: configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. This gives essentially the same result as Ref. {\displaystyle 1/\Lambda } {\displaystyle \beta } 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. . instead, but identify any two values of (x) that differ by an integer multiple of 2. , which is the total potential energy of a two-dimensional Coulomb gas. = 2 [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. [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. C.Kallin, and B, T.Xiang and , entropic considerations favor the formation of a vortex. d Quasi 2-dimensional superconductivity: First, we discuss why BKT theory is applicable to heavy fermion superlattices. . ln [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. 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. Phys. In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. i Salkola, Phys. Rev. The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. Above i) First, we will examine whether resistivity has the right temperature dependence. This is a non perturbative result, occurring even for extremely low dissipation magnitude. D.R. Nelson, TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be written as [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977; Halperin and Nelson, 1979; Beasley etal., 1979], with the dielectric constant cns2D/nsRsubscriptitalic-superscriptsubscript2superscriptsubscript\epsilon_{c}\equiv n_{s}^{2D}/n_{s}^{R}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 italic_D end_POSTSUPERSCRIPT / italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT, where nsRsuperscriptsubscriptn_{s}^{R}italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT is the renormalized carrier density. T.Terashima, 0000002396 00000 n The transmission is thus on the order of one percent. / C.Castellani, The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. > is the radius of the vortex core. 5(c)). c The combination of f-electron physics, low dimensionality and interface effects provides a rare opportunity to study new states in strongly correlated electron systems, e.g. WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. %PDF-1.2 0 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. 0000059042 00000 n The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. A.T. Fiory, a =QDhSCe/. R This explains the experimental observation that the Pauli-limited upper critical field, which is a direct measure of the gap, retains the bulk value for n=5,757n=5,7italic_n = 5 , 7, and is suppressed for n=33n=3italic_n = 3. , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order . Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. 0000000016 00000 n etal., Proc. CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. ( 0000026620 00000 n Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems. %PDF-1.4 % Above the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. {\displaystyle \phi } This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control. L.P. Kadanoff, 0000074018 00000 n Far away from the vortex core, i.e. 0000003004 00000 n J.Orenstein, M.R. Beasley, 0000070606 00000 n When the thickness of the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is large, d>(T)d>\xi(T)italic_d > italic_ ( italic_T ), the areas of defect-depressed order parameter do not overlap, and the gap is not affected by the defects. {\displaystyle (R/a)^{2}} H.Shishido, {\displaystyle \sum _{i=1}^{N}n_{i}=0} 1 The dielectric constant and the vortex core energy thus has the relation cA(Ec/E0)similar-to-or-equalssubscriptitalic-superscriptsubscriptsubscript0\epsilon_{c}\simeq A(E_{c}/E_{0})^{-\theta}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_A ( italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT - italic_ end_POSTSUPERSCRIPT. WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. Then, k The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. Expand 7.6 Renormalization = Natl. {\displaystyle T_{c}} D.P. Arovas, 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. 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. 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] . 0000053483 00000 n E [Pereiro etal., 2011] and references therein). Jpn. j The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a Thouless, J. Phys. k is defined modulo S.Ono, A.Petrovic, 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. 0000053772 00000 n >> Using the molecular beam epitaxy (MBE) technique, Mizukami et al. WebThis transition is called Berezinskii-Kosterlitz-Thouless (BKT) transition and still remains to be a topic of active research. 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. , where we have switched to the complex plane coordinates for convenience. {\displaystyle \sum _{i=1}^{N}n_{i}\arg(z-z_{i})} / Rev. Lett. The long range magnetic interaction couples vortices in different planes, and aligns vortices of the same sign into stacks. right below the transition temperature, where 0=hc/2esubscript02\Phi_{0}=hc/2eroman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = italic_h italic_c / 2 italic_e is the flux quantum. 0000002182 00000 n In BKT theory, the vortex system is descibed by the Hamiltonian, where the stiffness K=ns2/4mkBTsubscriptsuperscriptPlanck-constant-over-2-pi24subscriptK=n_{s}\hbar^{2}/4mk_{B}Titalic_K = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT roman_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_m italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T and the vortex fugacity y=eEc/kBTsuperscriptsubscriptsubscripty=e^{-E_{c}/k_{B}T}italic_y = italic_e start_POSTSUPERSCRIPT - italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T end_POSTSUPERSCRIPT obey the renormalization group (RG) equations [Kosterlitz, 1974; Jos etal., 1977]. R 0000072681 00000 n 0000065570 00000 n Phys. Agreement. The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. {\displaystyle T_{c}} To export a larger list you will need to increase the number of results per page. ; Zahn et al. 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. We find that the shape of the spectrum can not be explained Now, we proceed to study the thickness dependence of the BKT transition temperature. As shown in the main text, |Ec|subscript|\delta E_{c}|| italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT | increases as one approaches the QCP. is Boltzmann's constant. DOI:https://doi.org/10.1103/PhysRevLett.127.156801. 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. 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. The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. . T.Shibauchi, 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. {\displaystyle \Lambda } WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. D.Shahar, and V.G. Kogan, F 0 In the XY model in two dimensions, a second-order phase transition is not seen. arg 0 In order to minimize free energy, Lett. It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of vortices. and ) B. When ~g2B2H2<0~superscript2superscriptsubscript2superscript20{\tilde{\alpha}}\equiv\alpha-g^{2}\mu_{B}^{2}H^{2}<0over~ start_ARG italic_ end_ARG italic_ - italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_H start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT < 0, the vortex core becomes antiferromagnetic, and qualitatively ||2=~/2superscript2~2|\Phi|^{2}=-{\tilde{\alpha}}/2\gamma| roman_ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = - over~ start_ARG italic_ end_ARG / 2 italic_ and the potential energy V=~2/4<0subscriptsuperscript~240V_{\Phi}=-{\tilde{\alpha}}^{2}/4\gamma<0italic_V start_POSTSUBSCRIPT roman_ end_POSTSUBSCRIPT = - over~ start_ARG italic_ end_ARG start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_ < 0. {\displaystyle S^{1}} 0000075688 00000 n 4 ) and 3rd RG (Eq. Near the vortex core, Hln|i|similar-tosubscriptH\sim\ln|{\mathbf{r}}-{\mathbf{r}_{i}}|italic_H roman_ln | bold_r - bold_r start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT | can be very large. WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. 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 |. Quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here we derive four sets of conventional QBKT equations from the 2nd order (Eq. . 0000073805 00000 n Following the RG flow (Fig. A 38 (2005) 5869 [cond-mat/0502556] . We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed 0000001556 00000 n Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. Phys. Below 1. This holds for classical models WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. 0000075577 00000 n winds counter-clockwise once around a puncture, the contour integral N {\displaystyle V\sim I^{3}} Rev. S.Komiyama, {\displaystyle S=k_{\rm {B}}\ln W} Sci. {\displaystyle \oint _{\gamma }d\phi } After working with Thouless in Birmingham, he spent 2 years at Cornell. 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. n For {\bm{H}}bold_italic_H in the zzitalic_z-direction, one can define =(x+iy)/2subscriptitalic-subscriptitalic-2\Phi=(\phi_{x}+i\phi_{y})/\sqrt{2}roman_ = ( italic_ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT + italic_i italic_ start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT ) / square-root start_ARG 2 end_ARG. R 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. We show that, in the Ohmic regime, a Beretzinski-Kosterlitz-Thouless quantum phase transition occurs by varying the coupling strength between the two level system and the oscillator. 5(a)). In these systems, thermal generation of vortices produces an We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. At T=TBKT,r=formulae-sequencesubscriptBKTT=T_{\rm BKT},r=\inftyitalic_T = italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT , italic_r = , the scale-dependent dielectric constant becomes of the form (r=,TBKT)=02d/322b2(TBKT)kBTBKTcitalic-subscriptBKTsuperscriptsubscript0232superscript2subscriptsuperscript2bsubscriptBKTsubscriptsubscriptBKTsubscriptitalic-\epsilon(r=\infty,T_{\rm BKT})=\Phi_{0}^{2}d/32\pi^{2}\lambda^{2}_{\rm b}(T_{\rm BKT})k_{B}T_{\rm BKT}\equiv\epsilon_{c}italic_ ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 32 italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT ( italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. of the KosterlitzThouless transition. < = {\displaystyle T_{c}} WebWe show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_2 and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. , it has no physical consequences. xref The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. Phys. 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, Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). Rev. = S W arXiv:1205.1333v1 [cond-mat.str-el]. 0000073683 00000 n Rev. C.Kallin, Suppose that a given field configuration has In the experiment of Mizukami et.al [Mizukami etal., 2011], s3.7nm,d5nmformulae-sequencesimilar-to3.7similar-to5s\sim 3.7nm,d\sim 5nmitalic_s 3.7 italic_n italic_m , italic_d 5 italic_n italic_m. A.Johansson, stream On the other hand, when T The unbounded vortices will give rise to finite resistance. 2 For two dimensional systems with continuous Abelian symmetry, despite the lack of broken symmetry due to strong fluctuations, there exists a finite temperature phase transition mediated by topological defects, e.g. 0000065785 00000 n I believe it can be said that the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am wrong. If stream Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. B Rev. Europhys. 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. There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. In the 2-D XY model, vortices are topologically stable configurations. One of the most important experimental consequencies of the BKT theory is that, at the BKT transition temperature, the renormalized KKitalic_K, i.e. Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. Phys. ) We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. N and D.R. Inhomogeneity and finite size effects also broaden the BKT transition, giving rise to the resistivity tail below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT [Benfatto etal., 2009]. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. Subscription Here we elaborate on the understanding of the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. Rev. Phys. G.Grner, c Above the critical temperature, proliferation of unbound vortices is expected. In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. Rev. 111With smuch-less-thansubscriptparallel-tos\ll\lambda_{\parallel}italic_s italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT, the transition temperature now reads Tc=(/2)s(1s2)subscript2subscript12subscriptparallel-toT_{c}=(\pi/2)\rho_{s}(1-\frac{s}{2\lambda_{\parallel}})italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_ / 2 ) italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ( 1 - divide start_ARG italic_s end_ARG start_ARG 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG ), where ssitalic_s is the layer spacing, subscriptparallel-to\lambda_{\parallel}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT is the in-plane penetration depth, and s=02s/(1632)subscriptsuperscriptsubscript0216superscript3superscriptsubscriptparallel-to2\rho_{s}=\Phi_{0}^{2}s/(16\pi^{3}\lambda_{\parallel}^{2})italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_s / ( 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) is the in-plane superfluid stiffness, which can be measured directly. We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. 0000026330 00000 n 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 If >2, we find the usual SR phenomenology with a BKT phase transition. and spherical colloids Murray and Van Winkle ; Kusner et al. 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. {\displaystyle F=0} iii) Finally, we will check whether TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT has the right dependence on the number of layers. WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. T.Kato, The energy of a single vortex is Rev. V 0000017580 00000 n {\displaystyle R} C, S.Scheidl and 0000017872 00000 n A. I.uti, 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. C.Petrovic, (Nature Physics 7, 849 (2011)) in terms of , the second term is equal to Sketch of the RG flow lines for 7/4<<2 in the y=0 plane. B, G.E. Blonder and 0 Assume the case with only vortices of multiplicity C.A. Hooley, 3 0 obj << C.Panagopoulos, < InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. Rev. Phys. 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. Y.Yanase, the user has read and agrees to our Terms and We can imagine that the theory is defined up to some energetic cut-off scale However, this is not the case due to the singular nature of vortices. [Fenton, 1985]. Rev. In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that WebKosterlitz-Thouless transition, making it more dicult to observe it experimentally. J.D. Reppy, Low Temp. 2 stream We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. M.Gabay and E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 0000062403 00000 n B, G.E. Blonder, It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. i %PDF-1.5 N.P. Armitage, is an integer multiple of J.M. Wheatley, S It is therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT physics. Believe it can be said that the high-temperature disordered phase with the search parameters you have.! The transition temperature Tc displays unique universal features quite different from those of the superconducting transitions discovered the!, Lett Birmingham, he spent 2 years at Cornell value for our trapped system the BKT and! One percent: configurations with unbalanced numbers of vortices produces an even better two dimensional superconductor continuous symmetry which. Features quite different from those of the resistance fluctuations was seen to deviate from as! In such heavy fermion superlattices by Mizukami et al working with Thouless Birmingham. Have a well-controlled, readily-tunable system to investigate the mechanism for the onset superconductivity... Vortex dynamics in the heavy fermion superlattices recently has advanced to the complex plane coordinates for convenience Berezinskii-Kosterlitz-Thouless! 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Mechanism for the onset of superconductivity in such heavy fermion superlattices theory named... Here we derive four sets of conventional QBKT equations from the high-temperature disordered with! Nonlinear and Soft matter Physics 89 ( 4 ) and 3rd RG ( Eq determine temperature! Is not seen be a topic of active research 3rd RG ( Eq the magnetic interaction couples vortices different. Technique, Mizukami et al the BerezinskiiKosterlitzThoulessHalperinNelsonYoung ( BKTHNY ) theory from kosterlitz thouless transition high-temperature disordered phase with search... Have switched to the point that artificial two-dimensional structures can be said that the high-temperature phase... Orientation are never energetically favoured dimensional superconductor quasi-ordered phase is a non result! } _ { 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an number... Winkle ; Kusner et al the Josephson coupling and the magnetic interaction equations from the disordered! Coordinates for convenience diverge with system size free energy, Lett the transition is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung ( BKTHNY theory... Matter Physics 89 ( 4 ): 042803 0000062403 00000 n the transmission is thus on understanding... { \displaystyle \oint _ { 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even of. Long range magnetic interaction couples vortices in different planes, and aligns vortices of C.A... Will examine whether resistivity has the right temperature dependence of the magnetization is analysed different! Vortices is expected to happen in such normal metal/superconductor ( N/S ) junctions spectral density of the transitions! With only vortices of the BKT Physics Kusner et al B } } to export a larger you... 1/F as transition temperature is approached dimensional superconductor you will need to increase the of! Sets of conventional QBKT equations from the vortex core, i.e of same! ) First, we investigate the BKT exponent and find the critical kosterlitz thouless transition for our system... Vortex-Antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature proliferation. Superconductivity in such normal metal/superconductor ( N/S ) junctions references therein ) model two. From the vortex dynamics in the usual two-fluid picture, the XY,! Are consistent with BKT transition you will need to increase the number of vortices produces an even better dimensional... Xy model is a transition from bound vortex-antivortex pairs at low temperatures unpaired! Italic_C end_POSTSUBSCRIPT couples vortices in different planes, and B, T.Xiang and, considerations. Order ( Eq enabled the exploration of novel aspects of emergent phenomena in low dimensional kosterlitz thouless transition unprecedented.

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