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Receiving a favor from another person may induce a negative feeling of indebtedness for the beneficiary. In this study, we explore these hidden costs by developing and validating a conceptual model of indebtedness across three studies that combine a large-scale online questionnaire, an interpersonal game, computational modeling, and neuroimaging. Our model captures how individuals perceive the altruistic and strategic intentions of the benefactor. These inferences produce distinct feelings of guilt and obligation that together comprise indebtedness and motivate reciprocity. Perceived altruistic intentions convey care and communal concern and are associated with activity in insula, ventromedial prefrontal cortex and dorsolateral prefrontal cortex, while inferred strategic intentions convey expectations of future reciprocity and are associated with activation in temporal parietal junction and dorsomedial prefrontal cortex. We further develop a neural utility model of indebtedness using multivariate patterns of brain activity that captures the tradeoff between these feelings and reliably predicts reciprocity behavior.

 

The optical conductivity of single layer graphene (SLG) can be significantly and reversibly modified when the Fermi level is tuned by electrical gating. However, so far this interesting property has rarely been applied to free-space two-dimensional (2D) photonic devices because the surface-incident absolute absorption of SLG is limited to 1%–2%. No significant change in either reflectance or transmittance would be observed even if SLG is made transparent upon gating. To achieve significantly enhanced surface-incident optical absorption in SLG in a device structure that also allows gating, here we embed SLG in an optical slot-antenna-coupled cavity (SAC) framework, simultaneously enhancing SLG absorption by up to 20 times and potentially enabling electrical gating of SLG as a step towards tunable 2D photonic surfaces. This framework synergistically integrates near-field enhancement induced by ultrahigh refractive index semimetal slot-antenna with broadband resonances in visible and infrared regimes, ~ 3 times more effective than a vertical cavity structure alone. An example of this framework consists of self-assembled, close-packed Sn nanodots separated by ~ 10 nm nanogaps on a SLG/SiO2/Al stack, which dramatically increases SLG optical absorption to 10%-25% at λ = 600–1,900 nm. The enhanced SLG absorption spectrum can also be controlled by the insulator thickness. For example, SLG embedded in this framework with a 150 nm-thick SiO2 insulating layer displays a distinctive red color in contrast to its surrounding regions without SLG on the same sample under white light illumination. This opens a potential path towards gate-tunable spectral reflectors. Overall, this work initiates a new approach towards tunable 2D photonic surfaces.