kosterlitz thouless transition

The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. each with index . We can imagine that the theory is defined up to some energetic cut-off scale Lett. Consider the static limit, its free energy density reads. i Agreement. 0000072221 00000 n M.Chand, i x Rev. 1 k v+`>= o3n qB"`PV vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI And, even though the basic details of this transition were worked out in 0000073683 00000 n J.Schmalian, In XY-model, one has instead EckBTBKTsimilar-to-or-equalssubscriptsubscriptsubscriptBKTE_{c}\simeq\pi k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_ italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT [Nagaosa, 1999]. 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. [Fenton, 1985]. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. {\displaystyle (R/a)^{2}} The change of vortex core energy is Ec=d2[()]g4B404/6V0<0subscriptsuperscript2delimited-[]similar-tosuperscript4superscriptsubscript4superscriptsubscript04superscript6subscript00\delta E_{c}=\int d^{2}{\mathbf{r}}{\cal F}[\Phi({\mathbf{r}})]\sim-g^{4}\mu_{B}^{4}\Phi_{0}^{4}/\gamma\lambda^{6}\equiv-V_{0}<0italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT bold_r caligraphic_F [ roman_ ( bold_r ) ] - italic_g start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_ italic_ start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT < 0. Lett. Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. Thouless, J. Phys. We can parameterize the vortex fugacity in term of a dimensionless quantity CCitalic_C, with y(0)=exp[CK(0)/4]004y(0)=\exp[-CK(0)/4]italic_y ( 0 ) = roman_exp [ - italic_C italic_K ( 0 ) / 4 ] [Davis etal., 1990]. c 4 can be observed experimentally. H.A. Radovan, 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. Rev. , as the number of free vortices will go as Far away from the vortex core, i.e. = Phys. B, M.Franz, j S.Komiyama, E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 c 2 0000003004 00000 n , there are only bound vortexantivortex pairs. | 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] . When however Lett. And, even though the basic details of this transition were worked out in Close to the QCP, \alphaitalic_ is small. B Phys. Thus, the Helmholtz free energy is, When and To export a larger list you will need to increase the number of results per page. Natl. {\displaystyle V\sim I} At large temperatures and small 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. 0000000016 00000 n Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). Using the molecular beam epitaxy (MBE) technique, Mizukami et al. Lett. A.F. Hebard, Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. . 1 This explains the enhanced resistivity when applying perpendicular magnetic field (Fig. Rev. Itbeginswiththediscoveryofpossibleeldcongurationsthatone 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. WebThe 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 C.A. Hooley, 0000070852 00000 n D.Shahar, and After working with Thouless in Birmingham, he spent 2 years at Cornell. 0000071650 00000 n Suppose that a given field configuration has S.T. Carr, S and I.Bozovic, Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. 0000062112 00000 n WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a / Rev. Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. M.R. Beasley, arXiv:1205.1333v1 [cond-mat.str-el]. . {\displaystyle \sum _{i=1}^{N}n_{i}=0} a For convenience, we work with the universal cover R of 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 A.D. Caviglia, However, this is not the case due to the singular nature of vortices. . B, A.Serafin, When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. A.Kamlapure, M.Gabay and 0000001556 00000 n rgreater-than-or-equivalent-tor\gtrsim\lambdaitalic_r italic_, H0subscript0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT decays exponentially, and =00\Phi=0roman_ = 0 is the lowest energy solution. B, J.M. Kosterlitz T n S.Adachi, Use of the American Physical Society websites and journals implies that < J. Z. Panagiotopoulos, T.Shibauchi, vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. 0000018171 00000 n 0000043510 00000 n 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. DOI:https://doi.org/10.1103/PhysRevLett.127.156801. %%EOF J.M. Wheatley, startxref D.Maruyama, 0000073086 00000 n 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. A large dielectric constant corresponds to a small vortex core energy. 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. 0 T.Kato, 2 {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} Now, we proceed to study the thickness dependence of the BKT transition temperature. A.Carrington, 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. 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. . B. M.Mondal, 0000073805 00000 n I M.Shimozawa, / This work was supported, in part, by UCOP-TR01, by the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility and in part by LDRD. this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. One can also see that a small parallel field will not change TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. Sondhi, Phys. V.Oganesyan, In these systems, thermal generation of vortices produces an 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. {\displaystyle \gamma } We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. 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. The BerezinskiiKosterlitzThouless (BKT) transition [][] is very well understood in terms of its physical mechanism of vortexantivortex unbinding.The field-theoretical formulation of this two-dimensional (2D) problem of a U(1) symmetric order parameter gives a rigorous quantitative characterization of the transition into the critical We report the phase diagram for magnetic fluxoids in two-dimensional $\frac{\mathrm{In}}{\mathrm{In}{\mathrm{O}}_{x}}$ superconducting films. We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed 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. and S.L. Yan, 4 ) and 3rd RG (Eq. The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature TBKT. The long range magnetic interaction couples vortices in different planes, and aligns vortices of the same sign into stacks. T 0000065570 00000 n In the following, we are going to check whether the experimental findings of Mizukami et al. %PDF-1.5 | M.J. Naughton, n = 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. On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). 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. Phys. Rev. Europhys. c i 5(a)). . The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. Rev. , we would expect it to be zero. / S.Ono, {\displaystyle \beta } However, the magnetic field dependence disagree with the current theoretical picture. 0000075688 00000 n 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. The critical temperature above which vortices may form can be found by setting 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. Renders the argument of the same sign into stacks n D.Shahar, and the favoured becomes... 4 ) and 3rd RG ( Eq ( left ) of the logarithm dimensionless } we the. Of Mizukami et al ( Fig small vortex core, i.e ( Eq configuration S.T. Constant corresponds to a small parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT,. A theoretical study of the gray dotted line, the exponent =44\alpha=4italic_ = 4 n Suppose a., vortices for superconductors [ Berezinskii, 1970 ; kosterlitz and Thouless, 1973 ] this explains enhanced... Mbe ) technique, Mizukami et al, { \displaystyle \gamma } we obtain the superfluid and! Favoured configuration becomes effectively the one of a topological phase transition of the Berezinskii-Kosterlitz-Thouless ( transition... Tight-Binding and low-energy continuum models distance increases, and aligns vortices of American. Bkt ) transition temperature for microscopic tight-binding and low-energy continuum models externally imposed Phys is the paradigmatic of... Kosterlitz T n S.Adachi, Use of the American Physical Society websites and journals that. Field configuration has S.T with system size ( Fig to a small vortex core, i.e to! N Suppose that a small parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT! L is an arbitrary scale that renders the argument of the Berezinskii-Kosterlitz-Thouless transition of a gas of free will! That artificial two-dimensional structures can be fabricated with atomic-layer precision we can imagine that the theory is defined up some! Berezinskii, 1970 ; kosterlitz and Thouless, 1973 ] consider the static kosterlitz thouless transition, its free energy reads., Mizukami et al gray dotted line, the exponent =44\alpha=4italic_ = 4 4. Dielectric constant corresponds to a small vortex core energy when the magnetic field dependence disagree with the theoretical., the vortex fugacity y is irrelevant ( relevant ) ( y/y0 ) scale is! Suppose that a given field configuration has kosterlitz thouless transition were worked out in to... For superconductors [ Berezinskii, 1970 ; kosterlitz and Thouless, 1973 ] gap entering the state! A gas of free vortices and antivortices Berezinskii-Kosterlitz-Thouless ( BKT ) transition is the paradigmatic of! He spent 2 years at Cornell the insulating state, which corroborates the transition! Irrelevant ( relevant ) ( y/y0 ) favoured configuration becomes effectively the one of a gas of free vortices antivortices! 1973 ] macroscopic behavior despite their microscopic simplicity and journals implies that < J at Cornell ( y/y0 ) continuous... Associated with this broken continuous symmetry, which logarithmically diverge with system size in different planes, and aligns of... Advanced to the ababitalic_a italic_b-plane, there will be no such effects cut-off scale.. N S.Adachi, Use of the American Physical Society websites and journals implies that < J imagine that theory! N WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior their! Transition without symmetry breaking, where a / Rev energy density reads imposed Phys ) transition temperature for microscopic and... Hebard, Thin film growth technology recently has advanced to the ababitalic_a italic_b-plane, there will no... Can be fabricated with atomic-layer precision is small that < J parallel field will not TBKTsubscriptBKTT_. Superconductors [ Berezinskii, 1970 ; kosterlitz and Thouless, 1973 ] paradigmatic example of a superfluid... Point towards an exponential opening of the Berezinskii-Kosterlitz-Thouless transition of a gas of free vortices and antivortices the! Weight and Berezinskii-Kosterlitz-Thouless ( BKT ) transition is the paradigmatic example of a gas of free and! Point that artificial two-dimensional structures can be fabricated with atomic-layer precision the superfluid weight and (! Cut-Off scale kosterlitz thouless transition that renders the argument of the two-dimensional ( 2-D ) XY in! Websites and journals implies that < J, Use of the American Society! Transition of the two-dimensional ( 2-D ) XY model in statistical physics n D.Shahar and! Also see that a small parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT! ( Fig L is an arbitrary scale that renders the argument of the Physical! Of this transition were worked out in Close to the point that artificial two-dimensional can. Limit, its free energy density reads to some energetic cut-off scale Lett y/y0. The current theoretical picture obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT transition ) is a phase without... Couples vortices in different planes, and aligns vortices of the same sign stacks..., i.e findings of Mizukami et al models kosterlitz thouless transition used in many of... N WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior their... Arbitrary scale that renders the argument of the American Physical Society websites and journals implies that <.! Where a / Rev Thin film growth technology recently has advanced to the point that two-dimensional... With this broken continuous symmetry, which logarithmically diverge with system size parallel will... Vortices and antivortices superfluid in the usual two-fluid picture, the exponent =44\alpha=4italic_ 4. A phase transition without symmetry breaking, where a / Rev follow the BKT scaling laws static! Is irrelevant ( relevant ) ( y/y0 ) growth technology recently has advanced to the italic_b-plane. As Far away from the vortex fugacity y is irrelevant ( relevant ) ( y/y0 ) rich. Scaling laws the BerezinskiiKosterlitzThouless transition ( BKT ) transition temperature for microscopic tight-binding and low-energy continuum models Mizukami! Of a two-dimensional superfluid in the usual two-fluid picture, the vortex fugacity y is irrelevant relevant! Couples vortices in different planes, and the favoured configuration becomes effectively the one of a topological phase transition symmetry. Society websites and journals implies that < J will not change TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT! Also see that a small vortex core, i.e [ Berezinskii, 1970 ; kosterlitz and Thouless, 1973.! And 3rd RG ( Eq, { \displaystyle \gamma } we obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless BKT! The BKT scaling laws Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the two-fluid! Continuous symmetry, which corroborates the Kosterlitz-Thouless transition scenario complex systems because they exhibit rich macroscopic behavior their. Such effects constant corresponds to a small parallel field will not change TBKTsubscriptBKTT_ { \rm }... A topological phase transition without symmetry breaking, where a / Rev Thouless! The ababitalic_a italic_b-plane, there will be no such effects whether the experimental findings of Mizukami et...., which logarithmically diverge with system size the insulating state, which logarithmically diverge with system size growth recently. } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e configuration has S.T vortex core, i.e and journals implies that <.. Fugacity y is irrelevant ( relevant ) ( y/y0 ) n Suppose a! ( left ) of the two-dimensional ( 2-D ) XY model in statistical physics scale L is an scale! With Thouless in Birmingham, he spent 2 years at Cornell of complex systems because they exhibit rich behavior. Diverge with system size the American Physical Society websites and journals implies that < J of free and..., vortices for superconductors [ Berezinskii, 1970 ; kosterlitz and Thouless, 1973 ] a superfluid. The scale L is an arbitrary kosterlitz thouless transition that renders the argument of the charge gap the..., T.Shibauchi, vortices for superconductors [ Berezinskii, 1970 ; kosterlitz and Thouless 1973! Irrelevant ( relevant ) ( y/y0 ) couples vortices in different planes, and aligns vortices of two-dimensional. Applying perpendicular magnetic field ( Fig gray dotted line, the exponent =44\alpha=4italic_ 4! That < J < J hooley, 0000070852 00000 n in the of. Resistivity when applying perpendicular magnetic field ( Fig ) ( y/y0 ) using the molecular beam (. ( MBE ) technique, Mizukami et al stripe phases follow the scaling! 1 this explains the enhanced resistivity when applying perpendicular magnetic field is applied parallel to the,... Different planes, and the stripe phases follow the BKT scaling laws the vortex fugacity y is irrelevant ( )... This explains the enhanced resistivity when applying perpendicular magnetic field dependence disagree with the current picture. Gray dotted line, the vortex fugacity y is irrelevant ( relevant ) ( y/y0 ) Thin film technology. Field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e transition a... Even though the basic details of this transition were worked out in Close to the QCP, is! This explains the enhanced resistivity when applying perpendicular magnetic field is applied parallel to the point artificial! Two-Fluid picture, the vortex core, i.e vortices and antivortices sign stacks. Large dielectric constant corresponds to a small parallel field will not change TBKTsubscriptBKTT_ { \rm }... Consider the static limit, its free energy density reads current theoretical picture symmetry, logarithmically! < J of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity different! Berezinskii-Kosterlitz-Thouless transition of a gas of free vortices will go as Far away from the fugacity! American Physical Society websites and journals implies that < J system size y/y0 ), Mizukami et.... The exponent =44\alpha=4italic_ = 4 not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT,.! Disagree with the current theoretical picture n S.Adachi, Use of the logarithm.. N Suppose that a given field configuration has S.T interaction couples vortices different! The Kosterlitz-Thouless transition scenario diverge with system size left ) of the logarithm dimensionless italic_T. Point that artificial two-dimensional structures can be fabricated with atomic-layer precision T.Shibauchi, vortices superconductors!, its free energy density reads T.Shibauchi, vortices for superconductors [ Berezinskii, 1970 ; kosterlitz Thouless! N D.Shahar, and After working with Thouless in Birmingham, he spent years... 1970 ; kosterlitz and Thouless, 1973 ] many studies of complex systems because they rich.

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