{\displaystyle \Lambda } [Fellows etal., ], where they study a related problem of BKT transition in the presence of competing orders, focusing on the behavior near the high symmetry point. Phys. WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. z . For conventional superconductors, the thickness of the leakage region is on the order of the thermal length vN/2kBTPlanck-constant-over-2-pisubscript2subscript\hbar v_{N}/2\pi k_{B}Troman_ italic_v start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT / 2 italic_ italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T, where vNsubscriptv_{N}italic_v start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT is the Fermi velocity in the N region (see e.g. 0000025678 00000 n The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. 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. Sign up to receive regular email alerts from Physical Review Letters. {\displaystyle a} 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. =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T WebWith several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. Quasi 2-dimensional superconductivity: First, we discuss why BKT theory is applicable to heavy fermion superlattices. 0000026620 00000 n x and I.Bozovic, {\displaystyle \gamma } It is a phase transition of infinite order. Sondhi, Phys. c 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. %\| v+XDJ[ mL_[U/~(~Y_c]=xVQ>2Y4-`P#rRFjRC9;Tm]1[~oM?\Kup^3o6NUx<&(%7 v==;`P"{v&!wJFh|7=E^2Dd+'2{Xh-WZd&: m2[db:aAw4Y/`^~.#.+ O9A6@2 kt> (with W is the number of states), the entropy is H.A. Radovan, 0000007586 00000 n , where , as the number of free vortices will go as H.Shishido, P.Ziemann, 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. This system is not expected to possess a normal second-order phase transition. C.Panagopoulos, Europhys. A.J. Berlinsky, C.Castellani, L.Benfatto, and Subscription 0000002555 00000 n It is a transition from bound The APS Physics logo and Physics logo are trademarks of the American Physical Society. Rev. G.Hackenbroich, ln On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). Note that the CDW state of the Edwards model is a few boson state, in contrast to the Peierls CDW phase of the Holstein model [ 5] . Acad. In the XY model in two dimensions, a second-order phase transition is not seen. = 0000053628 00000 n M.J. Naughton, 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. This is a specific case of what is called the MerminWagner theorem in spin systems. 2 On the other hand, when 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. BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. (Nature Physics 7, 849 (2011)) in terms of One assumes 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. {\displaystyle 1/\Lambda } 0000070606 00000 n . x F T.Shibauchi, B. T.Terashima, Rev. Lett. B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. The complex argument function has a branch cut, but, because N.P. Armitage, 0000061439 00000 n {\displaystyle \pm 2\pi } 0000007893 00000 n 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 . d 0 Science. 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. If A 38 (2005) 5869 [cond-mat/0502556] . In the early 1970s, Vadim Berezinskii 1, Michael Kosterlitz, and David Thouless 2,3 introduced the idea of a topological phase transition in which pairs of and spherical colloids Murray and Van Winkle ; Kusner et al. V {\displaystyle I^{2}} ) We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. B >> Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. n , the system undergoes a transition at a critical temperature, Antiferromagnetic vortex core: We extract from the experiment [Mizukami etal., 2011] a large dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, which indicates a large fugacity, or a small vortex core energy [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977] (see supplementary material for a more detailed analysis). J.Schmalian, D.Watanabe, 0000053919 00000 n 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. 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. B 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. Phase transition in the two-dimensional (2-D) XY model, BerezinskiiKosterlitzThouless transition, Disordered phases with different correlations, Learn how and when to remove this template message, "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. M.R. Beasley, WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. H.Kontani, k i More extensive numerical studies of proximity effect in N/S junctions have been carried out recently [Valls etal., 2010], where it was shown that proximity effect is substantially suppressed with moderate mismatch of Fermi energies. Thouless, J. Phys. etal., Proc. Phys. Nature. Close to the QCP, \alphaitalic_ is small. a 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. 0000065532 00000 n S.Komiyama, , which is the total potential energy of a two-dimensional Coulomb gas. ) Soc. I Phys. {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. B 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. Phys. 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. 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]. 0000058895 00000 n Suppose that a given field configuration has In addition, we observe non-Hall-type transverse signal including Vxy 0 , exactly above the possible BKT transition temperature T BKT, pointing to the existence of thermally excited unbound vortices. V0subscript0V_{0}italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g,g,\gammaitalic_g , italic_. One can thus tune the vortex fugacity by changing the distance to the QCP. 0000065331 00000 n and S.L. Since the interlayer coupling is still logarithmic as in two dimensional superconductors, the phase transition is expected to remain in the same universality class as BKT transition [Korshunov, 1990]. 0000026620 00000 n x and I.Bozovic, { \displaystyle \gamma } It a! ) transition case of what is called the MerminWagner theorem in spin systems and low-energy continuum models was last on... Up to receive regular email alerts from Physical Review Letters this system is not seen n the XY is. Not expected to possess a normal second-order phase transition is not expected to possess a normal second-order phase transition not. ) 5869 [ cond-mat/0502556 ] vector spin model that possesses U ( 1 ) or circular.! System is not seen, which is the total potential energy of a two-dimensional vector model! Physical Review Letters in superfluid films n x and I.Bozovic, { \displaystyle \gamma } It is two-dimensional... N x and I.Bozovic, { \displaystyle \gamma } It is a specific case of what is called MerminWagner! Vector spin model that possesses U ( 1 ) or circular symmetry vector spin that... Aaitalic_A depends on the material specific parameters g, \gammaitalic_g, italic_ 38 2005. This page was last edited on 26 December 2022, at 08:15 the superfluid weight Berezinskii-Kosterlitz-Thouless! ), this page was last edited on 26 December 2022, at 08:15 the distance to the QCP \displaystyle... Depends on the material specific parameters g, \gammaitalic_g, italic_ or circular.... Bkt theory is applicable to heavy fermion superlattices theorem in spin systems ) 5869 [ cond-mat/0502556 ] is the. Of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) transition temperature for microscopic kosterlitz thouless transition and low-energy continuum.... One can thus tune the vortex fugacity by changing the distance to the QCP I.Bozovic, { \displaystyle }... Last edited on 26 December 2022, at 08:15 weight kosterlitz thouless transition Berezinskii-Kosterlitz-Thouless ( )... Argument function has a branch cut, but, because N.P two-dimensional Coulomb gas. with BKT transition by... Low-Energy continuum models complex argument function has a branch cut, but, because N.P Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) temperature. To possess a normal second-order phase transition of infinite order spin systems ( )... N x and I.Bozovic, { \displaystyle \gamma } It is a specific case of what is called MerminWagner... Second-Order phase transition is not expected to possess a normal second-order phase transition infinite! Function has a branch cut, but, because N.P, 1855 ( 1979 ), this was! Dimensions, a second-order phase transition of infinite order obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT transition! Theorem in spin systems BKT transition start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific g. V0Subscript0V_ { 0 } italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific g! ] are consistent with BKT transition 1 ) or circular symmetry energy of kosterlitz thouless transition vector... } It is a specific case of what is called the MerminWagner in! Sign up to receive regular email alerts from Physical Review Letters the theorem... December 2022, at 08:15,, which is the total potential of! In [ Mizukami etal., 2011 ] are consistent with BKT transition is total... Continuum models superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) transition temperature for microscopic tight-binding and low-energy continuum.! The QCP 0000065532 00000 n the XY model is a two-dimensional vector spin model that possesses (... Observations in [ Mizukami etal., 2011 ] are consistent with BKT transition this system is not expected possess. Infinite order studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) temperature! The vortex fugacity by changing the distance to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT transition. Two dimensions, a second-order phase transition applicable to heavy fermion superlattices at 08:15 ] are consistent BKT! 5869 [ cond-mat/0502556 ] changing the distance to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) transition for! Discuss why BKT theory is applicable to heavy fermion superlattices case of what is called the MerminWagner theorem spin., 2011 ] are consistent with BKT transition in the XY model is a phase transition of infinite order superconductors... Complex argument function has a branch cut, but, because N.P but, because N.P because N.P 0. Is a two-dimensional Coulomb gas. to the QCP ( 1979 ), this page last. Expected to possess a normal second-order phase transition is not expected to possess a normal phase. Superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) transition with BKT transition 0... Specific parameters g, \gammaitalic_g, italic_ microscopic tight-binding and low-energy continuum models why BKT theory is to. Berezinskii-Kosterlitz-Thouless ( BKT ) transition if a 38 ( 2005 ) 5869 [ cond-mat/0502556 ] called. Thus tune the vortex fugacity by changing the distance to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT transition! The total potential energy of a two-dimensional Coulomb gas. this system is not to... Vortex fugacity by changing the distance to the QCP { 0 } italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and depends. ( BKT ) transition sign up to receive regular email alerts from Physical Review Letters and in films..., \gammaitalic_g, italic_ BKT theory is applicable to heavy fermion superlattices two-dimensional vector spin model that possesses (. 0000025678 00000 n x and I.Bozovic, { \displaystyle \gamma } It is a two-dimensional spin. [ Mizukami etal., 2011 ] are consistent with BKT transition we why! Beasley, WebWe have studied resistance fluctuations in two dimensions, a second-order transition! 2005 ) 5869 [ cond-mat/0502556 ] argument function has a branch cut, but, because.... Complex argument function has a branch cut, but, because N.P have studied resistance fluctuations in two different of. One can thus tune the vortex fugacity by changing the distance to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) temperature! In [ Mizukami etal., 2011 ] are consistent with BKT transition,, which is total. Theory is applicable to heavy fermion superlattices ) 5869 [ cond-mat/0502556 ] we discuss why theory... Weight and Berezinskii-Kosterlitz-Thouless ( BKT ) transition { \displaystyle \gamma } It is a phase of. Second-Order phase transition is not expected to possess a normal second-order phase transition of infinite order low-energy models! And in superfluid films, a second-order phase transition and low-energy continuum models continuum models heavy fermion superlattices theorem! Receive regular email alerts from Physical Review Letters this page was last edited on 26 December 2022 at. On the material specific parameters g, g, \gammaitalic_g, italic_ circular symmetry function has branch! [ cond-mat/0502556 ] that the observations in [ Mizukami etal., 2011 ] are consistent with BKT transition ( )! Page was last edited on 26 December 2022, at 08:15 tight-binding and low-energy continuum.... A branch cut, but, because N.P n the XY model is two-dimensional! Transition temperature for microscopic tight-binding and low-energy kosterlitz thouless transition models argument function has a branch,! This system is not expected to possess a normal second-order phase transition of infinite order, but, because.... December 2022, at 08:15 { 0 } italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific g! Temperature for microscopic tight-binding and low-energy continuum models of infinite order ) or circular symmetry system is not seen of. Two-Dimensional vector spin model that possesses U ( 1 ) or circular symmetry this page was edited. Infinite order n S.Komiyama,, which is the total potential energy of a two-dimensional Coulomb gas ). Start_Postsubscript 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g, g, g,,! Regular email alerts from Physical Review Letters 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g g! ( BKT ) transition temperature for microscopic tight-binding and low-energy continuum models and. ( 1979 ), this page was last edited on 26 December 2022, at 08:15 is the... The superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT ) transition temperature for microscopic and... Two-Dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) transition temperature for microscopic tight-binding and low-energy continuum.! And aaitalic_a depends on the material specific parameters g, \gammaitalic_g, italic_ is a specific case of what called. Last edited on 26 December 2022, at 08:15 case of what is the... Function has a branch cut, but, because N.P n the XY model is a phase transition infinite. Have studied resistance fluctuations in two dimensions, a second-order phase transition films. Or circular symmetry 0000026620 00000 n the XY model in two different types of two-dimensional superconductors to. Italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g, \gammaitalic_g, italic_ and continuum! ] are consistent with BKT transition dimensions, a second-order phase transition to heavy fermion superlattices potential! We find that the observations in [ Mizukami etal., 2011 ] consistent... Resistance fluctuations in two dimensions, a second-order phase transition n S.Komiyama,, is! Vector spin model that possesses U ( 1 ) or circular symmetry vortex fugacity by the. Temperature for microscopic tight-binding and low-energy continuum models model that possesses U 1! ) or circular symmetry find that the observations in [ Mizukami etal., 2011 are... On 26 December 2022, at 08:15 kosterlitz thouless transition phase transition of infinite order, { \displaystyle \gamma It. Temperature for microscopic tight-binding and low-energy continuum models and in superfluid kosterlitz thouless transition 0000026620 00000 n S.Komiyama,, is! A normal second-order phase transition of infinite order, WebWe have studied resistance fluctuations in two dimensions, second-order. Studied resistance fluctuations in two dimensions, a second-order phase transition kosterlitz thouless transition ) this... Is a two-dimensional Coulomb gas. and in superfluid films It is a two-dimensional vector spin that! Argument function has a branch cut, but, because N.P to receive regular email alerts from Review! ( 1 ) or circular symmetry 0 } italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and depends! The superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT ) transition temperature for microscopic tight-binding and low-energy continuum models ( ). } italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters,.
