Floquet Superconductor in Holography

Transcription

1 Floquet Superconductor in Holography Takaaki Ishii (Utrecht) arxiv: [hep-th] w/ Keiju Murata 11 June 2018, Nonperturbative QCD Paris

2 Motivations Holography in time dependent systems To understand nonequilibrium phenomena from nonlinear dynamics in holographic theory. e.g.) QGP, quench, thermalization Condensed matter ideas Apply time dependent perturbation (laser-pulse) nonequilibrium states. e.g.) ARPES, superconductivity enhancement

3 <latexit sha1_base64="h2g6ok+dozauz2jpv0pswcbeit4=">aaacfxicsyriyswumtc4ycjezmlkxs7bycxnw8vhlyaoffacx1qunbqanj+txxsrlficmpozlxpaklmskxprujsamjuukxqelo0mkg8vsy0qzszpcympleinzu1mz8tmy0xolaekxqtiumzxage6xlfauiqkxlvnxvjnpqynkptuxgsog+gzgiecjsmqylbmgikafihlddemkqz5dmkmpqy5dkkmeqwlqhyoqyjdmrbgmxgygdauamvigaqbykvavizyppwhloelqlcuqcovqcirkjonjnobvgioab6qdzkzgkw7gwhldhaxaxuqmkgaxdvyafdz4itbaooxbn9wmlunngpklkognqtrm1oqz98lefydok5cif3ckihqhdfnjqxpdbzgt2yc3v4afgh5ihmiv6xq+ <latexit sha1_base64="agzqwv/iwbumnklaubdnvqc/znq=">aaacinichvhlshxbfd121oj4memyedw0diocmnwwis8cylziboijo4jjmu62hav7rxfnkhhwb5ipymkvgkhw5vax2eqhxpgj4tkagxfe6wkqfc0tquruqxtunaqyq1fgiui8q3vr2dx9sqc309c/mjjnvxq9fae1ybflj3cdamw2yufkx5svvk5ycsnhebyrlu2tz6395bqiyhn4x1ujfguevfxlhnqsxzszk5tm7+oyzdy+lxtxrskrxzxrtxslj+tsr6hnosyztgpm8lskjpthwehbhmnmbbldvlcoaa5q8cdgqzf2yshmtgodhjc5ntszixjjzf9gbxnw1jhlcibf7bapvv6tpqzp61bnofe7firlpwkljgkd0w+6or90rbd082stzlkj5axbs93witdm/hhavp6vyunzyfno9axnhq28s7xk9h4mtoswtltf3/51tfhhodacpx26zp97de5/+az+/z9zmc8wd <latexit sha1_base64="lrqkihwhm3+mvfioayvzhxlqc2y=">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</latexit> <latexit sha1_base64="oecxv5io/9lt1wbah2yiminuw0e=">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</latexit> We consider rotating electric field J θj Ωt E In gauge potential We include this rotating electric field to a holographic model of superconductivity (SC). c.f.) Linear polarization:

4 Rotating sources in holography Complex scalar with phase rotation [Biasi-Carrecedi-Mas-Musso-Serantes] c.f.) Spontaneous phase rotation: Boson star [Astefanesei-Radu, Buchel-Liebling-Lehner] D3/D7+rotating cpx scalar: Chiral magnetic effect [Hoyos-O'Bannon-Nishioka] D3/D7+rotating electric field for Weyl semimetal [Hashimoto-Kinoshita-Murata-Oka] [ Murata's talk]

5 Gauge/gravity duality Gravity Classical gravity in curved spacetime (AdS) Field (gauge) theory Large-N of strongly interacting field theory Local symmetry Field Global symmetry Operator OΔ Nonnormalizable mode Source of OΔ Normalizable mode VEV of OΔ

6 Holographic superconductor(/superfluid) Gravity Field (gauge) theory U(1) gauge field U(1) global symmetry and/or external U(1)em Complex scalar Cooper pair Nontrivial scalar solution despite trivial scalar boundary condition Spontaneous symmetry breaking

7 <latexit sha1_base64="nht+e42fmb5qgax1vey8t2ldtsg=">aaacynichvhpt9rafh4uevxqvrmyejm4gwamm+lme5gehkghxkgw1gusyjztms4t+ouz6ca125sn/wepnjqhhphnephg1qn/auegjh7k4gu3xchrx9oz733zvjffznirx6wi9hhig742cn107ezpfolmrcny7tvrmoyfw1po6ivi07yk83jawoorj21gglm+7bene+9ptr7rzulymhihehhb9q1owf3uwaops+w2ysixekditrv+khhyx6hkrpmsw2oumivzxhcf5sr6mtrtsmwmhh8bqzwuty8rlvsfmvnsklzfrpghpeb6l4khegdxptdlfvqlezcrqc9abypohovdmgahqnagbh8ybkaqe2cbxg8ldkaqibcncxicec/xgarqqm2mvqwrlgt3coxgtlwwaezzt5mrhdzfw1+gksa0/uqp6dn9td/se3rx115j3ipz0spzhmhzze6+udv8/l+vj7oc3v+qf3pw4mj87pwj9yhnslm4a3331dvz5sladdjdp9bt9p+ehtnpeikg+805wgvr76ced6d/ed1xqatwfvzvv+uvpsffs4zbpbgps3jdj2ajnkmdwrjtfzidh3chrwhs62njofqbkjrt8ftor38cz/evmq==</latexit> <latexit sha1_base64="fwjq4rihjoe89higlykoza14alu=">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</latexit> <latexit sha1_base64="s/gyanjszoo2alqsnjb0kzi3lqg=">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</latexit> sha1_base64="ql/codavxlprhox+mjxzigey6ya=">aaacbnichvhlssnafd2n7/qqcikiwcyvuik3iiicilpxwa1voupj4lqh0yqkauglp+bexaikgoj4gw78ard+grgrkrhx4w0aebx1hsmcoxppntn3dmeunk/0gfgamlta29o7op1d3t29sb7+nc8uu4bigbzpuxu65gltwilns98ug44rtjju sha1_base64="ei+pjuqm47+e/9z0kam4+pjsl9i=">aaacg3ichvhlsinbfd3p8rhjk6mbywaodioihtsijawi6mxmgr9rwujobiva2c+6k4ekujvv/ialvwrdolmc/8cnpzalp2fwqedghtedblfrb1fvp07dc+tulrk4dqsirllah47oru50t6a3r39gmptxad3yq6eli5bv+ogmautsst1zvlzy5gyqssm1hblh7n9r7w/uzbjzvrem6ohcdo1dz67ylqgykmc/l5bvrgnsziuswxxtohtu+aihpktj2vfvvm7mke9xijdat0aosrt87g+usamffqpwiefbmxzgiok2br2eglltnjklgdnxvsqbmqytcpbkdipzfr53ebwvsb6vwzwjwg3xkq73kjucy/sptumglukp/af7v2s14xotl3wezbzwbuxbnyord++qxj4v9h5vb3pwqgau9mqz9ybmwrew2vpa4/bm9evkwhoctuia/r/tfv3wdbzarfvrwa4cicmfod Simplest model [Hartnoll-Herzog-Horowits] Abelian Higgs model in AdS4 black hole geometry 2+1D field theory in finite temperature Introduce chemical potential <latexit Ψ eq: High temperature: <latexit

8 <latexit sha1_base64="s/gyanjszoo2alqsnjb0kzi3lqg=">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</latexit> <latexit sha1_base64="j64vl4ieavrx5gis2pu06urzwbc=">aaaccxichvhlssnafd2nr1pfvtekm2brfkhcikc4et247moqyfwsoopgmsqkldjid/gdcq4siiif4cyfcoenimskblx4mwzerb3dzjw5c8+dmzoga0k/ihqkkw3thz1d8e5et29f/0bycgjdd8qekqqmyznepqh7wpk2kaqysmsm6wm9zfhi Spontaneous condensation This has solution in low temperature = spontaneous condensation <O> Features as superconductivity: Infinite DC conductivity, mass gap Δ~<O>

9 <latexit sha1_base64="nht+e42fmb5qgax1vey8t2ldtsg=">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</latexit> sha1_base64="nnqj2inz0ekdvm9lqssbphyl2ay=">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</latexit> <latexit sha1_base64="wzp2ahd3lemwboyt5gfcovxuujw=">aaadjxichvhlbtnafl02r2ietwgdxmyialiunzpysaukpaibfid6ie2ltbkn3xeyql/yk0it4x/gb1iwagkb4isqg1asakkr1ohlkdiw4hpsfuefjowze88958ydgtvyrcij2dp0i0epht8xc9i4dfrm2dnk3lmnjbzhdm87orfgmzzluccc3pzcenwzijnzby937o3beb0z4xeiwucb3il4z2fdqljcyrkhqeun9zkcocxl72zm7yaxafi3zk7ayliruzmq9ttrw6brkfa3r6d2fdq3dpj0vs+hrg9hyc3mqz3xkdvqjn04zluna7tdpfcpu7jrucanelfhysnu0ikslrzcq+aazypn5obotwmxhmnlspxvotleofiltakgetholuevyresvl4ahs0iwyex+mahaimxbwws/lrqagiryj1ieysxeqroiqmdtwnkcwqwrldxhmlwldea89wzuwohd/hwj1fpwjz5sf6rffkovczfyi+/eqxki+9lb1e70pjompvowvr3/6p8xcwmfqn+2bmef66qxgx2hikkp4vt6ce7j/fxr6/npzxyjhzf/p+spfiwtxbmvjnpv/naezdwavp/xvfhog01rzvbq1eqy7fkl5ibi3ajfvc6l2az7saktmhr6to9bupr6c/19/oh/vnb1bvscx5+g/rnn4lzzqq=</latexit> <latexit sha1_base64="ky8rywozefaiwc9p6wbxsfmf5eq=">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</latexit> Our setup Ansatz: <latexit With this rotating ansatz, (z,t) variables separate. EOM reduces to ODEs rather than PDEs Ψ eq:

10 <latexit sha1_base64="m3m12nebnbiesi4k5kfm5ls4dng=">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</latexit> <latexit sha1_base64="excksd7koipar0r/ehn9npq4qp8=">aaacjhicsyriyswumtc4ycjezmlkxs7bycxnw8vhlyaoffacx1qunbqanj+txxsrlficmpozlxpaklmskxprujsamjuukxqelo0mkg8vsy0qzszpcympleinzu1mz8tmy0xolaekxquof9rg+oempicqemxhlgskliqq2crelkumv7vwxisn5jea2v618qlkbnogykcaytcempqzocagx2a5qwxdckm+qzjdkumuqypdhkmjkj3dkmhqditrdiymbgwfqlfyhmqgwbgqlqmwt2wozeac6i0fqkofqkgeimydyxqglxoqmgfkg8wsbutobtqsa8rfqj0kdkogvw1wgnw2oggw2uclwr+czlwdzqc5prjij0h0phbe83djbh Holographic steady state BH is heat bath. (No metric backreaction.) E There is a steady flux flow to BH. Constant flux in the holographic direction: This gives Joule heating:

11 A=0 Review: Ω=0 case Corresponds to a constant gauge potential. [Basu-Mukherjee-Shieh, Herzog-Kovtun-Son] In our setup, (E,Ω) 0 with A =E/Ω fixed. A increased As A is increased, phase transition becomes 1st order.

12 <latexit sha1_base64="btjghs18+yazvchctn9vip1qzo8=">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</latexit> To calculate phase transition Evaluate free energy, which is well-defined at Ω= ΔF T T/μ μ nd order 1st order 0.02 T/μ Example of F for 1st order phase transition A/μ E/(Ωμ) A(=E/Ω) dependence of Tc

13 When Ω> A/μ= A/μ= Larger Ω pushes back normal-to-sc phase transition (which is 1st order because of A) to 2nd order. At large A and Ω, the condensate is multivalued inside the SC phase: 1st order (phase) transition

14 <latexit sha1_base64="tjxiy6ngwnjkx0ohsd5fiewoc7u=">aaacfhicsyriyswumtc4ycjezmlkxs7bycxnw8vhlyaoffacx1qunbqanj+txxsrlficmpozlxpaklmskxprujsamjuukxqelo0mkg8vsy0qzszpcympleinzu1mz8tmy0xolaekxquifyrykssupszxu9bgjkfkl4dzxrxxasogegzgoidjmiqylbmgicbfydldd E and J get out of phase A/μ=0.53 J θj E Joule heating q is suppressed in the SC phase, consistent with the suppression of normal current. This means that E and J are 90 degrees out of phase, consistent with the London equation.

15 Phase diagram B C A Quantum phase transition A

16 <latexit sha1_base64="nyzelcmbhnpg42rp+wwhfprqt6o=">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</latexit> <latexit sha1_base64="mkzpnwflwkbjbjqkll19we37rue=">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 <latexit sha1_base64="3ri7vyhegz1apzy444jhf7gof4o=">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 <latexit sha1_base64="1tmycyv022+7wg084juvskdefk0=">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</latexit> Ω=0 phase transition revisited Free energy can be given in variational form Integrability of df is satisfied when Ω=0: Maxwell construction:

17 <latexit sha1_base64="yqqrs9lbyky0gqqapp0v++wm+my=">aaacjxicsyriyswumtc4ycjezmlkxs7bycxnw8vhlyaoffacx1qunbqanj+txxsrlficmpozlxpaklmskxprujsamjuukxqelo0mkg8vsy0qzszpcympleinzu1mz8tmy0xolaekxqtopljzkujgfgxkk6qoxoswkugqxjsljld71cykp+sxgarbxmfaeaflaz0dmfdazbhcgcomubcql7cciyyhhsgfizmhlcgxizuhj6eeym5hsgqobsjobkmga4ycofgsqzvqrajiygtlpzlumnab9zycvaucvsqcrbobzdqqfw0vzqpyqwywg3una23jaeiioe4fblwdqwyrdt4bndbybfds4a9os6rbzodcugmkkyb6uwvi+bskgr8t1julpesymhc68lq5hcgnwqls1kyg2wvaiibfjep0l1vn/xxsfararwawyoa10p0ldw4ahab6ik/ss/lswnsg2qxcwagwra9uteaykz6h Free energy for Ω 0? Integrability for ρ(μ,a), J(μ,A) is violated if Ω 0. Violation is larger in the region q is not small. No df exists which satisfies

18 <latexit sha1_base64="ihfdgmcezzsthewdixcw2nt1btc=">aaacl3ichvhnsinbep6cxtub/+j62wuvg0erxfajgikisgulr2m2khgzzsaogezmddodyay+gc+gskcvrgtfys8e9au8+aiyrwuvhqxmbkrfraa7q76qr/rrbjuqbqsirjq0dx87u7ptn9i9vx39a5nbzyurxwsduxr86ydrthuj6xqiqfwlxvoqcqtqs7fqb/9o5vfrioxc3/ulgohyqfpbnlt2husxzgyms5tckksvmculdltt9yaiipbyt5/tk1rk2vr4y1axm1nkuwz6s8dincwsw/izjyhhez4c1fcfgaffvosfimc6dbacxjbqzcxkz43zantim7fgvyirlea3ed3iad1bpy5bpaoy7fapkmfitb0jdemndemx9jeu6f7vxs24r0tlg3e7zrwbobd/pxd3lqvku0llkfwmzouyzmkt <latexit sha1_base64="7ezcprydhyr7oi8vq8nfq+cve/q=">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</latexit> <latexit sha1_base64="ru36wtl2zcqo18knhzs0spepay4=">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</latexit> Why? AdS/CFT dictionary Derive the field theory quantity from δsb. Horizon is included as ingoing wave condition rather than δsh. But δsb does not behave as df because of δsh. Therefore df is not given by -δsb.

19 <latexit sha1_base64="e78fuss4p3ag5chxfbd+pp+jmpg=">aaacd3ichvhlsgmxfd0d3/xrajecm8fs6apkrfalgiiiy/qocq2umtfqcf7mpiva/af/wiuluravp8onp+dctxcxcok48hy6ifrug5kcnnxzc5iyniucydhjtono7oru6e2l9w8mdiwswymbgvv1tv40xcv1tww94jzwefekafetz+e6bvh80zhybo5v1rgfcndzl3wpb9v6nin2halloirj1jkan1plwpfq2d931 Phase transition temperature To reasonably estimate the temperature of the 1st order transition, we try B C A A nd order transition temperature in region A is not shown here.

20

21 Re σ Im σ

22

23 Summary We applyed a rotating electric field a to holographic superconducting model and constructed a superconducting steady state. Nonequilibrium "thermodynamics" (free energy) for quantifying phase transition is challenging. Future plan Vortex formation, turbulence, boson star. How to enhance SC, lattice structure.