Vortices in Classical Systems

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Phillip Gaines
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1 Vortices in Classical Systems

2 4 He-II vortices: Vortices in Quantum Systems STM of NbSe 2 vortices: G. A. Williams, R. E. Packard, Hess PRL (1989). Phys. Rev. Lett. 33, 280 (1974) Pan, Hudson, Davis, RSI (1999) Hall probe image of YBCO film at T = 40 K: Checkerboards in Bi 2 Sr 2 CaCu 2 O 8+x vortices: Gauss s Hoffman et al, Science (2002) 20 um B applied = 1 Gauss

3 Single Vortex Manipulation in Superconducting Nb Vortices in Nb Film Cooled to 5.3K in 100G Eric Straver Jenny Hoffman Dan Rugar Kathryn Moler Δf=2.01Hz 1μm Stanford University Funded by Packard and AFOSR

4 Goals Part I: eliminate i uncontrolled vortex motion bigger magnets efficient power lines quieter sensors & circuits Part II: controlled single-vortex manipulation model for soft condensed matter vortex entanglement t vortex ratchet automaton Luttinger liquid FermiLab

5 Part I: eliminate uncontrolled vortex motion

6 Motivation: eliminate uncontrolled vortex motion H c2 H* (where vortices move) Field (T) 20 YBCO Temperature (K) Larbalestier, Nature 414, 368 (2001)

7 Motivation: eliminate uncontrolled vortex motion H c2 H* (where vortices move) Field (T) 20 YBCO Temperature (K) Larbalestier, Nature 414, 368 (2001) e- e- e- e-

8 Motivation: eliminate uncontrolled vortex motion H c2 H* (where vortices move) Field (T) 20 YBCO Temperature (K) Larbalestier, Nature 414, 368 (2001) Apply current I: Cooper pairs flow without dissipation e- e- e- e-

9 Motivation: eliminate uncontrolled vortex motion H c2 H* (where vortices move) Field (T) 20 YBCO Temperature (K) Larbalestier, Nature 414, 368 (2001) Apply current I: Cooper pairs flow without dissipation Normal electrons in vortex core cause dissipation when moved e- e- e- e- e e- ē- e- e-

10 Vortex Pinning Measurements: Bulk Transport 10 GB, B = 0 Tesla 4 GB, B = 1 Tesla intra-grain (upper scale) grain boundary Redwing et al, APL 75, 3171 (1999). Hogg et al, APL 78, 1433 (2001).

11 Vortex Pinning Measurements: Bulk Transport 10 GB, B = 0 Tesla 4 GB, B = 1 Tesla intra-grain (upper scale) grain boundary Redwing et al, APL 75, 3171 (1999). Hogg et al, APL 78, 1433 (2001). What s really going on here? First detectable Voltage = many, many vortices

12 Examples of Previous Single Vortex Depinning Force Measurements with Transport Current Finnemore and coworkers ongoing work (1988-present) Cabrera and coworkers several other groups

13 Examples of Previous Single Vortex Depinning Force Measurements with Transport Current Finnemore and coworkers ongoing work (1988-present) Cabrera and coworkers 1992 But we d like a more reliable way to know the force at the vortex location; and to detect vortex motion with finer spatial resolution on order ξ ~ nm + several other groups

14 Vortex Pinning Measurements: STM Imaging g reduce field from 3Teslato15Tesla 1.5 estimate pinning force from flux density gradient across twin boundary Maggio-Aprile et al, Nature 390, 487 (1997)

15 Vortex Pinning Measurements: STM Imaging g reduce field from 3Teslato15Tesla 1.5 estimate pinning force from flux density gradient across twin boundary Maggio-Aprile et al, Nature 390, 487 (1997) But we d like a more versatile way to directly measure pinning forces at arbitrary defects.

16 Magnetic Force Microscopy Pros and Cons of MFM Force between tip and sample: F = ( m B) Other signals Image cantilever resonant frequency Δff 0 ~ df z /dz better signal-to-noise Vertical force gradient imaging Horizontal force manipulation Tip Geometry Con: Imperfectly known Pro: Up to 20 nm spatial resolution Signal to Noise Con: Not as good as SQUIDs, Hall probes Pro: Good enough to see vortices Con: See atomic forces too Pro: Simultaneous topography Invasiveness Con: Tip exerts force on vortex Pro: Tip exerts force on vortex

17 Vortex Depinning in Nb T: Decreasing Pinning 5.2K 5.5K 6.0K 6.5K 7.0K 7.5K 4 μm Colormap adjusted separately for each image.

18 Vortex Pinning vs. Height at T = 5.5 K A z=576nm B z=518nm C z=461nm D z=403nm E z=346nm F z=288nm G z=230nm H z=173nm 2μ m Δ f (Hz) Δ f=0.63hz I x (μ m) x y Δ f=0.73hz J x (μ m) Δ f=0.85hz -0.2 K x (μ m) Δ f=0.97hz Δ f=1.22hz 0.4 L 1.0M x (μ m) x (μ m) Δ f=1.50hz N x (μ m) Δ f=2.02hz 30O 3.0O x (μ m) Δ f=2.79hz P 500nm vortex motion event Important parameters: k spring = 2.1±0.7 N/m f 0 = Hz λ Nb = 90 nm

19 Model: Monopole Tip Monopole Vortex +M d offset z λ B -M superconductor vortex model vortex as monopole distance λ beneath surface --J. Pearl, J. Appl. Phys. 37, 4139 (1966). df dz z = 2k spr df f = M zφ 2π 0 ( x x 0 ) 2 ( y ( x x ) + ( y y ) + ( z + λ + d ) 5/ offset ) y 0 ) 2 + 2( z + λ + d offset ) 2 )

20 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B G vs. z 4G vs. z z+λ+d (nm) min

21 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B G vs. z 4G vs. z 17G vs. z+λ+d λ min 4G vs. z+λ+d 10-5 min z+λ+d (nm) min df z /dz ~ (z+λ+d) -3

22 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B z (nm) G vs. z G vs. z G vs. z+λ+d λ min 20 4G vs. z+λ+d min z+λ+d (nm) min F z (pn) 10 4 Gauss 17 Gauss df z /dz ~ (z+λ+d) z+λ+d min (nm)

23 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B z (nm) G vs. z G vs. z G vs. z+λ+d λ min 20 4G vs. z+λ+d min z+λ+d (nm) min df z /dz ~ (z+λ+d) -4 F z (pn) Gauss 17 Gauss fit bound z+λ+d min (nm)

24 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B G vs. z 4G vs. z 17G vs. z+λ+d λ min 4G vs. z+λ+d 10-5 min z+λ+d (nm) min df z /dz ~ (z+λ+d) -4 F z (pn) z (nm) Gauss 17 Gauss fit bound 5 k spring bound z+λ+d min (nm)

25 Depinning Forces in Two Datasets at 5.5 K z=576nm z=518nm z=461nm z=403nm z=346nm z=288nm z=230nm z=173nm A B C D E F G H 2μ m Δ f=0.63hz Δ f=0.73hz Δ f=0.85hz Δ f=0.97hz Δ f=1.22hz Δ f=1.50hz Δ f=2.02hz Δ f=2.79hz # vortices # vort tices 8 17 Gauss 6 4 Gauss F z (pn) F lateral,max = 0.38*F z,max F depin ranges from 4 to 12 pn at 5.5 K

26 Nb Depinning Forces: Quantitative Comparison f p (pn/μ μm) Breitwisch (PRB 2000): T = 8.55 K; t = 400 nm c Park (PRL 1992): T c = 7.35 K; t = 20 nm Breitwisch Allen (PRB (PRB 1989): 2000): T c = 8.55 T K; t = 400 nm Park (PRL 1992): T c = 7.35 c = 8.91 K; t = 20 nm K; t = 20 nm Allen (PRB 1989): T Allen (PRB 1989): T c = 8.91 c = 5.86 K; t = 50 nm K; t = 20 nm Stoddart (SST 1995): T c = 9.20 K; t = 700 nm Allen (PRB 1989): T c = 5.86 K; t = 50 nm Stoddart (SST 1995): T c = 9.20 K; t = 700 nm T/T c F depin ranges from 15 pn/μm to 40 pn/μm # vort rtices Limits on motion detection from bootstrapping vortex fits: limited by S/N, can be improved r(95%) 60 (nm) z (nm) 8 17 Gauss 6 4 Gauss F z (pn) z (pn)

27 Part II: controlled single-vortex manipulation

28 Motivation: soft condensed matter physics Do vortices split or tilt and do vortices entangle? surface pancake vortex vortex core interlayer Josephson vortex Clem, PRB 43, 7837 (1991) Reichhardt & Hastings, PRL 92, (2004)

Motivation: Luttinger liquid physics STM: twin boundary

29 Motivation: Luttinger liquid physics STM: twin boundary in CuO chain plane of YBa 2 Cu 3 O 7-x y pin vortices in twin boundary plane x 0.21nm 100 Å Eric Hudson, et al Vortices are like 1D bosons in Luttinger liquid!! L τ nm z x L x Polkovnikov, PRB 71, (2005) vortex wandering in z-direction 1D particles moving in time y x

30 Motivation: vortex ratchet computing Fabricated defects in a superconductor, used to pin vortices Real material parameters for MgB 2 : Maximum speed: simulations show 315 MHz, pair-breaking is in the THz range. Minimum size: λ ~ 100nm Power dissipation: Joules / single cell flip NAND gate: Hastings, Reichhardt, Reichhardt, PRL 90, (2003)

31 Our Procedure for Single Vortex Manipulation using Magnetic Force Microscopy surveillance height manipulation height

32 Vortex Manipulation Results A B C D E Δ f=79mhz Δ f=87mhz Δ f=96mhz Δ f=74mhz Δ f=70mhz 2μ m T = K h = 288 nm 1μm T = 5.53 K h = 86.4 nm Δf=3.21Hz Δf = Hz

33 Goals Part I: eliminate i uncontrolled vortex motion bigger magnets efficient power lines quieter sensors & circuits Part II: controlled single-vortex manipulation model for soft condensed matter vortex entanglement t vortex ratchet automaton Luttinger liquid FermiLab

Vortex studies in YBCO Future directions Better

topography 100 nm Hawley, Science, 1991 STM

34 Vortex studies in YBCO Future directions Better MFM tips: - model as monopole 20μm 200nm Deng, APL (2004) nanotube on cantilever tip - better AFM spatial resolution, correlate with topography 100 nm Hawley, Science, 1991 STM studies: image with ξ ~ 15 Å resolution, 100 better than λ ~ 150 nm

35 Spatial Resolution 8μm SQUID 0.5μm Hall Probe MFM STM 0.5 Gauss 1.1 Gauss 100 Gauss 5 Tesla 10μm 550Å

36 Future: How to Pin Vortices in YBCO? (1) Screw dislocations (2) Chemical inclusions (3) Oxygen dopants (4) Twin boundaries STM: spiral growth patterns 100 nm Hawley, Science, 1991 STM: impurities in Bi 2 Sr 2 CaCu 2 O 8+x Ni 10Å Zn Vacancy(?) Hudson et al, Nature 411, 920 (2001). Pan et al, Nature 403, 746 (2000). Hudson et al, Physica B 329, 1365 (2003). STM: superconducting gap STM: twin boundary in CuO inhomogeneity in Bi 2 Sr 2 CaCu 2 O 8+x chain plane of YBa 2 Cu 3 O 7-x Vortex imaging in Bi 2 Sr 2 CaCu 2 O 8+x 0.21nm 100 Å 20 Δ (mev) Lang et al, Nature 415, 412 (2002) Å Eric Hudson, unpublished. 0.00nm 100Å Hoffman, Science (2002).

higher fields (Hoffman) 12 10 500nm 8 17

37 ummary Manipulate single vortices with nanoscale control Measured directly the depinning i forces in Nb 1μm already applying same technique to YBCO P Δf=3.21Hz Δf = Hz Eric Straver Nick Koshnick Ophir Ausleander # vort tices Next: correlate depinning forces with topography (Moler) STM studies to explore higher fields (Hoffman) nm 8 17 Gauss 6 4 Gauss 4 2 vortex motion event F z (pn)

Introduction to Superconductivity. Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance

Introduction to Superconductivity Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance Meissner Effect Magnetic field expelled. Superconducting surface current ensures