Confined vacuum resonances as artificial atoms with tunable lifetime

Abstract

Atomically engineered artificial lattices are a useful tool for simulating complex quantum phenomena, but have so far been limited to the study of Hamiltonians where electron-electron interactions do not play a rolebut it's precisely the regime in which these interactions do matter where computational times lend simulations a critical advantage over numerical methods. Here, we propose a new platform for constructing artificial matter that relies on the confinement of field-emission resonances, a class of vacuum-localized discretized electronic states. We use atom manipulation of surface vacancies in a chlorine-terminated Cu(100) surface to reveal square patches of the underlying metal, thereby creating atomicallyprecise potential wells that host particle-in-a-box modes. By adjusting the shape and size of the confining potential, we can access states with different quantum numbers, making these patches attractive candidates as quantum dots or artificial atoms. We demonstrate that the lifetime of electrons in these engineered states can be extended and tuned through modification of the confining potential, either via atomic assembly or by changing the tip-sample distance. We also demonstrate control over a finite range of state-filling, a parameter which plays a key role in the evolution of quantum many-body states. We model the transport through the localized state to disentangle and quantify the lifetime-limiting processes, illustrating the critical dependency of the electron lifetime on the properties of the underlying bulk band structure. The interplay with the bulk bands also gives rise to negative differential resistance,

Normalization procedure for obtaining the local density of states from high-bias scanning tunneling spectroscopy

“…However, it is in general possible to make a reasonable estimate of this parameter [5]. In the particular case of field-emission resonances, the absolute distance can be estimated by modelling the out-of-plane potential to match the experimental and calculated energies of the resonances [13]. In either case, the exact value of z 0 does not dramatically affect the spectral shape of the normalized differential conductance: for a wide range of z 0 values, the peak positions and widths remain roughly constant, while the relative height of the peaks are subject to variation (see Fig 2) [5].…”

“…Here, we focus specifically on laterally confined fieldemission resonances [13]: we arrange single vacancies on the chlorinated Cu(100) surface [25][26][27] to reveal square patches of the underlying metal surface, creating atomically precise potential wells, which we refer to by their size in unit cells. In doing so, we generate particle-in-abox states that carry some finite k .…”

“…Having ascertained that our normalization procedure is robust for different spectroscopic modes, and yields consistent results against a varying z 0 , we now focus on how it fares compared to the expected (calculated) local density of states. To calculate the local density of states, we model the potential landscape of the laterally confined field-emission resonances using a finite well with slanted walls where the depth of the well is set by the workfunction difference between the chlorinated and bare Cu(100) surfaces and the slope of the walls by the Fermi wavelength [13]. From this, we can calculate the expected eigenstates and energies to determine the LDOS, which is simply given by |Ψ| 2 .…”

“…We extend this model to account for the kselectivity of tunneling electrons, and apply it to spectroscopic measurements-performed in both measurement modes-of confined field emission resonances. The particle-in-a-box modes generated by this confinement have a well-defined in-plane momentum [13], a characteristic that makes them ideally suited to normalization via a k-dependent scheme.…”

“…2.Local density of states extracted from constant-height and constant-current spectroscopic data. a Constant-height (light green) and constant-current (dark blue) differential conductance spectroscopy probing confined fieldemission resonances on the chlorinated Cu(100) surface[13], obtained at current set-point of 250pA. b, c The raw dI/dV is normalized to obtain the local density of states, with (c) and without (b) considering the in-plane momentum of the probed state, for both the constant-height (light gray) and constant-current (maroon) measurements.…”