolved components are in-loop automated tip conditioning keyed to manipulation-efficiency metrics, sample-efficient adaptation of the manipulation policy to new tip apices, automated piezo-scanner calibration and throughput scaling for multi-day builds, computational inverse design of placement patterns from target spectra, and extension to magnetic adatoms on superconducting substrates. No cited work has demonstrated the closed loop, leaving the problem open.

Background

Since the first positioning of individual atoms with a scanning tunneling microscope (STM) — an instrument that images and modifies surfaces through the quantum tunneling current between an atomically sharp metal tip and the sample — researchers have built artificial lattices: ordered arrangements of adsorbed atoms or molecules on a crystal surface that impose a designer potential on the surface's two-dimensional electron gas (electrons quantum-mechanically confined to move only within the surface plane), thereby emulating engineered tight-binding models. On the standard Cu(111) platform each adsorbed carbon monoxide (CO) molecule acts as a repulsive scatterer for the surface-state electrons, so a patterned CO array realizes an essentially arbitrary periodic potential. Manually assembled landmarks include molecular graphene, in which CO-positioned 'artificial atoms' produce Dirac cones (energy bands dispersing linearly to a touching point, as in real graphene) at energies set by construction (Gomes et al., 2012); an electronic Lieb lattice with its signature flat band, i.e., a band with negligible dispersion that amplifies interaction effects (Slot et al., 2017); and electrons confined in fractal geometry (Kempkes et al., 2019). The electronic structure is read out by scanning tunneling spectroscopy, in which the differential conductance dI/dVdI/dV is recorded as a function of sample bias and tip position, mapping the local density of states.

This route to designer quantum matter is powerful but slow and artisanal. A human operator must position each molecule using the STM tip; the manipulation parameters (sample bias, current setpoint, speed) must be retuned whenever the fragile tip apex changes state; the piezoelectric scanner that positions the tip has calibration errors and nonlinearities that corrupt absolute placement; and thermal drift accumulates over multi-hour builds. Successive works have automated parts of the task: autonomous atom assembly by path planning (Celotta et al., 2014); reinforcement-learning (RL) control of molecule manipulation, in which an agent learns actions from reward feedback (Leinen et al., 2020; Ramsauer et al., 2023); deep-RL atom manipulation that learns the a-priori-unknown manipulation parameters while contending with spontaneous tip-apex changes (Chen et al., 2022); automated tip conditioning — procedures such as voltage pulses or controlled tip-sample contact that reshape or clean the apex — demonstrated for the imaging and spectroscopy modalities (Krull et al., 2020; Wang et al., 2021; Zhu et al., 2024); and Bayesian-optimization-based autonomous convergence of STM control parameters (Narasimha et al., 2024). None of these integrated conditioning into a manipulation loop, and all lattice patterns were forward-designed by humans.

Narasimha et al. (2025) advanced the state of the art to semi-autonomous fabrication: deep-learning object detection locates CO molecules, a linear-assignment algorithm allocates them to target sites, an offline-trained RL agent (DDPG, an actor-critic algorithm for continuous control) fine-tunes bias, setpoint, and speed in real time, and path planning with active drift compensation enabled a 37-molecule artificial graphene lattice with a spectroscopically confirmed Dirac point, at roughly 1-1.5 minutes per manipulation iteration (about 900 iterations, 25-30 hours total). The same work is explicit about what was not achieved: tip-state changes still required a human operator to intervene, condition the tip, and restart; installing a new tip forced retraining with about 2000 appended experimental transitions; a piezo-calibration error forced manual recalibration of the lattice constant (from 2.54 to 2.26 angstroms) and redesign of the lattice; and the pattern was forward-designed rather than computed from a target electronic structure. The authors identify the inverse problem — designing the artificial lattice structure given the electronic state of interest — as the most important open scientific direction, alongside extension to magnetic adatoms on superconducting substrates toward engineered topological and many-body states (Nadj-Perge et al., 2014 showed the manual version of such assemblies).

Problem Statement

Open problem: achieve fully autonomous, closed-loop fabrication of artificial lattices with prescribed electronic states by STM manipulation of adsorbed atoms or molecules on surfaces. Concretely, given a target electronic structure for an extended lattice — for example a Dirac cone at a specified energy, a flat band in a specified window, or topological edge states at a specified boundary — the task is to (1) compute a placement pattern of adsorbates (such as CO on Cu(111)) predicted to realize that target, where the inverse-design method must map an arbitrary target in this class to a pattern rather than recall an arrangement already known from the literature and must be demonstrated on at least one target whose adsorbate pattern is not already known; and (2) fabricate that pattern autonomously, meaning a system that detects tip-state changes from manipulation-efficiency metrics, performs in-situ tip conditioning appropriate to the current modality (imaging, spectroscopy, or manipulation) without human intervention and resumes fabrication, adapts its manipulation policy to a new tip apex or changed instrument state sample-efficiently rather than through approximately 2000 re-collected transitions with operator supervision, maintains placement precision through automated calibration that compensates piezo-scanner nonlinearities, and keeps cumulative drift and instabilities bounded over multi-day builds; so that (3) the finished lattice's dI/dVdI/dV spectra and maps can be verified against the target specified beforehand. The overarching objective is the closed loop itself — electronic-state specification in, autonomously designed, fabricated, and spectroscopically verified lattice out, with no human intervention during design or fabrication. The components are jointly necessary for that demonstration: an inverse-design method without autonomous fabrication, or autonomy without inverse design, each leaves the loop open. Extension of the same loop to magnetic adatoms on superconducting substrates, toward engineered topological and many-body states, is a further target named by the source but not part of the minimal completion boundary.

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