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

Transcription

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 = 2e 2 /h T T 1 Energy to switch a bit: E= k B T ln2 Time to switch one bit: t = h /E Energy to transport a bit: E= k B T /c d

4 Magnetic data storage Still 10 6 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)2x1 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. 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 attached 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 1/5 th -order pattern

12 Si(111)5x2-Au structure: Refinements The basic structure is 5x1,with 3 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)

13 Si(557) Au Simpler: Single Au chain Graphitic honeycomb chain Au chain

14 Why 1D, not 2D? Perfect lattice match along the chain, but complete mismatch perpendicular to it. Graphitic honeycomb chain

15 Futuristic transistor, made of graphene ribbons Geim and MacDonald, Physics Today, August 2007 Silicon ribbons instead?

16 The ultimate nanowire A single chain of orbitals 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, k x, k y Fermi surface: I(k y,k x ) Band dispersion: I(E, k x ) Phil Anderson: Photoemission data will provide the smoking gun for solving HiTc superconductivity.

21 Fermi surfaces from 2D to 1D 2D 2D + superlattice 1D

22 Band dispersions of atom chains Single Chain Double Chain Three Chains Si(557) -Au Si(553) Au Si(111) -Au E S E D b D a E D b S D a A 2 A 1 A 2 k A 2 A 1 A 2 k A 2 A 1 A 2 k S = Single Chain, D b = Double chain (bonding), D a = Double chain (antibonding), S. Erwin (unpublished)

23 What about the splitting? Prediction: It is magnetic! Spin-split band similar to that in photoemission 0 E F 0 k ZB 1x1 Crain et al., PRB 69, (2004). Sanchez-Portal et al., PRL 93, (2004)

24 Evidence for spin polarization Spin-polarized, angle-resolved photoemission Okuda et al. PRB 82, (R) (2010)

25 Various spin splittings Rashba (spin-orbit) Hamiltonian: H (k V) s Non-magnetic Exchange Splitting Rashba Splitting E k vertical shift horizontal shift W shape

26 Evidence for Rashba splitting (in k-space) Electron-like Rashba bands ( W ) E [ev] Two sets of bands: 1x2 back-folded direct k x [Å 1 ] Hole-like Rashba bands ( ) 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: P b -center at Si/SiO 2, seen by ESR

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

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

30 Empty minority spin state as hallmark of the magnetic exchange splitting E ex Magnetic Non-Magnetic E E ex E F 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 A Two-photon photoemission results Biedermann et al., PRB 85, (2012)

33 Two-photon photoemission IR UV A E Fermi Photoelectron Intensity at k =0 A High-resolution technique for unoccupied states. 25 fsec time resolution.

34 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)

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 exhibits an edge band straddling E F. That is not observed. The magnetic splitting avoids high-lying occupied states at E F, reducing the total energy (see the Stoner criterion). 0 ZB 2x1 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 Large current Small current Spin swapped Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009)