Atomic collapse in graphene.pdf

8/14/2019 Atomic collapse in graphene.pdf

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Atomic collapse in graphene

Andrey V. Shytov (BNL)Work done in collaboration with:

L.S. LevitovMIT

M.I. at!nel!on

"niver!ity o# Ni$%e&en'Netherland!

* Phys. Rev. Lett. 99, 236801; ibid. 99, 246802 (2007)


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Outline

1. Atomic collapse and Dirac vacuum reconstructionin high-energy physics

2. Charged impurities in graphene: manifestations of atomic

collapse a. ocal DO! "!#$% &. #ransport "conductivity% c. 'acuum polari(ation

). Conclusion


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*lectrons in graphene

+seudo-spin "su&lattice%

#,o su&lattices

!lo, &ut ultrarelativisticDirac fermions

Chirality conservation /0 no locali(ation "lein parado%


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3hy graphene4

5igh mo&ility tuna&le carrier density

inear spectrum /0 high 6uanti(ation energiesroom temperature mesoscopic physics

7eali(ation of relativistic 6uantum physics inta&le-top eperiments /0 unusual transportproperties

arge fine structure constant /0 strong field

regime inaccessi&le in high-energy physics


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Charged impurities

Dominant contri&ution to resistivity

"7+A screeningis not essential%

Nom!", #$%o&"'d (200)


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Charged impurities

Dominant contri&ution to resistivity

"7+A screeningis not essential%

Nom!", #$%o&"'d (200)

Any interesting non-linear effects444

8es Dirac vacuum reconstruction


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!ta&ility of AtomClassical physics: unsta&le

"energy is un&ounded%


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9$: sta&le or&its (ero

point motion stops thecollapse


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7elativity: collapsing or&its

v c


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7elativity: collapsing or&its 7elativity ; 9$: 444

v c

4


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7elativity: collapsing or&its 7elativity ; 9$: Collapse4

v c 444


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Dirac = epler pro&lem

%i!"$ (1929)

3hat happens at> 0 1)?4

D / )

+art @ "> 1)?%


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inite si(e of nucleus"regulari(ation%

!olution can &e continuedto > 0 1)?.

Pome!"&$h "&d mo!odi&sii (194)

+art @@ "1)? > 1?B%


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Atomic collapse:semiclassical picture

7elativistic particle may fallto the Coulom& center


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Atomic collapse:semiclassical picture

7elativistic particle may fallto the Coulom& center


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1! level merges intoDirac sea at > / 1?B


> 0 1?B4

+art @@ "1)? > 1?B%


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!olution can &e continuedto > 0 1)?. 1! level merges

into hole continuum at> / 1?B


> 0 1?B4

+art @@ "1)? > 1?B%


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Dirac = epler pro&lem+art @@@ "> 0 >c / 1?B%

+e!shtey&, e'dovi$h (1969)Po-ov (1970)

7esonant electron state in Dirac sea

!creening &y pair production4

9uasilocali(ed state


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Atomic collapse in graphene

o mass /0 no discrete states continuous

spectrum

$anifestations: 6uasistationary states resonances

!trong effects in vacuum polari(ation no cutoff at

Compton ,avelength

Can &e modeled &y charged impurities:


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Charged impurity in grapheneDirac e6uation:

Ansat(:


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#,o regimes

Critical value:

!u&critical:

!upercritical: Oscillations small r


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*act solution

!u&critical case:

!cale-invariant solution "depends only on kr%


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Density of states

!tanding ,aves


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Density of states

!tanding ,aves


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Density of states

!tanding ,aves


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9uasi-&ound states

#ype of carriers is reversed at small r

lein tunneling couples electron-lie states at small rto hole-lie states at large r

9


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9uasi-&ound states

Classical motion

9uanti(ation condition:

#ransparency:

*act result near criticality:


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#ransport

9uasi-&ound states sho, up as

ano resonances

Drude conductivity

!cattering phases "etracted from eact solution%


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'acuum polari(ation

7+A "$irlin et al%:

Eeneral form:

#homas-ermi "atsnelson%:

7+A and # give conflicting results ,hich is unusual

i d l l


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riedel sum rule

in "2BBF%:

#otal charge:

+hases etracted from eact solution:


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!u&rcritical case

7+A formula is valid.

umericall results:

Only deep states contri&ute

to polari(ation charge"confirmed &y a direct calculation%

e!ehov et "'/e"$t o!m'" o!

-o'"!i"tio& $h"!e


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!upercritical case

"only s-channel isovercritical%

#homas-ermi limit

7E flo, of the effective charge:

#he flo, terminates at finite distance:

#he charge of an overcritical impurity

is al,ays screened to the critical value.

Open questions:


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Open questions:

*citons4

*ffect of vacuum polari(ation on locali(ed states4

Other many-&ody effects4 ondo4

7ole of ,ater4 Capacitance4Eapped systems "&ilayers epitaial graphene%4

Conclusions:


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Conclusions:

#,o distinct regimes for Coulom& impurities:su&critical and supercritical

ocal DO!: 6uasilocali(ed states standing ,aves

ano-lie resonances in transport cross-sectionconductivity

!creening cloud in supercritical regime

!ignatures of atomic collapse can&e o&served.

Divalent and tri-valent impurities are needed"Ca 8& a Ed can &e intercalated e.g.

$cChesney et al "2BB?%%. Alternatively onecan use the charge on !#$ tip.

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Atomic collapse in graphene.pdf