Current address: ]Istituto di Scienze del Patrimonio Culturale, Consiglio
Nazionale delle Ricerche (ISPC-CNR), Via Biblioteca 4, 95124 Catania, Italy

# Correlation-Driven Electron-Hole Asymmetry in Graphene Field Effect Devices

Nicholas Dale1,2 Ryo Mori1,3 M. Iqbal Bakti Utama2,3,4 Jonathan D. Denlinger5
Conrad Stansbury1,2 Claudia G. Fatuzzo1,2 [  Sihan Zhao1 Kyunghoon Lee1,2
Takashi Taniguchi6 Kenji Watanabe7 Chris Jozwiak 5 Aaron Bostwick5 Eli
Rotenberg 5 Roland J. Koch5 Feng Wang1,2,8 Alessandra Lanzara1,2,8
<EMAIL_ADDRESS>1Department of Physics, University of California, Berkeley,
CA, 94720, USA  2Materials Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, CA, 94720, USA  3Graduate Group in Applied Science &
Technology, University of California, Berkeley, CA, 94720, USA  4Department of
Materials Science and Engineering, University of California at Berkeley,
Berkeley, CA, USA  5Advanced Light Source, Lawrence Berkeley National
Laboratory, Berkeley, CA, 94720, USA  6International Center for Materials
Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki,
Tsukuba 305-0044, Japan  7Research Center for Functional Materials, National
Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan  8Kavli
Energy NanoSciences Institute at University of California Berkeley and
Lawrence Berkeley National Laboratory, Berkeley, CA, USA

###### Abstract

Electron-hole asymmetry is a fundamental property in solids that can determine
the nature of quantum phase transitions and the regime of operation for
devices. The observation of electron-hole asymmetry in graphene and recently
in the phase diagram of bilayer graphene has spurred interest into whether it
stems from disorder or from fundamental interactions such as correlations.
Here, we report an effective new way to access electron-hole asymmetry in 2D
materials by directly measuring the quasiparticle self-energy in
graphene/Boron Nitride field effect devices. As the chemical potential moves
from the hole to the electron doped side, we see an increased strength of
electronic correlations manifested by an increase in the band velocity and
inverse quasiparticle lifetime. These results suggest that electronic
correlations play an intrinsic role in driving electron hole asymmetry in
graphene and provide a new insight for asymmetries in more strongly correlated
materials.

###### pacs:

Valid PACS appear here

##  I Introduction

Electron-hole asymmetry, or the difference in a material’s electronic
properties upon doping with electrons versus holes, profoundly impacts the
character of phase transitionsSharpe  _et al._ (2019)Sarkar  _et al._
(2020)Sajadi  _et al._ (2018)Hsu  _et al._ (2017), and the choice of doping
for devicesArora  _et al._ (1982)Larbalestier  _et al._ (2001). While it
typically arises from differing structures of bands containing electrons and
holesAshcroft and Mermin (1976)Jost  _et al._ (2017), in some cases this
asymmetry manifests from external sources such as impuritiesYazdani  _et al._
(1997)Novikov (2007), strainBai  _et al._ (2015)Jost  _et al._ (2017)Dasilva
_et al._ (2015), or simply from intrinsic many body interactionsAnderson and
Ong (2006)Kretinin  _et al._ (2013). Graphene is an interesting case in this
light, because its K point band structure is expected to be perfectly
electron-hole symmetricNeto  _et al._ (2007), but the combination of its
dimensionality and dispersion relation renders it highly susceptible to
symmetry-breaking perturbationsKotov  _et al._ (2012). Most experimental
realizations of the monolayerDeacon  _et al._ (2007) Kretinin  _et al._ (2013)
and bilayerZou  _et al._ (2011)Cao  _et al._ (2018a)Lu  _et al._ (2019)
exhibit electron hole asymmetry, even after vast improvements in sample
preparation, which reduce the effective strain and impurity concentrationWang
_et al._ (2013a)Kretinin  _et al._ (2013). Whether external sources or
intrinsic interactions such as correlationsZou  _et al._ (2011)Anderson and
Ong (2006)Cai  _et al._ (2016)Kretinin  _et al._ (2013) drive asymmetry
remains to be verified. This has become even more important with the recent
discovery of Mott-like physics and superconductivity in bilayer grapheneCao
_et al._ (2018a)Lu  _et al._ (2019), displaying a phase diagram which is
strongly electron-hole asymmetric and reminiscent of the cuprates Gooding  _et
al._ (1994).

The difficulty in addressing the origin of electron hole asymmetry in graphene
today is the requirement of a probe that has complete access to the material
self energy in both energy and momentum spanning over a large range of
electron and hole dopings. Some probes, including transport Deacon  _et al._
(2007) and quantum capacitance Kretinin  _et al._ (2013), can easily cover the
broad doping range via electrostatic gating, but are only sensitive to the
electronic states at the Fermi energy ($E_{F}$) and do not provide any
momentum information. In contrast, Angle Resolved Photoemission Spectroscopy
(ARPES) can provide access to the full quasiparticle spectral function
$A(k,\omega)$, but so far has resorted to methods of doping that modify the
fundamental properties of the system, including screeningHwang  _et al._
(2012)Siegel  _et al._ (2011) and impurity concentration Chen  _et al._
(2008)Siegel  _et al._ (2013). The very recent introduction of electrostatic
gating into ARPES experiments Nguyen  _et al._ (2019)Joucken  _et al._ (2019)
enables studies of the doping dependent self-energy with full energy and
momentum resolution while leaving the sample in pristine condition. Here we
report the first of such study, revealing significant asymmetries in the
quasiparticle self energy. The doping and momentum resolution of our
measurement enables us to effectively characterize the relationship between
electronic correlations and these asymmetries.

##  II Results

Figure 1: (a.,b.) schematic of experimental setup (a-) and optical micrograph
of the graphene/hBN sample (b-). Dashed lines outline regions of graphene
(black), hBN (blue), and graphite (purple) (c.-e.) ARPES spectra for S1 along
the $K-K^{\prime}$ direction (perpendicular $\Gamma-K$) at (c-) p doping
(-5V), (d-) equilibrium (0V), and (e-) n doping (8V). Blue dashed lines
indicate quasiparticle peak positions extracted from Lorentzian fits. (f.)
doping dependent MDCs spectra and quasiparticle peak positions (black arrows)
at $E_{F}$, indicated by the white dashed line in (b-d). (g.) ${E_{F}-E_{D}}$
as a function of gate voltage, extracted from linear fits to the graphene
spectra. Data for two different samples are shown (S1 and S2).

Fig. 1a presents an illustration of the sample geometry used for the ARPES
experiment and gating configuration, while panel b shows the optical
micrograph of the overall sample. The dashed contours identify regions of
monolayer graphene (black), hBN (blue) and graphite (purple) while the yellow
thick lines indicate the electrical contacts. The size of the sample is
smaller than 1200 $\mu\textnormal{m}^{2}$. The adopted beam size was 1
$\mu\textnormal{m}$ to allow measurements of each individual part of the
sample and disentangle different contributions. The equilibrium spectra for
the sample in Fig 1d clearly depicts the characteristic linear bands of
graphene’s Dirac fermions along the $K-K^{\prime}$ direction populated up to
near the charge neutrality point. A positive (negative) voltage established
between the graphite back gate and the graphene sample results in the
addition, panel e (subtraction, panel c) of electrons to (from) the sample.
Since the Fermi energy $E_{F}$ is held at ground, the additional negative
(positive) charges shift the Dirac spectrum downward (upward). The doping
change can be estimated by the peak separation at $E_{F}$ from momentum
distribution curves (MDCs), spectra at constant energy as a function of
momentum, shown in panel f for different gating values. At $V_{g}\,=\,0V$ the
Fermi surface is a point and the momentum separation between MDC peaks is
negligibly small. As electrons (holes) are added to the system, two peaks
emerge and the momentum separation increases, with a maximum at
$V_{g}\,=\,-5V(8V)$ corresponding to a p (n) doping of $2.2\pm 0.3\cdot
10^{12}\textnormal{cm}^{-2}\,(0.6\pm 0.3\cdot 10^{12}\textnormal{cm}^{-2})$.
The position of the Fermi energy $E_{F}\,-\,E_{D}$, displayed in Fig 1g, is
estimated by the intersection point of linear fits to the Dirac spectra (blue
dashed lines in Figs 1c-e). The scaling of $E_{D}$ with gate voltage away from
neutrality follows $E_{D}\sim\sqrt{V_{g}}$, suggesting that the charge doping
is well controlled, and a result of geometric capacitance Yu  _et al._ (2013).

Figure 2:  (a.-c.) graphene spectra at three representative dopings: (a.)
$-0.9\cdot 10^{12}\textnormal{cm}^{-2}$, (b.) $0.0\cdot
10^{12}\textnormal{cm}^{-2}$, (c.) $1.1\cdot 10^{12}\textnormal{cm}^{-2}$.
Black (red) dashed lines indicate linear fits to dispersions near $E_{D}$
($E_{F}$ in (a)). Inset cartoons illustrate the deviations from Dirac cone
dispersions at respective dopings. (d.) $E_{D}$ dispersions near the charge
neutrality point indicate asymmetry in band velocity for electron and hole
dopings. (e.) Extracted band velocities as a function of doping. Grey (teal)
shaded regions indicate $1\sigma$ deviation of best fit to the $v_{F}$
($v_{D})$ data using the logarithm-based lineshape described in the text. (f.)
Graphene fine structure constant ($\alpha$) as a function of doping, is
extracted from band velocity fits.

Fig. 2 reports the detailed evolution of the K point electronic structure near
$E_{F}$ for different doping (gating) values. Figs 2a-c display raw image
plots near the K point for dopings of $-0.9\cdot 10^{12}\textnormal{cm}^{-2}$,
$0.0\cdot 10^{12}\textnormal{cm}^{-2}$, and $1.1\cdot
10^{12}\textnormal{cm}^{-2}$ (details on calculation of the carrier density
can be found in Supplementary Note 1). Already from the raw data one can see
that the spectrum in Fig 2a is linear, and at the neutrality point (Fig 2b)
the dispersion looks noticeably steeper near $E_{F}$ (= $E_{D}$) than at
higher binding energies, in agreement with previous reports Siegel  _et al._
(2011)Hwang  _et al._ (2012). The electron-doped spectrum (Fig 2c) presents
different structure for the valence band than does the spectrum at similar
hole doping: the valence band near the Dirac point (black dashed line) is
steeper than the valence band in Fig 2a (red dashed line).

These differences are better visualized by plotting the energy dispersion vs
momentum (Fig 2d), extracted by fitting the momentum distribution curves with
standard Lorentzian-like functions in the proximity of the Dirac point. A
clear departure from linearity is observed in the data starting at the
neutrality point, where the dispersion is steepest, and still observed in the
electron doped side. Band velocities can be directly extracted from these
data, being proportional to the slope of the ARPES dispersions. Because the
dispersions for hole dopings remain linear, the band velocity at the Dirac
point $v_{D}$ (which is above $E_{F}$ at these dopings) can be approximated by
the Fermi velocity $v_{F}$. In contrast, the dispersions at neutrality
(purple) and electron dopings (blue) show a large deviation from linearity,
with $v_{D}$ nearly twice as large as velocities at $E_{D}-0.5$ eV. These
results clearly indicate the presence of a distinct electron-hole asymmetry in
the electronic response and are summarized in panel e, where the band
velocities at the Dirac point ($v_{D}$), extracted from the slope of ARPES
dispersions, are plotted as a function of doping. Although a divergence of
$v_{D}$ is observed in the proximity of the charge neutrality point, as
previously reported Siegel  _et al._ (2013) for the electron doped side, a
clear asymmetry is revealed over the entire doping range, with $v_{D}$
$\sim$30% higher for electron dopings than for hole dopings. The large
renormalization of the Dirac spectra was previously reported at the neutrality
point and assigned to electron-electron interactions González  _et al._
(1994)Siegel  _et al._ (2013) leading to a logarithmic correction of the band
velocity. Using a similar model Siegel  _et al._ (2013)

$\frac{v}{v_{0}}=1+\frac{\alpha}{8}\log{(\frac{n_{0}}{n_{e}})}$ (1)

we extract the long-range coulomb coupling $\alpha=\frac{e^{2}}{\epsilon\hbar
v_{0}}$ (panel f), which is the primary contributor to the velocity
enhancement. The dielectric strength $\epsilon=\epsilon_{0}(1+a|n_{e}|^{1/2})$
is allowed to effectively increase as a function of doping Elias  _et al._
(2011)Yu  _et al._ (2013), and $v_{0}=1.0\cdot 10^{6}$ m/s is the local
density approximation of the bare band velocity. The long range coupling
strength $\alpha$ shows a strong asymmetry between the electron and hole side,
which is the driver for the asymmetry in the band dispersion discussed in
panel d. Though this result is in apparent contrast with some reports using
$E_{F}$ sensitive probes Elias  _et al._ (2011)Yu  _et al._ (2013), we note
that the real coulomb interaction strength $\alpha$ can be isolated more
reliably from energy states at the Dirac pointSiegel  _et al._ (2013) rather
than from states at $E_{F}$, which are affected by multiple different
interactions Calandra and Mauri (2007).

Figure 3:  Electron-Hole Asymmetry in Self Energy. (a.,b.) Normalized EDCs at
$k_{p}-K\,=-0.19$ (a-), and MDCs at $E_{F}$ (b-) for hole (red) and electron
(blue) doped graphene. (c.) Imaginary part of the self energy as a function of
doping for EDCs at $k_{p}-K\,=-0.19$ (black) and MDCs at $E_{F}$ (grey).
Shaded grey region indicates $1\sigma$ deviation of best fit to the square-
root based function described in the text. (d.) Imaginary part of the self
energy normalized by the Fermi energy. Blue (red) solid lines indicate fits to
the data, as described in the text.

Figure 3 reports the imaginary part of the self energy for holes and electrons
at several doping values. The MDC’s FWHM $\Delta k$, the EDC’s FWHM $\Delta E$
and the imaginary part of the self energy Im $\Sigma(\omega)$ are related by
$2\,\textnormal{Im}\Sigma(\omega)=\hbar v_{F}\Delta k=\Delta E$ Valla  _et
al._ (1999). A clear asymmetry between electrons and holes is already apparent
in the raw spectra, EDC (panel a) and MDC (panel b). The full doping
dependence of Im $\Sigma$ is plotted in Fig 3c for both the MDCs at $E_{F}$
(grey) and the EDCs at $k-K=-0.19\AA^{-1}$ (black), each showing a strong
electron hole asymmetry. Im $\Sigma$ at $E_{F}$ scales as
$a_{0}\sqrt{|n_{e}|}$ away from neutrality, with the amplitude $a_{0}=0.45\pm
0.05$ for electron dopings and $a_{0}=0.09\pm 0.02$ for hole dopings. This
doping dependence is in contrast to alkali-doped graphene samples, which
develop a $1/\sqrt{n}$ dependence from the added long range impuritiesSiegel
_et al._ (2013), and the $\sqrt{n}$ scaling of the self energy at $E_{F}$
observed in gate-tunable graphene samples Muzzio  _et al._ (2020) can be
attributed to either acoustic phononsHwang and Das Sarma (2008)Kaasbjerg  _et
al._ (2012) or short range impuritiesAdam  _et al._ (2007). However, since
both scattering sources are directly affected by the screening of the Coulomb
interactionAdam  _et al._ (2007)Hwang and Das Sarma (2008), we can confidently
conclude that the prominent electron-hole asymmetry in the self energy at
$E_{F}$ is due to the asymmetry in the correlation strength $\alpha$ (reported
in Fig 2). A similar asymmetry has been observed in a graphene sample nearly
aligned with the hBN substrate Muzzio  _et al._ (2020), which may be weaker
due to the competing asymmetry produced by the moiré potentialDasilva  _et
al._ (2015) and/or from the presence of a screening graphite back gateStepanov
_et al._ (2020).

Whereas techniques that are only sensitive to the low energy physics are often
marred by impurities Chen  _et al._ (2008)Deacon  _et al._ (2007), the ability
of ARPES to access the entire energy range allows us to extract the intrinsic
behavior of materials. Fig. 3d presents the energy dependence of the imaginary
self energy scaled by the position of the Fermi energy $E_{F}$ for different
doping values. That $\textnormal{Im}\Sigma/E_{F}$ collapses to two distinct
curves for electron and hole dopings provides further evidence for electron
hole asymmetry in the material. The reported energy dependence is
qualitatively similar to numerical calculations of the inverse quasiparticle
lifetime from dynamically screened electron-electron correlationsHwang  _et
al._ (2007)Tse  _et al._ (2008). From these calculations we can approximate
the scattering rate to an empirical form:

$\frac{\textnormal{Im
}\Sigma_{ee}}{E_{F}}=c_{1}\tanh{[c_{2}\cdot\frac{(E-E_{F})}{E_{F}}]}$ (2)

where $c_{1}$ and $c_{2}$ are fit parameters. The fit shows an overall good
agreement with the data and gives $c_{1h}=2.5\pm 0.2$ for hole dopings,
$c_{1e}=4.6\pm 0.3$ for electron dopings, and $c_{2}=0.11\pm 0.03$ for both
dopings. Such differences are another manifestation of the electron
correlation strength, as discussed in Ref. Tse  _et al._ (2008).

##  III Discussion

The data reported here provide evidence of a strong electron-hole asymmetry in
graphene that is driven, as we will argue below, by strong electronic
correlations. We now discuss the possible sources of such asymmetry and show
that it is an intrinsic property rather than driven by disorder or other
extrinsic effects.

As mentioned above, there are several mechanisms that break electron-hole
symmetry in graphene, and include intrinsic asymmetries in the band structure,
charged impurities, and electronic correlations. The asymmetries in the band
structure are induced by next nearest neighbor hopping Neto  _et al._
(2007)Reich  _et al._ (2002) which can be effectively enhanced by strainBai
_et al._ (2015), induced for example from alignment to a substrate with a
different lattice constant, and easily modeled by tight binding
calculationsDasilva  _et al._ (2015). When applying the latter to our
experimental data, it becomes clear that to account for the 30% asymmetry
between conduction and valence band velocity an unrealistic value of
$|t^{\prime}|\sim 3$ eV is needed. This is an order of magnitude larger than
values reported in the literature ($t^{\prime}\sim 0.3$ eV) Bostwick  _et al._
(2007)Deacon  _et al._ (2007)Kretinin  _et al._ (2013), and opposite in sign
to the asymmetries produced in graphene aligned to hBNDasilva  _et al._
(2015), and graphene strained via wrinklesBai  _et al._ (2015). Moreover, we
note that our samples are aligned at large twist angles to the hBN substrate,
where lattice reconstruction is negligibly small Jung  _et al._ (2015) (see
supplementary information for more details), and therefore the effect on
$t^{\prime}$ is negligible.

Another possible source of electron hole asymmetry is the presence of charged
impurities leading, in the case of very close ($<5$ nm) proximity, to changes
in the LDOS as large as 30% Wang  _et al._ (2013b)Bai  _et al._ (2015).
However, impurities produce an inverse quasiparticle lifetime that scales
inversely with $E\,-\,E_{D}$ Adam  _et al._ (2007), in contrast to the
empirical function in equation 2 used to fit our data. Additionally, the
impurity density required to produce this effect throughout a mesoscopic
sample ($\sim 10^{13}\,\textnormal{cm}^{-2}$) is large enough to produce
signatures in the spectral function in the form of resonance statesPeres  _et
al._ (2006)Skrypnyk and Loktev (2008)Wang  _et al._ (2013b) or impurity
bandsAvsar  _et al._ (2014)Hwang  _et al._ (2018), which are not observed in
our data.

These observations make electronic correlations the primary driver of
electron-hole asymmetry observed in our study. Indeed, this interaction can
consistently explain the asymmetric logarithmic renormalization of the
dispersions across charge neutralityGonzález  _et al._ (1994)Das Sarma  _et
al._ (2007), the nonlinear behavior of self energy at high binding
energiesHwang  _et al._ (2007), and likely the asymmetry in the self energy at
$E_{F}$. Finally, we note that though numerical calculations for $\Sigma_{el-
el}$Tse  _et al._ (2008) are much smaller than values found in our experiment,
reaching quantitative agreement between experimental and theoretical results
often requires additional scaling factors Calandra and Mauri (2007)Park  _et
al._ (2007).

In conclusion, we have demonstrated the power of electrostatic gated ARPES to
study the interplay of interactions and electron-hole symmetry in 2D
materials. Our results point to electronic correlations as the driving force
for an intrinsic electron-hole asymmetry in graphene, manifested in the
dispersion and inverse quasiparticle lifetime. These findings open the
intriguing possibility that electron-electron interactions might also be
responsible for the asymmetries found in the phase diagrams of twisted bilayer
graphene Cao  _et al._ (2018a)Lu  _et al._ (2019) and similar correlated 2D
moiré systems Wang  _et al._ (2020)Chen  _et al._ (2020), as is found in high
temperature cuprate superconductors Gooding  _et al._ (1994)Phillips
(2006)Anderson and Ong (2006)Cai  _et al._ (2016).

Acknowledgements:
We thank Salman Kahn for technical assistance in the sample fabrication setup.
This work was primarily supported by the U.S. Department of Energy, Office of
Science, Office of Basic Energy Sciences, Materials Sciences and Engineering
Division under Contract No. DEAC02- 05CH11231 (Ultrafast Materials Science
Program KC2203). K.W. and T.T. acknowledge support from the Elemental Strategy
Initiative conducted by the MEXT, Japan ,Grant Number JPMXP0112101001, JSPS
KAKENHI Grant Number JP20H00354 and the CREST(JPMJCR15F3), JST.

Competing Interests:
The authors declare that they have no competing financial interests.

Correspondence:
Correspondence and requests for materials should be addressed to A.L. (email:
alanzara@ lbl.gov).

Author Contributions:
N.D. and A.L. initiated and directed the research project. T.T. and K.W.
synthesized the hBN crystals. N.D., M.I.B.U., S.Z., and K.L. fabricated the
graphene samples. N.D., R.M., J.D.D., C.G.F, and A.B. performed the ARPES
measurements. N.D. analyzed the ARPES data using software designed by C.S.,
and inputs from A.L. N.D. and A.L. wrote the manuscript, with inputs from all
of the authors.

Data Availability:
The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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##  V Methods

Two devices were made for this experiment – for S1 refer to Fig 1 and for S2
refer to Figs 2 and 3
Sample Preparation:
Flakes of single-layer Graphene and hexagonal Boron Nitride were exfoliated
onto Silicon Wafers with 90nm-thick oxide. S1 was constructed using a method
similar to that used in Utama  _et al._ (2019). A stamp comprised of
Polypropylene carbonate (PPC), and Polydimethylsiloxane (PDMS), and
transparent tape was used to pick up Graphite, hBN, and Graphene in sequential
order. The PPC stamp holding the stack was flipped onto a 90nm oxidized Si
wafer with the Graphene facing up, and the polymer was subsequently removed by
annealing in a vacuum furnace at 350C for 10 hours. S2 was constructed using a
technique similar to that outlined in Zomer et. al Zomer  _et al._ (2014). A
stamp comprised of Polycarbonate (PC) and Polydimethylsiloxane (PDMS) was used
to pick up the Graphene, hBN, and Graphite to form a graphene/hBN/graphite
heterostructure, which was then placed onto a fresh 90nm-oxidized Si wafer. PC
polymer residue was removed by placing the stack-on-chip in Chloroform for
$>$60 minutes at room temperature. Contacts were patterned onto each sample
surface using electron-beam lithography followed by evaporation of 5nm Cr and
50nm Au.

ARPES Measurements and Analysis:
Sample 1 was measured using a Scienta R4000 Hemispherical Analyzer at the
nanoARPES branch of beamline 7.0.2 (MAESTRO) at the Advanced Light Source
using a photon energy of 74 eV, a temperature of 300K,and a pressure better
than 1e-10 Torr. The beam was capillary refocused Koch  _et al._ (2018) to a
spot size of $\sim 1\mu\textnormal{m x }\,1\mu\textnormal{m}$. The overall
energy and momentum resolution was 30meV and $0.014\AA^{-1}$, respectively.
The sample was doped electrostatically using a Keithley 2450 Source Meter.
Sample 2 was measured using a Scienta R8000 Hemispherical Analyzer at Beamline
4.0.3 (MERLIN)Reininger  _et al._ (2007) at the Advanced Light Source using a
photon energy of 94eV, a temperature of 20K, and a pressure better than 5e-11
Torr. The beamspot was $\sim 100\mu\textnormal{m x }\,50\mu\textnormal{m}$.
The overall energy and momentum resolution was 25meV and $0.017\AA^{-1}$,
respectively. The sample was doped electrostatically using a Keithley 2200
programmable power supply electrically connected to the cryostat.
All ARPES data in this paper were analyzed using pyARPES, an open-source
python-based analysis frameworkStansbury and Lanzara (2020). Spectra presented
in the figures have had a background (estimated by mean value of detector
counts $\simeq 0.5\AA^{-1}$ away from the K point) removed, and are smoothed
by a gaussian filter with windows in momentum and energy smaller than the
experimental resolution.

##  VI Supplementary Material

Supplementary Note 1: Carrier Density Measurements

Figure S1: (a.) Fermi surface for S1 at $V_{g}=-6V$. White lines indicate
Fermi wavevector $k_{F}$ measured as the radius of the Fermi surface. (b.)
Graphene spectra cut along $k_{x}=K$, with illustration of more accurate
method to extract $k_{F}$. The position of $k_{F}$ (white vertical line) is
determined from intersection of band dispersion (dashed black line) with the
Fermi level (horizontal grey line).(c.,d.) MDCs at $E_{F}$ as a function of
applied gate voltage for S1 (c-) and S2 (d-). Valence (conduction) band
positions labelled with red (blue) markers. (e.) Fermi wavevector $k_{F}$ as a
function of gate voltage for both samples. Error bars are estimated from the
experimental momentum resolution and the broadness of the MDC. (f.) Carrier
density $n_{e}$ as a function of gate voltage for both samples, calculated
using Luttinger’s theorem: $n_{e}=k_{F}^{2}/\pi$. Error bars represent errors
propagated from estimates of $k_{F}$, while shaded regions represent errors
propagated from uncertainty in the charge neutrality point.

The charge-carrier density can be obtained from the size of the Fermi surface
using Luttinger’s theorem. Assuming a conical dispersion for graphene, the
Fermi surface is a circle with a radius of the Fermi wavevector $k_{F}$, i.e.
$n_{e}=k_{F}^{2}/\pi$ (see Fig S1a, and S1b). We extract the Fermi wavevector
from the distance between peak positions at the Fermi level, which are
displayed in Fig S1c for S1 and Fig S1d for S2. Whereas data from S1 includes
contributions from both sides of the Dirac cone, data from S2 primarily
contains one band, and $k_{F}$ can be extracted more accurately as (see Fig
S1b) the intersection of the band dispersion (black dashed line) with the
Fermi level (grey line). The K point position for S2 is then extracted as
value of $k_{F}$ at the doping with the steepest $v_{D}$, which in our case
occurs at a gate voltage of 0.5V (see Figure 2). The summary of extracted
$k_{F}$ values, and calculated $n_{e}$ values are presented in Fig S1e and Fig
S1f, respectively. For S1, error bars for $k_{F}$ are estimated based on the
broadness of the bands and the momentum resolution, which was $\sim
0.014\,\AA^{-1}$, whereas for S2, error bars are extracted from the
statistical error in the linear fit to the dispersion. Error bars for $n_{e}$
are obtained by propagating errors in $k_{F}$. Away from charge neutrality,
both devices appear to have a roughly linear dependence between doping and
gate voltage i.e. $n_{e}\simeq CV_{g}$, which is expected when treating the
system as a parallel-plate capacitor with geometric capacitance $C$. The dip
in geometric capacitance near the neutrality point indicates contributions of
the quantum capacitance, which scale with the strength of electron-electron
interactionsYu  _et al._ (2013).

Supplementary Note 2: MDC and EDC Analysis

Figure S2: (a.) Graphene spectra for sample S2 at $V_{g}=0$. Dashed lines are
guides to eye for valence bands. Light blue horizontal lines indicate binding
energies at which band width $\Delta k$ is measured from MDC fits, red
vertical line indicates momentum at which band width ($\Delta E$) is measured
from EDC fits. (b.) Example of a Lorentzian lineshape fit to single MDC at
$E_{F}$ (c.) Example Voigt fit to EDC at $K-0.19\AA^{-1}$. (d.,e.) MDCs at
$E_{F}$ (d-) and EDCs at $K-0.19\AA^{-1}$ (e-) and peak fits (black), which
contribute to figure 3c in the primary manuscript. Peak positions are
indicated by navy and orange markers. Data from progressively higher dopings
are offset for clarity.

Graphene scattering rates described in the main text are extracted using the
following procedure. The quasiparticle scattering rate $\Gamma$ is
proportional to the width of MDCs $\Delta k$, which usually have a Lorentzian
lineshape Damascelli (2003). Fig S2a presents a typical graphene spectra for
S2, which has matrix elements strongly favoring the $k-K<0$ side of the Dirac
cone. The faint presence of the other side of the Dirac cone for $k-K>0$
requires MDCs at $E_{F}$ to be fit to two Lorentzians with an affine
background. We restrict the two peaks to have the same width and be placed
symmetrically about the Dirac point, (see Fig S2b). EDCs at higher binding
energies, for example at $K-0.19\AA^{-1}$ can simply be fit to a single Voigt
lineshape with an affine background (see Fig S2c). Figures S2d and S2e show
the MDCs (blue) and EDCs (red) as well as the fits (black) used to extract the
quasiparticle scattering rate in the main text. MDCs have been smoothed using
a gaussian filter with a momentum window sized smaller than the expermental
resolution, and EDCs have been smoothed using a window (60 meV) that is
smaller than the smallest recorded value of Im $\Sigma$ for sample S2. The
statistical error of the fit is used to make the error bars in Fig 3c. The
presence of hBN spectra can be seen in the MDCs at hole dopings
$n_{e}<-0.5\cdot 10^{12}\textnormal{cm}^{-2}$, and in the EDCs at hole dopings
$n_{e}<0.0\cdot 10^{12}\textnormal{cm}^{-2}$, though they do not strongly
affect the extracted MDC or EDC widths due to the large discrepancy in
broadness of hBN and graphene bands.

Supplementary Note 3: Alignment to the hBN Substrate

Figure S3: Constant energy maps for S1 for a gate voltage of $V_{g}=-6V$ at
$E_{F}$ (a.) and $E_{F}-2.2eV$ (b.). Black (blue) lines outline the graphene
(hBN) Brillouin Zone, with the K point labelled by the white (blue) dot. hBN
axes are rotated 6 degrees w.r.t. the Graphene ones. c. Photoemission spectra
along $k_{x}=K$ indicate conical graphene bands near the Fermi level and the
apex of parabolic hBN bands at $\sim$2.2 eV below $E_{F}$.

Alignment angle between the graphene sample and hBN substrate is extracted by
overlaying their respective Brillouin Zones atop of photoemission data in Figs
S3a, and S3b. The graphene K point is characterized by the radial center of
the Dirac cone dispersion near $E_{F}$ (Fig S3a) and the hBN K point is
characterized as the peak of a parabolloid band at a binding energy of $\sim$
2.2 eV as seen from Fig S3c. The angular orientation of the hBN can also be
determined using the equation $\theta\simeq 2\arcsin(\frac{\Delta k}{2K})$ Cao
_et al._ (2018b). Using the momentum separation $\Delta k\simeq 0.18\AA^{-1}$
extracted from Fig S3c, we obtain an relative alignment of $\sim 6$ degrees,
which agrees with the alignment of the overlaid Brillouin Zones in Figs S3a
and S3b. Using the same technique, we obtain a relative twist of $\sim 13$
degrees for sample S2.

Supplementary Note 4: Shift of K point upon Application of Gate Voltage

Figure S4: (a.-c.) Constant energy spectra for a gate voltage of
$V_{g}\,=\,-2\textnormal{V}$ at $E_{F}$ (a-), $E_{F}-0.3$ eV (b-), and
$E_{F}-0.6$ eV (c-). (d.-f.) Same as (a-c) but for
$V_{g}\,=\,3\textnormal{V}$. Black crosshairs indicate the location of the K
point, and dashed circles are guide to the eye. (g.) Spectral weight obtained
from the peak height of MDCs at $E_{F}$ as a function of momentum for
$V_{g}\,=\,-2\textnormal{V}$ (red), and $V_{g}\,=\,3\textnormal{V}$ (blue).
(d.) $k_{x}$ values for the center of Lorentzian peaks (dashed curves) fitted
to the data in the previous panel, with errors bars representative of the
statistical error of the peak fit.

The analysis presented here is very sensitive to the exact identification of
the K point. Indeed, given the linear dispersion of graphene, a small
misalignment within the sample can cause a large error in the doping value.
Previous gated ARPES experiments have suffered from stray fields that drive a
shift of the measured spectra with gating Muzzio  _et al._ (2020). To minimize
the effects of experimental stray fields, in our experiment we have adopted a
sample geometry with a sizeable sample grounding plane Nguyen  _et al._
(2019). The resulting constant energy maps for our sample S2 (see panels a-f)
show that the K point does not shift significantly for negative (-2V) and
positive (+3V) gate voltages, allowing a precise identification of the K point
from the peak in the spectral weight at $E_{F}$ (see panel g). With this
geometry we find that the K point shift is negligible and much less than our
momentum resolution ($\sim 0.017\AA^{-1}$).