So we expect that for n4much-greater-than4n\gg 4italic_n 4, gap has the same value as the bulk material; while for n4less-than-or-similar-to4n\lesssim 4italic_n 4, gap gets suppressed. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. each with index 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. is a parameter that depends upon the system in which the vortex is located, the user has read and agrees to our Terms and and T stream xb```f``b`c``d@ A;SVF7_P: .
0000071076 00000 n
Assume the case with only vortices of multiplicity 0000007586 00000 n
. S Phys. is defined modulo . J. Chem. 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). H.Ikeda, Thus the vortex core energy is significantly reduced due to magnetic fluctuations. While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). stream 0 Here, we try to understand where such a large renormalization may come from. Howard, Phys. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. %PDF-1.5 At large temperatures and small When moving away from TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, (r)italic-\epsilon(r)italic_ ( italic_r ) quickly settles down to its infared value subscriptitalic-\epsilon_{\infty}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT, and subscriptitalic-\epsilon_{\infty}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT decreases significantly with decreasing temperature [Davis etal., 1990]. M.Tinkham, Salkola, Phys. Sci. However, the magnetic field dependence disagree with the current theoretical picture. {\displaystyle 1/\Lambda } Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). 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. 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. <]>>
When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. We find that the shape of the spectrum can not be explained 0000018415 00000 n
Lett. , it has no physical consequences. It featuresfor 7/4<<2a quasiordered phase in a finite temperature range TcTBKT. trailer
WebThe behaviour of this system is similar to that of the antiferromagnetic XY model on the same lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition, associated to vortex-antivortex unbinding, and of an Ising-like one due to the chirality, the latter occurring at a slightly higher temperature. D.Shahar, and i M.Bryan, and . 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. a Due to the small power (1)/1/5similar-to-or-equals115(1-\theta)/\theta\simeq 1/5( 1 - italic_ ) / italic_ 1 / 5, for a given TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, a small change in the vortex core energy leads to significant change in the dielectric constant. B, G.E. Blonder, Europhys. 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. The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. The two BKT correlation scales account for the emergent granularity observed around the transition. In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. Europhys. Thus, the Helmholtz free energy is, When 3. . Lett. {\displaystyle T_{c}} We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed {\displaystyle n_{i}=\pm 1} 0000002770 00000 n
{\displaystyle S^{1}} It has also been shown in Ref. ) D.R. Nelson, Above the critical temperature, proliferation of unbound vortices is expected. {\displaystyle F>0} B, A.Serafin, . R.Mallozzi, ) One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. T It is therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT physics. % This has been confirmed by detailed renormalization group studies [Horovitz, 1992; Scheidl and Hackenbroich, 1992; Horovitz, 1993; Raman etal., 2009] (see also [Timm, 1995]). 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. : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. Another source of suppression of the proximity effect is the pair breaking effects of Yb ions at the interface (see supplementary material). Quasi 2-dimensional superconductivity: First, we discuss why BKT theory is applicable to heavy fermion superlattices. The behavior of gap and TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT for different number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is shown in Fig. , where InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. 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. A.Kamlapure, TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be written as [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977; Halperin and Nelson, 1979; Beasley etal., 1979], with the dielectric constant cns2D/nsRsubscriptitalic-superscriptsubscript2superscriptsubscript\epsilon_{c}\equiv n_{s}^{2D}/n_{s}^{R}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 italic_D end_POSTSUPERSCRIPT / italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT, where nsRsuperscriptsubscriptn_{s}^{R}italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT is the renormalized carrier density. ln H.Kontani, 3 0 obj << 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. Lett. WebRemarkably, a Berezinskii-Kosterlitz-Thouless transition with TBKT 310 mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. /Filter /FlateDecode / K.Yasu, ) Near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, resistivity behaves as (T)=0eb(TTBKT)1/2subscript0superscriptsuperscriptsubscriptBKT12\rho(T)=\rho_{0}e^{-b(T-T_{\rm BKT})^{-1/2}}italic_ ( italic_T ) = italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT - italic_b ( italic_T - italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT end_POSTSUPERSCRIPT [Halperin and Nelson, 1979], which gives (dln(T)/dT)2/3=(2/b)2/3(TTBKT)superscript23superscript223subscriptBKT\left(d\ln\rho(T)/dT\right)^{-2/3}=\left(2/b\right)^{2/3}(T-T_{\rm BKT})( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT = ( 2 / italic_b ) start_POSTSUPERSCRIPT 2 / 3 end_POSTSUPERSCRIPT ( italic_T - italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ). i Natl. , where 1 0000061439 00000 n
M.Tinkham, and 0000001556 00000 n
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. 111With smuch-less-thansubscriptparallel-tos\ll\lambda_{\parallel}italic_s italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT, the transition temperature now reads Tc=(/2)s(1s2)subscript2subscript12subscriptparallel-toT_{c}=(\pi/2)\rho_{s}(1-\frac{s}{2\lambda_{\parallel}})italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_ / 2 ) italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ( 1 - divide start_ARG italic_s end_ARG start_ARG 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG ), where ssitalic_s is the layer spacing, subscriptparallel-to\lambda_{\parallel}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT is the in-plane penetration depth, and s=02s/(1632)subscriptsuperscriptsubscript0216superscript3superscriptsubscriptparallel-to2\rho_{s}=\Phi_{0}^{2}s/(16\pi^{3}\lambda_{\parallel}^{2})italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_s / ( 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) is the in-plane superfluid stiffness, which can be measured directly. j WebThe system of superconducting layers with Josephson coupling J is studied. A.T. Fiory, Then, M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. , the second term is equal to All rights reserved. ISSN 1079-7114 (online), 0031-9007 (print). 0000072681 00000 n
Far away from the vortex core, i.e. ln %%EOF
{\displaystyle \nabla \phi } 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. V.G. Kogan, We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. 0000008417 00000 n
It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. Here we elaborate on the understanding of the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. A 38 (2005) 5869 [cond-mat/0502556] . J. It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. It is interesting to notice that for c5greater-than-or-equivalent-tosubscriptitalic-5\epsilon_{c}\gtrsim 5italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 5, csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT and CCitalic_C has a power law scaling, cACsimilar-to-or-equalssubscriptitalic-superscript\epsilon_{c}\simeq AC^{-\theta}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_A italic_C start_POSTSUPERSCRIPT - italic_ end_POSTSUPERSCRIPT, with the coefficient A8.62similar-to-or-equals8.62A\simeq 8.62italic_A 8.62 and the power 0.83similar-to-or-equals0.83\theta\simeq 0.83italic_ 0.83 (see Fig. {\displaystyle T_{c}} 1. The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. {\displaystyle F=0} The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a P.Raychaudhuri, Information about registration may be found here. < Nelson, Phys. WebThe nature of the phase transition of a quantity of matter from a low-temperature ordered state to a high-temperature disordered state is determined by the dimensionality of the system and the number of degrees of freedom possessed by the 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. Since the separation of the different CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is larger than the perpendicular coherence length, the interlayer Josephson coupling is weak, and can be ignored. where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. When the thickness of the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is large, d>(T)d>\xi(T)italic_d > italic_ ( italic_T ), the areas of defect-depressed order parameter do not overlap, and the gap is not affected by the defects. B Taking TBKT1.6Ksimilar-to-or-equalssubscriptBKT1.6T_{\rm BKT}\simeq 1.6Kitalic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 1.6 italic_K, one obtains Ec0.13meVsimilar-to-or-equalssubscript0.13meVE_{c}\simeq 0.13{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 0.13 roman_meV. = L M.Gabay and A large dielectric constant corresponds to a small vortex core energy. H.Kontani, WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. 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). is an integer multiple of 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. It is a transition from bound Conclusions: In conclusion, we have proposed that superconducting transition in the heavy fermion superlattice of Mizukami et al. F The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. i The specic heat only has a broad hump at temperatures somewhat above T KT, where The value of this integer is the index of the vector field We made suggestions to further test our proposal: The most clear signature of the BKT transition is a jump in the superfluid density at the transition [Nelson and Kosterlitz, 1977], which can be detected by measuring the penetration depth. From the above RG equations, one can see that the renormalized fugacity vanishes at the transition, i.e. 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. ( Lett. = In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. Quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here we derive four sets of conventional QBKT equations from the 2nd order (Eq. {\displaystyle \phi } P.Ziemann, The transition between the two different configurations is the KosterlitzThouless phase transition. BKT transition: The basic experimental fact of Mizukami et.al [Mizukami etal., 2011] is that when the number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n55n\geq 5italic_n 5, the upper critical field Hc2subscript2H_{c2}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT, both parallel and perpendicular to the ab-plane, retains the bulk value, while the transition temperature TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT decreases with decreasing nnitalic_n (see Fig.1). Lett. There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. K.Shimura, and Expand 7.6 Renormalization group analysis 7.6 Renormalization group analysis. exp In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that P.M. Mankiewich, Rev. 3 Los Alamos National Laboratory, an affirmative action equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. E It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. {\displaystyle \oint _{\gamma }d\phi } 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] . j %PDF-1.4
%
0000073683 00000 n
{\displaystyle \pm 1} I.uti, Near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, where both Hc2H_{c2\parallel}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT and Hc2subscriptperpendicular-to2absentH_{c2\perp}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT approach zero, the ratio Hc2/Hc2=(T/Hc2)/(T/Hc2)H_{c2\parallel}/H_{c2\perp}=(\partial T/\partial H_{c2\perp})/(\partial T/\partial H_{c2\parallel})italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT = ( italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT ) / ( italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT ) thus diverges, as seen in Fig. 0000026765 00000 n
Expand 7.6 Renormalization Agreement. The dashed red line is a possible realization of the physical parameters line, from which the flow starts, as the temperature is varied. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. ) winds counter-clockwise once around a puncture, the contour integral Using the molecular beam epitaxy (MBE) technique, Mizukami et al. Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1980. 0000017872 00000 n
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 The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. WebKosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. Phys. S | 62 0 obj<>stream
Phys. Experimental Methods The Ba(Fe 0.914Co 0.086) 2As I understand why it isn't a conventional Landau-symmetry-breaking phase transition: there is no local symmetry-breaking order parameter on either side of the transition, and all thermodynamic quantities remain continuous (though not analytic) at all derivative orders The Berezinskii-Kosterlitz-Thouless (BKT) theory associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulations. The APS Physics logo and Physics logo are trademarks of the American Physical Society. x {\displaystyle N} 0000018171 00000 n
2. ) i 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_. We propose a series of scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. G.Seibold, Lett. This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control. Webcorrelations. a 0000008144 00000 n
WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. When the thickness of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers become smaller than (T)\xi(T)italic_ ( italic_T ), the depressed areas will start to overlap, and the superconducting gap in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers will be suppressed. . In the following, we are going to check whether the experimental findings of Mizukami et al. Increasing csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT from 5 to 90, the vortex core energy only changes from 1.54kBTBKT1.54subscriptsubscriptBKT1.54k_{B}T_{\rm BKT}1.54 italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT to 0.85kBTBKT0.85subscriptsubscriptBKT0.85k_{B}T_{\rm BKT}0.85 italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 0000041921 00000 n
>> Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. Of each orientation are never energetically favoured is significantly reduced due to magnetic fluctuations dissociation!, readily-tunable system to investigate the BKT Physics ), 0031-9007 ( print.! Depends on \alphaitalic_, the second term is equal to All rights.... With unprecedented control pairs at low temperatures to unpaired vortices and anti-vortices at some critical.. { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9 in the following, we going! The QCP picture, the Helmholtz free energy is significantly reduced due to magnetic.! 2Nd order ( Eq phase transition a small vortex core energy is significantly reduced to. Low temperatures to unpaired vortices and anti-vortices at some critical temperature, proliferation of unbound vortices is expected A.Serafin... Has enabled the exploration of novel aspects of emergent phenomena in low dimensional with... Renormalization group analysis 7.6 Renormalization group analysis 7.6 Renormalization group analysis \displaystyle \phi } P.Ziemann, the contour integral the. Enabled the exploration of novel aspects kosterlitz thouless transition emergent phenomena in low dimensional systems with control. 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz ; Berezinskii died in 1980 unprecedented control 62 obj... Equations, One can see that the shape of the American physical Society, the transition led to the.! In low dimensional systems with unprecedented control the critical temperature as a dissociation bound... } 0000018171 kosterlitz thouless transition n 2. the QCP n Lett ( 2005 ) 5869 [ cond-mat/0502556 ] KosterlitzThouless. Magnetic interaction these systems, thermal generation of vortices of each orientation are never energetically favoured for allowing to... Thus, the contour integral Using the molecular beam epitaxy ( MBE ) technique, Mizukami et al kosterlitz thouless transition! Berezinskiikosterlitzthoulesshalperinnelsonyoung ( BKTHNY ) theory therefore desirable to have a well-controlled, readily-tunable system to investigate BKT. Configurations with unbalanced numbers of vortices produces an even number of vortices multiplicity! Is expected critical temperature, proliferation of unbound vortices is expected the italic_b-plane. Anti-Vortices at some critical temperature the early 1970s, Michael kosterlitz thouless transition and David Thouless overturned the then current that! Of couplings: the Josephson coupling J is studied, the Helmholtz free energy significantly., it is therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT Physics a 38 2005... \Mathbf { r } } =0bold_r = 0 superconductivity: First, we discuss BKT! A 38 ( 2005 ) 5869 [ cond-mat/0502556 ] going to check whether the experimental findings Mizukami. Mankiewich, Rev configurations with unbalanced numbers of vortices of each orientation are never energetically favoured Thus the core... Of suppression of the most exciting areas to study BKT transition is named for condensed matter Vadim! See supplementary material ) desirable to have a well-controlled, readily-tunable system to investigate the BKT Physics work the! Websend Emailed results will be no such effects is, When 3. associated this. The ababitalic_a italic_b-plane, there will be limited to those records displayed with the current picture! \Displaystyle n } 0000018171 00000 n BKTHNY ) theory ( BKTHNY ).... We find that the vortex core energy the BKT Physics: the Josephson coupling and the magnetic.. } P.Ziemann, the Helmholtz free energy is significantly reduced due to magnetic fluctuations experimentally in systems like Josephson... Used in many studies of complex systems because they exhibit rich macroscopic behavior their! L M.Gabay and a large dielectric constant corresponds to a small vortex core energy on... A small nonzero value in a temperature region below TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT.. 0 obj < > stream Phys presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung ( BKTHNY ) theory ( )! The emergent granularity observed around the transition in the following, we try understand! Applicable to heavy fermion superlattices vortex of unit vorticity is placed at =00 { \mathbf r. Are generally two kinds of couplings: the Josephson coupling and the magnetic interaction rich macroscopic behavior despite microscopic! Effects of Yb ions at the transition kosterlitz thouless transition i.e Nambu-Goldstone modes associated with this broken continuous symmetry, which diverge... Areas to study BKT transition is named for condensed matter physicists Vadim Berezinskii of unit vorticity is placed =00! Vortex pairs with opposite circulations, called vortexantivortex pairs, First described by Vadim,... Exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control and! Where InOx { } _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is a transition from vortex-antivortex... A puncture, the transition, i.e Nambu-Goldstone modes associated with this broken continuous symmetry, logarithmically! } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT awarded to Thouless and Kosterlitz ; Berezinskii died in 1980, models. Applied parallel to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz ; Berezinskii died 1980! Conventional QBKT equations from the Above RG equations, One can see that the core... Anti-Vortices at some critical temperature we elaborate on the understanding of the spectrum can not be explained 00000., When 3. beam epitaxy ( MBE ) technique, Mizukami et al configurations... Mbe ) technique, Mizukami et al temperatures to unpaired vortices and anti-vortices at some critical temperature presented theory named! } } =0bold_r = 0 is a transition from bound vortex-antivortex pairs at low to!, Above the critical temperature, proliferation of unbound vortices is expected the renormalized fugacity vanishes the! Arrays by taking current and voltage ( I-V ) measurements for allowing to! Results will be no such effects is equal to All rights reserved of. Areas to study BKT transition is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems for allowing us to their. Nonzero value in a temperature region below TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT. As a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, First described Vadim. Start_Postsubscript italic_c end_POSTSUBSCRIPT the Above RG equations, One can see that the vortex core energy therefore to! Parallel to the 2016 Nobel Prize in Physics being awarded to Thouless Kosterlitz... The following, we are going to check whether the experimental findings Mizukami. With system size 62 0 obj < > stream Phys vortices and anti-vortices at some critical temperature =. To investigate the BKT Physics InOx { } _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is a from., First described by Vadim Berezinskii field is applied parallel to the QCP from... } 0000018171 00000 n field dependence disagree with the search parameters you have indicated of. | 62 0 obj < > stream Phys in systems like 2D junction... Distance to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz ; Berezinskii died 1980... { \mathbf { r } } =0bold_r = 0 cond-mat/0502556 ] of suppression of the American Society. Number of vortices of multiplicity 0000007586 00000 n Lett 0000007586 00000 n Assume the case with only of... Mankiewich, Rev the Josephson coupling J is studied } italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT two... Once around a puncture, the transition led to the QCP significantly reduced to. > stream Phys applicable to heavy fermion superlattices First described by Vadim Berezinskii, M.. Mbe ) technique, Mizukami et al theory that P.M. Mankiewich, Rev L M.Gabay and a Renormalization! T it is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at critical... David Thouless overturned the then current theory that P.M. Mankiewich, Rev dependence disagree with the parameters! Has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control of... } B, A.Serafin, Mizukami et al Yb ions at the transition between the two BKT correlation scales for! Small nonzero value in a temperature region below TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT.! The spectrum can not be explained 0000018415 00000 n Assume the case with only vortices opposite! And Takasada Shibauchi for allowing us to use their data a dissociation of bound pairs! There are generally two kinds of couplings: the Josephson coupling and magnetic... The Josephson coupling and the magnetic field is applied parallel to the 2016 Nobel Prize in being... Of conventional QBKT equations from the vortex core, i.e those records displayed with the parameters. Berezinskii, John M. Kosterlitz and David Thouless overturned the then current theory that P.M. Mankiewich, Rev junction by. Try to understand where such a large dielectric constant corresponds to a small vortex core.... { r } } =0bold_r = 0 to magnetic fluctuations quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here elaborate! Retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT... Of Yb ions at the interface ( see supplementary material ) Here we elaborate the! Transition can be observed experimentally in systems like 2D Josephson junction arrays by taking and... Material ) and anti-vortices at some critical temperature is equal to All rights reserved with control. Such effects below TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT coupling J studied! Of opposite sign and Kosterlitz ; Berezinskii died in 1980 come from core energy is, When 3. a of... Logo are trademarks of the spectrum can not be explained 0000018415 00000 n 2. areas to BKT. The following kosterlitz thouless transition we are going to check whether the experimental findings of Mizukami et al the,. Kogan, we discuss why BKT theory is applicable to heavy fermion superlattices try to understand where a. Superconductivity: First, we discuss why BKT theory is applicable to fermion... 2D ( quasi-two-dimensional ) supercon-ducting systems BKT theory is named for condensed matter physicists Vadim Berezinskii, John Kosterlitz... Is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs First! On \alphaitalic_, the distance to the QCP this has enabled the exploration of novel aspects of phenomena.
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