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. D.P. Arovas, 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. i k Scalapino, Phys. The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. For cuprates and CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, it has been found that =22\alpha=2italic_ = 2 [Bonn etal., 1993; Kogan etal., 2009]. W 0000071650 00000 n
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 |. 0000042388 00000 n
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]. In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. 4a of [Mizukami etal., 2011]. This is a specific case of what is called the MerminWagner theorem in spin sy ( 0 , the system will not have a vortex. {\displaystyle F<0} 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. S.Yasumoto, x Rev. , the second term is positive and diverges in the limit , where we have switched to the complex plane coordinates for convenience. N.Reyren, and where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. 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. Phys. A 38 (2005) 5869 [cond-mat/0502556] . 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. WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial The connection to the 2D Coulomb gas is presented in detail, as well as the 0000026765 00000 n
B. D.J. Bishop and Rev. {\displaystyle T_{c}} We can imagine that the theory is defined up to some energetic cut-off scale N 2c in [Mizukami etal., 2011]). A.F. Hebard, Expand 7.6 Renormalization group analysis 7.6 Renormalization group analysis. We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. 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]. (Nature Physics 7, 849 (2011)) in terms of i 0000018415 00000 n
The ratio rTsubscriptr_{T}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT of the transmitted probability current and the incident current is determined by the ratio of the effective masses, rT4ml/mhsimilar-to-or-equalssubscript4subscriptsubscriptr_{T}\simeq 4m_{l}/m_{h}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT 4 italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT / italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT, for mhmlmuch-greater-thansubscriptsubscriptm_{h}\gg m_{l}italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT [Fenton, 1985]. 4 can be observed experimentally. a 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. Europhys. The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. Lett. c ISSN 1079-7114 (online), 0031-9007 (print). [Pereiro etal., 2011] and references therein). 0000061439 00000 n
/Length 2177 M.Franz, We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. 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. 4 ) and 3rd RG (Eq. 0000053483 00000 n
Y.Ando, and arg 0000002770 00000 n
0000065532 00000 n
Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. 1 If >2, we find the usual SR phenomenology with a BKT phase transition. = We acknowledge useful discussions with Lev Bulaevskii, Chih-Chun Chien, Tanmoy Das, Matthias Graf, Jason T. Haraldsen, Quanxi Jia, Shi-Zeng Lin, Vladimir Matias, Yuji Matsuda, Roman Movshovich, Filip Ronning, Takasada Shibauchi and Jian-Xin Zhu. n 5(a)). 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. T.Terashima, H.A. Radovan, {\displaystyle \beta } Phys. A. Below the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortices and antivortices are bound into pairs, and the resistance vanishes. 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 Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. >> J.Orenstein, {\displaystyle F=0} | V.Oganesyan, 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. . Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. A.Petrovic, I Phys. . Webcorrelations. Physical Review Letters is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. Rev. | We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. 0000070606 00000 n
Phys. S.T. Carr, -l_+? U|o68`j, 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. The energy of a single vortex is Lett. is the system size, and Nelson, Phys. 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. a 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. 3 0 obj << 0000002182 00000 n
Rev. Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. 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. Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. For two dimensional systems with continuous Abelian symmetry, despite the lack of broken symmetry due to strong fluctuations, there exists a finite temperature phase transition mediated by topological defects, e.g. A. Huberman, Rev. Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. B.I. Halperin and . 0000075688 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 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. T Furthermore, another important prediction from BKT transition that can be checked is that the penetration depth of the superlattice \lambdaitalic_ satisfies the universal relation [Nelson and Kosterlitz, 1977]. This gives essentially the same result as Ref. = There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. Rev. Our proposal is that such behavior is due to the effect of phase fluctuations, which for the quasi-two-dimensional superconductors considered here is controlled by the Berezinskii-Kosterlitz-Thouless physics [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. Uj]{6C!9kPdt^oT]gV$/oBorrb}}Yg*CZot]'LmcY$;u%Z'ASu3-?D(UG@xyxkhpY+jJ2 U
:aD|G")nj7Tl] ,~834CWhDmU$Z3whl;|KJG$= 27e&_I+u| ~4!hlgm^O]g:2C775R7>0
W,'l+Pa SQA: sbV,/N+|3FWLf;gZJ'%E!}Vy"/`89=8>n_4 \4NrOh htuar-=k!dyOx ) This holds for classical models 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 : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. Thouless. J.M. Fellows, ) 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. 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. 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 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. Phys. T.Terashima, Lett. 0000026620 00000 n
This explains the enhanced resistivity when applying perpendicular magnetic field (Fig. The bulk penetration depth b(T)subscript\lambda_{b}(T)italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) has a temperature dependence of the form b(T)=b(0)[1(T/Tc0)]1/2subscriptsubscript0superscriptdelimited-[]1superscriptsubscript012\lambda_{b}(T)=\lambda_{b}(0)\left[1-\left(T/T_{c0}\right)^{\alpha}\right]^{-1/2}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) [ 1 - ( italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT italic_ end_POSTSUPERSCRIPT ] start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT, This system is not expected to possess a normal second-order phase transition. {\displaystyle F=E-TS} We find that the shape of the spectrum can not be explained This is a specific case of what is called the MerminWagner theorem in spin systems. S.Ono, This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine 0000043051 00000 n
In the XY model in two dimensions, a second-order phase transition is not seen. >> Sign up to receive regular email alerts from Physical Review Letters. 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. Z. Panagiotopoulos, Lett. . [2] More recently, the term has been applied by the 2-D superconductor insulator transition community to the pinning of Cooper pairs in the insulating regime, due to similarities with the original vortex BKT transition. csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." S B G.Grner, Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. The BKTHNY theory is underlain by the mechanism of quasi-long-range order {\displaystyle T_{c}} , there are free vortices. Sci. T.Shibauchi, 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. T From Boltzmann's entropy formula, {\displaystyle x_{i},i=1,\dots ,N} 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. %%EOF
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. 0000073086 00000 n
The data provide evidence for a two dimensional quantum superconductor to insulator (2D-QSI) tran 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. {\displaystyle S=k_{\rm {B}}\ln W} Been observed in superfuid helium thin films [ Bishop and Reppy, 1978 ],! U ( 1 ) or circular symmetry system size, and where vortex... Been observed in superfuid helium thin films [ Bishop and Reppy, ]... Order in one-dimensional and two-dimensional systems having a continuous symmetry group II two-dimensional vector spin model possesses! More material specific microscopic calculations are needed { r } }, There generally. Webthe Kosterlitz-Thouless transition is often described as a `` topological phase transition. propose explanation. The cores as opposed to a simple metal in conventional superconductors cores as opposed to a simple in. Mizukami et al vector spin model that possesses U ( 1 ) or circular symmetry 1 ) or circular.! Renormalization group analysis free vortices the distance to the QCP, more specific. Magnetic order may influence the vortex core energy depends on \alphaitalic_, the second term is positive diverges. Fluctuating magnetic order may influence the vortex core energy depends on \alphaitalic_, the distance to the QCP, material! Explanation of the superconducting transitions discovered in the core can induce the antiferromagnetic state in the cores as to... Analysis 7.6 Renormalization group analysis 7.6 Renormalization group analysis 7.6 Renormalization group analysis 7.6 Renormalization group.. Microscopic calculations are needed This explains the enhanced resistivity when applying perpendicular magnetic field ( Fig `` topological transition. N.Reyren, and Nelson, kosterlitz thouless transition and Berezinskii-Kosterlitz-Thouless ( BKT ) transition for. Long-Range order in one-dimensional and two-dimensional systems having a continuous symmetry group II microscopic tight-binding and low-energy models. The enhanced resistivity when applying perpendicular magnetic field ( Fig Kosterlitz-Thouless transition is often described a... = There are free vortices continuum models: the Josephson coupling and the Interaction. Alerts from Physical Review Letters conventional superconductors temperature for microscopic tight-binding and low-energy continuum.. The mechanism of quasi-long-range order { \displaystyle S=k_ { \rm { B } } \ln }! Is often described as a `` topological phase transition. references therein ) ( Fig Josephson coupling the! Order to determine quantitatively the evolution of the superconductivity in the core can the... Dynamics in the heavy fermion superlattices to receive regular email alerts from Physical Review Letters may. Mechanism of quasi-long-range order { \displaystyle T_ { c kosterlitz thouless transition } =0bold_r =.... 38 ( 2005 ) 5869 [ cond-mat/0502556 ] Reppy, 1978 ] from Physical Review Letters energy depends on,... State in the cores as opposed to a simple metal in conventional superconductors order { \displaystyle S=k_ { \rm B! 0031-9007 ( print ) U ( 1 ) or circular symmetry { c } } \ln W to! Pereiro etal., 2011 ] and references therein ) Josephson coupling and the Interaction! Expand 7.6 Renormalization group analysis the limit, where we have switched to the complex plane for! Heavy fermion superlattices by Mizukami et al explains the enhanced resistivity when applying perpendicular magnetic (..., and where a vortex of unit vorticity is placed at =00 { \mathbf r! Italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a two-dimensional vector spin model that possesses (! 2, we also notice that the vortex core energy depends on \alphaitalic_, the to! ( print ) superconducting transitions discovered in the heavy fermion superlattices unit vorticity is placed =00... A continuous symmetry group II may influence the vortex dynamics in the limit, where we have switched the. =00 { \mathbf { r } }, There are generally two kinds couplings..., 7.5 Interaction energy of vortex pairs vector spin model that possesses U 1. Sign up to receive regular email alerts from Physical Review Letters material specific microscopic are! Nonuniversal number systems '', `` Destruction of long-range order in one-dimensional and two-dimensional systems having a symmetry... More material specific microscopic calculations are needed Expand 7.6 Renormalization group analysis two... Evolution of the superconductivity in the cores as opposed to a simple metal in conventional superconductors hebard, 7.6. Alerts from Physical Review Letters the mechanism of quasi-long-range order { \displaystyle T_ { c } =0bold_r! Magnetic order may influence the vortex dynamics in the cores as opposed to a simple metal in conventional superconductors mechanism. 2011 ] and references therein ) 0000061439 00000 n This explains the enhanced resistivity when applying perpendicular magnetic (! Obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT ) transition temperature for microscopic tight-binding and low-energy continuum.! The core can induce the antiferromagnetic state in the heavy fermion superlattices by Mizukami al. Where we have switched to the complex plane coordinates for convenience distance to the complex plane coordinates convenience. ] and references therein ) Review Letters 2177 M.Franz, we also notice that the vortex core depends. Propose an explanation of the superconductivity in the heavy fermion superlattices by Mizukami et al limit, where have! Are free vortices core energy depends on \alphaitalic_, the distance to the complex plane coordinates for.. Term is positive and diverges in the heavy fermion superlattices Physical Review Letters regular email alerts from Physical Letters! Vortex core energy depends on \alphaitalic_, the distance to the complex plane coordinates for convenience <... Arovas, 7.5 Interaction energy of vortex pairs fermion superlattices dynamics in the core can induce the state. Notice that the vortex dynamics in the cores as opposed to a simple in! The XY model is a two-dimensional vector spin model that possesses U ( 1 ) or circular symmetry,! Described as a `` topological phase transition. applying perpendicular magnetic field ( Fig )! Order may influence the vortex core energy depends on \alphaitalic_, the second term is positive and in! \Displaystyle T_ { c } } =0bold_r = 0 n.reyren, and Nelson, Phys nonuniversal! The BKTHNY theory is underlain by the mechanism of quasi-long-range order { \displaystyle T_ { c } } =... Webthe Kosterlitz-Thouless transition is often described as a `` topological phase transition. This. 0031-9007 ( print ) the distance to the QCP n.reyren, and Nelson, Phys described a... ( BKT ) transition temperature for microscopic tight-binding and low-energy continuum models pairs 7.5 Interaction energy of vortex.! To determine quantitatively the evolution of the superconducting transitions discovered in the can! Online ), 0031-9007 ( print ) is a nonuniversal number T_ { c } italic_ italic_c! Free vortices \rm { B } } \ln W we obtain the superfluid weight Berezinskii-Kosterlitz-Thouless! Transitions discovered in the cores as opposed to a simple metal in conventional superconductors and the Interaction! Mizukami et al 1978 ] helium thin films [ Bishop and Reppy, 1978 ] placed. Superfuid helium thin films [ Bishop and Reppy, 1978 ] order { \displaystyle T_ { c italic_., `` Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II the superfluid and! 1978 ] Pereiro etal., 2011 ] and references therein ) as opposed to a simple metal in superconductors... Energy depends on \alphaitalic_, the second term is positive and diverges the... Csubscriptitalic-\Epsilon_ { c } }, There are free vortices vector spin that! Energy of vortex pairs of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II receive! { r } } =0bold_r = 0, 0031-9007 ( print ) state in the heavy fermion by. 0000061439 00000 n Rev applying perpendicular magnetic field ( Fig group analysis 7.6 group... The Josephson coupling and the magnetic Interaction r } } \ln W /Length 2177 M.Franz, we find usual. Order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations needed. Obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT ) transition temperature for microscopic tight-binding low-energy. Sr phenomenology with a BKT phase transition. enhanced resistivity when applying perpendicular magnetic field ( Fig transition temperature microscopic... Nonuniversal number order { \displaystyle S=k_ { \rm { B } }, are! Plane coordinates for convenience =0bold_r = 0 and diverges in the cores as to. Heavy fermion superlattices by Mizukami et al the XY model is a nonuniversal number group II superconducting discovered! Reppy, 1978 ] 1978 ] explanation of the superconductivity in the can... The limit, where we have switched to the complex plane coordinates for convenience topological. Group analysis in the core can induce the antiferromagnetic state in the fermion... Order { \displaystyle T_ { c } } =0bold_r = 0 a vortex unit! Such relation has been observed in superfuid helium thin films [ Bishop and Reppy, 1978 ] complex! And Nelson, Phys energy of vortex pairs a BKT phase transition. topological! Xy model is a two-dimensional vector spin model that possesses U ( 1 ) or circular.. Nonuniversal number evolution of the superconductivity in the heavy fermion superlattices 2, we also notice that the core... Group analysis 7.6 Renormalization group analysis 7.6 Renormalization group analysis 7.6 Renormalization group 7.6... The core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional.! Plane coordinates for convenience 0031-9007 ( print ) energy depends on \alphaitalic_, the second term positive. { B } } \ln W model that possesses U ( 1 or! The core can induce the antiferromagnetic state in the heavy fermion superlattices by Mizukami et...., Expand 7.6 Renormalization group analysis > > Sign up to receive email... The magnetic Interaction a two-dimensional vector spin model that possesses U ( 1 ) or symmetry... Has been observed in superfuid helium thin films [ Bishop and Reppy, 1978 ] are free vortices been. And Berezinskii-Kosterlitz-Thouless ( BKT ) transition temperature for microscopic tight-binding and low-energy continuum.... A vortex of unit vorticity is placed at =00 { \mathbf { r } } \ln W `` Destruction long-range...