A new descriptor for unconventional superconductivity: calibration and testing
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1 A new descriptor for unconventional superconductivity: calibration and testing João N. B. Rodrigues Department of Physics University of Illinois at Urbana-Champaign 24 th August 2018
2 A new descriptor for unconventional superconductivity: calibration and testing Supported by the US Department of Energy
3 1 Unconventional SC may be due to interactions between spin and orbital degrees of freedom 2 Charge-spin susceptibility: a way of estimating spin-orbital coupling from first principles 3 Testing if charge-spin susceptibility can distinguish usc from non-usc Test set Charge-spin susceptibility Classifiers for usc
4 1 Unconventional SC may be due to interactions between spin and orbital degrees of freedom 2 Charge-spin susceptibility: a way of estimating spin-orbital coupling from first principles 3 Testing if charge-spin susceptibility can distinguish usc from non-usc Test set Charge-spin susceptibility Classifiers for usc
5 Finding new unconventional superconductors Finding new unconventional (high-t c ) superconductors.
6 Finding new unconventional superconductors [Norman, RPP 79, (2016)] Heavy fermions, Organic, Cuprates, Iron-based.
7 Finding new unconventional superconductors [Norman, RPP 79, (2016)] Heavy fermions, Organic, Cuprates, Iron-based. }{{} Only two really high-t c
8 Finding new unconventional superconductors [Norman, RPP 79, (2016)] Heavy fermions, Organic, Cuprates, Iron-based. }{{} Only two really high-t c Data-poor situation! unlike conventional superconductivity
9 Finding new unconventional superconductors [Norman, RPP 79, (2016)] Heavy fermions, Organic, Cuprates, Iron-based. Not clear what to look for!
10 Finding new unconventional superconductors [Norman, RPP 79, (2016)] Heavy fermions, Organic, Cuprates, Iron-based. Not clear what to look for! Main issue we will discuss today.
![Finding new unconventional superconductors [Norman, RPP 79, 074502 (2016)] Heavy fermions, Organic, Cuprates,](/docs-images/95/125145887/images/11-0.jpg "Iron-based. Not clear what to look for! Up to now, many similarity-based searches.")
11 Finding new unconventional superconductors [Norman, RPP 79, (2016)] Heavy fermions, Organic, Cuprates, Iron-based. Not clear what to look for! Up to now, many similarity-based searches. But no prediction verified so far.
12 Finding new unconventional superconductors Commonalities between cuprates and iron-based superconductors: Layered materials with 2D arrays of transition metals. Partially filled d-levels stable local magnetic moments. Majority have long-range magnetic order when undoped. SC when long-range magn. order paramagnetic. Adapted from [Norman, RPP 79, (2016)]
13 Finding new unconventional superconductors Commonalities between cuprates and iron-based superconductors: Layered materials with 2D arrays of transition metals. Partially filled d-levels stable local magnetic moments. Majority have long-range magnetic order when undoped. SC when long-range magn. order paramagnetic. Crucial role of spin fluctuations in electron pairing. [Scalapino, RMP 84, 1383 (2012)]
14 Finding new unconventional superconductors Commonalities between cuprates and iron-based superconductors: Layered materials with 2D arrays of transition metals. Partially filled d-levels stable local magnetic moments. Majority have long-range magnetic order when undoped. SC when long-range magn. order paramagnetic. Crucial role of spin fluctuations in electron pairing. [Scalapino, RMP 84, 1383 (2012)] Conventional (BCS) Superconductivity Unconventional Superconductivity
15 1 Unconventional SC may be due to interactions between spin and orbital degrees of freedom 2 Charge-spin susceptibility: a way of estimating spin-orbital coupling from first principles 3 Testing if charge-spin susceptibility can distinguish usc from non-usc Test set Charge-spin susceptibility Classifiers for usc
16 "All happy families are alike; each unhappy family is unhappy in its own way." Leo Tolstoy in Anna Karenina.
17 "All happy families are alike; each unhappy family is unhappy in its own way." Leo Tolstoy in Anna Karenina. Hypothesis: Some ingredients need to be present for high-t c usc.
18 "All happy families are alike; each unhappy family is unhappy in its own way." Leo Tolstoy in Anna Karenina. Hypothesis: Some ingredients need to be present for high-t c usc. What should those ingredients be?
19 Parent compounds of cuprates and iron-based SCs: are layered with arrays of transition metals. have stable local magnetic moments.
20 Parent compounds of cuprates and iron-based SCs: are layered with arrays of transition metals. have stable local magnetic moments. Simplistic classifier: layered + magnetic Superconducting? no yes 10 Counts No Yes Local moments in ground state
21 Parent compounds of cuprates and iron-based SCs: are layered with arrays of transition metals. have stable local magnetic moments. Simplistic classifier: layered + magnetic Superconducting? no yes 10 Counts No Yes Local moments in ground state Bad at distinguishing usc from other materials.
22 Detecting spin-orbital coupling Parent compounds of cuprates and iron-based SCs: are layered with arrays of transition metals. have stable local magnetic moments. spin fluctuations crucial in pairing.
23 Detecting spin-orbital coupling Parent compounds of cuprates and iron-based SCs: are layered with arrays of transition metals. have stable local magnetic moments. spin fluctuations crucial in pairing. Spin-orbital coupling.
24 Detecting spin-orbital coupling Parent compounds of cuprates and iron-based SCs: are layered with arrays of transition metals. have stable local magnetic moments. spin fluctuations crucial in pairing. Spin-orbital coupling. For concreteness consider the model Hamiltonian H = H o + H S + λh os with λ coupling orbital and deep spin levels.
25 Detecting spin-orbital coupling Parent compounds of cuprates and iron-based SCs: are layered with arrays of transition metals. have stable local magnetic moments. spin fluctuations crucial in pairing. Spin-orbital coupling. For concreteness consider the model Hamiltonian H = H o + H S + λh os with λ coupling orbital and deep spin levels. Hole-doped cuprates: conduction holes mostly oxygen-p; half-filled Cu-d as local magn. moments; Iron-pnictides: minority spin levels as conduction electrons; majority spin levels as local magn. moments;
26 Detecting spin-orbital coupling Parent compounds of cuprates and iron-based SCs: are layered with arrays of transition metals. have stable local magnetic moments. spin fluctuations crucial in pairing. Spin-orbital coupling. For concreteness consider the model Hamiltonian H = H o + H S + λh os with λ coupling orbital and deep spin levels. One can show that ρ i (r) = λ w X i s i (r)
27 Detecting spin-orbital coupling Parent compounds of cuprates and iron-based SCs: are layered with arrays of transition metals. have stable local magnetic moments. spin fluctuations crucial in pairing. Spin-orbital coupling. For concreteness consider the model Hamiltonian H = H o + H S + λh os with λ coupling orbital and deep spin levels. One can show that ρ i (r) = λ w X i s i (r) Can spin-orbital coupling separate cuprates and iron-based SCs from other materials?
28 Detecting spin-orbital coupling Approximate spin-orbital coupling λ w by charge-spin susceptibility χ cs χ cs 1 N χ i = 1 N ρ i N N s i i=1 N is the number of different magnetic textures considered, ρ i ( s i ) is stands for the spatial fluctuations in charge (spin) density relative to that of lowest-energy magnetic order.the former are given by ρ i = dr ρi (r) ρ 0 (r) s i = dr s i (r) s 0 (r) where ρ 0 (r) and s 0 (r) are the charge and spin distributions of the lowest-energy state. i=1
29 Detecting spin-orbital coupling Approximate spin-orbital coupling λ w by charge-spin susceptibility χ cs χ cs 1 N χ i = 1 N ρ i N N s i i=1 i=1 E Emin (ev/f.u.) BaMn2As2 Ca2CuCl2O2 (x=0.0) BaCr2As2 FeSe FeTe BaFe2As2 Ca2CuCl2O2 (x=0.125) BaCo2As2 BaNi2As2 Ca2CuCl2O2 (x=0.25) Magnetic order checkerboard flip collinear bicollinear tetris fm block Average charge-spin susceptibility χ (e/µb) [Narayan et al., arxiv: ]
30 1 Unconventional SC may be due to interactions between spin and orbital degrees of freedom 2 Charge-spin susceptibility: a way of estimating spin-orbital coupling from first principles 3 Testing if charge-spin susceptibility can distinguish usc from non-usc Test set Charge-spin susceptibility Classifiers for usc
31 Results Calculating descriptors How are we going to calculate these properties? (Local magnetic moments and charge-spin susceptibility)
32 Results Calculating descriptors How are we going to calculate these properties? (Local magnetic moments and charge-spin susceptibility) Accurate method (like QMC) is expensive. If large-scale search = have to use DFT. (at least as a first filter)
33 Results Calculating descriptors How are we going to calculate these properties? (Local magnetic moments and charge-spin susceptibility) Accurate method (like QMC) is expensive. If large-scale search = have to use DFT. (at least as a first filter) Multiple-DFT calculations to control errors.
34 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Example: Find if there are stable local magnetic moments with multiple DFT+U. [Cococcioni and Gironcoli PRB 71, (2005)] Lowest-energy state: is non-magnetic stable magnetic moments absent. is magnetic stable magnetic moments exist. (a) U=0 (b) U=5 (c) U=10 (d) Multiple DFT+U Experiment No Material BaCu2As2 No Calculation No Calculation No Calculation No Uncertain Calculation
35 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Example: Find if there are stable local magnetic moments with multiple DFT+U. [Cococcioni and Gironcoli PRB 71, (2005)] Lowest-energy state: is non-magnetic stable magnetic moments absent. is magnetic stable magnetic moments exist. (a) U=0 (b) U=5 (c) U=10 (d) Multiple DFT+U Experiment No Material BaCu2As2 La2NiO4 No Calculation No Calculation No Calculation No Uncertain Calculation
36 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Example: Find if there are stable local magnetic moments with multiple DFT+U. [Cococcioni and Gironcoli PRB 71, (2005)] Lowest-energy state: is non-magnetic stable magnetic moments absent. is magnetic stable magnetic moments exist. (a) U=0 (b) U=5 (c) U=10 (d) Multiple DFT+U Experiment No Material BaCu2As2 La2NiO4 SrCuO2 No Calculation No Calculation No Calculation No Uncertain Calculation
37 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Example: Find if there are stable local magnetic moments with multiple DFT+U. [Cococcioni and Gironcoli PRB 71, (2005)] Lowest-energy state: is non-magnetic stable magnetic moments absent. is magnetic stable magnetic moments exist. (a) U=0 (b) U=5 (c) U=10 (d) Multiple DFT+U Experiment No Material BaCu2As2 La2NiO4 SrCuO2 NbSe2 No Calculation No Calculation No Calculation No Uncertain Calculation
38 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Example: Find if there are stable local magnetic moments with multiple DFT+U. [Cococcioni and Gironcoli PRB 71, (2005)] Lowest-energy state: is non-magnetic stable magnetic moments absent. is magnetic stable magnetic moments exist. (a) U=0 (b) U=5 (c) U=10 (d) Multiple DFT+U Experiment No Material BaCu2As2 La2NiO4 SrCuO2 NbSe2 TiSe2 No Calculation No Calculation No Calculation No Uncertain Calculation
39 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Example: Find if there are stable local magnetic moments with multiple DFT+U. [Cococcioni and Gironcoli PRB 71, (2005)] Lowest-energy state: is non-magnetic stable magnetic moments absent. is magnetic stable magnetic moments exist. (a) U=0 (b) U=5 (c) U=10 (d) Multiple DFT+U Experiment No Material BaCu2As2 La2NiO4 SrCuO2 NbSe2 TiSe2 No Calculation No Calculation No Calculation No Uncertain Calculation Lower rate of false positives and false negatives.
40 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Example: Find if there are stable local magnetic moments with multiple DFT+U. [Cococcioni and Gironcoli PRB 71, (2005)] Lowest-energy state: is non-magnetic stable magnetic moments absent. is magnetic stable magnetic moments exist. (a) U=0 (b) U=5 (c) U=10 (d) Multiple DFT+U Experiment No Material BaCu2As2 La2NiO4 SrCuO2 NbSe2 TiSe2 No Calculation No Calculation No Calculation No Uncertain Calculation Lower rate of false positives and false negatives. But large rate of uncertain.
41 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Improved estimator for existence of magnetic moments (multi DFT+U):
42 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Improved estimator for existence of magnetic moments (multi DFT+U): P(M NNN NNY ) 0.0, P(M NYY ) 0.6, P(M YYY ) 1.0.
43 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Improved estimator for existence of magnetic moments (multi DFT+U): This is our biggest source of error.
44 Results Example: Controlling inaccuracies in magnetic moments prediction with multiple-dft Improved estimator for existence of magnetic moments (multi DFT+U): This is our biggest source of error. Can use QMC in those with most uncertainty. [Narayan et al., arxiv: ]
45 1 Unconventional SC may be due to interactions between spin and orbital degrees of freedom 2 Charge-spin susceptibility: a way of estimating spin-orbital coupling from first principles 3 Testing if charge-spin susceptibility can distinguish usc from non-usc Test set Charge-spin susceptibility Classifiers for usc
46 Test set 35 pure materials (all layered, some magnetic, some usc): Cuprates: CaCuO 2, SrCuO 2, T-La 2 CuO 4, T -La 2 CuO 4.
47 Test set 35 pure materials (all layered, some magnetic, some usc): Cuprates: CaCuO 2, SrCuO 2, T-La 2 CuO 4, T -La 2 CuO 4. All are antiferromagnetic (AFM) insulators. All turn superconductor upon doping.
48 Test set 35 pure materials (all layered, some magnetic, some usc): Cuprates: CaCuO 2, SrCuO 2, T-La 2 CuO 4, T -La 2 CuO 4. Ba-122s: BaM 2 As 2 (M=Cr,Mn,Fe,Co,Ni,Cu). Typically AFM or paramagnetic metals. BaFe 2 As 2 turns superconductor under pressure or doping.
49 Test set 35 pure materials (all layered, some magnetic, some usc): Cuprates: CaCuO 2, SrCuO 2, T-La 2 CuO 4, T -La 2 CuO 4. Ba-122s: BaM 2 As 2 (M=Cr,Mn,Fe,Co,Ni,Cu). FeX: FeSe, FeTe, FeS. All magnetic metals. Turn superconductor upon charge doping. FeSe turns SC in pure form.
50 Test set 35 pure materials (all layered, some magnetic, some usc): Cuprates: CaCuO 2, SrCuO 2, T-La 2 CuO 4, T -La 2 CuO 4. Ba-122s: BaM 2 As 2 (M=Cr,Mn,Fe,Co,Ni,Cu). FeX: FeSe, FeTe, FeS. 214s: La 2 MO 4 (M=Co,Ni), Sr 2 MO 4 (M=V,Cr,Mn,Fe,Co) and K 2 MF 4 (M=Co,Ni,Cu). All are AFM insulators. Were never made superconducting.
51 Test set 35 pure materials (all layered, some magnetic, some usc): Cuprates: CaCuO 2, SrCuO 2, T-La 2 CuO 4, T -La 2 CuO 4. Ba-122s: BaM 2 As 2 (M=Cr,Mn,Fe,Co,Ni,Cu). FeX: FeSe, FeTe, FeS. 214s: La 2 MO 4 (M=Co,Ni), Sr 2 MO 4 (M=V,Cr,Mn,Fe,Co) and K 2 MF 4 (M=Co,Ni,Cu). TMDCs: MSe 2 (M=Ti,Nb,Ta,W) and MS 2 (M=Mo,Ta). Nonmagnetic metals and insulators. Conventional superconductor under charge doping or pressure.
52 Test set 35 pure materials (all layered, some magnetic, some usc): Cuprates: CaCuO 2, SrCuO 2, T-La 2 CuO 4, T -La 2 CuO 4. Ba-122s: BaM 2 As 2 (M=Cr,Mn,Fe,Co,Ni,Cu). FeX: FeSe, FeTe, FeS. 214s: La 2 MO 4 (M=Co,Ni), Sr 2 MO 4 (M=V,Cr,Mn,Fe,Co) and K 2 MF 4 (M=Co,Ni,Cu). TMDCs: MSe 2 (M=Ti,Nb,Ta,W) and MS 2 (M=Mo,Ta). MPX 3 : VPS 3, NiPSe 3, CdPSe 3, CrGeTe 3. Magnetic and non-magnetic insulators. Superconductivity unknown. We suspect they cannot be made usc.
53 1 Unconventional SC may be due to interactions between spin and orbital degrees of freedom 2 Charge-spin susceptibility: a way of estimating spin-orbital coupling from first principles 3 Testing if charge-spin susceptibility can distinguish usc from non-usc Test set Charge-spin susceptibility Classifiers for usc
54 Charge-spin susceptibility Charge-spin susceptibility: χ cs 1 N N i=1 χ i = 1 N N i=1 ρ i s i. Count U=0 Count U=5 Superconducting no yes 0 Count 4 2 U= Charge spin susceptibility, cs (e/ B )
55 Charge-spin susceptibility Charge-spin susceptibility: χ cs 1 N N i=1 χ i = 1 N N i=1 ρ i s i. Count U=0 Count U=5 Superconducting no yes 0 Count 4 2 U= Charge spin susceptibility, cs (e/ B) χ cs distinguishes cuprates and iron-based SCs from other materials! usc seems to require intermediate spin-orbital coupling. (similar to e-ph coupling conventional SCs. [Esterlis et al., arxiv: ])
56 1 Unconventional SC may be due to interactions between spin and orbital degrees of freedom 2 Charge-spin susceptibility: a way of estimating spin-orbital coupling from first principles 3 Testing if charge-spin susceptibility can distinguish usc from non-usc Test set Charge-spin susceptibility Classifiers for usc
57 Classifiers for unconventional superconductivity Classifiers for usc based on three ingredients: layered structure (with TMs); stable local magnetic moments; charge-spin susceptibility; Quantified as: P(SC χ U cs, M, 2D) P(SC χ U cs) P(M).
58 Classifiers for unconventional superconductivity Classifiers for usc based on three ingredients: layered structure (with TMs); stable local magnetic moments; charge-spin susceptibility; Quantified as: P(SC χ U cs, M, 2D) P(SC χ U cs) P(M). P(SC χ cs ) from charge-spin susceptibility: P(SC χ U cs) = ρ U sc ρ U sc + ρ U sc
59 Classifiers for unconventional superconductivity Classifiers for usc based on three ingredients: layered structure (with TMs); stable local magnetic moments; charge-spin susceptibility; Quantified as: P(SC χ U cs, M, 2D) P(SC χ U cs) P(M). P(SC χ cs ) from charge-spin susceptibility: P(SC χ U cs) = Probability local moments exist P(M): From experiment ρ U sc ρ U sc + ρ U sc From DFT+U P(M exp ) = 1 or 0 P(M calc ) { P(M NNN NNY ) 0.0 P(M NYY ) 0.6 P(M YYY ) 1.0
60 Classifiers for unconventional superconductivity Assessing quality of different classifiers: F1 = 2TP 2TP+FP+FN Exp,U=5 Exp,U=10 F1 score Calc,U=0 Calc,U=5 Calc,U=10 naive 0.2 Exp,U= Best classifier is P(SC χ U=5 cs ) P(M exp ).
61 Classifiers for unconventional superconductivity Assessing quality of different classifiers: F1 = 2TP 2TP+FP+FN Exp,U=5 Exp,U=10 F1 score Calc,U=0 Calc,U=5 Calc,U=10 naive 0.2 Exp,U= Best classifier is P(SC χ U=5 cs ) P(M exp ). P(M calc ) with DFT+U is inaccurate. QMC can help.
62 Ranking test set materials Ranking test set according to best classifier: P(SC χ U=5 cs ) P(M exp ). P(SC, Mexp) Superconducting? no yes 0.0 TaSe2 TiSe2 BaNi2As2 CdPSe3 VPS3 BaCu2As2 NbSe2 WSe2 MoS2 CrGeTe3 K2CuF4 K2NiF4 Sr2MnO4 La2CoO4 NiPSe3 BaMn2As2 La2NiO4 BaCr2As2 Sr2CrO4 TaS2 K2CoF4 T La2CuO4 SrCuO2 BaCo2As2 CaCuO2 Sr2VO4 BaFe2As2 T La2CuO4 Sr2FeO4 o FeSe FeTe Sr2CoO4 FeS t FeSe Material Clearly distinguishes known uscs from other materials!
63 Ranking test set materials P(SC, Mexp) Superconducting? no yes 0.0 TaSe2 TiSe2 BaNi2As2 CdPSe3 VPS3 BaCu2As2 NbSe2 WSe2 MoS2 CrGeTe3 K2CuF4 K2NiF4 Sr2MnO4 La2CoO4 NiPSe3 BaMn2As2 La2NiO4 BaCr2As2 Sr2CrO4 TaS2 Material K2CoF4 T La2CuO4 SrCuO2 BaCo2As2 CaCuO2 Sr2VO4 BaFe2As2 T La2CuO4 Sr2FeO4 o FeSe FeTe Sr2CoO4 FeS t FeSe A few comments on highly ranked non-uscs: DFT+U too inaccurate false prediction. Clarifiable with QMC.
64 Ranking test set materials P(SC, Mexp) Superconducting? no yes 0.0 TaSe2 TiSe2 BaNi2As2 CdPSe3 VPS3 BaCu2As2 NbSe2 WSe2 MoS2 CrGeTe3 K2CuF4 K2NiF4 Sr2MnO4 La2CoO4 NiPSe3 BaMn2As2 La2NiO4 BaCr2As2 Sr2CrO4 TaS2 Material K2CoF4 T La2CuO4 SrCuO2 BaCo2As2 CaCuO2 Sr2VO4 BaFe2As2 T La2CuO4 Sr2FeO4 o FeSe FeTe Sr2CoO4 FeS t FeSe A few comments on highly ranked non-uscs: DFT+U too inaccurate false prediction. Clarifiable with QMC. necessary ingredient (that we didn t consider) and material lacks.
65 Ranking test set materials P(SC, Mexp) Superconducting? no yes 0.0 TaSe2 TiSe2 BaNi2As2 CdPSe3 VPS3 BaCu2As2 NbSe2 WSe2 MoS2 CrGeTe3 K2CuF4 K2NiF4 Sr2MnO4 La2CoO4 NiPSe3 BaMn2As2 La2NiO4 BaCr2As2 Sr2CrO4 TaS2 Material K2CoF4 T La2CuO4 SrCuO2 BaCo2As2 CaCuO2 Sr2VO4 BaFe2As2 T La2CuO4 Sr2FeO4 o FeSe FeTe Sr2CoO4 FeS t FeSe A few comments on highly ranked non-uscs: DFT+U too inaccurate false prediction. Clarifiable with QMC. necessary ingredient (that we didn t consider) and material lacks. Good spin-orbital coupling but other instability dominates over SC.
66 Ranking test set materials P(SC, Mexp) Superconducting? no yes 0.0 TaSe2 TiSe2 BaNi2As2 CdPSe3 VPS3 BaCu2As2 NbSe2 WSe2 MoS2 CrGeTe3 K2CuF4 K2NiF4 Sr2MnO4 La2CoO4 NiPSe3 BaMn2As2 La2NiO4 BaCr2As2 Sr2CrO4 TaS2 Material K2CoF4 T La2CuO4 SrCuO2 BaCo2As2 CaCuO2 Sr2VO4 BaFe2As2 T La2CuO4 Sr2FeO4 o FeSe FeTe Sr2CoO4 FeS t FeSe A few comments on highly ranked non-uscs: DFT+U too inaccurate false prediction. Clarifiable with QMC. necessary ingredient (that we didn t consider) and material lacks. Good spin-orbital coupling but other instability dominates over SC. Charge doping issue: Charge doping degrades spin-orbital coupling. Material not amenable to doping for chemical reasons. Can be made usc (with correct doping) but never attempted.
67 Summary Classifier for usc with 3 ingredients: layered, LMs and spin-orbital. LMs prediction introduces most inaccuracies. QMC-improvable? Sufficiently specific to distinguish cuprates and iron-based SCs. Singles a few non-usc. Experimentalists should look at them.
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