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Adiabatic pumping in the mixed-valence and Kondo regimes

We investigate adiabatic pumping through a quantum dot with a single level in the mixed-valence and Kondo regimes using the slave-boson mean field approximation. The pumped current is driven by a gauge potential due to time-dependent tunneling barriers as

Adiabaticpumpinginthemixed-valenceandKondoregimes

TomosukeAono

DepartmentofPhysics,Ben-GurionUniversityoftheNegev,Beer-Sheva84105,Israel

(Dated:February6,2008)

2004

Weinvestigateadiabaticpumpingthroughaquantumdotwithasinglelevelinthemixed-valenceandKondoregimesusingtheslave-bosonmean eldapproximation.Thepumpedcurrentisdrivenbyagaugepotentialduetotime-dependenttunnelingbarriersaswellasbythemodulationoftheFriedelphase.ThesignoftheformercontributiondependsonthestrengthoftheCoulombinteraction.Under nitemagnetic elds,theseparationofthespinandchargecurrentspeculiartoltheKondoe ectoccurs.

Ju 9PACSnumbers:72.15.Qm,73.23.Hk,73.40.Gk,

1 ]Introduction.—Adiabaticpumpinginaquantumdotllsystemoccurswhenthedotisunderslowlyvaryingexter-ahnalgatevoltageswithzerobiasvoltage.Afteracertain-periodwhenthesystemreturnstoitsinitialstate,a niteschargeistransferredbyelectroninterferencethroughtheem

Adiabatic pumping in the mixed-valence and Kondo regimes

system.Inrecentexperiments,bothcharge[1]andspinpumpingarerealizedinopenquantumdotsystems..taThispumpinghasbeeninvestigatedtheoretically;chargempumping10,aswellasspinpump-ing13,14,16,17,18].Ithasbeenelucidatedthat-dthepumpingcanbeunderstoodinofBerrynphaseargumentinRef.andRefs.[19,20,21,22].ocAdiabaticpumpingisinvestigatedforthesystemsun-[derelectron-electroninteractions14,23,24,25, 2Inquantumdots,theinteractionsintroduceaprominentvfeature,theKondoe ect28,29,30],wherethe6spin-exchangebetweenelectronsintheleadsandthedot2resultsinanenhancementoftheconductanceatlowtem-5peratures.Weinvestigatetheadiabaticpumpinginthe11mixed-valenceandtheKondoregimestodemonstratean3interplaybetweentheKondoe ectandagaugepoten-0tialassociatedwiththeBerryphase,thoughthissystem/titselfispartlystudiedinRef.[26].Tothisend,wewillashowexplicitlytheappearanceoftheBerryphasetermmduetotime-dependenttunnelingbarriersandelucidate-dtheconnectionwiththeadiabaticpumpingunderthenelectroncorrelations.Wewillthenshowthatthespin-chargeseparationpeculiartotheKondoe ectemergesascotheseparationofpumpedspinandchargeundera nite:vmagnetic eld.

iXModel.—Weconsiderasystemwhichconsistsarquantumdotwhichhasasingleenergylevelandacouplestotwoleads,model [27,28]:H= describedbythek,σα=L,R[ k µ(t)]c Anderson

kσαckσα+ k,σα=L,RVα(t) c

kσαdσ+h.c. +HdotwithHdot=σ=±E0d

σdσ+un+n .Herec kσαcreatesanelectronwithenergy kandspinσinleadα=L,R,d electroninthedotwithspinσ,nσcre-atesanσ=d

σdσ,anduisthestrengthoftheCoulombinteraction.Wehaveintroducedtime-dependentsources,acommonchemicalpotentialµ(t)andtunnelingbarriersVα(t),whichare

drivingforcesforelectronpumping.

Letus rst ndoutasource-drainvoltageembeddedinthemodel.Tothisend,weapplythefollowingunitarytransformation ckσ+ckσ for= electronsξη

intheckσL leads:

1 ckσL

ηξckσR

≡U

ckσR (1)withξ=VL/V,η=VR/VandV=

2(ckσ++isckσ )(s=±),resultinginH=k,σ,s b

kσs[ k=±

(µ(t)+s a(t))]bkσs

+V(t)2 b

kσs

dσ+h.c. +Hdot.

(2)

k,σ,s=±Equationde nesthatthegaugepotentiala(t),whichoriginatesfromthetime-dependentbarriers,actsasa nitebiasvoltagebetweenbkσ+andbkσ elds.Hencea nitecurrent owsthroughthedotevenwhenarealbiasvoltageiszero.Inthefollowing,weassumeu=0forawhile.

AdiabaticCurrentandpumpedcurrentIσ charge.—The

σ,Lie/ = I σ,R /2withI σ;αkVα(t) I=d

σckσα c kσαdσbyb canberepresentedkσs elds:

IieV(t)σ=2 [(ξ+isη)2k

d σbkσs (ξ isη)2

b kσsdσ ].

s=±

(3)

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