Physics Department, University of Basel Intrinsic Charge Fluctuations and Nuclear Spin Order in GaAs Nanostructures Dominik Zumbühl Department of Physics, University of Basel Basel QC2 Center and Swiss Nanoscience Institute SNI Scuola Enrico Fermi, Varenna, 21.6.2012 Quantum Spintronics and Related Phenomena fundamental, intrinsic double-dot physics nuclear spin order in a Luttinger liquid?
500 nm 50 nm
Device: Double Dot with Charge Sensors surface-gate defined on a GaAs 2D electron gas (2DEG) charge sensors: quantum dots wafer material from Zimmermann, Gossard, UCSB device layout: Barthel, Marcus et al. PRL 2009, PRB2010
GaAs 2D Electron Gas (2DEG) A. Johnson density n = 2 x 10 11 cm -2 mobility ~ 200 000 cm 2 /(Vs) Fermi wavelength F ~ 50 nm mean free path ~ micron J. Zimmerman and A. C. Gossard, UC Santa Barbara
Lateral Depletion Gating, Ohmic Contacts depletion region A. Johnson quantum point contact voltage adjustable depletion area B. van Wees et al., PRL 1988 D. Wharam et al., J. Phys. C
Forming a Quantum Dot
Coulomb Blockade, Charging Energy capacitance of dot C small size of dot ~ 10 nm charging energy ~ mev Coulomb blockade peaks: resonant transport through dot 0.15 g (e 2 /h) 0.10 0.05 0 N = 1 2 3... classical, not quantum 0.00-200 -198-196 -194 V (mv)
Quantum Confinement Energy harmonic potential complicated potential average level spacing ev to mev quantum mechanics
Coulomb Diamonds kt ~ ev ~ mev Ec ~ mev 200nm V SD I differential conductance: peaks when current through dot is changing
Sequential Tunneling, Excited-State Spectroscopy lab to investigate quantum levels in device!! A B C quantum confinement energies internal excitations (spin) A B C 2ES 1ES 2ES GS 1ES -ev SD GS -ev SD 2ES 1ES GS -ev SD only one excess electron can be on dot (charging energy)
Charge sensing of Single Electrons QPC g QPC sensor sensitivity quantum point contact g / g QPC ~ 5 % QPC conductance add one electron to dot N empty dot g dot N+1 time one-electron dot
T E ~ 50 mk dot charge sensor: sensitivity dg/g ~100% Barthel, Marcus et al. PRL 2009, PRB2010 M. Field et al., PRL 1993. Elzermann et al., PRB, Nature 2003/2004
Charge Stability Diagram (0,2) (1,2) (2,2) (0,1) (1,1) (2,1) (2,0) (0,0) (1,0) can empty both dots add electrons one by one Elzermann et al., PRB, Nature 2003/2004
(0,0) (1,1) Transition lock-in measurement ( 1, 1 ) ( 0, 1 ) ( 1, 0 ) ( 0, 0 ) Van der Wiel et al., RMP2003
Time scale of charge fluctuations: an example assumptions: dot levels E ~100 ev below reservoirs electron 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 positions e.g. for T = 100 mk, 10 ms fluctuations destroy spin qubit information appear 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) if excited-state not metastable fluctuations present, but not directly visible (interdot tunneling faster than detector) charge fluctuations present throughout charge stability diagram rate strongly energy dependent fluctuations destroy spin qubit information but easy to remedy: lower tunneling rates / temperatures / level energies
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, temperature b) linear in bare reservoir tunnel rate work in progress to be submitted
Nuclear Helimagnets induced by hyperfine coupling and strongly interacting electron system (ee interaction) in Luttinger liquids (1D) GaAs wire carbon nanotube Braunecker, Simon & Loss, PRB2009, PRL 2008
Spin-Selective Peierls Transition in a Luttinger Liquid Peierls: metal insulator transition induced by F /2 periodic potential spin selective Peierls transition Braunecker, Japardize, Klinovaja & Loss, PRB 2010 induced by - spin-orbit coupling - nuclear Helimagnet (equivalent) freeze ½ of modes spin selective, g = 1 e 2 /h
GaAs Cleaved Edge Overgrowth Quantum Wires ultraclean, ballistic, micron long wires, density-tunable with gate probably the best established realization of a Luttinger liquid in nature Pfeiffer et al., JCG 1993 Yacoby et al., SSC 1996 Yacoby et al., PRL 1996 Picciotto et al., PRL 2000 Picciotto et al., Nature 2001 Auslaender et al., Science 2002 Tserkovnyak et al., PRL 2002 Tserkovnyak et al., PRB 2003 Auslaender et al., Science 2005 Steinberg et al., PRB 2006 Steinberg et al., NP 2008 Barak et al., NP 2010
GaAs Cleaved Edge Overgrowth (CEO) Quantum Wires a) AlGaAs/GaAs quantum well Si doping above well 2D electron gas (2DEG) 500 nm deep n ~ 2 10 11 cm -2, > 10 6 cm 2 /(Vs) tungsten surface gate cleave in UHV b) overgrow cleavage plane with modulation doping sequence gives charges at edge few modes strong overlap 2DEG to edge intimate 2D-1D coupling c) use gate to deplete 2DEG below control edge density & # modes Pfeiffer et al., JCG 1993 Yacoby et al., SSC 1996 Yacoby et al., PRL 1996
Gate-Voltage: Conductance Plateaus varying side-gate V S 300 mk y mean free path >10 m (flat plateaus) rectangular (QW)/ triangular (heterointerface) modes conductance quantization not universal (not 2e 2 /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 V G y z x UW LW long, flat plateaus (2 m wire) V G tunes simultaneously UW and LW density additional complication: both wires conduct in parallel most simple model: g = g UW + g LW
Identify Modes / Wires y z x LW mode 1 + UW mode 1
Identify Modes: B-dependence y z x
Identify Modes / Wires y z x LW mode 1 + UW mode 1 + LW + UW mode 2 mode 2 (weak coupling)
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 temperatures much smaller than 80 mk
Cool Metallic CBT thermometer to 7.5 ± 0.2 mk M. Meschke, J. Pekola Aalto University
Nuclear Ordering Temperature: Theory Estimates Braunecker, Simon & Loss, PRB 2009
Non-Universal Conductance Quantization A. Yacoby, L. Pfeiffer et al., PRL 1996 T = 0.3K NMR & magnon experiments in progress, C. Scheller
Reduced Conductance Quantization Model 1: non-interacting electrons non-interacting electron in both contacts and wires Landauer Formula, no disorder: multiples of 2e 2 /h reduced 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 2e 2 /h (Luttinger interaction parameter K 1) Apel & Rice, PRB 1982 Kane & Fisher, PRL, PRB 1992 clean, finite wire with Fermi liquid (non-interacting) leads g = N 2e 2 /h Maslov & Stone, PRB 1995 with weak disorder: reduced g with power-law due to wire ee only (contact resistance outside wire, unaffected by wire interactions plus weak scattering inside wire with LL features) finite conductance ~ 1/L at T = 0 Ogata & Fukuyama PRL 1994 Tarucha et al., SSC 1994 Maslov, PRB 1995 ruled out by long, flat plateaus (K would depend on plateau position)
Reduced Conductance Quantization Model 3: Boltzmann 2D-1D contact scattering model 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 BS : wire back scattering LL enhanced at low-t 2D : 2D-1D scattering LL suppressed at low-t (vanishing LL DOS) G arising from contacts, not single mode wire 2D-1D coupling requires momentum scattering rule out, since this predicts G -> 0 at T -> 0 (not seen) Yacoby et al., PRL 1996 Picciotto et al., PRL 2000
Reduced Conductance Quantization Model 4: Wigner Crystal, Heisenberg Chain at very low densities, large r S finite length Wigner Crystal antiferromagnetic Heisenberg chain, exponentially small exchange coupling J Matveev PRL, PRB 2004 present wires not in this very low density regime also, this model predicts qualitatively opposite T-dependence: low T<<J: 2e 2 /h high T>>J: 1e 2 /h
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 ~ 1e 2 /h for T < 80 mk (g ~ 2 e 2 /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 fluctuations GaAs double dots Daniel Biesinger, Basel Christian Scheller, Basel theory B. Braunecker, UA Madrid GaAs 2DEG wafers J. Zimmermann, A. C. Gossard, UC Santa Barbara nuclear spins quantum wires experiments C. Scheller, Basel samples, discussions G. Barak, A. Yacoby Harvard University theory B. Braunecker, UA Madrid D. Loss, Basel P. Simon, U Paris Sud CEO wires growth L. Pfeiffer, K. West Bell Labs & Princeton CBT thermometers M. Meschke, J. Pekola Aalto University, Helsinki Daniel Biesinger Christian Scheller