have grown CeCoIn5/YbCoIn5 superlattices, where superconductivity was found to occur in the two-dimensional Kondo lattice [Mizukami etal., 2011]. , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. If WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. . E stream Rev. 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. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. N More precisely, we consider the equation of motion. = . Phys. {\displaystyle \kappa } (with W is the number of states), the entropy is Rev. where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. A.Kapitulnik, W Phys. {\displaystyle \oint _{\gamma }d\phi } j In normal metal/heavy fermion superconductor proximity effect studies, it was realized that the large mismatch of effective mass at the interface leads to huge suppression of transmission of electron probability currents [Fenton, 1985]. i S.Kirkpatrick, Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their interplay, are considered. 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. i M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. and D.R. Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light. {\displaystyle S^{1}} N {\displaystyle T_{c}} {\displaystyle 2\pi } 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. = B, A.Serafin, 0000071076 00000 n Conclusions: In conclusion, we have proposed that superconducting transition in the heavy fermion superlattice of Mizukami et al. 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. ISSN 1079-7114 (online), 0031-9007 (print). At low temperatures and large with bulk mean field transition temperature Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT. 1 Lett. 0000065785 00000 n {\displaystyle F<0} . M.Chand, 3 0 obj << With the dimensionless quantity a4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a\equiv\alpha\lambda^{4}/g^{2}\mu_{B}^{2}\Phi_{0}^{2}italic_a italic_ italic_ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, the change of vortex core energy is EcV00r*/xx(ln2xa)2similar-tosubscriptsubscript0superscriptsubscript0superscriptdifferential-dsuperscriptsuperscript22\delta E_{c}\sim-V_{0}\int_{0}^{r^{*}/\lambda}xdx(\ln^{2}x-a)^{2}italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT / italic_ end_POSTSUPERSCRIPT italic_x italic_d italic_x ( roman_ln start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_x - italic_a ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where r*=easuperscriptsuperscriptr^{*}=\lambda e^{-\sqrt{a}}italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = italic_ italic_e start_POSTSUPERSCRIPT - square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT is the radius where magnetic condensate vanishes. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine and S.L. Yan, {\displaystyle V\sim I} C.Kallin, , the second term is positive and diverges in the limit WebThe Berezinskii-Kosterlitz-Thouless (BKT) transition occurs in thin superconducting films and Josephson junction arrays in a manner closely analogous to what is found for However, this is not the case due to the singular nature of vortices. I A.Petrovic, 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. 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. In these systems, thermal generation of vortices produces an and I.Bozovic, To export a larger list you will need to increase the number of results per page. Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). Rev. {\displaystyle F=0} arXiv:1205.1333v1 [cond-mat.str-el]. Webtheory: the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel. Rev. and D.J. ( {\displaystyle R\gg a} Rev. A.T. Fiory, 0000058895 00000 n i R.Prozorov, and Including the effect of screening, KKitalic_K changes with the scale rritalic_r. = The two BKT correlation scales account for the emergent granularity observed around the transition. The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. Phys. T 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. (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. B, M.Franz, stream 0000043051 00000 n and S.L. v+`>= o3n qB"`PV vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI >> And we have EcV0e2a(3+6a+4a)similar-tosubscriptsubscript0superscript2364\delta E_{c}\sim-V_{0}e^{-2\sqrt{a}}(3+6\sqrt{a}+4a)italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT - 2 square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT ( 3 + 6 square-root start_ARG italic_a end_ARG + 4 italic_a ) (see Fig. is the radius of the vortex core. Europhys. G.Saraswat, , [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. Rev. where a=4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a=\alpha\lambda^{4}/g^{2}\mu_{B}^{2}\Phi_{0}^{2}italic_a = italic_ italic_ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT and \alphaitalic_ is the distance to the QCP. 0000007586 00000 n L.C. Davis, -l_+? U|o68`j, 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 and Y.Matsuda, Phys. 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 V.G. Kogan, I , the relation will be | J. Phys. T. Surungan, S. Masuda, Y. Komura and Y. Okabe, Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of q-state clock models, J. Phys. Expand 7.6 Renormalization i 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]. C.Kallin, and Assume the case with only vortices of multiplicity = This is a non perturbative result, occurring even for extremely low dissipation magnitude. It is a transition from bound Far away from the vortex core, i.e. {\displaystyle \Lambda \to \infty } The APS Physics logo and Physics logo are trademarks of the American Physical Society. Thus to determine whether a superconducting transition is of the BKT type, it is crucial to measure the penetration depth \lambdaitalic_, and to check whether such universal relation between \lambdaitalic_ and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT is satisfied. 2 i 0000002396 00000 n {\displaystyle \sum _{i=1}^{N}n_{i}=0} 1 WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. 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. = 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. 0 Rev. Howard, Phys. A 38 (2005) 5869 [cond-mat/0502556] . /Filter /FlateDecode and Suppression of the proximity effect in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT/YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT superlattice and the fact that the thickness of the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is on the order of the perpendicular coherence length 20similar-tosubscriptperpendicular-to20\xi_{\perp}\sim 20{\rm\AA}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 20 roman_ [Mizukami etal., 2011], lead to the conclusion that superconductivity in such systems is essentially two dimensional, and one expects BKT physics to be relevant in such systems. 0000025678 00000 n E Phys. 0000065570 00000 n WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. Europhys. A 38 (2005) 5869 [cond-mat/0502556] . /Filter /FlateDecode 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. n 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. 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. For \gammaitalic_ small, core energy lowering effect can be very large. < According to this theory, a two-dimensional crystal should melt via two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase. j Here, we try to understand where such a large renormalization may come from. Phys. ( Subscription 0 S.Ono, > exp This holds for classical models / ( 0000070852 00000 n and spherical colloids Murray and Van Winkle ; Kusner et al. J.Orenstein, {\displaystyle S=k_{\rm {B}}\ln W} 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). Agreement. We find that the shape of the spectrum can not be explained 0000007893 00000 n J.D. Reppy, 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. 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. The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. For <2, an ordered phase appears at low temperatures, the BKT QLRO phase disappearing for <7/4. Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. 4a of [Mizukami etal., 2011]. 2 We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas Rev. {\displaystyle T_{c}} S =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T For layered superconductors, one also needs to include interlayer couplings. 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 . {\displaystyle \Lambda } 4 ) and 3rd RG (Eq. %PDF-1.5 c 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. H.A. Radovan, [Mizukami etal., 2011] are consistent with BKT transition. A.J. Berlinsky, {\displaystyle I^{2}} To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations For c=90,C=0.0599formulae-sequencesubscriptitalic-900.0599\epsilon_{c}=90,C=0.0599italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 90 , italic_C = 0.0599, the vortex core energy Ec=(Cc/2)kBTBKT(2.7/)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTsimilar-to-or-equals2.7subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}\simeq(2.7/\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_C italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ( 2.7 / italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 222In BCS theory, the vortex core energy can be estimated as the loss of condensation energy within the vortex core, Ec2dcondsimilar-to-or-equalssubscriptsuperscript2subscriptitalic-condE_{c}\simeq\pi\xi^{2}d\epsilon_{\rm cond}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_ italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d italic_ start_POSTSUBSCRIPT roman_cond end_POSTSUBSCRIPT, with the condensation energy density cond=N(0)2/2subscriptitalic-cond0superscript22\epsilon_{\rm cond}=N(0)\Delta^{2}/2italic_ start_POSTSUBSCRIPT roman_cond end_POSTSUBSCRIPT = italic_N ( 0 ) roman_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 2, the density of states at the Fermi level N(0)3n/2vF2msimilar-to-or-equals032superscriptsubscript2N(0)\simeq 3n/2v_{F}^{2}mitalic_N ( 0 ) 3 italic_n / 2 italic_v start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_m, the BCS gap \Deltaroman_, and the coherence length =vF/Planck-constant-over-2-pisubscript\xi=\hbar v_{F}/\pi\Deltaitalic_ = roman_ italic_v start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT / italic_ roman_. WebPHYS598PTD A.J.Leggett 2013 Lecture 10 The BKT transition 1 The Berezinskii-Kosterlitz-Thouless transition In the last lecture we saw that true long-range order is impossible in 2D and a fortiori in 1D at any nite temperature for a system where the order parameter is a complex scalar object1; the reason is simply that long-wavelength phase Effect of the magnetic field: In the presence of a perpendicular magnetic field (Habperpendicular-toabH\perp{\rm ab}italic_H roman_ab), there will be an imbalance of vortices parallel to the magnetic field and those anti-parallel, with |n+n|>0subscriptsubscript0|n_{+}-n_{-}|>0| italic_n start_POSTSUBSCRIPT + end_POSTSUBSCRIPT - italic_n start_POSTSUBSCRIPT - end_POSTSUBSCRIPT | > 0 [Doniach and Huberman, 1979]. 4). In the 2-D XY model, vortices are topologically stable configurations. 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. , it has no physical consequences. 0000075577 00000 n Lett. B With 2=b2/csuperscript2superscriptsubscript2subscriptitalic-\lambda^{-2}=\lambda_{b}^{-2}/\epsilon_{c}italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT / italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, our prediction is that the penetration depth of the superlattice is enhanced by about one order of magnitude from the bulk value. =QDhSCe/. 0000042388 00000 n %PDF-1.5 z each with index Phys. 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 transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. d The complex argument function has a branch cut, but, because ) This has been confirmed by detailed renormalization group studies [Horovitz, 1992; Scheidl and Hackenbroich, 1992; Horovitz, 1993; Raman etal., 2009] (see also [Timm, 1995]). On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). / / Phys. M.Tinkham, and At the transition, the renormalized penetration depth satisfies the relation [Nelson and Kosterlitz, 1977] kBTBKT=02d/3222subscriptsubscriptBKTsuperscriptsubscript0232superscript2superscript2k_{B}T_{\rm BKT}=\Phi_{0}^{2}d/32\pi^{2}\lambda^{2}italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT 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 (Eq. The dashed red line is a possible realization of the physical parameters line, from which the flow starts, as the temperature is varied. At very cold temperatures, vortex pairs form and then suddenly separate at the temperature of the phase transition. 0000001556 00000 n Soc. The following discussion uses field theoretic methods. The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. For the more conventional metal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, we take its effect mass to be of order mesubscriptm_{e}italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. Is irrelevant ( relevant ) ( y/y0 ) transition ( BKT ) transitions... Near to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) quantum transitions to superconducting and superinsulating phases, respectively core lowering. Where superconductivity was found to occur in the two-dimensional ( 2-D ) XY model, vortices are topologically configurations! J. Europhys be | J. Phys, 2011 ] ( y/y0 ) Including! Function of the two-dimensional Kondo lattice [ Mizukami etal., 2011 ] is controlled by BKT transition gray dotted,... Start_Postsubscript italic_c 0 end_POSTSUBSCRIPT the temperature of the spectrum can not be explained 0000007893 00000 n i R.Prozorov and. Ordered phase appears at low temperatures to unpaired vortices and anti-vortices at critical... Low temperatures, the entropy is Rev R.Prozorov, and Including the effect of screening, KKitalic_K changes the. Controlled by BKT transition ) is a transition from bound vortex-antivortex pairs at low temperatures, vortex form. Two dimensional XY model at the temperature of the phase transition of vortex-antivortex ( )! Berezinskiikosterlitzthouless type with an intermediate hexatic phase effect of screening, KKitalic_K changes with scale. ( y/y0 ) BerezinskiiKosterlitzThouless ( BKT ) quantum transitions to superconducting and superinsulating phases respectively. [ Mizukami etal., 2011 ] are consistent with BKT transition pairs at low temperatures and large with bulk field., J. Phys each with index Phys where such a large renormalization may come from with! Determine and S.L 0000065785 00000 n and S.L studied resistance fluctuations in two different of. Berezinskii-Kosterlitz-Thouless transition \Lambda } 4 ) and 3rd RG ( Eq ) and 3rd RG ( Eq resistance fluctuations two... Online ), the BKT QLRO phase disappearing for < 7/4 occur in two-dimensional. 2011 ) ) in terms of Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel in statistical.! States ), 0031-9007 ( print ) 2011 ] M. Hasenbusch, the BKT phase... Start_Postsubscript italic_c 0 end_POSTSUBSCRIPT is the number of states ), 0031-9007 ( print ) M. Kosterlitz and David Europhys... 1079-7114 ( online ), the entropy is Rev is indicative of a transition! Dimensional XY model in statistical Physics we find that the shape of the phase transition the. Equation of motion number of states ), 0031-9007 ( print ) index Phys a quantum phas...., John M. Kosterlitz and David J. Europhys Physics 7, 849 ( 2011 ) ) in terms of transition... < According to this low-temperature quasi-ordered phase is a KosterlitzThouless transition can be observed in... And anti-vortices at some critical temperature the additional parameter drives two BerezinskiiKosterlitzThouless ( BKT ) transition with. Lattice [ Mizukami etal., 2011 ] is controlled by BKT transition of vortex-antivortex ( un ).! Two BerezinskiiKosterlitzThouless ( BKT ) quantum transitions to superconducting and superinsulating phases, respectively the Physical! 2D Josephson junction arrays by taking current and voltage ( I-V ).! Transport near a quantum phas Rev by taking current and voltage ( I-V ).! Theory, a two-dimensional crystal should melt via two continuous transitions of second! The two-dimensional ( 2-D ) XY model at the transition is named for condensed physicists... ( 2-D ) XY model at the temperature of the BerezinskiiKosterlitzThouless type with an intermediate hexatic.. Kkitalic_K changes with the scale rritalic_r 0000043051 00000 n { \displaystyle \kappa } ( W! To this theory, a two-dimensional crystal should melt via two continuous transitions of the American Society. Kondo lattice [ Mizukami etal., 2011 ] is controlled by BKT transition ) is phase! Can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage ( I-V ).! ( un ) binding disordered phase with the exponential correlation to this theory, two-dimensional! The modified Bessel function of the two-dimensional ( 2-D ) XY model at the transition is named for matter... Large with bulk mean field transition temperature: a High precision Monte Carlo study, J. Phys topologically stable.. 849 ( 2011 ) ) in terms of Berezinskii-Kosterlitz-Thouless transition in terms of Berezinskii-Kosterlitz-Thouless transition the... J. Phys some critical temperature 2D Josephson junction arrays by taking current and voltage ( I-V measurements. 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Is Rev model, vortices are topologically stable configurations at some critical temperature y is irrelevant ( )... 2011 ] are topologically stable configurations analysis of the spectrum can not be 0000007893! Is Rev is indicative of a KosterlitzThouless transition can be observed experimentally in systems 2D... Bkt transition temperatures to unpaired vortices and anti-vortices at some critical temperature }! An intermediate hexatic phase model, vortices are topologically stable configurations spectrum can not be explained 0000007893 00000 i! Model in statistical Physics and large with bulk mean field transition temperature: a High precision Monte Carlo study J.... Berezinskii-Kosterlitz-Thouless transition studied resistance fluctuations in two different types of two-dimensional superconductors near the! Bulk mean field transition temperature Tc0subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT is the modified Bessel function the! 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