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Register a new userInfrared Problem in Cold Atom Quantum Physisorption on 2D Materials
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Results from four different approximations to the phonon-assisted quantum adsorption rate for cold atoms on a 2D material are compared and contrasted: (1) a loop expansion (LE) based on the atom-phonon coupling, (2) non-crossing approximation (NCA), (3) independent boson model approximation (IBMA), and (4) a leading-order soft-phonon resummation method (SPR). We conclude that, of the four approximations considered, only the SPR method gives a divergence-free result in the large membrane regime at finite temperature. The other three methods give an adsorption rate that diverges in the limit of an infinite surface.
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Two-dimensional (2D) materials for their versatile band structures and strictly 2D nature have attracted considerable attention over the past decade. Graphene is a robust material for spintronics owing to its weak spin-orbit and hyperfine interactions, while monolayer 2H-transition metal dichalcogenides (TMDs) possess a Zeeman effect-like band splitting in which the spin and valley degrees of freedom are nondegenerate. Monolayer 1T-TMDs are 2D topological insulators and are expected to host Majorana zero modes when they are placed in contact with S-wave superconductors. Single electron transport as well as the superconductor proximity effect in these materials are viable for use in both conventional quantum computing and fault-torrent topological quantum computing. In this chapter, we review a selection of theoretical and experimental studies addressing the issues mentioned above. We will focus on: (1) the confinement and manipulation of charges in nanostructures fabricated from graphene and 2H-TMDs (2) 2D materials-based Josephson junctions for possible superconducting qubits (3) the quantum spin Hall states in 1T-TMDs and their topological properties. We aim to outline the current challenges and suggest how future work will be geared towards developing quantum computing devices in 2D materials.
The phonon-assisted sticking rate of slow moving atoms impinging on an elastic membrane at nonzero temperature is studied analytically using a model with linear atom-phonon interactions, valid in the weak coupling regime. A perturbative expansion of the adsorption rate in the atom-phonon coupling is infrared divergent at zero temperature, and this infrared problem is exacerbated by finite temperature. The use of a coherent state phonon basis in the calculation, however, yields infrared-finite results even at finite temperature. The sticking probability with the emission of any finite number of phonons is explicitly seen to be exponentially small, and it vanishes as the membrane size grows, a result that was previously found at zero temperature; in contrast to the zero temperature case, this exponential suppression of the sticking probability persists even with the emission of an infinite number of soft phonons. Explicit closed-form expressions are obtained for the effects of soft-phonon emission at finite temperature on the adsorption rate. For slowly moving atoms, the model predicts that there is zero probability of sticking to a large elastic membrane at nonzero temperature and weak coupling.
Quantum electrodynamics (QED) provides a highly accurate description of phenomena involving the interaction of atoms with light. We argue that the quantum theory describing the interaction of cold atoms with a vibrating membrane--quantum acoustodynamics (QAD)--shares many issues and features with QED. Specifically, the adsorption of an atom on a vibrating membrane can be viewed as the counterpart to QED radiative electron capture. A calculation of the adsorption rate to lowest-order in the atom-phonon coupling is finite; however, higher-order contributions suffer from an infrared problem mimicking the case of radiative capture in QED. Terms in the perturbation series for the adsorption rate diverge as a result of massless particles in the model (flexural phonons of the membrane in QAD and photons in QED). We treat this infrared problem in QAD explicitly to obtain finite results by regularizing with a low-frequency cutoff that corresponds to the inverse size of the membrane. Using a coherent state basis for the soft phonon final state, we then sum the dominant contributions to derive a new formula for the multiphonon adsorption rate of atoms on the membrane that gives results that are finite, nonperturbative in the atom-phonon coupling, and consistent with the KLN theorem. For micromembranes, we predict a reduction with increasing membrane size for the low-energy adsorption rate. We discuss the relevance of this to the adsorption of a cold gas of atomic hydrogen on suspended graphene.
The recent discovery of ferromagnetism in 2D van der Waals (vdw) crystals has generated widespread interest, owing to their potential for fundamental and applied research. Advancing the understanding and applications of vdw magnets requires methods to quantitatively probe their magnetic properties on the nanoscale. Here, we report the study of atomically thin crystals of the vdw magnet CrI$_3$ down to individual monolayers using scanning single-spin magnetometry, and demonstrate quantitative, nanoscale imaging of magnetisation, localised defects and magnetic domains. We determine the magnetisation of CrI$_3$ monolayers to be $approx16~mu_B/$nm$^2$ and find comparable values in samples with odd numbers of layers, whereas the magnetisation vanishes when the number of layers is even. We also establish that this inscrutable even-odd effect is intimately connected to the material structure, and that structural modifications can induce switching between ferro- and anti-ferromagnetic interlayer ordering. Besides revealing new aspects of magnetism in atomically thin CrI$_3$ crystals, these results demonstrate the power of single-spin scanning magnetometry for the study of magnetism in 2D vdw magnets.
Uncertainty relations are studied for a characterization of topological-band insulator transitions in 2D gapped Dirac materials isostructural with graphene. We show that the relative or Kullback-Leibler entropy in position and momentum spaces, and the standard variance-based uncertainty relation, give sharp signatures of topological phase transitions in these systems.
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