1. Electronic Properties of Ultimate Nanowires
F. J. Himpsel, S. C. Erwin, I. Barke, …

2. Nanostructures with Atomic Precision
Single-Atom Wire, Single Wave Function
Ultimate Limits of Electronics, Data Storage
Combine spectroscopic methods:
Filled vs. empty states, spatial vs. momentum resolution
- Angle-resolved photoemission
- Two-photon photoemission
- Scanning tunneling spectroscopy

3. Limits of electronics from information theory
Conductance/Channel: G = 2 e2/h ∙T T Energy to switch a bit: E = kBT ∙ ln2 Time to switch one bit: t = h / E Energy to transport a bit: E = kBT ∙ /c ∙ d

4. Magnetic data storage
Still 106 Atoms/Bit

5. Use bond rearrangement at silicon surfaces to reach atomic precision
Si=Si dimers -bonded chain graphitic silicon  
Si(100)2x1 Si(111)2x Si(111)5x1-Au
(cleaved)
Conventional wisdom tells us that -bonds form only in carbon.
Silicon surfaces break the rule.

6. Si(111)7x7 The most stable surface of clean silicon. Bumps and holes
Perfect rearrangement of >100 atoms.
Bumps and holes
Adatoms convert three broken bonds into one.
Holes eat broken bonds.

7. Si(111)7x7 as 2D Template
Aluminum sticks to one of the two 7x7 triangles.
Mn atoms can be at-tached to aluminum.
Jia et al.

8. Stepped Si(111)7x7 as 1D Template
Straight steps because of the large 7x7 cell.
Wide kinks cost energy.
1 kink in atoms
15 nm

9. Atomic perfection by self-assembly Smaller is easier (“bottom up”)nm
One 7x7 cell per terrace

10. 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: Bi
TM: Ir
on Ge(100):
NM: Au TM: Pt

11. Si(111)5x2-Au : Found in 1969, still being refined
a 1/5th-order pattern

12. Si(111)5x2-Au structure: Refinements
The basic structure is 5x1, with Au atom chains (yellow) and a graphitic silicon ribbon (pink).
Add Si adatoms (blue)
Squeeze in extra Au atoms (orange)
Erwin et al., PRB 80, (2009)
Kwon, Kang, PRL 113, (2014) 12

13. Si(557) – Au Simpler: Single Au chain Graphitic honeycomb chain
Working on structural model s to explain fractional filling. Previous x-ray diffraction showed gold sat in the middle of the terrace (for 557) rather than at the step edge.
One possible model adds 2 extra silicon adatoms every 3 unit cells.
Such a model gives the correct electron count, explains the x3 periodicity as observed by STM. Also give favorable energy in LDA calculations by Steve Erwin as compared to say surface without adatoms or x2 adatom chains

14. Why 1D , not 2D ?
Perfect lattice match along the chain, but complete mismatch perpendicular to i t .
Graphitic
honeycomb chain
Working on structural model s to explain fractional filling. Previous x-ray diffraction showed gold sat in the middle of the terrace (for 557) rather than at the step edge.
One possible model adds 2 extra silicon adatoms every 3 unit cells.
Such a model gives the correct electron count, explains the x3 periodicity as observed by STM. Also give favorable energy in LDA calculations by Steve Erwin as compared to say surface without adatoms or x2 adatom chains

15. Futuristic transistor, made of graphene ribbons
Working on structural model s to explain fractional filling. Previous x-ray diffraction showed gold sat in the middle of the terrace (for 557) rather than at the step edge.
One possible model adds 2 extra silicon adatoms every 3 unit cells.
Such a model gives the correct electron count, explains the x3 periodicity as observed by STM. Also give favorable energy in LDA calculations by Steve Erwin as compared to say surface without adatoms or x2 adatom chains
Geim and MacDonald, Physics Today, August 2007
Silicon ribbons instead ?

16. A single chain of orbitals
The ultimate nanowire
A single chain of orbitals
Working on structural model s to explain fractional filling. Previous x-ray diffraction showed gold sat in the middle of the terrace (for 557) rather than at the step edge.
One possible model adds 2 extra silicon adatoms every 3 unit cells.
Such a model gives the correct electron count, explains the x3 periodicity as observed by STM. Also give favorable energy in LDA calculations by Steve Erwin as compared to say surface without adatoms or x2 adatom chains
Graphitic
ribbon
Si(557)-Au

17. The Haiku structure, a buried wire
Si(100)- Bi
Owen, Miki, Bowler

18. 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

19. Electrons cannot avoid each other in 1D
Delocalized electrons:
Tomonaga-Luttinger model
in reciprocal space
Localized electrons:
Hubbard model
in real space

20. Mapping out electrons at surfaces
Angle-resolved photoemission
measures 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.

21. Fermi surfaces from 2D to 1D
2D + super-lattice 1D

22. Band dispersions of atom chains
Single Chain Double Chain E
 A A A2 k
Db S Da
Si(111) -Au
Three Chains
Si(557) -Au Si(553) –Au
Working on structural model s to explain fractional filling. Previous x-ray diffraction showed gold sat in the middle of the terrace (for 557) rather than at the step edge.
One possible model adds 2 extra silicon adatoms every 3 unit cells.
Such a model gives the correct electron count, explains the x3 periodicity as observed by STM. Also give favorable energy in LDA calculations by Steve Erwin as compared to say surface without adatoms or x2 adatom chains S
Db Da E E k k
 A A A2
 A A A2
S = Single Chain, Db = Double chain (bonding), Da = Double chain (antibonding), S. Erwin (unpublished)

23. What about the splitting ? Prediction: It is magnetic !EF
Spin-split band similar to that in photoemission
Crain et al., PRB 69, (2004).
k ZB1x1
Sanchez-Portal et al., PRL 93, (2004)

24. Evidence for spin polarization
Backfolded dashed bands are weak, since the 2x1 lattice potential is weak.
Spin-polarized, angle-resolved photoemission
Okuda et al. PRB 82, (R) (2010)

25. Various spin splittings
Rashba (spin-orbit) Hamiltonian: H  (k  V)  s
V = crystal potential. Gradient of V on average perpendicular to the surface. Inversion of s changes sign of H, i.e. splitting. Invert p and s gives same H.
Non-magnetic Exchange Splitting Rashba Splitting
 E  k
vertical shift horizontal shift
“ W ” shape

26. Evidence for Rashba splitting ( in k-space)
E [eV]
kx [Å−1]
1x2 back-folded
direct
Two sets of bands:
Electron-like Rashba bands (“ W ”)
Hole-like Rashba bands (“ ”)
Backfolded dashed bands are weak, since the 2x1 lattice potential is weak. W
Barke et al., PRL 97, (2006)

27. 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

28. Look for isolated broken bonds
Graphitic
ribbon
Focus on the step edge

29. Prediction: Si edge atoms with an unpaired electron become spin-polarized
Erwin, Himpsel, Nature Comm. 1:58 (2010) 29

30. Empty minority spin state as hallmark
of the magnetic exchange splitting Eex
Eex E EF
Magnetic Non-Magnetic
Snijders, Erwin, et al., New Journal of Physics 14, (2012).

31. Scanning tunneling spectroscopy of edge states
dI/dV
I/V
 D(E)
V [V]
Spin-polarized edge atoms appear bright.
Their broken bonds stick out, forming a magnetic superlattice.

32. Magnetic band structure
Two-photon photoemission results A
Biedermann et al., PRB 85, (2012)

33. Two-photon photoemission
Photoelectron Intensity at k|| = 0 A
EFermi IR UV A
High-resolution technique for unoccupied states f sec time resolution.

34. 12 spins/bit, antiferromagnetic, color = spin polarization
Europhysics News 39, 31 (2008)
Loth et al., Science 335, 196 (2012)
12 spins/bit, antiferromagnetic,
color = spin polarization

35. Backup Slides

36. Spin-Charge Separation via Tunneling between two Quantum Wires
Use B-field to transfer momentum: p  (p + eA) E p
Auslaender et al., Science 308, 88 (2005)

37. Increase spinon-holon splitting by Coulomb U
TTF-TCNQ
Claessen et al., PRL 88, (2002), PRB 68, (2003)

38. Zero-dimensional “surface state” at the end
of a one-dimensional chain
End atoms disappear at certain bias voltages
Crain and Pierce, Science 307, 703 (2005)

39. 1x3 superlattice formation at the step edge
What are these distortions ?
Atoms ? (Reconstruction) Electrons ? (Charge density wave)
Magnetic ? (Spin density wave)
Ahn, Kang, Ryang, & Yeom, PRL 2005
300 K
45 K 39

40. Low-lying magnetic configurations of Si edge states
Erwin, Himpsel, Nature Comm. 1:58 (2010)

41. Empty states from two-photon photoemission
The magnetic splitting shifts the minority spin states up and the majority states down.
The unpolarized surface ex-hibits an edge band stradd-ling EF . That is not observed. The magnetic splitting avoids high-lying occupied states at EF , reducing the total energy (see the Stoner criterion).
ZB2x1
Rügheimer et al., PRB 75, (R) (2007), Sanchez-Portal et al., PRL 93, (2004).

42. Two-photon photoemission processes

43. Spin-polarized scanning tunneling spectroscopy
Spin swapped
Large current
Small current
Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009)