四川大学：Establishing Gauge Invariant Linear Response of Fermionic Superuids with Pair Fluctuations（贺言）

Establishing Gauge Invariant Linear Response of Fermionic Superuids with Pair Fluctuations Yan he贺言 Sichuan University四川大学

Establishing Gauge Invariant Linear Response of Fermionic Superuids with Pair Fluctuations Yan He 贺言 Sichuan University 四川大学

Collaborators Chih-Chun Chien简志钧 UC Merced Hao guo郭吴, Southest u东南大学 This talk is based on the following papers H Guo, C.C.Chien, YH, J. Low Temp. Phys. 172, 5(2013) H Guo, C.C. Chien, YH, K Levin, Int J. Mod. Phys. B, 27, 1330010(2013) YH. H. Guo. arXiv 1505: 04080

Collaborators ◼ Chih-Chun Chien 简志钧 UC Merced ◼ Hao Guo 郭昊，Southest U东南大学 This talk is based on the following papers H. Guo, C.C.Chien, YH, J. Low Temp. Phys. 172, 5 (2013) H. Guo, C.C.Chien, YH, K. Levin, Int. J. Mod. Phys. B,27,1330010 (2013) YH, H. Guo, arXiv: 1505:04080

Outline BCS-BEC crossover theory and pair fluctuation theory a Gauge invariant linear response in bCs mean field theory: Consistent Fluctuation of Order parameter (CFOP a diagrammatic derivation of CFOP Gauge invariant linear response with pair fluctuation Summary

Outline ◼ BCS-BEC crossover theory and pair fluctuation theory ◼ Gauge invariant linear response in BCS mean field theory: Consistent Fluctuation of Order parameter (CFOP) ◼ A diagrammatic derivation of CFOP ◼ Gauge invariant linear response with pair fluctuation ◼ Summary

a brief introduction to bcs-beC crossover and pair fluctuation

A brief introduction to BCS-BEC crossover and pair fluctuation

Tunable attractive interaction via Feshbach resonance Feshbach resonance involves a bound state near a continuum level Unitary limit BEC Contact potential intermediate nteraction is described BCS by scattering length 60 100 magnetic field (mT) ← ncreasing attraction

Tunable attractive interaction via Feshbach resonance Increasing attraction k -k Feshbach resonance involves a bound state near a continuum level. Contact potential. Interaction is described by scattering length. R Unitary limit

What is BCs-BEC crossover Interpolation between fermionic superfluids to bosonic superfluids Transition from loosely bound Cooper pairs to tightly bound molecules The schematic excitation spectrum BCS intermediate BEC ◎a ●● ○o

What is BCS-BEC Crossover ◼ Interpolation between fermionic superfluids to bosonic superfluids ◼ Transition from loosely bound Cooper pairs to tightly bound molecules. ◼ The schematic excitation spectrum:

Physical picture of BCS-BEC crossover Pairs are formed before condensation E nergy gap is different from order acD) parameter a This combination defines bcs-bec crossover

Physical picture of BCS-BEC crossover ◼ Pairs are formed before condensation. ◼ Energy gap is different from order parameter. ◼ This combination defines BCS-BEC crossover

BCS-BEC crossover at t=0 Based on BCS-Leggett ground state BCS)=Tu+vs* ck) Self-consistently solve for chemical potential 2E g Ek IkEa l/k

BCS-BEC crossover at T=0 ◼ Based on BCS-Leggett ground state ◼ Self-consistently solve for chemical potential ( )  + − +  = + k k k k k 0 , , BCS u v c c E g 1 2 1  = − k k          = − k k k E n  1

Generalization of bcs-bec crossover to finite temperatures: GOG pairing fluctuation t-matrix(ladder approx. for non-condensed pairs to=:+ +·· pg tn(Q1+8@),tlo)=2G(0-K)G(K) g a Fermion self-energy pg ∑三

Generalization of BCS-BEC Crossover to finite temperatures: G0G pairing fluctuation ◼ t-matrix (ladder approx.) for non-condensed pairs ◼ Fermion self-energy = − + = K p g Q G Q K G K g Q g t Q , ( ) ( ) ( ) 1 ( ) ( )  0 

Properties of GOG Pair fluctuations It reduce to bcs mean field at t=o It generates pseudogap at finite t a The superfluid transition is a continuous transition Consistency requires a gauge invariant linear response theory

Properties of G0G Pair fluctuations ◼ It reduce to BCS mean field at T=0 ◼ It generates pseudogap at finite T ◼ The superfluid transition is a continuous transition. ◼ Consistency requires a gauge invariant linear response theory