PNR synthesis
PNRs were synthesized as reported in ref. 21. In short, in an argon glovebox (less than 0.1 ppm O2, less than 0.1 ppm H2O) black phosphorus (2D Semiconductors Ltd or Smart Elements) was ground using a pestle and mortar into roughly 1-mm flakes and 124 mg (in a typical synthesis) was transferred to a glass tube fitted with a metal Swagelok valve, alongside 3.5 mg freshly cut lithium metal (Sigma Aldrich, 99% rod). The tube was evacuated (roughly 10−7 mbar) and cooled to −50 °C and ammonia gas (Sigma Aldrich, 99.95%, precleaned by condensation over excess lithium metal) was condensed to submerge the lithium and phosphorus. The solution immediately turned dark blue from the formation of lithium-ammonia solution, and slowly turned orange over 16 h. The ammonia was then evaporated and the LiP8 salt was dried under vacuum (roughly 10−7 mbar) at room temperature. The LiP8 (10 mg) was then placed in 10 ml of either NMP (Sigma Aldrich, 99.5% anhydrous) or DMF (Sigma Aldrich, 99.9% anhydrous) that had been dried with 4-Å molecular sieves for 1 week. The mixtures were bath sonicated for 30 min, before centrifuging (100g, 10 min) and decanting in a glovebox to give solutions of PNRs.
Single PNR AFM
PNR samples were prepared by means of dropcasting from solution onto freshly cleaved graphite (HOPG) substrates as discussed in ref. 21. High-resolution topography maps were then collected using contact-mode high-speed AFM (HS-AFM; Bristol Nano Dynamics Ltd) with silicon nitride microcantilevers (MSNL-10, Bruker) with nominal tip radii of 2 nm. To ensure that the images obtained featured tip-limited lateral resolution scan sizes of 0.8 × 0.5 µm were used, corresponding to pixel sizes of roughly 1 × 1 nm.
HS-AFM images containing ribbons selected for analysis were input into custom LabVIEW image analysis software (National Instruments) that isolated the ribbon from the background in an automated fashion before generating histograms of ribbon height and width. In brief, the algorithm consisted of: a local thresholding step to identify the ribbon; a mask step to separate pixels corresponding to the background from the ribbon; an erosion step to remove the edge pixels where the AFM tip traverses the slope between the background and ribbon; calculation of height histograms for both the background and ribbon pixels and finally Gaussian fits to the histograms to recover the mean height of each and enable calculation of the height of the ribbon with respect to the background.
The width of the ribbon was analysed in parallel using the same algorithm. After the masking step the central axis of the isolated ribbon was determined by fitting cubic splines to the two edges of the ribbon and calculating the mean of these two edges. Then, the width of the ribbon was determined by calculating the distance to the central axis from each edge. Measurements of the width of the ribbon along its entire length were then input into a histogram and fit with a Gaussian distribution to identify the mean width of the PNR.
Magnetic linear dichroism and birefringence
The degree of magnetic alignment is measured optically through the magnetic field-induced linear dichroism and birefringence by using green and red Helium Neon lasers (wavelengths 543 and 632.5 nm, respectively). The solution samples were contained in an optical cuvette (thickness 5 or 10 mm) positioned within a temperature-controlled environment at 20.0 ± 0.1 °C in a 33-T Florida–Bitter electromagnet or a Varian V-3900 2-T magnet. The linear dichroism and linear birefringence signals were measured using standard polarization modulation techniques using a photo-elastic modulator50.
SQUID magnetometry
Magnetization measurements were obtained in a Quantum Design Magnetic Properties Measurement System (MPMS 3) using a SQUID magnetometer. Measurements were performed down to 1.8 K and up to 350 K, in various applied magnetic field strengths up to 7 T. Data for two magnetization–temperature curves of PNRs are shown in the inset of Fig. 1d. Each magnetization–temperature curve was measured starting at 1.8 K and increasing the temperature in a constant probing field of 50 mT. Before beginning any new magnetic field or temperature scan the system was taken to 300 K and the magnet was reset to remove any stray flux from the SQUID. Samples were secured on an MPMS quartz sample holder using GE varnish, and care was taken to ensure that they were not touched by any magnetic material throughout the mounting and loading procedure. For each measurement, several d.c. magnetization measurements were averaged, providing a reliable measure of the bulk magnetization of the PNR samples.
For measuring the PNRs in the DMF and NMP solutions (Supplementary Fig. 23), 10 μl were pipetted into a plastic (polypropylene) straw or capsule (polypropylene). The capsule was fixed to a quartz rod using GE varnish, and the presence of PNRs increased the magnetization by two orders of magnitude when compared to the GE and straw or capsule by itself. The d.c. moment was averaged over several scans, and between each experimental run the MPMS was brought to 300 K and the magnet was reset to remove any remaining flux in the SQUID. Oxygenation of the PNR was performed by bubbling air through PNRs in the plastic capsule for roughly 20 min while ensuring the sample it did not come into contact with any metallic substances. See also Supplementary Notes 10, 11 and 24 for further details.
EPR
For the cwEPR experiments, 100 µl of PNR in DMF solution was placed into a 3.9-mm-outer-diameter (2.9-mm-inner-diameter) quartz EPR tube inside a nitrogen glovebox. The sample tube was attached to a custom adaptor and transferred to a pumping station outside the glovebox. The custom adaptor keeps the sample in the inert glovebox environment. The solution was evaporated under vacuum (using a pumping station), resulting in a film on the inner walls of the EPR tube. The procedure was repeated four times to achieve a thicker film and in total 400 µl was evaporated. The inner wall sample was then left to pump to a pressure of 6 × 10−4 mbar and flame sealed.
Narrow magnetic field scan rotation and temperature series (setup 1)
The cwEPR spectra were recorded at X-band (roughly 9.4 GHz) using a laboratory-built EPR spectrometer (all narrow scan cwEPR spectra were rescaled to 9.4 GHz). The setup for the rotation and temperature series consisted of a Bruker ER 041 MR microwave bridge together with an ER 048R microwave controller and an AEG electromagnet together with a Bruker BH 15 Hall effect field controller. The magnetic field was also monitored with a Bruker ER 035M NMR Gaussmeter. The resonator used was a Bruker ER 4122-SHQE resonator. The static magnetic field was modulated at 100 kHz and lock-in detection was carried out using a Stanford Research SR810 lock-in amplifier in combination with a Wangine WPA-120 audio amplifier. An ESR 900 helium flow cryostat together with a ITC503 temperature controller (Oxford Instruments) was used for low-temperature measurements. The spectra were acquired at a frequency of roughly 9.4 GHz with a microwave power of 7.96 mW and 1-mT modulation amplitude. The magnetic field was calibrated using a standard N@C60 sample with a known g factor.
The narrow magnetic field scans presented in the main text (Fig. 2c) have had the FMR signal (slope) removed from them using an appropriate polynomial fit. See Supplementary Note 15 for further details.
Wide magnetic field scan rotation study (setup 2)
The cwEPR spectra were recorded at the X-band (roughly 9.55 GHz) using a laboratory-built EPR spectrometer (all wide-scan cwEPR spectra were rescaled to 9.55 GHz). The setup for the rotation study consisted of a Bruker ER 046 XK-T microwave bridge together with an ER 048R microwave controller and a Varian electromagnet together with a Bruker ER 032M Hall effect field controller. The resonator used was a Bruker MD5 dielectric ring resonator. The static magnetic field was modulated at 99 kHz and lock-in detection was carried out using a Stanford Research SR830 lock-in amplifier in combination with a Wavetek 50 MHz function generator model 80. The wide magnetic field measurement was carried out at 296 K. The spectra were acquired at a frequency of roughly 9.55 GHz with a microwave power of 7.96 μW and 0.4-mT modulation amplitude.
Wide magnetic field scan without low-temperature insert rotation series (setup 3)
The wide magnetic field scan without a low-temperature insert (rotation series) was carried out on a Bruker ElexSys E580 spectrometer, with a Bruker ER 4122-SHQE resonator. The SHQE cavity is the same type of cavity as used in the narrow field range setup ‘setup 1’. However, this time we used the cavity without the low-temperature Dewar insert, as this insert can have background signals. The reason for using the Bruker ElexSys E580 is that it allowed us to do the full magnetic field sweep using the SHQE resonator. The spectra were acquired at a frequency of roughly 9.85 GHz with a microwave power of 8.05 μW and 0.4-mT modulation amplitude.
Scanning tunnelling microscopy
All scanning tunnelling microscopy (STM) experiments were performed on a commercial Omicron LT-STM at 4.2 K using PtIr STM tips. Samples were prepared by aerosolizing PNRs dispersed in NMP onto a HOPG substrate to minimize aggregation on the surface51. The deposition parameters and the concentration and/or density of PNRs on the surface were optimized using ambient AFM imaging. For ultra-high vacuum-STM experiments PNRs were aerosolized onto a freshly cleaved HOPG substrate using an Iwata Custom Micron CM-C airbrush. The coated substrate was immediately transferred into the vacuum chamber and annealed for more than 1 h at 150 °C before transferring the substrate to the STM sample stage (extended annealing or heating greater than 150 °C led to partial degradation of PNRs). Supplementary Note 5 contains further details on the STM imaging.
Transient absorption spectroscopy
The transient absorption measurements from 550 to 930 nm were performed using a home-built setup around a Yb-doped potassium gadolinium tungstate (Yb:KGW) amplifier laser (1,030 nm, 38 kHz, 15 W, Pharos, LightConversion). The probe pulse was a chirped seeded white light continuum created using a 4-mm yttrium aluminium garnet (YAG) crystal that spanned from 500 to 950 nm. For the source of the pump pulse (roughly 200 fs) a commercial optical parametric amplifier OPHEUS ONE (LightConversion) was used.
The transient absorption measurements from 400 to 550 nm were performed using a home-built setup around a Ti-sapphire (800 nm, 1 kHz, Spectra-Physics, Solstice Ace). The probe pulse was a chirped seeded white light continuum created using a 4-mm CaF2 crystal that spanned from 400 to 600 nm. For the source of the pump pulse (roughly 100 fs), the fundamental of the laser was doubled in a β-barium borate crystal.
The sub-1-T magnetic field was generated using an electromagnet from GMW Model 3470 with 1-cm distance between cylindrical poles and the field strength calibrated with a Gaussmeter.
Impulsive Raman spectroscopy
Femtosecond time-domain Raman spectroscopy measurements were performed using a home-built setup around a Yb:KGW amplifier laser (1,030 nm, 38 kHz, 15 W, Pharos, LightConversion). The probe pulse was a chirped seeded white light continuum created using a 4-mm YAG crystal that spanned from 500 to 950 nm. The pump pulse for the resonant experiment was created using a non-collinear optical parametric amplifier where the 1,030 nm seeded a white light continuum stage in sapphire that was subsequently amplified with the third harmonic of the 1,030-nm laser in a β-barium borate crystal to create a broad pulse centred at 550 nm. The pump pulse for the off-resonant experiment was created using a non-collinear optical parametric amplifier where the 1,030 nm seeded a white light continuum stage in a YAG crystal that was subsequently amplified with the third harmonic of the 1,030-nm laser in a β-barium borate crystal to create a broad pulse centred at 750 nm. Both pulses were compressed using a chirped mirror and wedge prism (Layerterc) combination to a temporal duration of under 15 fs. Compression was determined by second-harmonic generation frequency-resolved optical gating (upper limit) and further confirmed by reference measurements on acetonitrile where the 2,200 cm−1 mode could be resolved. The probe white light was delayed using a computer-controlled piezoelectric translation stage (Physik Instrumente), and a sequence of probe pulses with and without pump was generated using a chopper wheel (Thorlabs) on the pump beam. The average fluence of the pump 10 μJ cm−2.
Transient absorption microscopy
Pulses were delivered by a Yb:KGW amplifier (Pharos, LightConversion, 1,030 nm, 5 W, 200 kHz) that seeded two broadband white light stages. The probe white light was generated in a 3-mm YAG crystal and adjusted to cover the wavelength range from 650 to 950 nm by a fused-silica prism-based spectral filter. By contrast, the pump white light was generated in a 3-mm sapphire crystal to extend the white light in the high frequency to 500 nm, with pulse short-pass filtered at 650 nm (Thorlabs, FESH650). The pump pulses were focused onto the sample using a single-lens oil-immersion objective (×100, numerical aperture (NA) 1.1) to a diffraction-limited spot of roughly 270 nm (full-width at half-maximum, full bandwidth). By contrast, the counter-propagating probe pulses were loosely focused onto the sample by a concave mirror (full-width at half-maximum, roughly 15 μm). A set of third-order corrected chirped mirrors (pump white light, Layertec; probe white light, Venteon) in combination with a pair of fused-silica wedge prisms (Layertec) compressed the pulses to sub-15 fs at the sample. The transmitted probe light was collected by the same objective used to focus the pump pulses. The probe was then relayed to a spectrometer consisting of a slit in the intermediate image plane and a F2 prism to disperse the light perpendicular to the slit. This allowed us to access spectrally dispersed transient absorption microscopy images of the PNRs over a selected region. The differential nature of the imaging was achieved by modulating the pump beam at 45 Hz by a mechanical chopper. All recording was performed with an EMCCD camera (Qimaging Rolera Thunder, Photonmetrics). The axial focus position was maintained by an extra auto-focus line based on total internal reflection of a 405-nm continuous wave laser beam.
Ensemble photoluminescence measurements
Steady-state photoluminescence
Photoluminescence experiments were performed using a home-made confocal-like setup using a large working-distance microscope objective (NA roughly 0.55) to focus light on the nanoribbons and collect the emission in a reflection configuration. In the studies, PNRs are dispersed (dropcasting method) on glass slides (thickness roughly 100 μm) and glued (with silver lacquer) on the cold finger of a cryostat designed for thermal expansion compensation (from Oxford Instruments). The photoluminescence signal was analysed by using a 75-cm focal length spectrometer (Acton sp2750i, Princeton Instruments) itself coupled to a nitrogen cooled CCD (Spec10, Princeton Instruments), a combination that leads to a roughly 100 μeV energy resolution, well beyond the resolution required to address the broad PNRs photoluminescence components. To minimize the scattered light, the excitation was tuned to 416 nm (second-harmonic generation of a Ti:sapphire laser, pulse width of roughly 2 ps, 80-MHz repetition rate) and a dichroic filter (Semrock FF01-430/LP-25, 50% cut-off at 437 nm) was placed in the detection path. The photoluminescence polarization was analysed using a classical scheme: a motorized half-waveplate, positioned upstream along the detection beam path, allowing us to rotate the polarization of the PNR emission that was further analysed using a polarizer (Glan-Taylor, calcite) placed in front of the spectrometer slit (with its direction set parallel to the grating grooves to enhance the CCD response).
Time-resolved photoluminescence
The spectro-temporal photoluminescence maps were measured using a streak-camera synchronized with the high repetition rate Ti:sapphire laser (C5680 model from Hamamatsu incorporating a M5675 synchroscan unit). All measurements were carried out in the confocal configuration described above, the camera being directly coupled to the Acton spectrometer, using a deflection mirror and imaging the nanoribbons’ spectra on the entrance slit of the camera. The response function of the camera was measured as the response to laser excitation with an instrument response function curve that demonstrates a time resolution of roughly 22 ps across the detection range to the setup. The same cryostat and mounting as for steady-state photoluminescence measurements were used for the time-resolved measurements.
Single PNR photoluminescence imaging and spectroscopy
Spinning disk confocal photoluminescence measurements were performed with a commercial Nikon X-Light V2 microscope, with a ×100 1.52 NA oil-immersion objective. Excitation in all cases was at 390 nm with nominal laser powers (at the laser output) between 20 and 50 mW. Imaging was performed with a 40 μm confocal pinhole and iXon 897 EMCCD Camera (Andor). The lateral resolution in such measurements was around 120 nm. For the measurement of photoluminescence spectra from individual PNRs, the microscope emission outcoupling-arm was modified to pass the photoluminescence to a spectrograph (Kymeria 193i; 600 lines per millimetre grating; 600-nm blaze) with the emission once again measured by an iXon 897 EMCCD. Typical accumulation times of 1–2 min were used to collect spectra from the PNRs with a collection area on the sample of 0.1 μm.
Absorption spectroscopy
Temperature dependent PNR absorption
An Agilent Cary 6000i ultraviolet–visible light with near infrared spectrophotometer with blank substrate correction was used. Here 400 μl of PNR solution was dropcast onto fused-silica substrates and placed in a continuous-flow cryostat (Oxford Instruments Optistat CF-V) under a continuous inert atmosphere. Samples were cooled to 6 K with the temperature dependent absorption taken on heating.
Individual PNR absorption spectroscopy
Absorption spectroscopy of individual (large, greater than 300 nm wide) PNRs was performed on a customized Zeiss Axio microscope with illumination provided by a halogen lamp (Zeiss HAL100). Transmitted light was collected using a ×50/0.4 objective (Nikon, T Plan SLWD) and spatially filtered using a 100-μm-diameter optical fibre (Avantes FC-UV100-2-SR) mounted in confocal configuration and connected to a spectrometer (Avantes AvaSpec-HS2048). PNR samples were prepared by means of dropcasting from solution onto cleaned (Acetone/IPA) 0.17-mm-thick glass slides.
Pressure dependent absorption
To study the pressure dependence of the PNRs, transmittance spectra were measured with a LAMBDA 750 ultraviolet–visible light with near infrared spectrophotometer (Perkin Elmer). The PNR solutions were dried in an inert atmosphere and then placed inside a high-pressure cell (ISS Inc.) filled with an inert liquid, Fluorinert FC-72 (3 M). Hydrostatic pressure was generated through a pressurizing liquid using a manual pump. Before using, the liquid was degassed in a Schlenk line to remove oxygen that caused, from 300 MPa onwards, scattering of a fraction of light and therefore a reduction of the transmitted signal from the sample. The pressure was applied from ambient pressure to 300 MPa in steps of 50 MPa. Before the measurement, we waited 7 min for equilibration of the material under pressure. We estimated an error of the pressure reading to be 20 MPa.
Raman measurements
Temperature-dependent Raman spectroscopy
Raman spectra were measured as a function of temperature from 4 to 300 K. Raman measurements were conducted by backscattering (T64000, Horiba) a continuous wave diode line (532 nm, 1 mW). Spectra were collected at more than 200 cm−1, where the CCD detector (Horiba Synapse Open-Electrode) had a monotonically increasing quantum efficiency of 0.43–0.50. Acquisitions used a ×100 optical objective and used minimal laser intensity to avoid sample degradation.
Raman imaging
For Raman imaging a standard layout of an epi-detected Raman microscope was used. A pump laser beam (wavelength 532 nm, Coherent Mira) was spectrally cleaned up by a bandpass filter (FLH05532-4, Thorlabs), and its beam width was expanded to 7.2 mm before entering a home-built inverted microscope. Further waveplates (half-waveplate and quarter-waveplate for 532 nm, Foctek Photonics) precompensated the ellipticity introduced by the dichroic filter (F38-532_T1, AHF) and also generated circularly polarized light. We used high NA oil-immersion objectives (Nikon ×60/1.4 NA oil) to ensure high-resolution imaging and increase collection efficiency. The pump power before the objective was 30 mW, a power level that ensured no degradation of samples. The samples were scanned with galvanometric mirrors (Thorlabs). The Raman inelastic backscattered light was collected by the same objective and focused with the microscope tube lens onto the slit of a spectrometer (Andor, Shamrock 303i, grating 300 lines mm−1; the slit also acts an effective pinhole for confocal detection). The spectrometer is equipped with a high-sensitivity charge-coupled camera (Andor, iXon 897). The image presented was taken with an integration time per pixel of 500 ms. Recording of data was performed by a custom MATLAB program. For Raman imaging, black phosphorous flakes (300–600-nm thickness; 2D Semiconductors Ltd) were mechanically exfoliated inside a nitrogen glovebox and transferred onto a Si substrate. A 0.15-mm-thick coverslip was placed over the flakes and sealed with epoxy glue to act as an encapsulant. The polarization of the pump and Raman light was not strongly controlled, but simply adjusted to maximize the respective signals.
