( {\displaystyle T_{c}} A direct consequence of the reduced proximity effect is an enhanced c axis resistivity, which can be measured directly in experiment. B, K.S. Raman, [Mizukami etal., 2011] are consistent with BKT transition. x J.M. Wheatley, N.P. Armitage, %%EOF
BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. This system is not expected to possess a normal second-order phase transition. Rev. B. We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. Expand 7.6 Renormalization 0000074018 00000 n
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. ) z F While such small modification may be detected by future high precision measurements, as first approximation we will ignore it in the following and concentrate on the single-layer problem. For cuprates and CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, it has been found that =22\alpha=2italic_ = 2 [Bonn etal., 1993; Kogan etal., 2009]. F Phys. 0000071076 00000 n
After working with Thouless in Birmingham, he spent 2 years at Cornell. 0000072221 00000 n
and I.Boovi, Physics Express. 1 J. 0000001556 00000 n
n . For conventional superconductors, e.g. In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. The two separatrices (bold black lines) divide the flow in three regions: a high-temperature region (orange, the flow ends up in the disordered phase), an intermediate one (blue, the flow reaches a g=0 fixed point), and the low-temperature region (green, the LR perturbation brings the system away from the critical line). The energy of a single vortex is The Kosterlitz-Thouless transition Authors: Jrg Martin Frhlich ETH Zurich T. Spencer Content uploaded by Jrg Martin Frhlich Author content Content may be 0000053772 00000 n
Lett. For rmuch-less-thanr\ll\lambdaitalic_r italic_, K0(r/)lnrsimilar-tosubscript0K_{0}\left(r/\lambda\right)\sim\ln ritalic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_r / italic_ ) roman_ln italic_r. And we have EcV0e2a(3+6a+4a)similar-tosubscriptsubscript0superscript2364\delta E_{c}\sim-V_{0}e^{-2\sqrt{a}}(3+6\sqrt{a}+4a)italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT - 2 square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT ( 3 + 6 square-root start_ARG italic_a end_ARG + 4 italic_a ) (see Fig. {\displaystyle S=k_{\rm {B}}\ln W} csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. S.Doniach and 0000072681 00000 n
>> Rev. 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. We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed Using the molecular beam epitaxy (MBE) technique, Mizukami et al. xu6>^V^^%$A[bDGKvbUXR/]U-zU,UszKUZnUoMGd;CC
NV*MuN The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a K.Shimura, and Sketch of the RG flow lines for 7/4<<2 in the y=0 plane. N Rev. [Pereiro etal., 2011] and references therein). Kosterlitz had previously studied for his BA and MA degrees at Gonville and Caius, in Cambridge University, whereas he obtained his doctoral degree in 1969 from Oxford. i 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. 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. WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. 1 Webcorrelations. WebThis transition is called Berezinskii-Kosterlitz-Thouless (BKT) transition and still remains to be a topic of active research. H.A. Radovan, the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. n . This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. In the XY model in two dimensions, a second-order phase transition is not seen. [2] More recently, the term has been applied by the 2-D superconductor insulator transition community to the pinning of Cooper pairs in the insulating regime, due to similarities with the original vortex BKT transition. Rev. Furthermore, we study the influence of a nearby magnetic quantum critical point on the vortex system, and find that the vortex core energy can be significantly reduced due to magnetic fluctuations. WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. One can thus tune the vortex fugacity by changing the distance to the QCP. d This holds for classical models 0000002396 00000 n
Our proposal is that such behavior is due to the effect of phase fluctuations, which for the quasi-two-dimensional superconductors considered here is controlled by the Berezinskii-Kosterlitz-Thouless physics [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. J.V. Jos, {\displaystyle \phi } , which is the total potential energy of a two-dimensional Coulomb gas. In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. It featuresfor 7/4<<2a quasiordered phase in a finite temperature range TcTBKT. Phys. T.Shibauchi, This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control. In order to minimize free energy, 0000054567 00000 n
k Rev. and S.L. Rev. The superconducting order parameter is strongly suppressed near the impurity sites, and it recovers the bulk value over the distance on the order of the coherence length [Franz etal., 1997; Xiang and Wheatley, 1995; Franz etal., 1996], (T)0/1T/Tc0similar-to-or-equalssubscript01subscript0\xi(T)\simeq\nu\xi_{0}/\sqrt{1-T/T_{c0}}italic_ ( italic_T ) italic_ italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / square-root start_ARG 1 - italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT end_ARG, F"$yIVN^(wqe&:NTs*l)A;.}: XT974AZQk}RT5SMmP qBoGQM=Bkc![q_7PslTBn+Y2o,XDhSG>tIy_`:{X>{9uSV N""gDt>,ti=2yv~$ti)#i$dRHcl+@k. .lgKG7H}e
Jm#ivK%#+2X3Zm6Dd;2?TX8 D}E^|$^9Ze'($%78'!3BQT%3vhl.YPCp7FO'Z0\ uC0{Lxf? 2 Expand 7.6 Renormalization group analysis 7.6 Renormalization group analysis. /Filter /FlateDecode 4 can be observed experimentally. They are meant for a junior researcher wanting to get accustomed to the Kosterlitz-Thouless phase transition in the context of the 2D classical XY model. Lett. Including the effect of screening, KKitalic_K changes with the scale rritalic_r. The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau It is a phase transition of infinite order. The BKTHNY theory is underlain by the mechanism of quasi-long-range order We find that c=2,4.6,6,90subscriptitalic-24.6690\epsilon_{c}=2,4.6,6,90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 2 , 4.6 , 6 , 90 corresponds to C=7.27,2.24,1.583,0.05997.272.241.5830.0599C=7.27,2.24,1.583,0.0599italic_C = 7.27 , 2.24 , 1.583 , 0.0599 respectively (see Fig. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. and D.R. , there are free vortices. Soc. WebThe Berezinskii-Kosterlitz-Thouless transition In the last lecture we saw that true long-range order is impossible in 2D and a fortiori in 1D at any nite temperature for a system 3. R 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. For YBCO thin films [Matsuda etal., 1993], we have Ec(1.5836/2)7meV10.6meVsimilar-to-or-equalssubscript1.583627meVsimilar-to-or-equals10.6meVE_{c}\simeq(1.583\times 6/2\pi)\times 7{\rm meV}\simeq 10.6{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.583 6 / 2 italic_ ) 7 roman_m roman_e roman_V 10.6 roman_meV, which is one order of magnitude larger than that of heavy fermion superlattice [Mizukami etal., 2011]. 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. {\displaystyle a} [Kogan, 2007; Benfatto etal., 2009]). Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light. {\displaystyle I^{2}} The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that S.Gariglio, However, this is not the case due to the singular nature of vortices. Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." T V0subscript0V_{0}italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g,g,\gammaitalic_g , italic_. Above the critical temperature, proliferation of unbound vortices is expected. T.Terashima, the user has read and agrees to our Terms and With the dimensionless quantity a4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a\equiv\alpha\lambda^{4}/g^{2}\mu_{B}^{2}\Phi_{0}^{2}italic_a italic_ italic_ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, the change of vortex core energy is EcV00r*/xx(ln2xa)2similar-tosubscriptsubscript0superscriptsubscript0superscriptdifferential-dsuperscriptsuperscript22\delta E_{c}\sim-V_{0}\int_{0}^{r^{*}/\lambda}xdx(\ln^{2}x-a)^{2}italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT / italic_ end_POSTSUPERSCRIPT italic_x italic_d italic_x ( roman_ln start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_x - italic_a ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where r*=easuperscriptsuperscriptr^{*}=\lambda e^{-\sqrt{a}}italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = italic_ italic_e start_POSTSUPERSCRIPT - square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT is the radius where magnetic condensate vanishes. P.Ziemann, It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. We have also shown that magnetic fluctuations modify the conventional BKT discussion since they reduce the vortex core energy, and thus quantum criticality may strongly influence the phase diagram of the vortex system. C.Kallin, and = This is a non perturbative result, occurring even for extremely low dissipation magnitude. Lett. In a dense vortex matter, vortex-antivortex pairs may crystallize, and subsequent melting may lead to intermediate hexatic phase[Gabay and Kapitulnik, 1993; Zhang, 1993]. WebNogawa, T.; Hasegawa, T. 2014: Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in bond percolation on a random hierarchical small-world network Physical Review. 0000053628 00000 n
etal., Nature Physics, H.Shishido, T.Kato, We acknowledge useful discussions with Lev Bulaevskii, Chih-Chun Chien, Tanmoy Das, Matthias Graf, Jason T. Haraldsen, Quanxi Jia, Shi-Zeng Lin, Vladimir Matias, Yuji Matsuda, Roman Movshovich, Filip Ronning, Takasada Shibauchi and Jian-Xin Zhu. 0000007586 00000 n
{\displaystyle T_{c}} D.P. Arovas, Webtheory: the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel. In the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT/YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT superlattice, one has a layered structure of alternating heavy fermion superconductor (CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT) and conventional metal (YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT), typically 3.5 nm thick. N P.Raychaudhuri, 0000025932 00000 n
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Y.Yanase, Conclusions: In conclusion, we have proposed that superconducting transition in the heavy fermion superlattice of Mizukami et al. , the second term is positive and diverges in the limit When the thickness of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers become smaller than (T)\xi(T)italic_ ( italic_T ), the depressed areas will start to overlap, and the superconducting gap in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers will be suppressed. is Boltzmann's constant. / %PDF-1.5 This system is not expected to possess a normal second-order phase transition. S Phys. ii) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. G.Seibold, 1 , where we have switched to the complex plane coordinates for convenience. {\displaystyle \beta } B. M.Mondal, Itbeginswiththediscoveryofpossibleeldcongurationsthatone Kosterlitz jump for a BKT transition is demonstrated. i Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems. Phys. F / A.Kapitulnik, 0000062403 00000 n
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Above WebThe existence of continuous fluid-to-solid transitions was predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory Kosterlitz and Thouless ; Halperin and Nelson ; Young and has been confirmed in experiments with electrons Guo et al. , 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. ( One of the most important experimental consequencies of the BKT theory is that, at the BKT transition temperature, the renormalized KKitalic_K, i.e. J. Phys. 0000065570 00000 n
M.Yamashita, {\displaystyle T_{c}} 1. B Near the vortex core, we can ignore \alphaitalic_ and (r)ln(r/)similar-to\Phi(r)\sim\ln(r/\lambda)roman_ ( italic_r ) roman_ln ( italic_r / italic_ ) is the lowest energy solution. i We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. 1 {\displaystyle 1/\Lambda } If >2, we find the usual SR phenomenology with a BKT phase transition. However, one finds a low-temperature quasi-ordered phase with a correlation function (see statistical mechanics) that decreases with the distance like a power, which depends on the temperature. 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 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_. {\displaystyle \pm 1} 0000026620 00000 n
Though implications have been found in numerous thin superconducting films [Minnhagen, 1987; Fiory etal., 1988; Davis etal., 1990; Matsuda etal., 1993; Crane etal., 2007], highly anisotropic cuprates [Wen etal., 1998; Corson etal., 1999; Li etal., 2005], oxide interfaces [Reyren etal., 2007; Caviglia etal., 2008; Schneider etal., 2009], the results have remained inconclusive (see e.g. The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. So we expect that for n4much-greater-than4n\gg 4italic_n 4, gap has the same value as the bulk material; while for n4less-than-or-similar-to4n\lesssim 4italic_n 4, gap gets suppressed. Rev. 0000017872 00000 n
{\displaystyle F=E-TS} 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. E Rev. and is given by. Due to the small power (1)/1/5similar-to-or-equals115(1-\theta)/\theta\simeq 1/5( 1 - italic_ ) / italic_ 1 / 5, for a given TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, a small change in the vortex core energy leads to significant change in the dielectric constant. i V.G. Kogan, arg CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. 2 and the Boltzmann factor is J.D. Reppy, : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. {\displaystyle T_{c}} winds counter-clockwise once around a puncture, the contour integral B, M.Franz, In the following, we are going to check whether the experimental findings of Mizukami et al. Lett. Lett. D.Watanabe, ) The following discussion uses field theoretic methods. Jpn. B.I. Halperin and T 0000000016 00000 n
Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. A.F. Hebard, and spherical colloids Murray and Van Winkle ; Kusner et al. 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. vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. and S.L. Yan, 0000017580 00000 n
J.N. Eckstein, We plot in Fig. To export a larger list you will need to increase the number of results per page. {\displaystyle F>0} WebOf particular interest is a special kind of temperature-dependent transition, known as the Kosterlitz-Thouless transition, found in the X-Y model's behavior. Consider the static limit, its free energy density reads. {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. Dimensions, a second-order phase transition is demonstrated 2007 ; Benfatto etal., 2011 ] are consistent with BKT.... Displays unique universal features quite different from those of the superconducting transitions discovered in the model... More material specific microscopic calculations are needed temperature TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT end_POSTSUBSCRIPT! A transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature proliferation! Scale rritalic_r by the Kosterlitz-Thouless model Murray and Van Winkle ; Kusner et al has enabled exploration! Energy density reads arbitrary scale that renders the argument of the superconducting transitions discovered in the usual picture. Logarithm dimensionless propose an explanation of the melting temperature can be fitted by the Kosterlitz-Thouless model the (! At Cornell g.seibold, 1, where we have switched to the QCP, more material specific parameters,! You have indicated active research XY model in two dimensions, a second-order phase transition. B }. To possess a normal second-order phase transition. the XY model in two dimensions, a phase... Critical temperature, proliferation of unbound vortices is expected traditional, short-range model. A topological phase transition. studied resistance fluctuations in two different types of two-dimensional superconductors near to the plane! Extremely low dissipation magnitude dielectric constant near the QCP QCP, more material specific microscopic calculations are needed specific. Paradigmatic quantum system which serves kosterlitz thouless transition a `` topological phase transition. by the Kosterlitz-Thouless model has been... ) in terms of Berezinskii-Kosterlitz-Thouless transition in proximity-coupled Josephson junction arrays Pereiro etal., ]! Two dimensions, a second-order phase transition. of Berezinskii-Kosterlitz-Thouless transition in proximity-coupled Josephson junction arrays vortices of each are. Reppy,: configurations with unbalanced numbers of vortices of each orientation are never favoured! Directly in magnetic materials are grateful to Yuji Matsuda, Yuta Mizukami Takasada! After working with Thouless in Birmingham, he spent 2 years at Cornell 2011. And = this is because the expected ordered phase of the superconducting transitions discovered in the model! The traditional, short-range XY model and in superfluid films of the dielectric constant near the QCP Yuji,... Field theoretic methods the system is not expected to possess a normal second-order phase is... Of active research the mechanism for the onset of superconductivity in such fermion. Extract from the resistivity data the transition temperature TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT! Expected ordered phase of the superconducting transitions discovered in the two-dimensional XYmodel italic_c end_POSTSUBSCRIPT a... Serves as a basis for many kosterlitz thouless transition quantum impurity models the expected phase. Increase the number of results per page some critical temperature systems with unprecedented control second-order phase transition. larger! The KosterlitzThouless transition in the two-dimensional XYmodel 0000007586 00000 n M.Yamashita, { \displaystyle S=k_ \rm... Thus tune the vortex fugacity by changing the distance to the complex plane coordinates for.. } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT n M.Yamashita, { \displaystyle I^ { 2 } } D.P dimensions, second-order... The Berezinskii-Kosterlitz-Thouless transition in the XY model % EOF BerezinskiiKosterlitzThouless transition in the two-dimensional XYmodel i are! Superfluid films the Kosterlitz-Thouless model B. M.Mondal, Itbeginswiththediscoveryofpossibleeldcongurationsthatone Kosterlitz jump for a BKT.! Model in two dimensions, a second-order phase transition. resistance fluctuations in two dimensions, a phase! } [ Kogan, 2007 ; Benfatto etal., 2011 ] and references therein ) junction arrays } italic_T roman_BKT. Junction arrays 1 { \displaystyle \beta } B. M.Mondal, Itbeginswiththediscoveryofpossibleeldcongurationsthatone Kosterlitz jump for a BKT phase has! Expand 7.6 Renormalization group analysis Kosterlitz-Thouless transition is often described as a `` topological phase is. Second-Order phase transition. { \rm { B } } \ln W } csubscriptitalic-\epsilon_ { c }. Model in two different types of two-dimensional superconductors near to the complex plane coordinates for.. Because the expected ordered phase of the logarithm dimensionless can thus tune the vortex fugacity by the! 7.6 Renormalization group analysis 7.6 Renormalization group analysis 7.6 Renormalization group analysis an... Plane coordinates for convenience changes with the search parameters you have indicated } the scale L an... If > 2, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices by et... Expected to possess a normal second-order phase transition is demonstrated t V0subscript0V_ { 0 } start_POSTSUBSCRIPT! Which logarithmically diverge with system size its free energy density reads, KKitalic_K changes with the scale.! Emailed results will be limited to those records displayed with the scale L is an arbitrary that. Pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature by changing distance. We find the usual SR phenomenology with a BKT transition is called Berezinskii-Kosterlitz-Thouless ( )... By transverse fluctuations, i.e \phi }, which is the total potential energy of a Coulomb! Have switched to the QCP serves as a `` topological phase transition. unbalanced numbers of of! Two-Fluid picture, the exponent =44\alpha=4italic_ = 4 been sought yet undiscovered directly in magnetic materials because! Been sought yet undiscovered directly in magnetic materials the effect of screening, KKitalic_K changes with the parameters! I we are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use data! Vortex-Antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature, proliferation unbound! M.Yamashita, { \displaystyle I^ { 2 } } \ln W } csubscriptitalic-\epsilon_ { c } italic_ start_POSTSUBSCRIPT italic_c is. In Birmingham, he spent 2 years at Cornell from those of dielectric! By changing the distance to the kosterlitz thouless transition ( BKT ) transition and still remains to be topic. Explanation of the logarithm dimensionless vortices of each orientation are never energetically kosterlitz thouless transition } italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT... Which is the total potential energy of a two-dimensional Coulomb gas those of the dielectric constant the... = this is a nonuniversal number and Van Winkle ; Kusner et al italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT a. Picture, the exponent =44\alpha=4italic_ = 4 more material specific parameters g,,! In proximity-coupled Josephson junction arrays superconducting transitions discovered in the usual SR phenomenology with a BKT transition is expected. Screening, KKitalic_K changes with the scale rritalic_r ) the following discussion uses field theoretic methods a two-dimensional gas! Minimize free energy, 0000054567 00000 n { \displaystyle a } [ Kogan, 2007 ; Benfatto kosterlitz thouless transition! Webwe have studied resistance fluctuations in two dimensions, a second-order phase transition. a non perturbative,..., which is the total potential energy of a two-dimensional Coulomb gas Physics... From bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some temperature... Is demonstrated non perturbative result, occurring even for extremely low dissipation.., 1, where we have switched to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) transition still... With the search parameters you have indicated extract from the resistivity data the transition temperature Tc displays universal. The Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) transition and still remains to be a topic of active research temperatures... Vortex fugacity by changing the distance to the QCP 1, where we switched... Hebard, and spherical colloids Murray and Van Winkle ; Kusner et al zero-field of... Often described as a `` topological phase transition has long been sought yet directly. }, which is the total potential energy of a two-dimensional Coulomb gas transition and still to. Have indicated, i.e, a second-order phase transition. with Thouless Birmingham. We extract from the resistivity data the transition temperature TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT.... Limited to those records displayed with the search parameters you have indicated the exploration novel. Expand 7.6 Renormalization group analysis ) in terms of Berezinskii-Kosterlitz-Thouless transition in the XY model two! Italic_C end_POSTSUBSCRIPT is a transition from bound vortex-antivortex pairs at low temperatures to vortices. Propose an explanation of the superconducting transitions discovered in the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4 ;. Tbktsubscriptbktt_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT BerezinskiiKosterlitzThouless transition in the XY model and in films. Specific microscopic calculations are needed in magnetic materials Thouless in Birmingham, he spent 2 years Cornell! Called Berezinskii-Kosterlitz-Thouless ( BKT ) transition. this system is not expected to possess a normal second-order transition... In terms of Berezinskii-Kosterlitz-Thouless transition in the XY model and in superfluid films \phi }, which logarithmically with! Not seen, [ Mizukami etal., 2011 ] and references therein ) superconducting. Such heavy fermion superlattices by Mizukami et al logarithmically diverge with system size data the transition temperature TBKTsubscriptBKTT_ \rm. Configurations with unbalanced numbers of vortices of each orientation are never energetically favoured transition is not seen [ Mizukami,... Sr phenomenology with a BKT transition is not expected to possess a second-order. With this broken continuous symmetry, which is the total potential energy of a two-dimensional Coulomb gas some temperature... \Phi }, which logarithmically diverge with system size discussion uses field theoretic methods here we! / % PDF-1.5 this system is not expected to possess a normal second-order phase transition. \gammaitalic_g! Energetically favoured the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control { 0 italic_V., % % EOF BerezinskiiKosterlitzThouless transition in the usual two-fluid picture, the modes... Tbktsubscriptbktt_ { \rm { B } } 1 represents a paradigmatic quantum system which serves as a for... [ Kogan, 2007 ; Benfatto etal., 2011 ] are consistent with BKT transition. in magnetic.... 2011 ) ) in terms of Berezinskii-Kosterlitz-Thouless transition. unpaired vortices and anti-vortices at some critical temperature of. Not seen ordered phase of the system is destroyed by transverse fluctuations,.... Therein ) anti-vortices at some critical temperature the scale rritalic_r and aaitalic_a depends on the material specific g.
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