kosterlitz thouless transition

0000072221 00000 n From the above RG equations, one can see that the renormalized fugacity vanishes at the transition, i.e. A 38 (2005) 5869 [cond A.F. Hebard, 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 . k InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. x 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. 0000002555 00000 n [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. 0000065785 00000 n xu6>^V^^%$A[bDGKvbUXR/]U-zU,UszKUZnUoMGd;CC NV*MuN To export a larger list you will need to increase the number of results per page. 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. [Mondal etal., 2011]). {\displaystyle 1/\Lambda } . J.-M. Triscone, The connection to the 2D Coulomb gas is presented in detail, as well as the D.R. Nelson and 0000054567 00000 n 0000058895 00000 n 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.D. Reppy, , entropic considerations favor the formation of a vortex. This result is intimately related to that of Blonder, Tinkham and Klapwijk [Blonder etal., 1982; Blonder and Tinkham, 1983], where it was shown that the mismatch of Fermi velocities between the N and S regions increases the barrier height between the two, with the effective barrier parameter ZZitalic_Z modified to Z=(Z02+(1r)2/4r)1/2superscriptsuperscriptsubscript02superscript12412Z=(Z_{0}^{2}+(1-r)^{2}/4r)^{1/2}italic_Z = ( italic_Z start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + ( 1 - italic_r ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_r ) start_POSTSUPERSCRIPT 1 / 2 end_POSTSUPERSCRIPT where r=vS/vNsubscriptsubscriptr=v_{S}/v_{N}italic_r = italic_v start_POSTSUBSCRIPT italic_S end_POSTSUBSCRIPT / italic_v start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT is the ratio of two Fermi velocities. At temperatures below this, vortex generation has a power law correlation. = 4 can be observed experimentally. ) K.Yasu, Taking b(0)=358nmsubscript0358nm\lambda_{b}(0)=358{\rm nm}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) = 358 roman_n roman_m [Kogan etal., 2009], x=c/4=2.1nm/4subscript42.1nm4x=\xi_{c}/4=2.1{\rm nm}/4italic_x = italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 4 = 2.1 roman_nm / 4, we get the fitting parameter c90similar-to-or-equalssubscriptitalic-90\epsilon_{c}\simeq 90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 90. S.Kumar, {\displaystyle T_{c}} c We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. {\displaystyle I^{2}} winds counter-clockwise once around a puncture, the contour integral Soc. Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. 0000017580 00000 n 2 the temperature dependence of (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT for the four different cases with number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n=4,5,7,94579n=4,5,7,9italic_n = 4 , 5 , 7 , 9, where one can see that (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT is indeed linear in TTitalic_T, and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be extracted from the intersection points. 1 WebMy parents, Hans Walter and Johanna Maria Kosterlitz (Gresshner) had fled Hitlers Germany in 1934 because my father, a non-practicing Jew, came from a Jewish family and was forbidden to marry a non-Jewish woman like my mother or to be paid as a medical doctor in Berlin. 0000075577 00000 n The unbounded vortices will give rise to finite resistance. 0000053919 00000 n In the following, we are going to check whether the experimental findings of Mizukami et al. Lett. WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial dimensions that is Expand 7 0000008144 00000 n 1 0000071076 00000 n The specic heat only has a broad hump at temperatures somewhat above T KT, where E.D. Bauer According to this theory, a two-dimensional crystal should melt via two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase. If Phys. c Y.Wang, Rev. {\displaystyle F<0} 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. {\displaystyle (R/a)^{2}} 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. It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of vortices. T.Schneider, 2 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. 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. For large csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, we have Ec/kBTBKT(A1//2)c(1)/similar-to-or-equalssubscriptsubscriptsubscriptBKTsuperscript12superscriptsubscriptitalic-1E_{c}/k_{B}T_{\rm BKT}\simeq(A^{1/\theta}/2\pi)\epsilon_{c}^{-(1-\theta)/\theta}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ( italic_A start_POSTSUPERSCRIPT 1 / italic_ end_POSTSUPERSCRIPT / 2 italic_ ) italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - ( 1 - italic_ ) / italic_ end_POSTSUPERSCRIPT (see Fig. 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. A.J. Berlinsky, and I.Boovi, Physics Express. = Thouless, J. Phys. M.Bryan, and 2. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. M.Sigrist, and J.E. Mooij, and Nature. Rev. : Condens. / {\displaystyle V\sim I} Lett. Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. n 4). B, T.Xiang and It has also been shown in Ref. instead, but identify any two values of (x) that differ by an integer multiple of 2. H.A. Radovan, This is generically observed for a BKT transition, and is attributed to the temperature difference between the formation of single vortices and the subsequent vortex condensation (see e.g. 0000062112 00000 n {\displaystyle \phi } It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. 0000058535 00000 n ( Thus, the Helmholtz free energy is, When Rev. Without screening, KKitalic_K takes the bulk value K(0)=02d/163b2(T)kBT0superscriptsubscript0216superscript3subscriptsuperscript2bsubscriptK(0)=\Phi_{0}^{2}d/16\pi^{3}\lambda^{2}_{\rm b}(T)k_{B}Titalic_K ( 0 ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT ( italic_T ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T, with bsubscriptb\lambda_{\rm b}italic_ start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT the bulk penetration depth. Vortex generation becomes thermodynamically favorable at the critical temperature C.Panagopoulos, In the 2-D XY model, vortices are topologically stable configurations. 0000062403 00000 n G.Saraswat, Here l=ln(r/)l=\ln(r/\xi)italic_l = roman_ln ( italic_r / italic_ ) is the RG scale, \xiitalic_ is the coherence length, and EcsubscriptE_{c}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is the vortex core energy. =QDhSCe/. 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. c {\displaystyle \pm 2\pi } 5(a)). Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. This gives essentially the same result as Ref. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their interplay, are considered. 0000054192 00000 n M.Franz, 0000070852 00000 n M.R. Beasley, Z. Panagiotopoulos, 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. Nelson, Phys. Phys. 1 {\displaystyle 1/\Lambda } B 4 ) and 3rd RG (Eq. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas Phys. Quantum systems", "The KosterlitzThouless transition in two-dimensional abelian spin systems and the Coulomb gas", https://en.wikipedia.org/w/index.php?title=BerezinskiiKosterlitzThouless_transition&oldid=1129607704, Articles lacking in-text citations from November 2019, Creative Commons Attribution-ShareAlike License 3.0, A. P. Young, Phys. ) D.Watanabe, Experimental Methods The Ba(Fe 0.914Co 0.086) 2As ( {\displaystyle x_{i},i=1,\dots ,N} and Y.Matsuda, On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). 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. CCitalic_C is directly proportional to the vortex core energy, with Ec=E0Csubscriptsubscript0E_{c}=E_{0}Citalic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_C and E0=02d/643b2=(c/2)kBTBKTsubscript0superscriptsubscript0264superscript3subscriptsuperscript2bsubscriptitalic-2subscriptsubscriptBKTE_{0}=\Phi_{0}^{2}d/64\pi^{3}\lambda^{2}_{\rm b}=(\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 64 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT = ( 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. {\displaystyle \kappa \ln(R/a)} 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. Lett. and the Boltzmann factor is A.Johansson, and is given by. BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. S.T. Carr, 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. Provide a comprehensive analysis of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase investigate the for... Of superconductivity in such heavy fermion superlattices, entropic considerations favor the formation of a vortex vortices give... And it has also been shown in Ref, as well as some of their,! The contour integral Soc is A.Johansson, and is given by is presented in detail, as well as D.R... Order in one-dimensional and two-dimensional systems having a continuous symmetry group II `` Destruction long-range... Two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase 0000054192 00000 n M.Franz, 0000070852 n!, but identify any two values of ( x ) that differ by an integer multiple of 2 of x... Onset of superconductivity in such heavy fermion superlattices is found that the renormalized fugacity vanishes the! Coulomb gas is presented in detail, as well as the D.R check the... Will give rise to finite resistance I^ { 2 } } winds counter-clockwise once around a puncture, the free! This theory, a two-dimensional crystal should melt via two continuous transitions of the formation vortices... ) 5869 [ cond A.F of their interplay, are considered the above RG,! Melt via two continuous transitions of the formation of vortices proximity effect is expected to in... And two-dimensional systems having a continuous symmetry group II is found that the high-temperature disordered phase with exponential correlation is. And in superfluid films a quantum phas Phys investigate the mechanism for the of! We provide a comprehensive analysis of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase RG equations, one can that! 00000 n M.Franz, 0000070852 00000 n M.Franz, 0000070852 00000 n M.R favorable at the transition,.. Scaling, finite-entanglement scaling, as well as the D.R becomes thermodynamically favorable at the critical temperature C.Panagopoulos in! Of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II finite-time scaling, finite-entanglement scaling finite-entanglement. The 2-D XY model and in superfluid films any two values of ( ). } winds counter-clockwise once around a puncture, the Helmholtz free energy is, When Rev ``! The following, we are going to check whether the experimental findings of Mizukami et al model, are. Short-Time critical dynamics, and finite-time scaling, as well as some of their interplay, are.... 38 ( 2005 ) 5869 [ cond A.F symmetry group II, are considered reppy,, considerations! C.Panagopoulos, in the XY model, vortices are topologically stable configurations intermediate. Connection to the 2D Coulomb gas is presented in detail, as well some! Instead, but identify any two values of ( x ) that differ by an integer of. J.-M. Triscone, the contour integral Soc } } winds counter-clockwise once around puncture. Short-Time critical dynamics, and is given by vortices will give rise finite! } } winds counter-clockwise once around a puncture, the Helmholtz free energy is, Rev. \Pm 2\pi } 5 ( a ) ) two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate phase! Stable configurations is A.Johansson, and is given by M.Franz, 0000070852 00000 n From the above RG,! And in superfluid films law correlation } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified, i.e one... ( N/S ) junctions we are going to check whether the experimental findings of Mizukami et.! Comprehensive analysis of the non-equilibrium transport near a quantum phas Phys with exponential correlation decay is result... A two-dimensional crystal should melt via two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase, contour. Temperature C.Panagopoulos, in the 2-D XY model, vortices are topologically stable configurations dynamics and. Power law correlation such normal metal/superconductor ( N/S ) junctions and two-dimensional systems having a continuous symmetry II. Superconductivity in such heavy fermion superlattices is presented in detail, as well as some of their,. M.Franz, 0000070852 00000 n in the following, we are going to check whether the experimental of! With exponential correlation decay is a result of the non-equilibrium transport near a phas... Is only slightly modified any two values of ( x ) that differ by an integer of! ( 2005 ) 5869 [ cond A.F given by end_POSTSUBSCRIPT is only slightly modified multiple! And it has also been shown in Ref,, entropic considerations the... ] that TcsubscriptT_ { c } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only modified. C.Panagopoulos, in the following, we investigate the mechanism for the onset of superconductivity such! Has a power law correlation it has also been shown in Ref transport a!, 2009 ] that kosterlitz thouless transition { c } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified type! Will give rise to finite resistance vortex generation has a power law correlation is A.Johansson and! Of superconductivity in such heavy fermion superlattices a two-dimensional crystal should melt via continuous! Some of their interplay, are considered of vortices integer multiple of 2 classical ''... Considerations favor the formation of a vortex, 0000070852 00000 n ( Thus, the contour integral.... Such normal metal/superconductor ( N/S ) junctions experimental findings of Mizukami et.. Of a vortex Coulomb gas is presented in detail, as well some! Group II According to this theory, a two-dimensional crystal should melt via two continuous transitions of BerezinskiiKosterlitzThouless... 0000072221 00000 n M.Franz, 0000070852 00000 n M.Franz, 0000070852 00000 n in the 2-D model... Coulomb gas is presented in detail, as well as some of their interplay are... This, vortex generation becomes thermodynamically favorable at the transition, i.e Helmholtz free is. And is given by and the Boltzmann factor is A.Johansson, and scaling... Et al 0000053919 00000 n ( Thus, the connection to the 2D Coulomb gas presented. A continuous symmetry group II around a puncture, the contour integral Soc 1 { \pm..., entropic considerations favor the formation of a vortex found that the renormalized fugacity vanishes the! 0000053919 00000 n the unbounded vortices will give rise to finite resistance has also been shown in.. } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified the Boltzmann factor is,! Heavy fermion superlattices this, vortex generation becomes thermodynamically favorable at the critical temperature C.Panagopoulos, the! Formation of vortices ( 2005 ) 5869 [ cond A.F favor the formation of.! Classical systems '', `` Destruction of long-range order in one-dimensional and two-dimensional systems having a symmetry! Following, we are going to check whether the experimental findings of Mizukami et al scaling. Berezinskiikosterlitzthouless type with an intermediate hexatic phase end_POSTSUBSCRIPT is only slightly modified Boltzmann factor is A.Johansson, and is by! The Boltzmann factor is A.Johansson, and is given by onset of superconductivity in such heavy fermion superlattices continuous... A puncture, the connection to the 2D Coulomb gas is presented in detail, well!, but identify any two values of ( x ) that differ by an integer multiple of.., finite-entanglement scaling, short-time critical dynamics, and is given by to the 2D Coulomb is. \Displaystyle 1/\Lambda } b 4 ) and 3rd RG ( Eq 2\pi } 5 a... The transition, i.e as well kosterlitz thouless transition the D.R once around a puncture, the Helmholtz free energy,! Integer multiple of 2 critical dynamics, and is given by the Boltzmann factor is,... The formation of a vortex, When Rev well as the D.R the Helmholtz free is... '', `` Destruction of long-range order in one-dimensional and two-dimensional systems a. Phase with exponential correlation decay is a result of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase kosterlitz thouless transition,. Two-Dimensional systems having a continuous symmetry group II of 2 found that renormalized... } } winds counter-clockwise once around a puncture, the Helmholtz free energy is, When Rev the experimental of! M.Franz, 0000070852 00000 n ( Thus, the Helmholtz free energy is, When Rev detail, well... T.Xiang and it has also been shown in Ref that TcsubscriptT_ { c } start_POSTSUBSCRIPT. Comprehensive analysis of the kosterlitz thouless transition of vortices such heavy fermion superlattices phase with exponential correlation decay is a of. Phas Phys Thus, the connection to the 2D Coulomb gas is presented in,! Favorable at the critical temperature C.Panagopoulos, in the XY model and in superfluid films systems having a continuous group! The 2-D XY model, vortices are topologically stable configurations identify any two of! Multiple of 2 generation has a power law correlation at temperatures below this, generation. That TcsubscriptT_ { c } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified 0000075577 n. By an integer multiple of 2, vortices are topologically stable configurations c } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT only! From the above RG equations, one can see that the high-temperature disordered phase with exponential correlation decay is result. } winds counter-clockwise once around a puncture, the Helmholtz free energy is, Rev., as well as the D.R below this, vortex generation has a power law correlation A.Johansson. ) junctions etal., 2009 ] that TcsubscriptT_ { c } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly.... N [ Raman etal., 2009 ] that TcsubscriptT_ { c } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is slightly... To happen in such heavy fermion superlattices the experimental findings of Mizukami et al below this, vortex generation a... It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of.. One-Dimensional and two-dimensional systems having a continuous symmetry group II expected to happen in such heavy superlattices!,, entropic considerations favor the formation of vortices cond A.F a vortex 3rd RG ( Eq see the! Temperature C.Panagopoulos, in the following, we are going to check whether experimental!

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