SS ii fl id i f ifl id i f iSuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphenegraphenegraphene

X. C. Xie International Center for Quantum Materials Peking University International Center for Quantum Materials, Peking University Institute of Physics, Chinese Academy of Sciences Department of Physics, Oklahoma State University

In collaboration with:Qing-feng Sun (Institute of Physics, CAS)Zh t Ji (B iji I tit t f T h l ) Zhao-tan Jiang (Beijing Institute of Technology) Yue Yu (Institute of Theoretical Physics,CAS)

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

OutlineOutlineOutlineOutline

MotivationMotivation

SuperSuper--SpinSpin--Fluid (SSF)Fluid (SSF)

Results and DiscussionResults and Discussion

ConclusionConclusion

AcknowledgementAcknowledgement

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

MotivationMotivationMotivationMotivation

S-wave Cooper Pairs, 2e, spin singlet, BCS ground state

Exciton electron-hole pair charge-neutral spin singlet or triplet Exciton, electron-hole pair, charge-neutral, spin singlet or triplet

A spin triplet exciton condensate is named as

Super-Spin-Fluid (SSF)

General drawback of the exciton condensate in many physical systems is its instability because of the electron-hole (e-h) recombination

Typical exciton lifetime: picosecond~microsecond, short

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Exciton in normal graphene

Spin-singlet exciton excitation:The charge carriers are spin-unpolarized in normal grapheneg p p g p

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

I th f ti (FM) hIn the ferromagnetic (FM) graphene,the carriers are spin polarized.

Electron-like

Exciton:

Hole-likeThese positive and negative carriers attract and form excitons that are attract and form excitons that are stable against the e-h recombination due to the Coulomb interaction.

If a carrier jumps from the electron-like state to the hole-like one, the total energy of the system rises, which prevents the e h recombination and means the exciton in the FM graphene e-h recombination and means the exciton in the FM graphene is stable.

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

SuperSuper SpinSpin Fluid (SSF)Fluid (SSF)SuperSuper--SpinSpin--Fluid (SSF)Fluid (SSF)

HamiltonianHamiltonian

with

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Diagonalization of the free Hamiltonian

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Electron annihilation operator

Hole creation operator

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Zero momentum e-h pair

Mean field approximation

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

The total mean field Hamiltonian

The corresponding energy spectrum is shown by the solid curves.

An energy gap is opened.

This means the exciton condensed state of the e-h pairs is more stable than the unpaired state.

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Th d t t f th FM h i t l fl id The ground state of the FM graphene is a neutral superfluid with spin ћ per pair ------SSF

The spin current is dissipationless and the spin resistance is zero.

The energy gap can be obtained self-consistently

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Self-consistent numerical results

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Result and DiscussionResult and DiscussionResult and DiscussionResult and Discussion1 Meissner Effect1. Meissner Effect

The criterion that a superconductor differs from a perfect metal

Described by the London equations.

Is there a Meissner-like effect for the SSF?Is there a Meissner like effect for the SSF?

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Consider a SSF with the superfluid carrier density in an Consider a SSF with the superfluid carrier density in an external electric field E and a magnetic field B

Magnetic force on a spin carrierMagnetic force on a spin carrier

(a)

(b)

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Example for this electric Meissner effect: Example for this electric Meissner effect:

Consider a positive charge Q at the origin andan infinite FM graphene in the x-y plane at z = Z

super-spin-currentsuper-spin-current

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

2. Josephson Effect

SSF/Normal Conductor/SSF junction

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

The weakly coupled junction

where

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

The spin-dependent particle current:

The spin current

The charge current

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

There is a super-spin-There is a super spincurrent flowing through the junction that resembles the Josephson tunneling inthe Josephson tunneling in a conventional superconductor junction.

Fig. 3(c) shows the super-spin-current Js can also be observed in non-zero mdobserved in non zero md as far as Δ ̸= 0 and Δϕ ̸= 0, π.

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

ConclusionConclusionConclusionConclusion

We predict a super-spin-fluid (SSF) state in theferromagnetic graphene as the counterpart toferromagnetic graphene, as the counterpart tothe (charge) superconductor. The SSF cancarry the dissipationless super-spin-current atequilibrium.

A BCS-type theory for the SSF is presented,and an electrical ‘Meissner effect’ and a spin-and an electrical Meissner effect and a spincurrent Josephson effect in SSF device aredemonstrated.

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

AcknowledgementAcknowledgementAcknowledgementAcknowledgementNSFNSF ChiChi NSFNSF--ChinaChina

ChinaChina--973 program 973 program

USUS--DOE DOE

SuperSuper--spinspin--fluid in a ferromagnetic fluid in a ferromagnetic graphenegraphene

Thank you!Thank you!

Nov. 24, 2010