Let There Be Topological Superconductors

Transcription

1 Let There Be Topological Superconductors K K d Γ ~q c µ arxiv: arxiv: Eun-Ah Kim (Cornell) Boulder

2 Q. Topological Superconductor material? Bulk 1D proximity 2D proximity?

3 Designing 2D topological SC's 2D topological SC - odd-parity SC of spinless fermions - Majorana bound state Strategies: 1) interaction, 2) spinlessness

4 Strategy I Manipulate the pairing interaction: target non-phononic mechanism

5

6 Topological Superconductivity in Metal/ Quantum-Spin-Ice Heterostructures Jian-Huang She, Choonghyun Kim, Craig Fennie, Michael Lawler, E-AK (arxiv: )

7 Wanted: non-phononic mechanism Dope a Quantum spin liquid P.W.Anderson RVB singlet Cooper pair single

8 Wanted: non-phononic mechanism Use Quantum spin liquid E F E F, J ex, J K Characteristic energy scales: J e x Perturbative limit: J K / E F <<1 Spin-fermion model

9 Spin-fermion model for J ex =0 FL PM& &&&&HFL& (=FL PM)& AFM& RKKY interaction Kondo-Singlet Doniach (1977)

10 Spin-fermion model for Jex+ Frustration For JRKKY~ JK2N(0) <Jex AFM order suppressed. FL PM% %%%%HFL% (=FL PM)% FL PM& &&&&HFL& (=FL PM)& 2 FL SL% SC SL% SC SL% &&&&HFL& (=FL PM)& AFM& (b) Superconduct or riding on FL PM& QSL (a) Kondo-Singlet + RVB singlet+cooper pair (1989) singletcoleman & Andrei FL PM& Senthil, Vojta, Sachdev (2003) FL

11 How to predictively materialize SC QSL? Simple isotropic metal 1. <S>=0 2. Dynamic spin fluctuation <S i S j > 3. Gapped spectrum 4. Well understood Quantum Spin Ice

12 Emergent Gauge Field in Spin Ice 2-in 2-out ice rule Kimura et al (2013) Gauge Field Propagator Spin-spin correlation

13 Elastic neutron: pinch points (spin-ice like) Inelastic neutron: over 90% weight

14 No order down to 20mK Gapped quantum paramagnet ωs=0.17mev Inelastic spectra peaked at Q=0

15 Effective Continuum Theory Integrate out spins >> Effective e-e interaction h i H int (t) = (JKv 2 cell/2}) X Z Z 2 dt 0 d 2 rd 2 r 0 s a (r,t)hs a (r, 0,t)S b (r 0, 0,t 0 )is b (r 0,t 0 ), ab P

16 Unusual Gauge-Matter Coupling Minimal Coupling Spin-ice/electron Repulsion against Cooper pairing Electrons are not magnetic monopoles Attractive equalspin interaction!

17 Selection Rule Dictated Odd-Parity Pair binding problem with dipole-dipole interactio Wigner-Eckart thm:

18 Dealing with interacting electrons? h H int (t) = i (J 2 Kv 2 cell/2}) X ab P Z dt 0 Z Separation of scale: ωs/ef <<1 Migdal theorem d 2 rd 2 r 0 s a (r,t)hs a (r, 0,t)S b (r 0, 0,t 0 )is b (r 0,t 0 ), Dimensionless ratio: N(0)V J 2 K N(0)/J ex < 1 Full problem solving the BCS mean-field theory T c! s e 1/

19 Leading channels

20 Can we persuade a material synthesis person?

21 Criteria for Metal Structural Lattice match A2B2O7 No orphan bonds Electronic Simple isotropic Fermi surface Wave function penetration Odd-# FS around high symmetry points

22 Non-magnetic s-electrons: large overlap, isotropic FS.

23 Band structure for the Proposal x=0.2 Isotropic single pocket centered at Γ- point

24 Wave function penetration

25 Topological Superconductivity in Metal/Quantum-Spin-Ice Heterostructures Topological superconductor riding on QSL Selection Rule Dictated Intrinsic Topo SC. Substantial phase space.

26 Acknowledgements Jian-huang SheChoonghyun KimCriag Fennie Michael Lawler Funding: DOE, CCMR (NSF)

27 Strategy II Manipulate the band structure

28 Topological superconductivity in group-vi TMDs Yi-Ting Hsu, Abolhassan Vaezi, E-AK (arxiv: )

29 Spin-degenerate Fermi surface Singlet superconductor Q. What if the band structure is spin-split?

30 Spinless fermion via real space splitting TI surface states Proximity induce topo SC Fu & Kane, PRL (2008) Experiments: Wang et al Science 336, 52 (2012) Xu et al, Nat.Phys 10, 943 (2014)

31 Spinless fermion via k-space splitting? k y K' Γ K k x

32 Monolayer group VI TMD's MoS 2, WS 2, MoSe 2, WSe 2 Non-centro symmetric Direct Gap ~2eV Dresselhaus spin-orbit

33 Band-selective spin-splitting Partially filled crystal-field-split d-bands - Conduction band : l z =0 - Valence band : l z = 1 Spin-orbit coupling 150~460meV

34 Confirmation of the band structure ` Iwasa group N. Nano (2014)

35 k-space spin-split FS? p-doped group VI- TMD!

36 Juice for superconductivity? d electrons => expect correlation effects n-doped J.T.Ye et al. (Science 2012)

37 p-doped TMD k-space spin-split Fermi surfaces + Moderate correlation (d-electron) Topological SC? Yi-Ting Hsu Mark Fischer Abolhassan Vaezi

38 Model Kinetic term Band-basis Spin-basis Repulsive interaction term

39 Superconductivity out of repulsive interaction? Kohn-Luttiger: singularity in scattering amplitude (~q) Non-s wave (Kohn &Luttinger 1965 Two-step RG formulation : Fe-based SC, doped graphene, SrRuO Chubukov & Nandkishore, Raghu & Kivelson ( )

40 Two-step RG on p-doped TMD

41 Step I: W -> Λ0 d c At scale W: Microscopic model At scale Λ0: Effective model

42 Step I: W -> Λ0 d c gintra,0 and ginter,0 at two-loop g (0) inter (~q, ~q0 )=U + U 3 f inter (~q, ~q 0 ) g (0) intra (~q, ~q0 )=U 3 f intra (~q, ~q 0 ) f s <0 -> g (0) s<0 in anisotropic channel

43 Step 2: Λ0 ->0 RG flow Divergence if λ (0) <0

44 Two possibilities Intra-pocket p+ip Inter-pocket p wave -T-breaking -Modulated - C=2 -C=\pm 1 per pocket

45 this additional phase below. below. Also Also note note that that the the phase phase has an overall gauge freedom freedom so so that that uniform uniform changes changes in in phase amount to a gauge gauge transformation. transformation. DMRG results U=-2 (a) (a) Pairing Pairing phase phase at at U=-2. U=-2. U=+4 (b) (b) Pairing Pairing phase phase at at U=+4. U=+4. FIG. 3. ) for the nearest-neighbor j depicted FIG. 3. Arg( Arg( i,i+ i,i+ jj ) for the nearest-neighbor j depicted above. Both repulsive and regimes Jordan Venderley, E-AK above. Both the the moderately moderately repulsive and attractive attractive regimes are translationally invariant, but clearly di er in phase.

46 Designing 2D topological SC's Control interaction k-space spin split TMD