Ohm's law describes the proportionality of current density and electric field.  In solid-state conductors, Ohm's law emerges due to electron scattering processes that relax the electrical current.  Here, we use nitrogen-vacancy center magnetometry to directly image the local breakdown of Ohm's law in a narrow constriction fabricated in a high mobility graphene monolayer.  Ohmic flow is visible at room temperature as current concentration on the constriction edges, with flow profiles entirely determined by sample geometry.  However, as the temperature is lowered below 200 K, the current concentrates near the constriction center.  The change in the flow pattern is consistent with a crossover from diffusive to viscous electron transport dominated by electron-electron scattering processes that do not relax current.

GENERAL INFORMATION

1. Title of Dataset: Imaging the breakdown of ohmic transport in graphene

2. Author Information
    A. Name: Alec Jenkins
        Institution: Department of Physics, University of California, Santa Barbara CA

    B. Name: Susanne Baumann
        Institution: Department of Physics, University of California, Santa Barbara CA
    
    C. Name: Haoxin Zhou
        Institution: Department of Physics, University of California, Santa Barbara CA

    D. Name: Simon A. Meynell
        Institution: Department of Physics, University of California, Santa Barbara CA

    E. Name: Daipeng Yang
        Institution: Department of Physics, University of California, Santa Barbara CA

    F. Name: Kenji Watanabe
        Institution: Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

    G. Name: Takashi Taniguchi
        Institution: International Center for Materials Nanoarchitectonics, National Institute for Materials Science,  1-1 Namiki, Tsukuba 305-0044, Japan

    H. Name: Andrew Lucas
        Institution: Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder CO

    H. Name: Andrea F. Young
        Institution: Department of Physics, University of California, Santa Barbara CA

    H. Name: Ania C. Bleszynski Jayich
        Institution: Department of Physics, University of California, Santa Barbara CA

3. Date of data collection: 

4. Geographic location of data collection: 2019-04-21 to 2019-08-22

DATA & FILE OVERVIEW
 
All data files are included in this folder structure. The data are organized in the following structure:

graphene device -> data type (calibration, NV scanning, or transport) -> temperature -> gate voltage**

*transport data files contain a range of gate voltages.

1. A. NV scanning data files have the name format "scanData__[num]_[date]_[time].mat". These files contain data organized in a matlab struct format and can, for example, be accessed in python using the "loadmat" package. 

These files contain geometric scanning parameters:

scan.xLen, scan.yLen, scan.xSize, scan.ySize, scan.fineBox, scan.midBox, scan.xCenter, scan.yCenter, scan.xPos, scan.yPos, scan.direction, scan.stepNum, scan.theta

NV and device measurement parameters in scan.param:

scan.param.dwellTime, scan.param.baselineFreq, scan.param.deltaFreq, scan.param.deviceCurrent, scan.param.deviceCurrentOffset, scan.param.deviceCurrentOffset2, scan.param.measureTime, scan.param.numFreqs, scan.param.voltgatecenter, scan.param.voltgatemodulation, scan.param.esrWidth, scan.param.hfSplitting, scan.param.freqConversion, scan.param.maxSlopePos, scan.param.freqModDev, scan.param.freqDev, scan.param.frequencyDeviationSet, scan.param.frequencyDeviationActual, scan.param.pulseSequence, scan.param.FileName, scan.param.FilePath, scan.param.scanType, scan.param.scanTag, scan.param.RFAmplitude, scan.param.repsPerTau, scan.param.tipDiamond, scan.param.sample, scan.param.Tsample, scan.param.backgateV, scan.param.opticalP

and measured scan data in scan.scanData, in 2 X scan.xSize X scan.ySize arrays:

afmHeight, afmError, afmConstHeight, freq, freqError, PL, countDiff, contrast, sensitivity, hkResult

where the first and second indices correpsond to forward and backward (if measured) scan directions.

1. B. Associated with the NV scanning files are "PLvsZ__[num]_[date]_[time].mat" files that contain measured NV photoluminescence vs. tip retraction height. This data is used to calibrate the NV height above the graphene samples in a given scan using the measured NV photoluminescence in that scan.

2. Transport data files have the name format "TransportSaveFile_[num]_[date]_[time].mat". These files contain data organized in a matlab struct format and can, for example, be accessed in python using the "loadmat" package. 

These files contain parameters of the transport measurement in gateMeasurement.param, and measured device voltage values in gateMeasurement.data.Vmeasure for a given gate voltage in gateMeasurement.data.Vgate.

3. Calibration files are in a .json format and contain NV axis angles relative to the device and device geomtry parameters.

4. Analysis files are organized into a few python files. The classes contained in these files are used to reconstruct current densities in the graphene device from the raw data files described above.

METHODOLOGICAL INFORMATION

1. Description of methods used for collection/generation of data: 
The measurement methods and data generation are described in https://arxiv.org/abs/2002.05065

2. Methods for processing the data: 
The reconstructed current densities and uncertainties in https://arxiv.org/abs/2002.05065 are calculated using the "scan_current_reconstruction_err" function in the file "scan_current_reconstruction.py". This function takes args: scan data and PLvsZ data paths, NV and device parameters that are specified in the calibration files, and device boundary positions in the scan which are used to shift the zero spatial-frequency value of current which is not provided by Fourier reconstruction.