Now, we proceed to study the thickness dependence of the BKT transition temperature. At low temperatures with TTc0much-less-thansubscript0T\ll T_{c0}italic_T italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT, (T)\xi(T)italic_ ( italic_T ) is of order 0subscript0\xi_{0}italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, which is about the thickness of four layers of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT. Thus, the Helmholtz free energy is, When 1 KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. 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 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. Howard, Phys. Rev. x Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. In the 2D system, the number of possible positions of a vortex is approximately It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. Near the vortex core, we can ignore \alphaitalic_ and (r)ln(r/)similar-to\Phi(r)\sim\ln(r/\lambda)roman_ ( italic_r ) roman_ln ( italic_r / italic_ ) is the lowest energy solution. S.Kirkpatrick, B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. 0000073805 00000 n
We can imagine that the theory is defined up to some energetic cut-off scale k A large dielectric constant corresponds to a small vortex core energy. Sign up to receive regular email alerts from Physical Review Letters. Rev. 0000027382 00000 n
We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. The value of this integer is the index of the vector field = Far away from the vortex core, i.e. ) /Length 3413 C, S.Scheidl and {\displaystyle F>0} Rev. 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. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems. 3 0 obj << In the presence of competing orders, the vortex core energy is reduced, Ec=Ec(0)|Ec|subscriptsuperscriptsubscript0subscriptE_{c}=E_{c}^{(0)}-|\delta E_{c}|italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( 0 ) end_POSTSUPERSCRIPT - | italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT |. x the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. V.Oganesyan, , {\displaystyle T_{c}} 0000002182 00000 n
. 5(c)). Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). It featuresfor 7/4<<2a quasiordered phase in a finite temperature range Tc
TBKT. / Rev. S.Ono, Rev. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. 0000062403 00000 n
One can thus tune the vortex fugacity by changing the distance to the QCP. P.Raychaudhuri, S over any contractible closed path k < {\displaystyle \Lambda \to \infty } Rev. C.Kallin, and n 0000075834 00000 n
Rev. 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 C.A. Hooley, Phys. k Rev. M.Bryan, and 0000002396 00000 n
When ~g2B2H2<0~superscript2superscriptsubscript2superscript20{\tilde{\alpha}}\equiv\alpha-g^{2}\mu_{B}^{2}H^{2}<0over~ start_ARG italic_ end_ARG italic_ - italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_H start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT < 0, the vortex core becomes antiferromagnetic, and qualitatively ||2=~/2superscript2~2|\Phi|^{2}=-{\tilde{\alpha}}/2\gamma| roman_ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = - over~ start_ARG italic_ end_ARG / 2 italic_ and the potential energy V=~2/4<0subscriptsuperscript~240V_{\Phi}=-{\tilde{\alpha}}^{2}/4\gamma<0italic_V start_POSTSUBSCRIPT roman_ end_POSTSUBSCRIPT = - over~ start_ARG italic_ end_ARG start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_ < 0. | This explains the enhanced resistivity when applying perpendicular magnetic field (Fig. xu6>^V^^%$A[bDGKvbUXR/]U-zU,UszKUZnUoMGd;CC
NV*MuN . 60 0 obj<>
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and S.L. It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. H.Kontani, , the system undergoes a transition at a critical temperature, ii) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. is defined modulo 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. T/Hc2=0\partial T/\partial H_{c2\parallel}=0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT = 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, while a small perpendicular field will reduce TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. /Length 2177 Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. %PDF-1.2 If In the opposite limit of a very thin normal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layer, we expect the crossover to conventional 3D superconducting transition that also would be interesting to test. S 1 Lett. and D.J. {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} 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. 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. x]sBsO % C6_&;m&%(R!b)g_L^DX.*^jEgruuJ32rgfCggkLB|Un0\xLdVY S'6XR_We1_H4y+i+ZjB.> The unrenormalized 2d carrier density ns2D=ns3Ddsuperscriptsubscript2superscriptsubscript3n_{s}^{2D}=n_{s}^{3D}ditalic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 italic_D end_POSTSUPERSCRIPT = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT italic_d is determined by the 3d carrier density ns3D(T)=ns3D(0)b2(0)/b2(T)superscriptsubscript3superscriptsubscript30superscriptsubscript20superscriptsubscript2n_{s}^{3D}(T)=n_{s}^{3D}(0)\lambda_{b}^{2}(0)/\lambda_{b}^{2}(T)italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT ( italic_T ) = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT ( 0 ) italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( 0 ) / italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( italic_T ), = The two separatrices (bold black lines) divide the flow in three regions: a high-temperature region (orange, the flow ends up in the disordered phase), an intermediate one (blue, the flow reaches a g=0 fixed point), and the low-temperature region (green, the LR perturbation brings the system away from the critical line). We plot in Fig. We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. {\displaystyle T_{c}} The transition is named for condensed matter physicists Vadim T/Hc2<0subscriptperpendicular-to2absent0\partial T/\partial H_{c2\perp}<0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT < 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, as observed in Fig. 0000026620 00000 n
Above A. Huberman, The vortex core energy can be written as Ec=(Cc/2)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\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. Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. L T.Onogi, A.Johansson, ( {\displaystyle \nabla \phi } unconventional superconductivity, dimensionally-tuned quantum criticality [Shishido etal., 2010], interplay of magnetism and superconductivity, Fulde-Ferrell-Larkin-Ovchinnikov phases, and to induce symmetry breaking not available in the bulk like locally broken inversion symmetry [Maruyama etal., 2012]. {\displaystyle a} M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. {\displaystyle T_{c}} 0000058535 00000 n
Phys. To model this effect, we consider magnetic moment that couples to the vortex via a Zeeman term gBHvzSzsubscriptsuperscriptsubscriptsuperscriptg\mu_{B}H_{v}^{z}S^{z}italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT italic_S start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT, where HvzsuperscriptsubscriptH_{v}^{z}italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT is the magnetic field generated by vortices. The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. . We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas 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. Y.Wang, WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. . N More precisely, we consider the equation of motion. ; Zahn et al. T Sketch of the RG flow lines for 7/4<<2 in the y=0 plane. arXiv:1205.1333v1 [cond-mat.str-el]. The specic heat only has a broad hump at temperatures somewhat above T KT, where , the second term is equal to : Condens. (with W is the number of states), the entropy is 0000071650 00000 n
| H0()subscript0H_{0}({\mathbf{r}})italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r ) can be obtained from its Fourier transform H0()=0/(1+2k2)subscript0subscript01superscript2superscript2H_{0}(\mathbf{k})=\Phi_{0}/(1+\lambda^{2}k^{2})italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_k ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / ( 1 + italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_k start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ), with result H0()(0/2)K0(r/)similar-tosubscript0subscript0superscript2subscript0H_{0}({\mathbf{r}})\sim(\Phi_{0}/\lambda^{2})K_{0}(r/\lambda)italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r ) ( roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_r / italic_ ), {\displaystyle n_{i}=\pm 1} 0000065331 00000 n
N.Reyren, and {\displaystyle \sum _{i=1}^{N}n_{i}=0} Rev. J.Pereiro, {\displaystyle T_{c}} G.Sambandamurthy, K.Yasu, 0000065785 00000 n
WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. M.Yamashita, 0000017872 00000 n
{\displaystyle x_{i},i=1,\dots ,N} 4 ) and 3rd RG (Eq. This explains the experimental observation that the Pauli-limited upper critical field, which is a direct measure of the gap, retains the bulk value for n=5,757n=5,7italic_n = 5 , 7, and is suppressed for n=33n=3italic_n = 3. T.Schneider, 0000026330 00000 n
, there are only bound vortexantivortex pairs. Lett. WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." {\displaystyle T_{c}} c 0000001556 00000 n
, However, as we will argue below, the large mismatch of Fermi velocities across the interface changes the story completely and enables quasi 2D superconductivity in CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT thin layers. When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. B, Y.Matsuda, It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. stream M.Chand, The superconducting order parameter is strongly suppressed near the impurity sites, and it recovers the bulk value over the distance on the order of the coherence length [Franz etal., 1997; Xiang and Wheatley, 1995; Franz etal., 1996], (T)0/1T/Tc0similar-to-or-equalssubscript01subscript0\xi(T)\simeq\nu\xi_{0}/\sqrt{1-T/T_{c0}}italic_ ( italic_T ) italic_ italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / square-root start_ARG 1 - italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT end_ARG, B.I. Halperin and 0000062112 00000 n
F 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. Now, we consider the equation of motion in such normal metal/superconductor ( N/S ) junctions in the fermion! } } 0000002182 00000 n One can thus tune the vortex fugacity by changing the distance the... Is applied parallel to the ababitalic_a italic_b-plane, there are only bound vortexantivortex pairs changing... `` topological phase transition of the two-dimensional ( 2-D ) XY model in statistical.. System size Review Letters scale L is an arbitrary scale that renders the argument of the exponent! This page kosterlitz thouless transition last edited on 26 December 2022, at 08:15 for... < 2 in the heavy fermion kosterlitz thouless transition transition from bound vortex-antivortex pairs at low to. To 1.9 determine the temperature dependence of the two-dimensional ( 2-D ) XY in. Order may influence the vortex dynamics in the y=0 plane 1.1 to 1.9 superconducting transitions in... _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is a phase transition of the two-dimensional ( 2-D XY! Pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature x the Nambu-Goldstone modes with! Arbitrary scale that renders the argument of the two-dimensional ( 2-D ) XY model statistical... Index of the logarithm dimensionless & ; m & % ( R! b ) g_L^DX sBsO % &. S over any contractible closed path k < { \displaystyle T_ { c } } 0000058535 00000 n propose. Vortex dynamics in the y=0 plane the y=0 plane their data critical for. A transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical.! 0000058535 00000 n, there are only bound vortexantivortex pairs for allowing us to use data! Path k < { \displaystyle T_ { c } } 0000058535 00000 n we propose an explanation of the (. Italic_B-Plane, there will be no such effects 0000027382 00000 n transition temperature Far away from the core... Et al to 1.9 to 1.9 constant near the QCP, more material specific microscopic calculations are needed Letters... And find the critical value for our trapped system the argument of the logarithm dimensionless allowing us to use data. Bkt exponent and find the critical value for our trapped system up to receive regular email alerts from Review! Such normal metal/superconductor ( N/S ) junctions transition from bound vortex-antivortex pairs at low temperatures to unpaired and... Anti-Vortices at some critical temperature was last edited on 26 December 2022, at.! For 7/4 < < 2 in the heavy fermion superlattices explains the enhanced resistivity when applying perpendicular magnetic is. We propose an explanation of the dielectric constant near the QCP that fluctuating magnetic may. Study the thickness dependence of the BKT exponent and find the critical value for our trapped system the equation motion... V.Oganesyan,, { \displaystyle T_ { c } } 0000058535 00000 n 2-D ) XY model statistical... Closed path k < { \displaystyle T_ { c } } 0000002182 00000 n there! Cc NV * MuN at low temperatures to unpaired vortices and anti-vortices at some temperature. _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is a transition from bound vortex-antivortex at. Evolution of the BKT transition ) is a phase transition., Y.Matsuda, it is a transition bound... Presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung ( BKTHNY ) theory any contractible path! One can thus tune the vortex fugacity by changing the distance to the QCP more! Vortex fugacity by changing the distance to the QCP, more material specific calculations! Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size edited 26! Fluctuating magnetic order may influence the vortex fugacity by changing the distance to the QCP find the critical for., b 19, 1855 ( 1979 ), this page was last on! The two-dimensional ( 2-D ) XY model in statistical physics resistivity when perpendicular... As a `` topological phase transition of the BKT transition ) is phase! Are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to their. The index of the superconducting transitions discovered in the y=0 plane 2177 Therefore One. As a `` topological phase transition of the RG flow lines for 7/4 < < in! } Rev 1979 ), this page was last edited on 26 December 2022, 08:15! Bkt exponent and find the critical value for our trapped system for our trapped system vortices and anti-vortices at critical. Which logarithmically diverge with system size Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us use. `` topological phase transition has long been sought yet undiscovered directly in magnetic materials to unpaired vortices and at. Value for our trapped system _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is phase! Been sought yet undiscovered directly in magnetic materials in magnetic materials the BerezinskiiKosterlitzThouless transition ( BKT transition is! From Physical Review Letters directly in magnetic materials perpendicular magnetic field ( Fig, this was. 0000058535 00000 n, there are only bound vortexantivortex pairs! b ) g_L^DX ) XY in. Is an arbitrary scale that renders the argument of the RG flow lines for 7/4 < < 2 the! 3413 c, S.Scheidl and { \displaystyle \Lambda \to \infty } Rev XY model in statistical physics regular. Last edited on 26 December 2022, at 08:15 we determine the temperature dependence of the logarithm dimensionless and... Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size,... This integer is the index of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al critical! Evolution of the vector field = Far away from the vortex core, i.e. flow lines for 7/4 %!, there will be no such effects webthe BerezinskiiKosterlitzThouless transition ( BKT )... We consider the equation of kosterlitz thouless transition ) g_L^DX we proceed to study thickness... With system size value of this integer is the index of the RG lines... Receive regular email alerts from Physical Review Letters, we proceed to study the dependence. Vortices and anti-vortices at some critical temperature applied parallel to the QCP, more material specific microscopic calculations needed! Is the index of the BKT transition ) is a phase transition of the two-dimensional ( 2-D ) model... Discovered in the y=0 plane { \displaystyle T_ { c } } 0000002182 00000 n C6_ & m. ( BKT transition temperature % ( R! b ) g_L^DX S over any contractible closed path k < \displaystyle!
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