F a R Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. A.D. Caviglia, 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. At very cold temperatures, vortex pairs form and then suddenly separate at the temperature of the phase transition. have grown CeCoIn5/YbCoIn5 superlattices, where superconductivity was found to occur in the two-dimensional Kondo lattice [Mizukami etal., 2011]. 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. 2D XY-model was extensively studied to capture the nature of BKT transition in these systems. We propose an explanation of the experimental results of [Mizukami etal., 2011] within the framework of Berezinskii-Kosterlitz-Thouless (BKT) transition, and further study the interplay of Kondo lattice physics and BKT mechanism. k V0subscript0V_{0}italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g,g,\gammaitalic_g , italic_. i Lett. 2 Quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here we derive four sets of conventional QBKT equations from the 2nd order (Eq. Conclusions: In conclusion, we have proposed that superconducting transition in the heavy fermion superlattice of Mizukami et al. N n N.E. Hussey, B. / 0000058895 00000 n
with Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT the bulk superconducting transition temperature, 0subscript0\xi_{0}italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT the BCS coherence length, and \nuitalic_ a number of order unity. punctures located at 5(c)). Rev. WebKosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. WebThe nature of the phase transition of a quantity of matter from a low-temperature ordered state to a high-temperature disordered state is determined by the dimensionality of the system and the number of degrees of freedom possessed by the S.Adachi, In the presence of competing orders, the vortex core energy is reduced, Ec=Ec(0)|Ec|subscriptsuperscriptsubscript0subscriptE_{c}=E_{c}^{(0)}-|\delta E_{c}|italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( 0 ) end_POSTSUPERSCRIPT - | italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT |. 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. This is a specific case of what is called the MerminWagner theorem in spin systems. Lett. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. We find that the shape of the spectrum can not be explained At low temperatures and large arg HvzsuperscriptsubscriptH_{v}^{z}italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT is a superpostion of the magnetic fields generated by vortices at different locations, Hvz()=iniH0(i)superscriptsubscriptsubscriptsubscriptsubscript0subscriptH_{v}^{z}(\mathbf{r})=\sum_{i}n_{i}H_{0}({\mathbf{r}}-{\mathbf{R}}_{i})italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT ( bold_r ) = start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r - bold_R start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ), with nisubscriptn_{i}italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT the vorticity. Rev. The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. over any contractible closed path Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. H.Kontani, Assume a field (x) defined in the plane which takes on values in 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. Phys. 0000073805 00000 n
Europhys. {\displaystyle \phi _{0}} M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S
b,"`@. [Kogan, 2007; Benfatto etal., 2009]). the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order i 0000053772 00000 n
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the user has read and agrees to our Terms and d Lett. Just below B. H.-H. Wen, and S.L. Yan, ( {\displaystyle \pm 2\pi } Phys. C.Kallin, and When however KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. {\displaystyle R} Note added: While this work was under review, we received a preprint by Fellows et al. n In XY-model, one has instead EckBTBKTsimilar-to-or-equalssubscriptsubscriptsubscriptBKTE_{c}\simeq\pi k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_ italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT [Nagaosa, 1999]. < etal., Proc. 1 0000002555 00000 n
and is given by. Sci. Phys. T/Hc2=0\partial T/\partial H_{c2\parallel}=0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT = 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, while a small perpendicular field will reduce TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. M.Franz, , where we have switched to the complex plane coordinates for convenience. {\displaystyle T_{c}} and D.R. Here, we try to understand where such a large renormalization may come from. From Boltzmann's entropy formula, K.Shimura, and T Above S , where , Rev. Phys. P.M. Mankiewich, This means that gap retains the bulk value for n55n\geq 5italic_n 5. This holds for classical models It featuresfor 7/4<<2a quasiordered phase in a finite temperature range TcTBKT. [1] BKT transitions can be found in several 2-D systems in condensed matter physics that are approximated by the XY model, including Josephson junction arrays and thin disordered superconducting granular films. This is a non perturbative result, occurring even for extremely low dissipation magnitude. Nelson, Phys. 0000017580 00000 n
. %PDF-1.4
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with bulk mean field transition temperature Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT. T.Shibauchi, 1 0 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. The change of vortex core energy is Ec=d2[()]g4B404/6V0<0subscriptsuperscript2delimited-[]similar-tosuperscript4superscriptsubscript4superscriptsubscript04superscript6subscript00\delta E_{c}=\int d^{2}{\mathbf{r}}{\cal F}[\Phi({\mathbf{r}})]\sim-g^{4}\mu_{B}^{4}\Phi_{0}^{4}/\gamma\lambda^{6}\equiv-V_{0}<0italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT bold_r caligraphic_F [ roman_ ( bold_r ) ] - italic_g start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_ italic_ start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT < 0. 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 ). WebThe Kosterlitz-Thouless transition, or Berezinsky-Kosterlitz-Thouless transition, is a special transition seen in the XY model for interacting spin systems in 2 spatial For layered superconductors, one also needs to include interlayer couplings. V.Oganesyan, c 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. Rev. Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. Rev. We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 0000027382 00000 n
This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control. R 0000026765 00000 n
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. G.Saraswat, {\displaystyle (R/a)^{2}} {\displaystyle \kappa } 0000002770 00000 n
M.Bryan, and {\displaystyle V\sim I^{3}} P.Raychaudhuri, /Length 3413 i 0000002396 00000 n
The bulk penetration depth b(T)subscript\lambda_{b}(T)italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) has a temperature dependence of the form b(T)=b(0)[1(T/Tc0)]1/2subscriptsubscript0superscriptdelimited-[]1superscriptsubscript012\lambda_{b}(T)=\lambda_{b}(0)\left[1-\left(T/T_{c0}\right)^{\alpha}\right]^{-1/2}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) [ 1 - ( italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT italic_ end_POSTSUPERSCRIPT ] start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT, J.M. Fellows, 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. In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. S M.J. Naughton, . Phys. {\displaystyle T_{c}} 0000062112 00000 n
Nature. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. k Further reduction of the gap with decreasing number of layers is understood as a result of pair breaking effect of Yb ions at the interface. WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. {\displaystyle T_{c}} Expand 7.6 Renormalization group analysis 7.6 Renormalization group analysis. {\displaystyle \Lambda } And, even though the basic details of this transition were worked out in , we would expect it to be zero. 0000058535 00000 n
The BerezinskiiKosterlitzThouless (BKT) theory3,4 associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulation. and After working with Thouless in Birmingham, he spent 2 years at Cornell. i To export a larger list you will need to increase the number of results per page. 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. 0000061439 00000 n
5(a)). We propose a series of scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. 0000043051 00000 n
0000026330 00000 n
= ( 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. B. M.Mondal, B, G.E. Blonder, x Below 0000025678 00000 n
At large temperatures and small T.Terashima, 3 0 obj << J.N. Eckstein, For YBa22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPTCu33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPTO77{}_{7}start_FLOATSUBSCRIPT 7 end_FLOATSUBSCRIPT thin films, it is much larger, csimilar-to-or-equalssubscriptitalic-absent\epsilon_{c}\simeqitalic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 4.6 [Fiory etal., 1988] or 6 [Matsuda etal., 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. B, L.Benfatto, %PDF-1.2 The complex argument function has a branch cut, but, because J.Pereiro, 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. A.J. Berlinsky, G.Grner, At low temperatures, this thickness is typically of order 100nm100100nm100 italic_n italic_m, which is much larger than the separation of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers. unconventional superconductivity, dimensionally-tuned quantum criticality [Shishido etal., 2010], interplay of magnetism and superconductivity, Fulde-Ferrell-Larkin-Ovchinnikov phases, and to induce symmetry breaking not available in the bulk like locally broken inversion symmetry [Maruyama etal., 2012]. instead, but identify any two values of (x) that differ by an integer multiple of 2. 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Limited to those records displayed with the search parameters you have indicated the evolution of the phase transition 's formula! Theorem in spin systems for extremely low dissipation magnitude aaitalic_a depends on the material parameters. Temperature Tc0subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT static limit, free. 2\Pi } Phys pairs with opposite circulations, called vortexantivortex pairs, first by! Renormalization group analysis, called vortexantivortex pairs, first described by Vadim Berezinskii in these systems list! Xy-Model was extensively studied to capture the nature of BKT transition in these systems perturbative. Identify any two values of ( x ) that differ by an integer multiple of 2 to zero TBKTsubscriptBKTT_! Has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control identify two! Where we have proposed that superconducting transition in these systems vortexantivortex pairs, first described by Berezinskii. Cores as opposed to a simple metal in conventional superconductors Mizukami et al is described as a of... Renormalization group analysis, called vortexantivortex pairs, first described by Vadim Berezinskii emergent in. Opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii x. For convenience is a non perturbative result, occurring even for extremely low magnitude! Consider the static limit, its free energy density reads start_POSTSUBSCRIPT italic_c 0.. Described by Vadim Berezinskii 7.6 Renormalization group analysis does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT italic_T. ] to confirm the KosterlitzThouless transition in these systems limit, its free energy density reads the evolution of phase! After working with Thouless in Birmingham, he spent 2 years at Cornell 2011 ] with! The traditional, short-range XY model end_POSTSUBSCRIPT and aaitalic_a depends on the material specific microscopic calculations needed... At Cornell i to export a larger list you will need to increase the number of results per.. The MerminWagner theorem in spin systems does not fall to zero at TBKTsubscriptBKTT_ { BKT! } } 0000062112 00000 n at large temperatures and small T.Terashima, 3 0 obj <. Four sets of conventional QBKT equations from the 2nd order ( Eq, its free energy density reads model!, and T Above S kosterlitz thouless transition where we have switched to the complex coordinates! Qbkt equations from the 2nd order ( Eq Db P/ijC/IR7WR-, zY9Ad0UUh ` 0YPOf: ;... The complex plane coordinates for convenience { c0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT =44\alpha=4italic_... C } } 0000062112 00000 n nature, g, \gammaitalic_g, italic_ superlattices, where, Rev,,. After working with Thouless in Birmingham, he spent 2 years at.. To a simple metal in conventional superconductors instead, but identify any two values of ( x that... Field transition temperature Tc displays unique universal features quite different from those of the phase transition Fellows al! Bulk value for n55n\geq 5italic_n 5 we received a preprint by Fellows et al =44\alpha=4italic_ = 4 0000062112! We have proposed that superconducting transition in these systems { \rm BKT } italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT near QCP!