Physics Department, University of Basel

Intrinsic Charge Fluctuations and Nuclear Spin Order

in GaAs Nanostructures

Dominik ZumbühlDepartment of Physics, University of Basel

Basel QC2 Center and Swiss Nanoscience Institute SNI

Scuola Enrico Fermi, Varenna, 21.6.2012Quantum Spintronics and Related Phenomena

fundamental, intrinsic double-dot physicsnuclear spin order in a Luttinger liquid?

50 nm

500 nm

device layout: Barthel, Marcus et al. PRL 2009, PRB2010

surface-gate defined on a GaAs 2D electron gas (2DEG)charge sensors: quantum dotswafer material from Zimmermann, Gossard, UCSB

Device: Double Dot with Charge Sensors

GaAs 2D Electron Gas (2DEG)

Fermi wavelength F ~ 50 nmmean free path ~ micron

A. Johnson

J. Zimmerman and A. C. Gossard, UC Santa Barbara

density n = 2 x 1011 cm-2

mobility ~ 200’000 cm2/(Vs)

Lateral Depletion Gating, Ohmic Contacts

B. van Wees et al., PRL 1988D. Wharam et al., J. Phys. C

quantum pointcontact

voltage adjustabledepletion area

depletion region

A. Johnson

Forming a Quantum Dot

0.15

0.10

0.05

0.00-200 -198 -196 -194

V (mV)

g (e

2 /h)

N = 1 2 3 . . .

Coulomb blockade peaks:resonant transport through dot

0

Coulomb Blockade, Charging Energy

small size of dot ~ 10 nm

charging energy

~ meV

classical, not quantum

capacitance of dot C

Quantum Confinement Energy

harmonic potential

eV to meV

complicated potential

average level spacing

quantum mechanics

200nm

VSD

I

kT ~ eV~ meVEc ~ meV

differential conductance: peaks when current through dot is changing

Coulomb Diamonds

GS1ES2ES

-eVSDGS1ES2ES

-eVSDGS1ES2ES

-eVSD

only one excess electron can be on dot (charging energy)

lab to investigatequantum levelsin device!!

A B C

A B C

quantum confinement energies

internal excitations (spin)

Sequential Tunneling, Excited-State Spectroscopy

Charge sensing of Single Electrons

quantum point contact QPC

QPC

co

nduc

tanc

e

time

empty dot

add oneelectronto dot

one-electron dotdot g

QPC gQPC sensorsensitivityg / g ~ 5 %

N N+1

TE ~ 50 mK

dot charge sensor: sensitivity dg/g ~100%Barthel, Marcus et al. PRL 2009, PRB2010M. Field et al., PRL 1993. Elzermann et al., PRB, Nature 2003/2004

Charge Stability Diagram

( 0 , 0 )

( 0 , 1 )

( 1 , 1 )

( 1 , 0 )

( 0 , 2 )( 1 , 2 )

( 2 , 2 )

( 2 , 1 )

( 2 , 0 )

can empty both dots add electrons one by one

Elzermann et al., PRB, Nature 2003/2004

(0,0) – (1,1) Transition

( 0 , 0 )

( 0 , 1 )

( 1 , 0 )

( 1 , 1 )

lock-in measurement

Van der Wiel et al., RMP2003

Time scale of charge fluctuations: an example

assumptions:dot levels E ~100 eV below reservoirselectron T = 150 mK (13 eV) ~ 10 MHz (100 ns, 0.5 mK)

charge fluctuation rate ~

here: ~ 200 s (average time for electron to leave dot)

but: exponentially sensitive to temperature, level positionse.g. for T = 100 mK, 10 ms

fluctuations destroy spin qubit informationappear in T1 measurement

but easy to remedy: lower tunneling rates / temperatures / level energies

Double Dot Charge Fluctuations and Metastable States

present for all vertices,not only for (0,0)-(1,1)

fluctuations destroy spin qubit information

but easy to remedy: lower tunneling rates / temperatures / level energies

if excited-state not metastablefluctuations present, but not directly visible(interdot tunneling faster than detector)

charge fluctuations present throughout charge stability diagramrate strongly energy dependent

external energy absorption

extrinsic effect, energy absorption

Summary

• intrinsic charge fluctuations and metastable states in GaAs few-electron double dots - charge fluctuations due to sequential tunneling exchange with reservoirs- intrinsic effect, no energy absorption, not sensor back-action- fluctuations easily visible for metastable states- experiment and model in quantitative agreement- control fluctuation rate

a) exponentially with level energy, temperatureb) linear in bare reservoir tunnel rate

work in progress… to be submitted

Nuclear Helimagnets

carbon nanotube

Braunecker, Simon & Loss, PRB2009, PRL 2008

GaAs wire

induced by hyperfine coupling and strongly interacting electron system (ee interaction)in Luttinger liquids (1D)

Spin-Selective Peierls Transition in a Luttinger Liquid

Peierls: metal – insulator transitioninduced by F/2 periodic potential

spin selective Peierls transition

induced by - spin-orbit coupling- nuclear Helimagnet (equivalent)freeze ½ of modesspin selective, g = 1 e2/h

Braunecker, Japardize,Klinovaja & Loss, PRB 2010

GaAs Cleaved Edge Overgrowth Quantum Wires

ultraclean, ballistic, micron long wires, density-tunable with gateprobably the best established realization of a Luttinger liquid in nature

Pfeiffer et al., JCG 1993Yacoby et al., SSC 1996 Yacoby et al., PRL 1996Picciotto et al., PRL 2000Picciotto et al., Nature 2001Auslaender et al., Science 2002Tserkovnyak et al., PRL 2002Tserkovnyak et al., PRB 2003Auslaender et al., Science 2005Steinberg et al., PRB 2006Steinberg et al., NP 2008Barak et al., NP 2010

GaAs Cleaved Edge Overgrowth (CEO) Quantum Wires

Pfeiffer et al., JCG 1993Yacoby et al., SSC 1996 Yacoby et al., PRL 1996

a) AlGaAs/GaAs quantum well Si doping above well2D electron gas (2DEG) 500 nm deepn ~ 2 1011 cm-2, > 106 cm2/(Vs)tungsten surface gatecleave in UHV

b) overgrow cleavage plane withmodulation doping sequencegives charges at edgefew modesstrong overlap 2DEG to edgeintimate 2D-1D coupling

c) use gate to deplete 2DEG belowcontrol edge density & # modes

Gate-Voltage: Conductance Plateaus

varying side-gate VS300 mK

rectangular (QW)/triangular (heterointerface) modes

y

mean free path >10 m (flat plateaus)

conductance quantization not universal (not 2e2/h multiples)but repeatable (QW width dependent)

very large subband spacing (many meV, from B-field data)Yacoby et al., SSC 1996

Low-Temperature T < 300 mK Wire Transport

Basel measurements on Yacoby / Pfeiffer wires

weak, short, not-flat plateaus, low density…

Two Parallel Wires: upper wire (UW), lower wire (LW)

more recently grown, higher quality samples

UW

LW

• long, flat plateaus (2 m wire)• VG tunes simultaneously UW and LW density• additional complication: both wires conduct in parallel

most simple model: g = gUW + gLW

VG xyz

Identify Modes / Wires

LWmode 1

+ UWmode 1

xyz

Identify Modes: B-dependence

xyz

Identify Modes / Wires

LWmode 1

+ UWmode 1

+ LWmode 2 (weak coupling)

+ UWmode 2

xyz

Electron Temperature Measurements

use two independent methods

1. on-chip FQHE thermometer: upper bound on T:T < 30 mK

2. independent cool down with Coulomb blockade thermometers(Meschke & Pekola, Aalto Univ., Finland)

T = 11 mK for identical setup, cold finger, chip carrier etc.

both of these independent measurements give temperaturesmuch smaller than 80 mK

Cool Metallic CBT thermometer to 7.5 ± 0.2 mK

M. Meschke, J. Pekola

Aalto University

Nuclear Ordering Temperature: Theory EstimatesBraunecker, Simon & Loss, PRB 2009

T = 0.3K

A. Yacoby, L. Pfeiffer et al., PRL 1996

NMR & magnon experiments in progress, C. Scheller

Non-Universal Conductance Quantization

Reduced Conductance Quantization Model 1: non-interacting electrons

non-interacting electron in both contacts and wiresLandauer Formula, no disorder: multiples of 2e2/hreduced g: transmission T < 1 (disorder)

ruled out by a) energy independence T (flat, long plateaus)b) temperature dependence for energy independent T

Reduced Conductance Quantization Model 2: interacting electrons, Luttinger liquid theory

infinite Luttinger liquid: g = N K 2e2/h (Luttinger interaction parameter K 1)

Apel & Rice, PRB 1982Kane & Fisher, PRL, PRB 1992

clean, finite wire with Fermi liquid (non-interacting) leadsg = N 2e2/h

with weak disorder: reduced g with power-law due to wire ee only(contact resistance outside wire, unaffected by wire interactionsplus weak scattering inside wire with LL features)

Maslov & Stone, PRB 1995

Ogata & Fukuyama PRL 1994Tarucha et al., SSC 1994Maslov, PRB 1995

ruled out by long, flat plateaus(K would depend on plateau position)

finite conductance ~ 1/L at T = 0

Reduced Conductance Quantization Model 3: Boltzmann 2D-1D contact scattering model

2D-1D coupling requires momentum scattering

BS : wire back scatteringLL enhanced at low-T

2D: 2D-1D scatteringLL suppressed at low-T(vanishing LL DOS)

coupling a) from 2D to few (~ 4 - 8) mode, semi-infinite wire, with weak LL correl.b) from semi-infinite wire to single mode wire

G arising from contacts, not single mode wire

rule out, since this predicts G -> 0 at T -> 0 (not seen)

Yacoby et al., PRL 1996Picciotto et al., PRL 2000

Reduced Conductance Quantization Model 4: Wigner Crystal, Heisenberg Chain

at very low densities, large rSfinite length Wigner Crystalantiferromagnetic Heisenberg chain, exponentially small exchange coupling J

present wires not in this very low density regime

also, this model predicts qualitatively opposite T-dependence:low T<<J: 2e2/hhigh T>>J: 1e2/h

Matveev PRL, PRB 2004

Summary & Outlook

• charge fluctuations in GaAs few-electron double dots - thermally activated, two-step sequential tunneling process- intrinsic effect, no energy absorption, not sensor back-action- causes qubit decoherence: improve with low tunneling, low T

• evidence for nuclear-spin order in GaAs quantum wires- wire g ~ 1e2/h for T < 80 mK (g ~ 2 e2/2 at high T)- sample electrons cool to ~ 10 mK (CBT)- not inconsistent with spin-selective Peierls transition in a Luttinger liquid

and a nuclear helimagnet

both experiments: work in progress

Acknowledgements

charge fluctuationsGaAs double dotsDaniel Biesinger, BaselChristian Scheller, Basel

theoryB. Braunecker, UA Madrid

GaAs 2DEG wafersJ. Zimmermann, A. C. Gossard, UC Santa Barbara

nuclear spinsquantum wiresexperimentsC. Scheller, Basel

samples, discussionsG. Barak, A. YacobyHarvard University

theoryB. Braunecker, UA MadridD. Loss, BaselP. Simon, U Paris Sud

CEO wires growthL. Pfeiffer, K. WestBell Labs & Princeton

CBT thermometersM. Meschke, J. PekolaAalto University, Helsinki

Daniel Biesinger Christian Scheller