Superlattice systems as a testbed of correlated topological - PowerPoint PPT Presentation

Superlattice systems as a testbed of correlated topological classification By Tsuneya Yoshida (Kyoto Univ.) Collaborators: A. Daido, I. Danshita, R. Peters, Y. Yanase, and N. Kawakami NQS2017 2017/11/06

Plan of this talk Main topic Experimental platform of reduction of topological classification Part 1 Part 2 Superlattice of CeCoIn 5 /YbCoIn 5 Ultracold dipolar fermions YbCoIn 5 TY-Danshita-Peters-Kawakami arXiv. 1711.xxxx TY-Daido-Yanase-Kawakami PRL 118, 147001 (2016)

Introduction Topological insulators Gapless edge states (robust against non-magnetic perturbations) Nontrivial band structure (Bulk) C. L. Kane et al. (2005) ～ Topological insulators in correlated systems ～ SmB 6 (Kondo insulator) LaPtBi etc. (Heusler compounds) La Pt Bi Dzero et al. (2010) S. Chadov et al. 2010

Topological phase in d,f electron systems Topological and strong correlation Coulomb interaction + Topology new phenomena ・ Fractional topological ins. ・ Topological Mott ins. ・ Reduction of topological classification e.g., 1D class BDI,

Classification of TIs/TSCs in free fermions Z 2 -insulator in 3D (Bi 2 Te 3 , Bi 2 Se 3 ) particle-hole time-reversal Energy Y. L. Chen et al. momentum (2009) A.P. Schyder et al. (‘08), A. Kitaev (‘09), S. Ryu et al. (‘10) Searching topological material nanowire Classifying TI/TSC : useful Reduction of topological classification ・ Correlation can reduce Z classification e.g., 1D class BDI, V. Mourik et al. (2012)

Fidkowski and Kitaev (2010) classification Z Kitaev chain (TRS, PHS) =[# of gapless edges] Majorana modes ・・・ × 8 ・・・ Time-reversal: ・・・ ・・・ Gap out edge modes Classification # of gapless edges result Z Free-fermions 1 ・・・ 8 9 2 10 ・・・ Z 8 correlated fermions 1 2 ・・・ 0 1 ・・・ 2 Kitaev chain × 8 : [no gapless edge]=[trivial phase] topologically trivial!

The reduction of topological classification is addressed by many groups. Y.-M Lu and A. V. Vishwanath (2012); C.-T. Hsieh, T. Morimoto, and S. Ryu (2014); M. Levin and A. Stern (2012); Y.-Z. You and C. Xu (2014); H. Yao and S. Ryu (2013); H. Isobe and L. Fu (2015); S. Ryu and S.-C. Zhang (2012); T. Y and A. Furusaki (2015); C. Wang, A. C. Potter, and T. Senthil (2014); T. Morimoto, A. Furusaki, and C. Mudry (2015) The periodic table in correlated systems is obtained in 1, 2, and 3D T. Morimoto, A. Furusaki, and C. Mudry (2015)

Motivation The reduction is a recent progress of the theoretical sides. But... No candidate materials for the reduction of the classification We propose The CeCoIn 5 /YbCoIn 5 superlattice as a candidate material

Experimental observations Correlated lectrons are confined in -layers reflection superconducting Y. Mizukami, et al., (2011) plane phase for T ~1K S.K. Goh et al., (2012) M. Shimozawa et al., (2014) We find that the superlattice: topological crystalline superconductor Correlation mean-field level # of # of CeCoIn 5 protection Majorana layers (4,0) yes 2 4 (1,0) 3 1 yes (8,0) 4 8 NO The superlattice: a candidate material for the reduction

Results ・ at a mean-field level Topological crystalline superconductor # of # of CeCoIn 5 protection Majorana layers (4,0) yes 2 4 (1,0) 3 1 yes (8,0) 4 8 NO

Non-interacting case: BdG-Hamiltonian with magnetic field BdG-Hamiltonian for CeCoIn 5 layers intra-layer: normal part Zeeman term magnetic field Rashba term Reflection plane intra-layer: pairing potential p-wave

Non-interacting case: symmetry of BdG-Hamiltonian Nambu operator reflection symmetry Symmetry class of and time-reversal × ✔ particle-hole Class D -classification …

Chern numbers in the superconducting phase PBC:Chern number ν ± Block-diagonalize with reflection is characterized by Chern# -classification OBC × 8 × 8 Topological crystalline superconductor [mirror Chern #] with and [total Chern #]

Results ・ At the mean-field level Topological crystalline superconductor Correlation mean-field level # of # of CeCoIn 5 protection Majorana layers (4,0) yes 2 4 (1,0) 3 1 yes (8,0) 4 8 NO

Gapping out respecting R- symmetry Two pairs of Majorana complex fermion Two helical Majorana modes E E Back scattering - + term breaks R-symmetry Symmetry protected gapless modes

# of helical Symmetry complex fermion protection Yes 1 Yes 2 3 Yes 4 NO 8 pairs of helical Majorana E(k) 1 E(k) + 1 ＋ - - 4 4 k k

Conclusion We propose the CeCoIn 5 /YbCoIn 5 superlattice system as a plat form of reduction of topological classification # of Protection # of CeCoIn 5 Majorana (correlated) layers (4,0) yes 2 4 (1,0) 3 1 yes (8,0) 4 8 NO This might be observed with systematic STM measurement for 2,3,4,5,6,…layers

Testbed of in cold atoms Part 2: TY-Danshita-Peters-Kawakami arXiv:1711.xxxx Motivation For more direct observation, it is better if the interaction can be tuned... difficult in real materials... Interactions can be tuned in cold atoms The testbed of can be build up by loading 161 Dy atoms to a one-dimensional lattice

Simple model of Toy model: 2-leg Su-Schrieffer-Heeger model with interactions Non-interacting part -t J U chain a ・・・ chain b ・・・ -V 1D class AIII: Z (for free fermions)

Simple model of Intuitive picture gapless modes (a ↑ ) (a ↓ ) U = J =0 (b ↑ ) (b ↓ ) (chain,spin) U >0 J =0 no gapless edge U >0 J >0

(1) How to prepare the above toy model or other similar? (2) How to observe the destruction of gapless edges?

(1) How to prepare the above toy model or other similar? (2) How to observe the destruction of gapless edges?

Similar model can be build up by loading 161 Dy : strong magnetic dipole-dipole interaction [optical pumping] + [Zeno effect] Effective two-leg ladder of spin-1/2 -t ・・・ -V ・・・ spin exchange interaction

Numerical results: bulk properties (PBC) bulk gap: finite ③ charge gap intra-Hubbard U/t ② para CDW spin gap U/t ① spin exchange J/t J/t Entanglement spectrum ① ③ ② 4-fold no degeneracy 16-fold

Energy gap (OBC) ② ③ J=0 para intra-Hubbard U/t charge gap CDW spin gap charge: gapped spin: gapless ② ① U/t U=5t spin exchange J/t ① Degeneracy parameter set of ES ③ 16-fold ① charge: gapped J/t 4-fold ② spin: gapped no degeneracy ③ All of edge modes are ※ Bulk is gapped destroyed by U and J

(2) How to observe the destruction of gapless edges? U=5t charge gap spin gap J/t Finite charge gap@ edges Radio frequency spectroscopy (~[ARPES measurement]) How to observe spin gap?

How to observe the spin gap? Energy Spin gap: Observing time evolution : Eigenstates of ・ Superposed state can be prepared by shining a half- π pulse ・ Oscillation of , tells us the gap size [gap size] ～ 1nK

Summary of part 2 para CDW loading 161 Dy atoms, one can prepare a testbed of * Interactions can be tuned in experiments!! can be observed by ・ Radio frequency spectroscopy: [charge gap] ～ 80nK ・ Time-evolution of the expectation [spin gap] ～ 1nK TY-Danshita-Peters-Kawakami arXiv 1711.xxxx

Thank you!