Electronic Properties of Ultimate Nanowires

F. J. Himpsel, S. C. Erwin, I. Barke, …

• Nanostructures with Atomic Precision

• Single Atom Wire, Single Wave Function

• Ultimate Limits of Electronics

The Goal

• Combine spectroscopic methodsSpatial vs. momentum resolution, filled vs. empty states, spin

-

Angle-resolved photoemission-

Two-photon photoemission-

Scanning tunneling spectroscopy

Conductance per Channel:

G = G0·T

G0

=

2e2/h

Energy to switch one bit:

E = kBT · ln2

Time to switch one bit:

t = h / E

Energy to transport a bit:

E = kBT · /c · d

Limits of Electronics from Information Theory

Transmission T1

Still 106 Atoms/BitMagnetic Data Storage

Use Bond Rearrangement on Silicon to Obtain Atomic Precision

Conventional wisdom tells us that -bonds

form only in carbon.

Silicon surfaces break the rule.

Si(100)2x1

Si(111)2x1

Si(111)5x2-Au(cleaved)

Si=Si

dimers

-bonded chain

graphitic silicon

Adatoms

convert three

broken bonds into one.

Holes

eat broken bonds.

Bumps and holes

Si(111)7x7

Most stable silicon surface.

Perfect rearrangement of >100 atoms.

Si(111)7x7 as 2D Template

Aluminum sticks to one of the two 7x7 triangles.

Can put Mn

atoms on top of the aluminum.

Jia

et al.

Straight steps because of the large 7x7 cell.

Wide kinks cost energy.

1 kink in 20 000 atoms

15 nm

Stepped Si(111)7x7as 1D Template

Atomic Perfection by Self-AssemblySmaller is easier (“bottom up”)

One 7x7 cell per terrace

5.731

592

8 nm

Metal atoms that produce 1D

chains on vicinal Si(111) :

I: Li, Na,…

II: Ca, Ba,…

III: In IV: Pb

NM: Ag,

Au TM: Pt RE: Gd, Dy,…

on Si(100):III: BiTM: Ir

on Ge(100):NM: Au TM: Pt

1/3rd-order pattern … was joined by a 1/5th-order pattern

Si(111)5x2-Au structure: found in 1969, still getting refined.

Three Au chains on Si(111)5x2-Au

Au chain

Graphitichoneycomb

chain

Si(557) – Au

Simpler: Single chain

Graphitichoneycomb

chain

Why are these surfaces 1D (not 2D) ?

Perfect lattice match along the chain,

but complete mismatch perpendicular to it

.

Geim

and MacDonald,Physics Today, August 2007

Futuristic molecular switch, made of graphene

ribbons

Maybe silicene

instead?

Graphiticribbon

Si(557)-Au

Single chain of orbitals

The ultimate nanowire

The Haiku structure, a buried wire

Si(100)- Bi

Owen, Miki, Bowler

Physics in One Dimension

• Elegant and simple

• Lowest dimension with translational motion

• Electrons cannot avoid each other

• No such thing as a single electron

• Spinons

and holons

instead

Electrons cannot avoid each other in 1D:

Delocalized electrons:Tomonaga-Luttinger

model

in reciprocal space

Localized electrons:Hubbard modelin real space

Mapping out Electrons at a Surface

Angle-resolved photoemissionmeasures all quantum numbers:

E, kx

, ky

Fermi surface: I (ky, kx

)Band dispersion:

I (E,

kx

)

Phil Anderson: Photoemission data will provide the “smoking gun”

for solving HiTc

superconductivity.

2D

Fermi Surfaces from 2D to 1D

2D + super-

lattice

1D

Single Chain Double Chain

Si(557)

-Au Si(553) –Au

S = Single Chain Db = Double chain bondingDa = Double chain antibonding

S

A2 A1 A2

E

k

EDb Da

A2 A1 A2

k

E

A2 A1 A2 k

Db S Da

Si(111)

-Au

Three Chains

0 k ZB1x1

EF

Spin-split band similar to that in photoemission

Sanchez-Portal et al. 2004

0

What about the splitting? Prediction: It is magnetic!

Evidence for spin polarization

Spin-polarized, angle-resolved photoemission

Okuda et al. 2010

Non-magnetic Exchange Splitting Rashba SplittingE k

vertical shift horizontal shift“

W”

shape

Various spin splittings

Rashba

(spin-orbit) Hamiltonian:

H

(k

V)

s

Evidence for Rashba splitting (in k-space)

Barke

et al. 2006

E [eV]

kx

[Å−1]

1x2 back-foldeddirect

Two sets of bands:

Electron-like Rashba

bands (“

W ”)

Hole-like Rashba

bands (“

”)

W

Spin-polarization of broken bonds in real space?

3D: No Spin-paired electrons in -bonds

2D: No Spin-paired electrons in -bonds

1D: ??

0D: Yes Isolated broken bond electron: Pb -center at Si/SiO2 , seen by ESR

GraphiticribbonFocus on the step edge

Look for isolated broken bonds

Si

SiSiSi

Au Au

Au Au

Au Au

Prediction: Magnetism triggers superlattice, couples atoms – electrons – spins

Erwin and Himpsel, Nature Comm. (2010)

Empty minority spin state is the hallmark of the magnetic splitting Eex

Eex

E

EF

Magnetic Non-Magnetic

Calculated magnetic band structure

Two-photon photoemission results

Biedermann

et al., PRB (2012)

A

Two-photon photoemission in k-space

High-resolution technique for unoccupied states. 25 fsec time resolution.

EFermiIR

UV

A

Pho

toel

ectro

n In

tens

ity a

t k |

|=0

A

Snijders

et al., New Journal of Physics (2012)

Scanning tunneling spectroscopy in real space

Spin-polarized edge atoms appear bright. Dangling bond sticks out !

V [V]

dI/dVI/V

D(E)

Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009)

Spin-polarized scanning tunneling spectroscopy

Spin swapped

Large current Small current

Loth

et al., Science 335, 196 (2012)

12 spins/bit, antiferromagnetic,color = spin polarization

Europhysics

News 39, 31 (2008)

Backups

Total filling of 5/3

e- per chain atom

• 5 electrons get distributed over 3 chain atoms (tripling of the unit cell).• Analogous to 1 electron being shared by

3 flux quanta

in the FQHE.

Band Dispersion

Fermi SurfaceFractional Band Filling

Spin-Charge Separation via Tunneling between two Quantum Wires

Auslaender

et al., Science 308, 88 (2005)

Use B-field to transfer momentum: p (p + eA)

E

p

Increase spinon-holon splitting by Coulomb U

TTF-TCNQ

Claessen

et al., PRL 88, 096402 (2002), PRB 68, 125111 (2003)

End atoms disappear at certain bias voltages

Zero-dimensional “surface state” at the end of a one-dimensional chain

Crain and Pierce, Science 307, 703 (2005)

Is there a connection to spin- polarized broken bonds in

irradiated graphite?

See also C-specific MCD results by Ohldag

et al., PRL 98, 187204 (2007); New J. Physics 12, 123012 (2010).

From Cervenka, Katsnelson, Flipse, Nature Physics 5, 840 (2009).

1x3 superlattice formation at the step edge

What are these distortions ?Atoms?

(Reconstruction) Electrons?

(Charge density wave)Magnetic?

(Spin density wave)

Empty StatesTwo-Photon

Photoemission

Rügheimer

et al., PRB 75, 121401(R) (2007)

0 ZB2x1

Predicted step edge band not seen at EF

. Would be rather unstable. How does the surface avoid such high density of states at EF

?

Magnetic splitting shifts minority spin states up

!

Two-photon photoemission processes

Low-lying magnetic states