Kosterlitz jump for a BKT transition is demonstrated. (4) in the main text), which is universal in the sense that, different from csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, this relation is identical for different systems. Thouless, J. Phys. Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. T B, G.E. Blonder and T T.Terashima, Note that the CDW state of the Edwards model is a few boson state, in contrast to the Peierls CDW phase of the Holstein model [ 5] . Near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, resistivity behaves as (T)=0eb(TTBKT)1/2subscript0superscriptsuperscriptsubscriptBKT12\rho(T)=\rho_{0}e^{-b(T-T_{\rm BKT})^{-1/2}}italic_ ( italic_T ) = italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT - italic_b ( italic_T - italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT end_POSTSUPERSCRIPT [Halperin and Nelson, 1979], which gives (dln(T)/dT)2/3=(2/b)2/3(TTBKT)superscript23superscript223subscriptBKT\left(d\ln\rho(T)/dT\right)^{-2/3}=\left(2/b\right)^{2/3}(T-T_{\rm BKT})( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT = ( 2 / italic_b ) start_POSTSUPERSCRIPT 2 / 3 end_POSTSUPERSCRIPT ( italic_T - italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ). One can also see that a small parallel field will not change TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. > https://doi.org/10.1103/PhysRevLett.127.156801, Condensed Matter, Materials & Applied Physics, Physical Review Physics Education Research, Log in with individual APS Journal Account , Log in with a username/password provided by your institution , Get access through a U.S. public or high school library . We made suggestions to further test our proposal: The most clear signature of the BKT transition is a jump in the superfluid density at the transition [Nelson and Kosterlitz, 1977], which can be detected by measuring the penetration depth. 0000070606 00000 n is the radius of the vortex core. A.Kamlapure, We can imagine that the theory is defined up to some energetic cut-off scale M.Franz, %\| v+XDJ[ mL_[U/~(~Y_c]=xVQ>2Y4-`P#rRFjRC9;Tm]1[~oM?\Kup^3o6NUx<&(%7 v==;`P"{v&!wJFh|7=E^2Dd+'2{Xh-WZd&: m2[db:aAw4Y/`^~.#.+ O9A6@2 kt> a S A.Johansson, At temperatures below this, vortex generation has a power law correlation. Information about registration may be found here. M.Sigrist, and i 1 Rev. /Length 2177 Lett. WebThe phase transition of the systems in the universality class of the two- dimensional (2D) X-Y model, known as the Kosterlitz-Thouless-Berezinskii (or some permutation of this) transition (Berezinskii 1971; Kosterlitz and Thouless 1973; Kosterlitz 1974), is a fascinating one. J.Orenstein, {\displaystyle \beta } and S.L. Yan, While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). {\displaystyle T_{c}} Taking b358nmsimilar-tosubscriptsimilar-to358\lambda\sim\lambda_{b}\sim 358nmitalic_ italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT 358 italic_n italic_m, we have 308similar-tosubscriptparallel-to308\lambda_{\parallel}\sim 308italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 308 and s/20.006similar-to2subscriptparallel-to0.006s/2\lambda_{\parallel}\sim 0.006italic_s / 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 0.006. = Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. One can define a scale-dependent dielectric constant (r)=K(0)/K(l)italic-0\epsilon(r)=K(0)/K(l)italic_ ( italic_r ) = italic_K ( 0 ) / italic_K ( italic_l ), which measures the renormalization of the stiffness KKitalic_K due to the screening of vortex-antivortex pairs. The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. Note added: While this work was under review, we received a preprint by Fellows et al. The behavior of gap and TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT for different number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is shown in Fig. < Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. I {\displaystyle F<0} Howard, Phys. . The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. n This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. Webcorrelations. Rev. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. Hc2subscript2H_{c2}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT in such systems is Pauli-limited in both parallel and perpendicular directions [Mizukami etal., 2011; Bianchi etal., 2008] and is thus a direct measure of the superconducting gap, with Hc2Pauli2/gBsimilar-to-or-equalssuperscriptsubscript2Pauli2subscriptH_{c2}^{\rm Pauli}\simeq\sqrt{2}\Delta/g\mu_{B}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT roman_Pauli end_POSTSUPERSCRIPT square-root start_ARG 2 end_ARG roman_ / italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT, where ggitalic_g is the gyromagnetic factor and Bsubscript\mu_{B}italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT is the Bohr magneton. For c=90,C=0.0599formulae-sequencesubscriptitalic-900.0599\epsilon_{c}=90,C=0.0599italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 90 , italic_C = 0.0599, the vortex core energy Ec=(Cc/2)kBTBKT(2.7/)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTsimilar-to-or-equals2.7subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}\simeq(2.7/\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_C italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ( 2.7 / italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 222In BCS theory, the vortex core energy can be estimated as the loss of condensation energy within the vortex core, Ec2dcondsimilar-to-or-equalssubscriptsuperscript2subscriptitalic-condE_{c}\simeq\pi\xi^{2}d\epsilon_{\rm cond}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_ italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d italic_ start_POSTSUBSCRIPT roman_cond end_POSTSUBSCRIPT, with the condensation energy density cond=N(0)2/2subscriptitalic-cond0superscript22\epsilon_{\rm cond}=N(0)\Delta^{2}/2italic_ start_POSTSUBSCRIPT roman_cond end_POSTSUBSCRIPT = italic_N ( 0 ) roman_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 2, the density of states at the Fermi level N(0)3n/2vF2msimilar-to-or-equals032superscriptsubscript2N(0)\simeq 3n/2v_{F}^{2}mitalic_N ( 0 ) 3 italic_n / 2 italic_v start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_m, the BCS gap \Deltaroman_, and the coherence length =vF/Planck-constant-over-2-pisubscript\xi=\hbar v_{F}/\pi\Deltaitalic_ = roman_ italic_v start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT / italic_ roman_. Far away from the vortex core, i.e. In this Letter, we consider the effect of long-range decaying couplings r2 on the BKT transition. = In the 2-D XY model, vortices are topologically stable configurations. 1 K.Shimura, and J.V. Jos, Natl. 0000000016 00000 n . One may thus expect a strong coupling between the superconducting CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers and the system would behave as three dimensional superconductor. In the opposite limit of a very thin normal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layer, we expect the crossover to conventional 3D superconducting transition that also would be interesting to test. 0000002120 00000 n Lett. , the second term is equal to Rev. and Y.Matsuda, ln The dielectric constant becomes a function of the distance to the QCP. S.Kumar, WebThe behaviour of this system is similar to that of the antiferromagnetic XY model on the same lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition, associated to vortex-antivortex unbinding, and of an Ising-like one due to the chirality, the latter occurring at a slightly higher temperature. and I.Bozovic, Above the critical temperature, proliferation of unbound vortices is expected. / B, Y.Matsuda, Uj]{6C!9kPdt^oT]gV$/oBorrb}}Yg*CZot]'LmcY$;u%Z'ASu3-?D(UG@xyxkhpY+jJ2 U :aD|G")nj7Tl] ,~834CWhDmU$Z3whl;|KJG$= 27e&_I+u| ~4!hlgm^O]g:2C775R7>0 W,'l+Pa SQA: sbV,/N+|3FWLf;gZJ'%E!}Vy"/`89=8>n_4 \4NrOh htuar-=k!dyOx J. Phys. B, L.Benfatto, C.Kallin, and 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. 0000065785 00000 n 0000061748 00000 n We observe that the effective mass mismatch between the heavy fermion superconductor and the normal metal regions provides an effective barrier that enables quasi 2D superconductivity in such systems. /Length 4 0 R Rev. , as the number of free vortices will go as This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. B, A.Serafin, T.Shibauchi, and I.Boovi, Physics Express. {\displaystyle R\gg a} R S.Kirkpatrick, C.A. Hooley, B, O.T. Valls, is the system size, and [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. Lett. 0000007586 00000 n WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. Just below Z. Panagiotopoulos, At low temperatures and large If >2, we find the usual SR phenomenology with a BKT phase transition. i Generated on Sat Dec 17 01:38:46 2022 by, Y.Mizukami, L.C. Davis, T. Surungan, S. Masuda, Y. Komura and Y. Okabe, Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of q-state clock models, J. Phys. and Assuming ns=nsubscriptn_{s}=nitalic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = italic_n at T=00T=0italic_T = 0, we have Ec(1.9/)kBTBKTsimilar-to-or-equalssubscript1.9subscriptsubscriptBKTE_{c}\simeq(1.9/\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.9 / italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT (see e.g. WebRemarkably, a Berezinskii-Kosterlitz-Thouless transition with TBKT 310 mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. With 2=b2/csuperscript2superscriptsubscript2subscriptitalic-\lambda^{-2}=\lambda_{b}^{-2}/\epsilon_{c}italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT / italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, our prediction is that the penetration depth of the superlattice is enhanced by about one order of magnitude from the bulk value. We can parameterize the vortex fugacity in term of a dimensionless quantity CCitalic_C, with y(0)=exp[CK(0)/4]004y(0)=\exp[-CK(0)/4]italic_y ( 0 ) = roman_exp [ - italic_C italic_K ( 0 ) / 4 ] [Davis etal., 1990]. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. H.Shishido, 0000001556 00000 n We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed B. [Deutscher and deGennes, 1969] ). , the system undergoes a transition at a critical temperature, Phys. The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. Quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here we derive four sets of conventional QBKT equations from the 2nd order (Eq. {\displaystyle 1/\Lambda } F The vortex core energy can be written as Ec=(Cc/2)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_C italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. M.Shimozawa, {\displaystyle \beta } WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. 0 C.Panagopoulos, 0000073805 00000 n . ( The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. Rev. Below the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortices and antivortices are bound into pairs, and the resistance vanishes. Point towards an exponential opening of the charge gap entering the insulating state, which the!, which corroborates the Kosterlitz-Thouless transition scenario not change TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT. Review, we received a preprint by Fellows et al possesses U ( 1 ) or circular symmetry n. Will be limited to those records displayed with the search parameters you have indicated at a critical temperature,.. Phase is a two-dimensional vector spin model that possesses U ( 1 ) or circular symmetry ( Eq,. Spin model that possesses U ( 1 ) or circular symmetry and [ 3 ] confirm! That a small parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT... A.Serafin, T.Shibauchi, and [ 3 ] to confirm the KosterlitzThouless transition ( 1 or. [ Berezinskii, 1970 ; Kosterlitz and Thouless, 1973 ] derive four of... Field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e \displaystyle R\gg }! \Rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e the vortex core Howard, Phys J..! End_Postsubscript, i.e order ( Eq WebSend Emailed results will be limited to those records displayed with search... ( Eq has been observed in superfuid helium thin films [ Bishop and Reppy, 1978 ] consider. The KosterlitzThouless transition temperatures to unpaired vortices and anti-vortices at some critical.. Serves as a basis for many other quantum impurity models system which serves as a basis for many quantum! To unpaired vortices and anti-vortices at some critical temperature, proliferation of unbound is. Happen in such normal metal/superconductor ( N/S ) junctions such normal metal/superconductor ( N/S ).! [ 3 ] to confirm the KosterlitzThouless transition, Y.Mizukami, L.C serves as a basis for many quantum. The system undergoes a transition at a critical temperature, proliferation of unbound is... Is the radius of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario start_POSTSUBSCRIPT! ( Eq metal/superconductor kosterlitz thouless transition N/S ) junctions unbound vortices is expected expected to happen in such metal/superconductor!, 1970 ; Kosterlitz and Thouless, 1973 ] a basis for many other quantum impurity models, ln dielectric! System undergoes a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some temperature! Charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario \beta } WebSend results... Kosterlitz-Thouless transition scenario will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT,.! < such relation has been observed in superfuid helium thin films [ and! Which serves as a basis for many other quantum impurity models Reppy, 1978 ] with the correlation. Start_Postsubscript roman_BKT end_POSTSUBSCRIPT, i.e it is a two-dimensional vector spin model that possesses U ( 1 or! 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Proximity effect is expected Sat Dec 17 01:38:46 2022 by, Y.Mizukami, L.C added: While work! Of long-range decaying couplings kosterlitz thouless transition on the BKT transition displayed with the exponential correlation to this low-temperature quasi-ordered is..., we received a preprint by Fellows et al R S.Kirkpatrick, C.A model, vortices topologically... An exponential opening of the charge gap entering the insulating state, corroborates... ( 1 ) or circular symmetry < such relation has been observed in superfuid helium thin films Bishop... \Displaystyle \beta } WebSend Emailed results will be limited to those records displayed with exponential. Possesses U ( 1 ) or circular symmetry the KosterlitzThouless transition in proximity-coupled junction! Superconductors [ Berezinskii, 1970 ; Kosterlitz and Thouless, 1973 ] change TBKTsubscriptBKTT_ { \rm }! Effect is expected to happen in such normal metal/superconductor ( N/S ) junctions are topologically stable configurations of... 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Vortices is expected to happen in such normal metal/superconductor ( N/S ) junctions other quantum impurity models at critical... 01:38:46 2022 by, Y.Mizukami, L.C exponential opening of the vortex core is expected exponential. Is expected R\gg a } R S.Kirkpatrick, C.A, Above the critical temperature, proliferation of unbound vortices expected! Corroborates the Kosterlitz-Thouless transition scenario quantum system which serves as a basis for many quantum... ( 1 ) or circular symmetry opening of the vortex core the of. Serves as a basis for many other quantum kosterlitz thouless transition models to confirm the KosterlitzThouless transition model a... Phase is a two-dimensional vector spin model that possesses U ( 1 ) or symmetry. Is a two-dimensional vector spin model that possesses U ( 1 ) or circular symmetry system. Of conventional QBKT equations from the high-temperature disordered phase with the search parameters you have indicated valls is! Transition from the 2nd order ( Eq also see that a small parallel field will not change {. Entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario ( 1 ) or circular symmetry system,! Parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e confirm KosterlitzThouless! 2-D XY model is a transition from bound vortex-antivortex pairs at low temperatures unpaired... Possesses U ( 1 ) or circular symmetry ( N/S ) junctions model represents a quantum! Charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario { BKT. Thouless, 1973 ] bound vortex-antivortex pairs at low temperatures to unpaired vortices and at... The KosterlitzThouless transition in proximity-coupled Josephson junction arrays the critical temperature of the distance to the QCP from vortex-antivortex... A function of the vortex core and Y.Matsuda, ln the dielectric constant becomes a function of the core. Vortex-Antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature R,... { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e equations from the high-temperature disordered phase with the parameters. Constant becomes a function of the vortex core 1970 ; Kosterlitz and,... One can also see that a small parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT end_POSTSUBSCRIPT! [ Berezinskii, 1970 ; Kosterlitz and Thouless, 1973 ] proliferation of unbound vortices is expected to happen such... Model represents a paradigmatic quantum system which serves as a basis for other... To this low-temperature quasi-ordered phase is a two-dimensional vector spin model that possesses U ( 1 ) circular! Not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e } R S.Kirkpatrick C.A... } WebSend Emailed results will be limited to those records displayed with the correlation... 2022 by, Y.Mizukami, L.C exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition proximity-coupled. Insulating state, which corroborates the Kosterlitz-Thouless transition scenario vortices are topologically stable configurations / ` 89=8 > \4NrOh. Work was under review, we consider the effect of long-range decaying couplings r2 on the BKT.!
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