Spin-orbit-mediated control of electron and hole spins in InSb ...

Spin-orbit-mediated control of electron and hole spins in
InSb nanowire quantum dots
Vlad Pribiag
Kavli Institute of Nanoscience,
Delft University of Technology
Stevan Nadj-Perge
Sergey Frolov
Johan van den Berg
Ilse van Weperen
Leo Kouwenhoven
Sébastien Plissard
Erik Bakkers
conduction band

Zincblende InSb nanowires (111)
nanowires are grown by
MOVPE
Au
InSb
InAs
• Strong spin-orbit coupling
• Smallest band gap of III-V semiconductors
• Very large g-factors
InP (111)
Qubits, Majorana fermions
Plissard et al., NanoLetters (2012).
see also: Caroff et al., Nanotechnology (2009).

Right Gate (mV)
300 400 500
InSb double quantum dots
3
2
4
1
5
D
S
1 µm
BG
300 400 500 600
Left gate (mV)
• easier to tune than InAs
(higher mobility, lower electron mass)
S. Nadj-Perge et al., PRL (2012).
(Few-electron single dot in InSb nw’s first realized in Xu group (Lund).)

Energy (μeV)
Electric dipole spin resonance
Weak interdot coupling
E ac = E 0 sin(ω L t)
gµ B B
• a.c. electric field drives spin resonance
mediated by the spin-orbit interaction
20
0
-20
(,)
(,)
(,)
(,)
0 5 10
B (mT)

Energy (μeV)
Electric dipole spin resonance
Detect spin rotations via spin blockade
Weak interdot coupling
E ac = E 0 sin(ω L t)
gµ B B
• a.c. electric field drives spin resonance
mediated by the spin-orbit interaction
20
0
-20
(,)
(,)
(,)
(,)
0 5 10
B (mT)

Frequency (GHz)
Energy (μeV)
Electric dipole spin resonance
Detect spin rotations via spin blockade
Weak interdot coupling
20
20
(,)
0
(,)
(,)
5
-50 50
B (mT)
-20
(,)
0 5 10
B (mT)

g-factor
g-factor anisotropy in an InSb double-dot
45
anisotropic g-factors in two dots:
30
-90° 0° 90° 180° 270°
Angle
nw B
nw
B
Similar measurements on g-factors from Petta group on InAs nanowires.

g-factor
g-factor anisotropy in an InSb double-dot
45
anisotropic g-factors in two dots:
30
-90° 0° 90° 180° 270°
Angle
left dot
right dot

Electric dipole spin resonance – stronger
interdot coupling
Stronger interdot coupling
• tunnel coupling hybridizes S(1,1) and S(0,2)
• SO mixes T - (1,1) and S

Frequency (GHz)
Electric dipole spin resonance – stronger
interdot coupling
Stronger interdot coupling
15
10
5
-20 B (mT) 20
• tunnel coupling hybridizes S(1,1) and S(0,2)
• SO mixes T - (1,1) and S
anticrossing size: l so ~ 230 nm
(cf. l SO ~ 10 µm for GaAs!)

Angular dependence of SOI
• anticrossing size depends on angle of B w.r.t. nanowire

Angular dependence of SOI
• anticrossing size depends on angle of B w.r.t. nanowire
• spin-blockade leakage current has similar angular dependence on B

Angular dependence of SOI
B SO
B
φ
T - (1,1)
B SO
S(1,1)
T 0 (1,1)
T + (1,1)
B SO
S(0,2)
• anticrossing and leakage current show same anisotropy
• common origin: mixing of T(1,1) and S by the SOI

Determining the spin-orbit field direction
k
E
111
B SO
• No BIA spin-orbit for [111] direction (the growth direction)
• Anisotropies consistent with Rashba spin-orbit interaction

Coherent control of electron spin in InSb
initialize manipulate readout
SB
CB
SB
• f Rabi up to 104 MHz (highest reported for single-spin qubit in a QD)
• fidelity of ~81%
J. van den Berg et al., PRL 2013 (in print).

Ramsey sequence
InSb qubit coherence
Ramsey fringe
vary the relative phase

Ramsey sequence
InSb qubit coherence
Ramsey fringe
vary the relative phase
Decay of Ramsey fringe contrast
vary the waiting time t
T 2 * ~ 6-9 ns

InSb qubit coherence
Ramsey sequence
Hahn echo sequence
Decay of Ramsey fringe contrast
Decay of Hahn echo fringe contrast
T 2 * ~ 6-9 ns
T echo ~ 32-35 ns
Similar to InAs nw qubits: suggests dephasing due to fast dynamics of nuclear spin bath

Selective coherent control
• large Δg between the two QD’s (due to difference in confinement)

Selective coherent control
• large Δg between the two QD’s (due to difference in confinement)
• allows selective driving of Rabi oscillations for each of the two qubits
• the large ΔE Z may enable CPHASE gate operation time of ~1 ns (Meunier et al., PRB 2011)

From electron spins to hole spins
Electron spins:
• very advanced platform for quantum information processing
(single-spin rotations, single-spin readout, coherent exchange)
• decoherence due to nuclear spins is a challenge in III-V semiconductors
Hole spins:
• weaker hyperfine interaction (longer spin coherence)
(e.g. Brunner et al., Science (2009); DeGreve et al., Nat. Phys. (2011))
• stronger spin-orbit coupling (enhanced spin control)
(e.g. Manaselyan et al., Europhys. Lett. (2009); Kloeffel et al., PRB (2011))
• control may facilitate spin-to-photon conversion
• … but challenging fabrication few spin transport studies to date
V.S.P. et al., Nature Nanotech., 2013 (in print).

From electrons to holes in InSb nw’s
hole
transport
electron
transport
S
D
Bipolar InSb nanowire FETs first demonstrated by
Nielsen et al., (2011).

Bandgap of our InSb nanowires
Bandgap ~ 200 meV (agrees with bulk values)

Schematic band diagram for hole QD.
Hole quantum dots

Hole quantum dots
Gate tuning from electron transport to hole QD.
Schematic band diagram for hole QD. • charging energies: ~20 meV
• orbital energies: ~3-8 meV

Double quantum dots with holes
Schematic band diagram for hole double QD.

Double quantum dots with holes
Schematic band diagram for hole double QD.
• charging energies: ~20 meV
• orbital energies: ~8 meV
• predominantly light hole character

Double quantum dots with holes
Schematic band diagram for hole double QD.
• charging energies: ~20 meV
• orbital energies: ~8 meV
• predominantly light hole character
Csontos et al., PRB (2009).

Hole spin blockade
• B = 0 peak is a typical signature of spin blockade for electron spins
(e.g. Koppens et al., Science (2005))

Hyperfine coupling: holes vs. electrons
• Peak width enables estimate of RMS fluctuations of hyperfine field

Hyperfine coupling: holes vs. electrons
• Peak width enables estimate of RMS fluctuations of hyperfine field
cf. optical measurements
Chekhovich et al., PRL 2011

Electric-dipole spin resonance of
hole spins

Electric-dipole spin resonance of
hole spins

Electric-dipole spin resonance of
hole spins: hole g-factors
Hole g-factors in QDs:
• Highly-anisotropic
• One order of magnitude smaller than for electrons
• Surprisingly small compared to bulk hole g-factor (~16) – likely subband mixing
• Strong gate-dependence: suggests g-tensor modulation contributes to EDSR

Electric-dipole spin resonance of
hole spins: hole g-factors
Csontos et al., PRB (2009).
Hole g-factors in QDs:
• Highly-anisotropic
• One order of magnitude smaller than for electrons
• Surprisingly small compared to bulk hole g-factor (~16) – likely subband mixing
• Strong gate-dependence: suggests g-tensor modulation contributes to EDSR

Spin-blockade – strong coupling
• Dip at B = 0
• Likely due to spin-orbit coupling (as also seen for electrons)
• But, very different angular dependence than electrons…

Spin-blockade anisotropy – strong coupling
Electrons:
B SO
B
k
T - (1,1)
E
B SO
S(1,1)
T 0 (1,1)
T + (1,1)
B SO
S(0,2)

Spin-blockade anisotropy – strong coupling
Electrons:
Holes:
B SO
B
k
T - (1,1)
E
B SO
S(1,1)
T 0 (1,1)
T + (1,1)
B SO
S(0,2)

Summary
InSb nanowires, so far:
• Mapped out anisotropy of spin blockade and g-factor (for e and h)
• Fast Rabi oscillations of single-electron-spin qubit (>100 MHz)
• Compared hyperfine coupling (e vs. h)
• Achieved electrical control of hole spins in InSb nanowires
– potential for enhanced control and coherence w.r.t. electron spins
Future directions:
• CPHASE gate (based on large ΔE Z )
• Coherent single hole spin rotations
• Study hole SOI strength and anisotropy (using EDSR)
• Single-shot spin readout (rf-SETs) – study entanglement correlations