Anomalous Metals and Failed Superconductors. With B. Spivak and A. Kapitulnik (also P. Oreto)

Transcription

1 Anomalous Metals and Failed Superconductors With B. Spivak and A. Kapitulnik (also P. Oreto) Tallahassee 2018

2 Pillars the Theory of Quantum Mater From B Spivak Α proof of the Fermi liquid theory is based on perturbative calculations of Feynman s diagrams. (349 pages). It is valid in the weakly interacting case where rs<<1. Most of experiments supporting the Fermi liquid theory are done at rs>1!

3 Pillars the Theory of Quantum Mater Weak localization implies no metals in 2D Small Ginzburg parameter implies there are no important superconducting fluctuations in conventional superconductors Both are seemingly wrong.

4 Anderson localization implies no metals in 2D?? Apparent Metal Insulator Transition in Clean 2DEGs with large r s

5 Anderson localization implies no metals in 2D?? Apparent Metal Insulator Transition in Clean 2DEGs with large r s Quantum Hall Metal in 2DEG in large H Quantum Superconductor to Insulator transitions in 2D

6 Anderson localization implies no metals in 2D?? Apparent Metal Insulator Transition in Clean 2DEGs with large r s Quantum Hall Metal in 2DEG in large H Quantum Superconductor to Insulator transitions in 2D Quantum Superconductor to Metal transitions in 2D (This is not in conflict with the observation that sometimes there is an apparent direct SIT.)

7 Small Ginzburg parameter implies there are no important superconducting fluctuations in conventional superconductors N = (E F )( 0 ) d 0 G =1/N

8 Small Ginzburg parameter implies there are no important superconducting fluctuations in conventional superconductors N = (E F )( 0 ) d 0 G =1/N Fluctuation Superconductivity of Aslamazov-Larkin and Maki-Thomson are small (Gaussian) corrections to mean-field theory except in parametrically narrow region around T c.

9 Small Ginzburg parameter implies there are no important superconducting fluctuations in conventional superconductors The case of the quantum transition is even worse: 0! 0 exp[ 1/ eff (x)] eff > 0 for x<x c eff < 0 and 0 = 0 for x<x c eff = 0 for x = x c Interactions in other channels are irrelevant. There are no quantum critical fluctuations at all!

10 Small Ginzburg parameter implies there are no important superconducting fluctuations in conventional superconductors The case of the quantum transition is even worse: 0! 0 exp[ 1/ eff (x)] eff > 0 for x<x c eff < 0 and 0 = 0 for x<x c eff = 0 for x = x c Because 0 p ~D/ 0 exp[ 1/2 (x)] as x! x c e ects of finite length scale inhomogeneities averaged over

11 Quantum phase transitions from SC state to non-superconducting state Varying gate voltage, magnetic field, film thickness As T tend to zero, Superconducting for x < x c Non superconducting for x > x c Normal state characterized by Drude conductivity: = h/e 2 (k F `) 1 h/e 2 25k

12 T The field driven transition Drude Metal Superconductor QSMT Anomalous Metal H

13 Magnetic Field Driven QSMT in amoge films h/e 2 25k Ephron et al, PRL (1996)

14 Magnetic Field Driven QSMT a-tan x and a-ino x films e 2 /h 25k Breznay and Kapitulnik, Science Advances (2017)

15 Magnetic Field Driven QSMT in crystalline films of NbSe 2 Figure 3. Magnetic field tuned phase transitions in 2D NbSe. a) 2D color plot of sheet resistance vs. h/e 2 25k Tsen et al, Nature Physics (2016)

16 Magnetic Field Driven QSMT in a highly crystalline ZrNCl electric double layer transistor (Ion gated) h/e 2 25k Saito et al, Science (2015)

17 T The field driven transition Drude Metal Failed Superconductor Superconductor QSMT Anomalous Metal H

18 T Without a magnetic field Drude Metal Superconductor Anomalous Metal QSMT x

19 Gate voltage driven QSMT in a WTe 2 flake h/e 2 25k Sajidi et al (D. Cobden group from U. Washington) unpublished

20 Gate voltage Driven QSMT in a SrTiO 3 -SrAlO 3 heterostructure Chen et al (H. Hwang s group at Stanford) submitted for publication) h/e 2 25k

21 Gate voltage Driven QSMT in a gated twodimensional semiconductorsuperconductor array (Al islands on InAs quantum well) Bottcher et al (C. Marcus s group at Niels Bohr Institute, submitted for publication arxiv: ) h/e 2 25k

22 Gate voltage Driven QSMT in an array of Sn discs on a graphene substrate Han, Z., A. Allain, H. Arjmandi-Tash, K. Tikhonov, M. FeigelMan, B. Sacepe, and V. Bouchiat, Nature Physics 10, 380 (2014). h/e 2 25k

23 FIG. 4. Normalized resistance as a function of temperature for SNS arrays of widely spaced islands. For spacings exceeding 700 nm, the BKT transition is interrupted by a low-temperature metallic state. The data for d 690 nm and for d 740 nm come from different substrates, having Nb island heights of 125 nm and 145 nm, respectively. Eley et al, arxiv But not in J. Phys.: Condens. Matter 25, (2013)

24 T Without a magnetic field Drude Metal Failed Superconductor Superconductor Anomalous Metal QSMT x

25 Other anomalous properties of the anomalous metal Anomalous Hall response Kapitulnik and Breznay Science Advances 3, e (2017). Anomalous optical response Y. Wang, I. Tamir, D. Shahar, N. P. Armitage arxiv:

26 Some aspects of the theory Since ρ D << h/e 2, and ρ << ρ D The question is why do these systems fail to become superconducting as T tends to 0? B. Spivak, P. Oreto, and S. A. Kivelson, Theory of quantum metal to superconductor transitions in highly conducting systems, Phys. Rev. B 77, (2008).

27 Some aspects of the theory Consider problem of superconducting grains embedded in good metal and tune QSMT as function of concentration j(t ) = SC susceptibility of grain j J ij (T ) = Josephson coupling between grain i and j Approximate estimate of T c X J ij (T c ) j (T c )=A c j B. Spivak, P. Oreto, and S. A. Kivelson, Theory of quantum metal to superconductor transitions in highly conducting systems, Phys. Rev. B 77, (2008).

28 j(t ) = SC susceptibility of grain j J ij (T ) = Josephson coupling between grain i and j Simple estimate of T c j(t ) < j (0) < 1 X J ij (T c ) j (T c )=A c j J ij (T ) ~ R ij d for ~ R ij <L T J ij (T ) exp[ ~ R ij /L T ] for ~ R ij >L T X J ij (T c ) j (T c ) log[l T ] j The ground state is always superconducting!

29 j(t ) = SC susceptibility of grain j J ij (T ) = Josephson coupling between grain i and j Simple estimate of T c j(t ) < j (0) < 1 X J ij (T c ) j (T c )=A c j J ij (T ) ~ R ij h d 1+µ log 2 R ~ i 1 ij for ~ R ij <L T X J ij (T ) j (T ) (T )J nn (T ) apple (0)J nn (0) j Presence of (weak) repulsive interactions in metals result in a failed superconductor and an anomalous metal near QSMT

30 This is a good theory in principle but it has problems with the broad stability of the experimentally observed anomalous metals

31 Simple estimate of T c j(t ) < j (0) < 1 J ij (T ) ~ R ij d h 1+µ log 2 ~ R ij i 1 X J ij (T c ) j (T c ) (T c )J nn (T c ) j for ~ R ij <L T Presence of (weak) repulsive interactions in metals result in a failed superconductor and an anomalous metal near QSMT Quantum critical regime : A c > (0)J nn (0) > small L T >R nn T<J nn (0) 1/ (0) (0) (E F )V exp[+ eff / q ] for large grain (0) (E F )V for small grain X J ij (T c ) j (T c )=A c j

32 For the most part, these are not strongly correlated materials What is needed is theory beyond ADG There are missing small effects which are larger than T* and larger than T c as T c tends to 0. Reference: Anomalous metals failed superconductors, A. Kapitulnik, S. A. Kivelson, and B. I. Spivak, ArXiv: Thank you.