DOI: 10.25349/d91k60
title: Imaging the breakdown of ohmic transport in graphene

description: 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.
description: GENERAL INFORMATION 1. Title of Dataset:
 Imaging the breakdown of ohmic transport in graphene 2.
 Author Information<br>     A. Name: Alec Jenkins<br>       
  Institution: Department of Physics, University of California, Santa
 Barbara CA     B. Name: Susanne Baumann<br>   
      Institution: Department of Physics, University of California, Santa
 Barbara CA<br>     <br>     C. Name: Haoxin Zhou<br>   
      Institution: Department of Physics, University of California, Santa
 Barbara CA     D. Name: Simon A. Meynell<br>   
      Institution: Department of Physics, University of California, Santa
 Barbara CA     E. Name: Daipeng Yang<br>       
  Institution: Department of Physics, University of California, Santa
 Barbara CA     F. Name: Kenji Watanabe<br>       
  Institution: Research Center for Functional Materials, National Institute
 for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
     G. Name: Takashi Taniguchi<br>         Institution:
 International Center for Materials Nanoarchitectonics, National Institute
 for Materials Science,  1-1 Namiki, Tsukuba 305-0044, Japan
     H. Name: Andrew Lucas<br>         Institution:
 Department of Physics and Center for Theory of Quantum Matter, University
 of Colorado, Boulder CO     H. Name: Andrea F.
 Young<br>         Institution: Department of Physics, University of
 California, Santa Barbara CA     H. Name: Ania C.
 Bleszynski Jayich<br>         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 <br> DATA
 & FILE OVERVIEW<br>  <br> All data files are included
 in this folder structure. The data are organized in the following
 structure: graphene device -&gt; data type
 (calibration, NV scanning, or transport) -&gt; temperature -&gt;
 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.
 <br> 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. <br> 3. Calibration
 files are in a .json format and contain NV axis angles relative to the
 device and device geomtry parameters. <br> 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.
 <br> METHODOLOGICAL INFORMATION 1.
 Description of methods used for collection/generation of data: <br>
 The measurement methods and data generation are described in
 https://arxiv.org/abs/2002.05065 <br> 2. Methods
 for processing the data: <br> 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. <br>