Nitrogen vacancy (NV) centres in diamond are attractive as quantum sensors owing to their superb coherence under ambient conditions. However, the NV centre spin resonances are relatively insensitive to some important parameters such as temperature. Here we design and experimentally demonstrate a hybrid nano-thermometer composed of NV centres and a magnetic nanoparticle (MNP), in which the temperature sensitivity is enhanced by the critical magnetization of the MNP near the ferromagnetic-paramagnetic transition temperature. The temperature susceptibility of the NV center spin resonance reached 14 MHz/K, enhanced from the value without the MNP by two orders of magnitude. The sensitivity of a hybrid nano-thermometer composed of a Cu1-xNix MNP and a nanodiamond was measured to be 11 mK/Hz 1/2 under ambient conditions. With such high-sensitivity, we monitored nanometer-scale temperature variation of 0.3 degree with a time resolution of 60 msec. This hybrid nano-thermometer 2 provides a novel approach to studying a broad range of thermal processes at nanoscales such as nano-plasmonics, sub-cellular heat-stimulated processes, thermodynamics of nanostructures, and thermal remanent magnetization of nanoparticles. MAIN TEXT:Nanoscale temperature sensing is important for studying a broad range of phenomena in physics, biology, and chemistry, such as the temperature heterogeneities 1-3 in living cells, heat dissipation in nano circuits 4 , nano-plasmonics, and nano-magnetism (like thermal remanent magnetism of nanoparticles). There have been a number of nanoscale temperature detection schemes 5, 6 , such as scanning thermal microscopy (SThM) 7-9 , SQUID based nano-thermometer 10 , and fluorescence thermometers 11 based on rare-

Diamond nitrogen-vacancy (NV) center-based magnetometry provides a unique opportunity for quantum bio-sensing. However, NV centers are not sensitive to parameters such as temperature and pressure, and immune to many biochemical parameters such as pH and non-magnetic biomolecules. Here, we propose a scheme that can potentially enable the measurement of various biochemical parameters using diamond quantum sensing, by employing stimulus-responsive hydrogels as a spacing transducer in-between a nanodiamond (ND, with NV centers) and magnetic nanoparticles (MNPs). The volume phase transition of hydrogel upon stimulation leads to sharp variation in the separation distance between the MNPs and the ND. This in turn changes the magnetic field that the NV centers can detect sensitively. We construct a temperature sensor under this hybrid scheme and show the proof-of-the-principle demonstration of reversible temperature sensing. Applications in the detection of other bio-relevant parameters are envisioned if appropriate types of hydrogels can be engineered.

Nitrogen-vacancy (NV) centers in diamond are promising quantum sensors for their long spin coherence time under ambient conditions. However, their spin resonances are relatively insensitive to non-magnetic parameters such as temperature. A magnetic-nanoparticle-nanodiamond hybrid thermometer, where the temperature change is converted to the magnetic field variation near the Curie temperature, was demonstrated to have enhanced temperature sensitivity ($11{\rm{\;mK\;H}}{{\rm{z}}^{ - 1/2}}$)  [Phys. Rev. X 8, 011042 (2018)], but the sensitivity was limited by the large spectral broadening of ensemble spins in nanodiamonds. To overcome this limitation, here we show an improved design of a hybrid nanothermometer using a single NV center in a diamond nanopillar coupled with a single magnetic nanoparticle of copper-nickel alloy, and demonstrate a temperature sensitivity of $76{\rm{\;\mu K\;H}}{{\rm{z}}^{ - 1/2}}$. This hybrid design enables detection of 2 millikelvin temperature changes with temporal resolution of 5 milliseconds. The ultra-sensitive nanothermometer offers a new tool to investigate thermal processes in nanoscale systems.

Motivated by the recent atomic-scale scanning tunneling microscope (STM) observation for a spatially localized in-gap state in an electron doped Mott insulator, we evaluate the local electronic state of the Hubbard model on the square lattice using the cluster perturbation theory. An in-gap state is found to exist below the upper Hubbard band around the dopant lattice site, which is consistent with the STM measurements. The emergence of this local in-gap state is accompanied with a rapid reduction of the double occupancy of electrons. A similar in-gap state is also found to exist on the triangular lattice. These results suggest that the in-gap state is an inherent feature of Mott insulators independent of the lattice structure.PACS numbers: 74.72. Cj, 71.27.+a, 71.10.Fd The mechanism underlying high-T c superconductivity in cuprates remains one of the most challenging and fundamental problems in condensed matter physics [1]. All cuprate superconductors have a layered structure made up of one or more CuO 2 planes. Their parent compounds have one unpaired electron per Cu unit cell, which constitutes a Mott insulating ground state with an antiferromagnetic (AF) long range order [2]. By doping holes or electrons to CuO 2 planes, the AF order is suppressed and a superconducting phase emerges above a critical doping concentration. The evolution from the AF Mott insulating phase to the superconducting phase induced by doping is highly non-trivial [1]. A thorough investigation on the charge and spin dynamics of doped Mott insulators is believed to be the key for the understanding of extraordinary phenomena observed in high-T c superconductors, such as the pseudogap effect.The dynamics of a single hole in an antiferromagnetic Mott insulator has been extensively studied using the self-consistent Born approximation [3][4][5][6][7][8], finite-size exact diagonalization [9][10][11] and quantum Monte Carlo [12,13] methods, based on the t−J-type model. It was predicted that the single-particle spectrum consists of a sharp coherent peak, corresponding to a quasiparticle excitation, and an incoherent background. But this sharp coherent peak was not observed in the spectrum of electrons measured by angle-resolved photoemission spectroscopy on Sr 2 CuO 2 Cl 2 [14] and Ca 2 CuO 2 Cl 2 [15,16]. To reconcile the difference between theory and experiments, two kinds of scenarios were proposed to explain why the sharp quasipartilcle peak is absent. One is to attribute this absence of sharp peak as an extrinsic effect induced by electron-phonon coupling [17]. The other regards this as an intrinsic effect resulting from a selflocalization of doped holes in an AF background which smears out the coherent peak. From the self-consistent mean-field approximation (SCMFA), indeed it was found that the charge excitations are self-localized in a staggered AF ordered state [18][19][20]. This kind of charge self-localization was also predicted to exist in a singlehole Hubbard model by considering the non-perturbative phase string effect [21] or i...

Spatially resolved information about material deformation upon loading is critical to evaluating mechanical properties of materials, and to understanding mechano-response of live systems. Existing techniques may access local properties of materials at nanoscale, but not at locations away from the force-loading positions. Moreover, interpretation of the local measurement relies on correct modeling, the validation of which is not straightforward. Here we demonstrate an approach to evaluating non-local material deformation based on the integration of nanodiamond orientation sensing and atomic force microscopy nanoindentation. This approach features a 5 nm precision in the loading direction and a sub-hundred nanometer lateral resolution, high enough to disclose the surface/interface effects in the material deformation. The non-local deformation profile can validate the models needed for mechanical property determination. The non-local nanometer-precision sensing of deformation facilitates studying mechanical response of complex material systems ranging from impact transfer in nanocomposites to mechano-response of live systems.