electrical transport near a pair-breaking superconductor-metal...
TRANSCRIPT
![Page 1: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/1.jpg)
Electrical transport near a pair-breaking superconductor-metal quantum phase transition
Emily Dunkel (Harvard)Joel Moore (Berkeley)
Daniel Podolsky (Berkeley)Subir Sachdev (Harvard)
Ashvin Vishwanath (Berkeley)Philipp Werner (ETH)Matthias Troyer (ETH)
Talk online at http://sachdev.physics.harvard.edu
Physical Review Letters 92, 237003 (2004)Physical Review B 73, 085116 (2006)
cond-mat/0510597.
See also talk by Daniel Podolsky, N38.00007, Wed 9:12 AM
![Page 2: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/2.jpg)
T
Superconductor
α
Tc
αc
Metal
![Page 3: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/3.jpg)
T
Superconductor
α
Tc
αc
Metal
![Page 4: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/4.jpg)
Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan, and H. Wang, Science 294, 2332 (2001).
![Page 5: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/5.jpg)
![Page 6: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/6.jpg)
I. Theory for the superconductor-metal quantum phase transition
![Page 7: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/7.jpg)
Computation of fluctuation conductivity in metal at low temperatures
T
Superconductor
α
Metal
Tc
αc
![Page 8: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/8.jpg)
Computation of fluctuation conductivity in metal at low temperatures
T
Superconductor
α
Metal
Tc
αc
![Page 9: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/9.jpg)
Computation of fluctuation conductivity in metal at low temperatures
T
Superconductor
α
Metal
Tc
αc
![Page 10: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/10.jpg)
Computation of fluctuation conductivity in metal at low temperatures
T
Superconductor
α
Metal
Tc
αc
![Page 11: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/11.jpg)
Theory for quantum-critical region, and beyond
T
Superconductor
α
Metal
Tc
αc
Quantum critical
![Page 12: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/12.jpg)
Theory for quantum-critical region, and beyond
T
Superconductor
α
Metal
Tc
αc
Quantum critical
In one dimension, theory reduces to the Langer-Ambegaokar-McCumber-Halperin theory (Model A dynamics), near mean-field Tc
![Page 13: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/13.jpg)
Role of charge conservation in quantum critical theory
Dynamics of quantum theory (and model A) does not conserve total charge.
2(related to the question of why dissipation is not )qω
Analogous the Fermi-liquid/spin-density-wave transition (Hertz theory), where dynamics of critical
theory does not conserve total spin.
![Page 14: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/14.jpg)
Role of charge conservation in quantum critical theory
Dynamics of quantum theory (and model A) does not conserve total charge.
2(related to the question of why dissipation is not )qω
Analogous the Fermi-liquid/spin-density-wave transition (Hertz theory), where dynamics of critical
theory does not conserve total spin.
Cooper pairs (SDW) fluctuations decay into fermionic excitations at a finite rate, before any appreciable phase precession due to changes in
chemical potential (magnetic field).
![Page 15: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/15.jpg)
II. Quantum criticality in d=1
![Page 16: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/16.jpg)
Theory for quantum-critical region, and beyond in d=1
T
Superconductor
α
Metal
Tc
αc
Quantum critical
![Page 17: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/17.jpg)
Theory for quantum-critical region, and beyond in d=1
T
Superconductor
α
Metal
Tc
αc
Quantum critical
![Page 18: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/18.jpg)
Superconductor
α
Metal
Tc
αc
Quantum critical
Theory for quantum-critical region, and beyond in d=1
T
![Page 19: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/19.jpg)
III. Nanowires near the superconductor-metal quantum critical point
![Page 20: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/20.jpg)
Nanowires near the quantum critical point in d=1
T
Superconductor
α
Metal
Tc
αc
Quantum critical
![Page 21: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/21.jpg)
Effect of the leads
![Page 22: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/22.jpg)
Large n computation of conductance
![Page 23: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/23.jpg)
Quantum Monte Carlo and large n computation of d.c. conductance
![Page 24: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/24.jpg)
IV. Quantum criticality in d=2
![Page 25: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/25.jpg)
Theory for quantum-critical region, and beyond in d=2
![Page 26: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/26.jpg)
Locus of points with U/R constant
![Page 27: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/27.jpg)
Locus of points with U/R constant
![Page 28: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/28.jpg)
Locus of points with U/R constant
![Page 29: Electrical transport near a pair-breaking superconductor-metal …qpt.physics.harvard.edu/talks/aps2006_1.pdf · Y. Liu, Yu. Zadorozhny, M. M. Rosario, B. Y. Rock, P. T. Carrigan,](https://reader036.vdocument.in/reader036/viewer/2022063015/5fd290afec2574380b61b1dd/html5/thumbnails/29.jpg)
Conclusions• Universal transport in wires near the superconductor-metal
transition
• Theory includes contributions from thermal and quantum phase slips ---- reduces to the classical LAMH theory at high temperatures
• Sensitivity to leads should be a generic feature of the ``coherent’’ transport regime of quantum critical points.
• Complete computation of electrical transport in d=2 to leading logarithmic accuracy.
Conclusions• Universal transport in wires near the superconductor-metal
transition
• Theory includes contributions from thermal and quantum phase slips ---- reduces to the classical LAMH theory at high temperatures
• Sensitivity to leads should be a generic feature of the ``coherent’’ transport regime of quantum critical points.
• Complete computation of electrical transport in d=2 to leading logarithmic accuracy.