Quantum theory of vortices in - Harvard...
Transcript of Quantum theory of vortices in - Harvard...
![Page 1: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/1.jpg)
Quantum theory of vortices in d-wave superconductors
Talk online at http://sachdev.physics.harvard.edu
Physical Review B 71, 144508 and 144509 (2005),Annals of Physics 321, 1528 (2006),
Physical Review B 73, 134511 (2006), cond-mat/0606001.
Leon Balents (UCSB) Lorenz Bartosch (Harvard) Anton Burkov (Harvard)
Predrag Nikolic (Harvard) Subir Sachdev (Harvard)
Krishnendu Sengupta (HRI, India)
![Page 2: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/2.jpg)
BCS theory of vortices in d-wave superconductors
+
periodic potential
+
strong Coulomb interactions
Vortices in BCS superconductors near a
superconductor-Mott insulator transition at finite doping
![Page 3: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/3.jpg)
The cuprate superconductor Ca2-xNaxCuO2Cl2
T. Hanaguri, C. Lupien, Y. Kohsaka, D.-H. Lee, M. Azuma, M. Takano, H. Takagi, and J. C. Davis, Nature 430, 1001 (2004). Closely related modulations in superconducting Bi2Sr2CaCu2O8+δ observed first by C. Howald, H. Eisaki, N. Kaneko, and A. Kapitulnik, cond-mat/0201546 and Physical Review B 67, 014533 (2003).
![Page 4: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/4.jpg)
The cuprate superconductor Ca2-xNaxCuO2Cl2
Evidence that holes can form an insulating state with period ≈ 4 modulation in the density
T. Hanaguri, C. Lupien, Y. Kohsaka, D.-H. Lee, M. Azuma, M. Takano, H. Takagi, and J. C. Davis, Nature 430, 1001 (2004). Closely related modulations in superconducting Bi2Sr2CaCu2O8+δ observed first by C. Howald, H. Eisaki, N. Kaneko, and A. Kapitulnik, cond-mat/0201546 and Physical Review B 67, 014533 (2003).
![Page 5: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/5.jpg)
STM around vortices induced by a magnetic field in the superconducting stateJ. E. Hoffman, E. W. Hudson, K. M. Lang, V. Madhavan, S. H. Pan,
H. Eisaki, S. Uchida, and J. C. Davis, Science 295, 466 (2002).
-120 -80 -40 0 40 80 1200.0
0.5
1.0
1.5
2.0
2.5
3.0
Regular QPSR Vortex
Diff
eren
tial C
ondu
ctan
ce (n
S)
Sample Bias (mV)
Local density of states (LDOS)
1Å spatial resolution image of integrated
LDOS of Bi2Sr2CaCu2O8+δ
( 1meV to 12 meV) at B=5 Tesla.
I. Maggio-Aprile et al. Phys. Rev. Lett. 75, 2754 (1995).S.H. Pan et al. Phys. Rev. Lett. 85, 1536 (2000).
![Page 6: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/6.jpg)
100Å
b7 pA
0 pA
Vortex-induced LDOS of Bi2Sr2CaCu2O8+δ integrated from 1meV to 12meV at 4K
J. Hoffman et al., Science 295, 466 (2002).G. Levy et al., Phys. Rev. Lett. 95, 257005 (2005).
Vortices have halos with LDOS modulations at a period ≈ 4 lattice spacings
Prediction of periodic LDOS modulations near vortices: K. Park and S. Sachdev, Phys. Rev. B 64, 184510 (2001).
![Page 7: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/7.jpg)
Questions on the cuprate superconductors
• What is the quantum theory of the ground state as it evolves from the superconductor to the modulated insulator ?
• What happens to the vortices near such a quantum transition ?
![Page 8: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/8.jpg)
OutlineOutline
• The superfluid-insulator transition of bosons
• The quantum mechanics of vortices near the superfluid-insulator transition
Dual theory of superfluid-insulator transition as the proliferation of vortex-anti-vortex pairs
• Influence of nodal quasiparticles on vortex dynamics in a d-wave superconductor
![Page 9: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/9.jpg)
I. The superfluid-insulator transition of bosons
![Page 10: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/10.jpg)
Bosons at filling fraction f = 1
M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
Weak interactions: superfluidity
Strong interactions: Mott insulator which preserves all lattice
symmetries
![Page 11: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/11.jpg)
Bosons at filling fraction f = 1
Weak interactions: superfluidity
0Ψ ≠
![Page 12: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/12.jpg)
Bosons at filling fraction f = 1
Weak interactions: superfluidity
0Ψ ≠
![Page 13: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/13.jpg)
Bosons at filling fraction f = 1
Weak interactions: superfluidity
0Ψ ≠
![Page 14: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/14.jpg)
Bosons at filling fraction f = 1
Weak interactions: superfluidity
0Ψ ≠
![Page 15: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/15.jpg)
Strong interactions: insulator
Bosons at filling fraction f = 1
0Ψ =
![Page 16: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/16.jpg)
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
Weak interactions: superfluidity
0Ψ ≠
![Page 17: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/17.jpg)
Weak interactions: superfluidity
0Ψ ≠
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 18: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/18.jpg)
Weak interactions: superfluidity
0Ψ ≠
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 19: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/19.jpg)
Weak interactions: superfluidity
0Ψ ≠
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 20: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/20.jpg)
Weak interactions: superfluidity
0Ψ ≠
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 21: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/21.jpg)
Strong interactions: insulator
0Ψ =
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 22: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/22.jpg)
Strong interactions: insulator
0Ψ =
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 23: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/23.jpg)
Strong interactions: insulator
0Ψ =
Insulator has “density wave” order
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 24: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/24.jpg)
Superfluid
Insulator
Interactions between bosons
?
Charge density Charge density wave (CDW) orderwave (CDW) order
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 25: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/25.jpg)
Superfluid
Insulator
Interactions between bosons
?
Charge density Charge density wave (CDW) orderwave (CDW) order
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 26: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/26.jpg)
Valence bond Valence bond solid (VBS) ordersolid (VBS) orderSuperfluid
Insulator
Interactions between bosons
?
12( + )=
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).
Bosons at filling fraction f = 1/2or S=1/2 XXZ model
![Page 27: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/27.jpg)
Valence bond Valence bond solid (VBS) ordersolid (VBS) orderSuperfluid
Insulator
Interactions between bosons
?
Bosons at filling fraction f = 1/2
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).
or S=1/2 XXZ model 12( + )=
![Page 28: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/28.jpg)
Valence bond Valence bond solid (VBS) ordersolid (VBS) orderSuperfluid
Insulator
Interactions between bosons
?
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).
Bosons at filling fraction f = 1/2or S=1/2 XXZ model 1
2( + )=
![Page 29: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/29.jpg)
Valence bond Valence bond solid (VBS) ordersolid (VBS) orderSuperfluid
Insulator
Interactions between bosons
?
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).
Bosons at filling fraction f = 1/2or S=1/2 XXZ model 1
2( + )=
![Page 30: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/30.jpg)
The superfluid-insulator quantum phase transition
Key difficulty: Multiple order parameters (Bose-Einstein condensate, charge density wave, valence-bond-solid order…) not related by symmetry, but clearly physically connected. Standard methods only predict strong first order transitions (for generic parameters).
![Page 31: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/31.jpg)
The superfluid-insulator quantum phase transition
Key difficulty: Multiple order parameters (Bose-Einstein condensate, charge density wave, valence-bond-solid order…) not related by symmetry, but clearly physically connected. Standard methods only predict strong first order transitions (for generic parameters).
Key theoretical tool: Quantum theory of vortices
![Page 32: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/32.jpg)
OutlineOutline
• The superfluid-insulator transition of bosons
• The quantum mechanics of vortices near the superfluid-insulator transition
Dual theory of superfluid-insulator transition as the proliferation of vortex-anti-vortex pairs
• Influence of nodal quasiparticles on vortex dynamics in a d-wave superconductor
![Page 33: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/33.jpg)
II. The quantum mechanics of vortices near a superfluid-insulator transition
Dual theory of the superfluid-insulator transition as the proliferation of vortex-anti-vortex-pairs
![Page 34: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/34.jpg)
Central question:In two dimensions, we can view the vortices as
point particle excitations of the superfluid. What is the quantum mechanics of these “particles” ?
Excitations of the superfluid: Vortices and anti-vortices
![Page 35: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/35.jpg)
In ordinary fluids, vortices experience the Magnus Force
FM
( ) ( ) ( )mass density of air velocity of ball circulationMF = i i
![Page 36: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/36.jpg)
![Page 37: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/37.jpg)
Dual picture:The vortex is a quantum particle with dual “electric”
charge n, moving in a dual “magnetic” field of strength = h×(number density of Bose particles)
C. Dasgupta and B.I. Halperin, Phys. Rev. Lett. 47, 1556 (1981); D.R. Nelson, Phys. Rev. Lett. 60, 1973 (1988); M.P.A. Fisher and D.-H. Lee, Phys. Rev. B 39, 2756 (1989)
![Page 38: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/38.jpg)
![Page 39: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/39.jpg)
![Page 40: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/40.jpg)
Bosons on the square lattice at filling fraction f=p/q
![Page 41: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/41.jpg)
Bosons on the square lattice at filling fraction f=p/q
![Page 42: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/42.jpg)
![Page 43: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/43.jpg)
![Page 44: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/44.jpg)
![Page 45: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/45.jpg)
![Page 46: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/46.jpg)
![Page 47: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/47.jpg)
![Page 48: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/48.jpg)
As a superfluid approaches an insulating state, the decrease in the strength of the condensate will lower the energy cost of creating vortex-anti-
vortex pairs.
Vortex theory of the superfluid-insulator transition
![Page 49: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/49.jpg)
Proliferation of vortex-anti-vortex pairs.
Vortex theory of the superfluid-insulator transition
![Page 50: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/50.jpg)
Vortex theory of the superfluid-insulator transition
Proliferation of vortex-anti-vortex pairs.
![Page 51: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/51.jpg)
Vortex theory of the superfluid-insulator transition
Proliferation of vortex-anti-vortex pairs.
![Page 52: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/52.jpg)
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).C. Lannert, M.P.A. Fisher, and T. Senthil, Phys. Rev. B 63, 134510 (2001)
S. Sachdev and K. Park, Annals of Physics, 298, 58 (2002)T. Senthil, A. Vishwanath, L. Balents, S. Sachdev and M.P.A. Fisher, Science 303, 1490 (2004).
![Page 53: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/53.jpg)
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).C. Lannert, M.P.A. Fisher, and T. Senthil, Phys. Rev. B 63, 134510 (2001)
S. Sachdev and K. Park, Annals of Physics, 298, 58 (2002)T. Senthil, A. Vishwanath, L. Balents, S. Sachdev and M.P.A. Fisher, Science 303, 1490 (2004).
![Page 54: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/54.jpg)
100Å
b7 pA
0 pA
Vortex-induced LDOS of Bi2Sr2CaCu2O8+δ integrated from 1meV to 12meV at 4K
Vortices have halos with LDOS modulations at a period ≈ 4 lattice spacings
Prediction of periodic LDOS modulations near vortices: K. Park and S. Sachdev, Phys. Rev. B 64, 184510 (2001).
J. Hoffman et al., Science 295, 466 (2002).G. Levy et al., Phys. Rev. Lett. 95, 257005 (2005).
![Page 55: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/55.jpg)
OutlineOutline
• The superfluid-insulator transition of bosons
• The quantum mechanics of vortices near the superfluid-insulator transition
Dual theory of superfluid-insulator transition as the proliferation of vortex-anti-vortex pairs
• Influence of nodal quasiparticles on vortex dynamics in a d-wave superconductor
![Page 56: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/56.jpg)
III. Influence of nodal quasiparticles on vortex dynamics in a d-wave
superconductor
P. Nikolic
![Page 57: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/57.jpg)
![Page 58: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/58.jpg)
![Page 59: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/59.jpg)
2
A effective mass
~
where ~ is a high energy cutoff
vF
finite
m vΛ
Λ Δ
![Page 60: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/60.jpg)
21
sub-Ohmic damping with
Universal function of FF
vC v v− Δ⎛ ⎞= ×⎜ ⎟
⎝ ⎠
![Page 61: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/61.jpg)
22
Bardeen-Stephen viscous drag with
Universal function of FF
vC v v− Δ⎛ ⎞= ×⎜ ⎟
⎝ ⎠
![Page 62: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/62.jpg)
22
Bardeen-Stephen viscous drag with
Universal function of FF
vC v v− Δ⎛ ⎞= ×⎜ ⎟
⎝ ⎠
Effect of nodal quasiparticles on vortex dynamics is relatively innocuous.
![Page 63: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/63.jpg)
![Page 64: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/64.jpg)
Influence of the quantum oscillating vortex on the LDOS
P. Nikolic, S. Sachdev, and L. Bartosch, cond-mat/0606001
Resonant feature near the vortex oscillation frequency
![Page 65: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/65.jpg)
Influence of the quantum oscillating vortex on the LDOS
Resonant feature near the vortex oscillation frequency
-120 -80 -40 0 40 80 1200.0
0.5
1.0
1.5
2.0
2.5
3.0
Regular QPSR Vortex
Diff
eren
tial C
ondu
ctan
ce (n
S)
Sample Bias (mV)
P. Nikolic, S. Sachdev, and L. Bartosch, cond-mat/0606001
I. Maggio-Aprile et al. Phys. Rev. Lett. 75, 2754 (1995)S.H. Pan et al. Phys. Rev. Lett. 85, 1536 (2000).
![Page 66: Quantum theory of vortices in - Harvard Universityqpt.physics.harvard.edu/talks/itzykson.pdfinsulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS](https://reader034.fdocuments.us/reader034/viewer/2022042105/5e831ea7b884ce6106762de2/html5/thumbnails/66.jpg)
Conclusions• Evidence that vortices in the cuprate superconductors carry a “flavor”
index which encodes the spatial modulations of a proximate insulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS modulations observed in STM experiments.
• Size of modulation halo allows estimate of the inertial mass of a vortex
• Direct detection of vortex zero-point motion may be possible in inelastic neutron or light-scattering experiments
• The quantum zero-point motion of the vortices influences the spectrum of the electronic quasiparticles, in a manner consistent with LDOS spectrum
• “Aharanov-Bohm” or “Berry” phases lead to surprising kinematicduality relations between seemingly distinct orders. These phasefactors allow for continuous quantum phase transitions in situations where such transitions are forbidden by Landau-Ginzburg-Wilson theory.
Conclusions• Evidence that vortices in the cuprate superconductors carry a “flavor”
index which encodes the spatial modulations of a proximate insulator. Quantum zero point motion of the vortex provides a natural explanation for LDOS modulations observed in STM experiments.
• Size of modulation halo allows estimate of the inertial mass of a vortex
• Direct detection of vortex zero-point motion may be possible in inelastic neutron or light-scattering experiments
• The quantum zero-point motion of the vortices influences the spectrum of the electronic quasiparticles, in a manner consistent with LDOS spectrum
• “Aharanov-Bohm” or “Berry” phases lead to surprising kinematicduality relations between seemingly distinct orders. These phasefactors allow for continuous quantum phase transitions in situations where such transitions are forbidden by Landau-Ginzburg-Wilson theory.