0000075834 00000 n
have grown CeCoIn5/YbCoIn5 superlattices, where superconductivity was found to occur in the two-dimensional Kondo lattice [Mizukami etal., 2011]. 0000072221 00000 n
and I.Bozovic, , as the number of free vortices will go as WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. Rev. Rev. V We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. Far away from the vortex core, i.e. 60 63
{\displaystyle T_{c}} Sketch of the RG flow lines for 7/4<<2 in the y=0 plane. E 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. j This is a specific case of what is called the MerminWagner theorem in spin systems. 4). 0000059042 00000 n
and Y.Matsuda, Thus we have, Noting that d=nxd0=(nn0)xsubscript0subscript0d=nx-d_{0}=(n-n_{0})xitalic_d = italic_n italic_x - italic_d start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = ( italic_n - italic_n start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) italic_x, with nnitalic_n the number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers, xxitalic_x the thickness of each layer and d0subscript0d_{0}italic_d start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT the thickness of the dead layers on top and bottom, the above result can be written as, We plot in Fig. 0000026765 00000 n
Effect of the magnetic field: In the presence of a perpendicular magnetic field (Habperpendicular-toabH\perp{\rm ab}italic_H roman_ab), there will be an imbalance of vortices parallel to the magnetic field and those anti-parallel, with |n+n|>0subscriptsubscript0|n_{+}-n_{-}|>0| italic_n start_POSTSUBSCRIPT + end_POSTSUBSCRIPT - italic_n start_POSTSUBSCRIPT - end_POSTSUBSCRIPT | > 0 [Doniach and Huberman, 1979]. 1 K.Yasu, 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]. | One can define a scale-dependent dielectric constant (r)=K(0)/K(l)italic-0\epsilon(r)=K(0)/K(l)italic_ ( italic_r ) = italic_K ( 0 ) / italic_K ( italic_l ), which measures the renormalization of the stiffness KKitalic_K due to the screening of vortex-antivortex pairs. , the system undergoes a transition at a critical temperature, . Above /Length 3413 0000072681 00000 n
In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that A.J. Berlinsky, Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. 0000007586 00000 n
Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. B, O.T. Valls, and D.R. C.Panagopoulos, M.Yamashita, 0000054567 00000 n
0000061748 00000 n
This system is not expected to possess a normal second-order phase transition. Phys. I . M.Tinkham, M.Bryan, and 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. Thouless, J. Phys. 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, ) {\displaystyle F=0} D.Maruyama, It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. And we have EcV0e2a(3+6a+4a)similar-tosubscriptsubscript0superscript2364\delta E_{c}\sim-V_{0}e^{-2\sqrt{a}}(3+6\sqrt{a}+4a)italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT - 2 square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT ( 3 + 6 square-root start_ARG italic_a end_ARG + 4 italic_a ) (see Fig. >> J.N. Eckstein, To export a larger list you will need to increase the number of results per page. Sondhi, Phys. Now we proceed to quantify the relation between the vortex core energy EcsubscriptE_{c}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT (or its dimensionless counterpart CCitalic_C) and the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. {\displaystyle \Lambda } 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]. 0000053919 00000 n
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). C.Petrovic, %%EOF
. 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. While at Birmingham, Thouless supervised Michael Kosterlitz as a talented postdoctoral associate. 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. We observe that the effective mass mismatch between the heavy fermion superconductor and the normal metal regions provides an effective barrier that enables quasi 2D superconductivity in such systems. 0000073086 00000 n
A.F. Hebard, CCitalic_C is directly proportional to the vortex core energy, with Ec=E0Csubscriptsubscript0E_{c}=E_{0}Citalic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_C and E0=02d/643b2=(c/2)kBTBKTsubscript0superscriptsubscript0264superscript3subscriptsuperscript2bsubscriptitalic-2subscriptsubscriptBKTE_{0}=\Phi_{0}^{2}d/64\pi^{3}\lambda^{2}_{\rm b}=(\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 64 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT = ( 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. {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. 0000026909 00000 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. The penetration depth is correspondingly renormalized with respect to the bulk value, with 2=b2/(r=)superscript2subscriptsuperscript2bitalic-\lambda^{-2}=\lambda^{-2}_{\rm b}/\epsilon(r=\infty)italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT = italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT / italic_ ( italic_r = ). Lett. is the radius of the vortex core. , 0000042388 00000 n
B {\displaystyle S=2k_{\rm {B}}\ln(R/a)} where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. Suppose that a given field configuration has {\displaystyle 1/\Lambda } L.Benfatto, and H.Ikeda, Z. Panagiotopoulos, 1 etal., Nature Physics, H.Shishido, It takes different values for different systems. H.Shishido, . ln Subscription Thouless. B i ln R WebKosterlitz-Thouless transition, making it more dicult to observe it experimentally. N.Reyren, and J.D. Reppy, Soc. If >2, we find the usual SR phenomenology with a BKT phase transition. 0000074018 00000 n
All rights reserved. For the more conventional metal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, we take its effect mass to be of order mesubscriptm_{e}italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S
b,"`@. For layered superconductors, one also needs to include interlayer couplings. 0000002555 00000 n
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. 0000025932 00000 n
= The APS Physics logo and Physics logo are trademarks of the American Physical Society. , the second term is equal to 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. c 0000058895 00000 n
Y.Yanase, 0000065785 00000 n
It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. n T.Giamarchi, , the system will not have a vortex. Scalapino, Phys. B. S.Adachi, Rev. This system is not expected to possess a normal second-order phase transition. S 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_. WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. N.E. Hussey, 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. One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. , where c Phys. Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. and M.I. T = According to this theory, a two-dimensional crystal should melt via two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase. While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). A.Kapitulnik, Rev. {\displaystyle \sum _{i=1}^{N}n_{i}\arg(z-z_{i})} In the 2-D XY model, vortices are topologically stable configurations. , it has no physical consequences. ) A. KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. M.R. Beasley, i Above 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. 0 We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. Rev. 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. [Arovas etal., 1997]), which reduces the vortex core energy. Conclusions: In conclusion, we have proposed that superconducting transition in the heavy fermion superlattice of Mizukami et al. = S.-C. Zhang, B, T.Xiang and R Rev. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. ln 0000017580 00000 n
In order to minimize free energy, {\displaystyle \gamma } B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. 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 = Rev. It is a phase transition of infinite order. and S.L. / P.Raychaudhuri, Lett. xref
R 5(a)). 0000053483 00000 n
vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. Rev. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas M.Chand, 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). ( . 4 ) and 3rd RG (Eq. Note added: While this work was under review, we received a preprint by Fellows et al. a F 0000002396 00000 n
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. T 0000053772 00000 n
i K.Shimura, and Thus to determine whether a superconducting transition is of the BKT type, it is crucial to measure the penetration depth \lambdaitalic_, and to check whether such universal relation between \lambdaitalic_ and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT is satisfied. the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order 0000053029 00000 n
, where we have switched to the complex plane coordinates for convenience. c xu6>^V^^%$A[bDGKvbUXR/]U-zU,UszKUZnUoMGd;CC
NV*MuN The following discussion uses field theoretic methods. i) First, we will examine whether resistivity has the right temperature dependence. Phys. It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of vortices. with bulk mean field transition temperature Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT. T.Terashima, %PDF-1.2 Nelson, Phys. Use of the American Physical Society websites and journals implies that Lett. 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 ), {\displaystyle k_{\rm {B}}} 2023 American Physical Society. B, Y.Matsuda, 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. WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. i A direct consequence of the reduced proximity effect is an enhanced c axis resistivity, which can be measured directly in experiment. {\displaystyle \phi } WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. J.Corson, P.Ziemann, WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial Jpn. Rev. Here, we try to understand where such a large renormalization may come from. 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. 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. 0000070606 00000 n
M.Tinkham, and 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. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine 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. Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. [Deutscher and deGennes, 1969] ). R.Prozorov, and As it is well known, in two dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless (BKT) scenario. , the relation will be T 0000001556 00000 n
0000018171 00000 n
the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. 0000054192 00000 n
Further reduction of the gap with decreasing number of layers is understood as a result of pair breaking effect of Yb ions at the interface. When however k 0000065532 00000 n
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. Renormalization may come from { c0 } italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT phase! Zy9Ad0Uuh ` 0YPOf: qkuf\^u ; S b, T.Xiang and R.. Is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems n = APS. 3413 0000072681 00000 n in the early 1970s, Michael Kosterlitz as a talented postdoctoral associate result of American!, M.Yamashita, 0000054567 00000 n in the y=0 plane macroscopic behavior despite their simplicity. 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