Inducing a Magnetic Monopole with Topological Surface States REPORTS

REPORTS

that such a general definition of a topological insulator reduces to the Z2 topological insulators described in (4–6) for non-interacting band Inducing a Magnetic Monopole with insulators; this finding is a three-dimensional (3D) generalization of the quantum spin Hall insulator in two dimensions (7–10). For generic Topological Surface States band insulators, the parameter q has a micro- scopic expression of the momentum space Xiao-Liang Qi,1 Rundong Li,1 Jiadong Zang,2 Shou-Cheng Zhang1* Chern-Simons form (3, 11). Recently, experimental evidence of the topologically nontrivial Existence of the magnetic monopole is compatible with the fundamental laws of nature; surface states has been observed in Bi Sb alloy however, this elusive particle has yet to be detected experimentally. We show theoretically that an 1−x x (12), which supports the theoretical prediction electric charge near a topological surface state induces an image magnetic monopole charge due that Bi Sb is a Z topological insulator (4). to the topological magneto-electric effect. The magnetic field generated by the image magnetic 1−x x 2 With periodic temporal and spatial boundary monopole may be experimentally measured, and the inverse square law of the field dependence conditions, the partition function is periodic in q can be determined quantitatively. We propose that this effect can be used to experimentally realize under the 2p shift, and the system is invariant a gas of quantum particles carrying fractional statistics, consisting of the bound states of the under the time-reversal symmetry at q = 0 and electric charge and the image magnetic monopole charge. q = p.However,withopenboundaryconditions, the partition function is no longer periodic in q, he electromagnetic response of a conven- Furthermore, when a periodic boundary condi- and time-reversal symmetry is generally broken tional insulator is described by a dielectric tion is imposed in both the spatial and temporal (but only on the boundary), even when q =(2n + Tconstant e and a magnetic permeability m. directions, the integral of such a total derivative 1)p.Ourworkin(3)givesthefollowingphysical An electric field induces an electric polarization, term is always quantized to be an integer; i.e., interpretation: Time-reversal invariant topologi- S q cal insulators have a bulk energy gap but have whereas a magnetic field induces a magnetic ℏ qn (where n is an integer). Therefore, the polarization. As both the electric field E(x)and partition¼ function and all physically measurable gapless excitations with an odd number of Dirac

the magnetic induction B(x)arewelldefinedinside quantities are invariant when the q parameter is cones on the surface. When the surface is coated on January 4, 2010 an insulator, the linear response of a convention- shifted by 2p times an integer (2). Under time- with a thin magnetic film, time-reversal sym- al insulator can be fully described by the effective reversal symmetry, eiqn is transformed into e–iqn metry is broken, and an energy gap also opens up 2 1 3 2 1 2 3 (here, i = –1). Therefore, all time-reversal in- at the surface. In this case, the low-energy theory action S0 8p ∫d xdt eE − m B ,whered xdt is ¼ variant insulators fall into two general classes, is completely determined by the surface term in the volume element of space and time. However, described by either q =0orq = p (3). These two Eq. 1. As the surface term is a Chern-Simons in general, another possible term is allowed in the time-reversal invariant classes are disconnected, term, it describes the quantum Hall effect on effective action, which is quadratic in the elec- and they can only be connected continuously by the surface. From the general Chern-Simons- tromagnetic field, contains the same number of time-reversal breaking perturbations. This classi- Landau-Ginzburg theory of the quantum Hall

derivatives of the electromagnetic potential, and fication of time-reversal invariant insulators in effect (13), we know that the coefficient q = www.sciencemag.org is rotationally invariant; this term is given by terms of the two possible values of the q (2n +1)p gives a quantized Hall conductance of q a 3 e2 1 e2 Sq ∫d xdtE⋅B.Here,a (where ħ parameter is generally valid for insulators with sxy n . This quantized Hall effect on ¼ 2p 2p ¼ ℏc ¼ þ 2 h is PlanckÀÁ’sconstantÀÁ h divided by 2p and c is the arbitrary interactions (3). The effective action the surfaceÀÁ is the physical origin behind the speed of light) is the fine-structure constant, and q contains the complete description of the topological magneto-electric (TME) effect. can be viewed as a phenomenological parameter electromagnetic response of topological insula- Under an applied electric field, a quantized in the sense of the effective Landau-Ginzburg tors. Topological insulators have an energy gap in Hall current is induced on the surface, which in theory. This term describes the magneto-electric the bulk, but gapless surface states protected by turn generates a magnetic polarization and vice effect (1), where an electric field can induce a the time-reversal symmetry. We have shown (3) versa. Downloaded from magnetic polarization, and a magnetic field can induce an electric polarization. Unlike conventional terms in the Landau- Fig. 1. Illustration of the image charge Ginzburg effective actions, the integrand in Sq and monopole of a point-like electric is a total derivative term, when E(x) and B(x) charge. The lower-half space is occupied are expressed in terms of the electromagnetic by a topological insulator (TI) with di- vector potential (where ∂m denotes the partial electric constant e2 and magnetic perme- derivative; m, n, r, and t denote the spacetime ability m2.Theupper-halfspaceisoccupied coordinates; F mn is the electromagnetic field by a topologically trivial insulator (or vac- tensor; and Am is the electromagnetic potential) uum) with dielectric constant e1 and magnetic permeability m1. A point electric q a 3 mn rt charge q is located at (0, 0, d). When seen Sq ∫d xdtemnrtF F from the lower-half space, the image ¼ 2p 16p (1) q a 3 m n r t electric charge q1 and magnetic monopole ∫d xdt∂ emnrsA ∂ A ¼ 2p 4p ð Þ g1 are at (0, 0, d); when seen from the upper-half space, the image electric charge q2 and magnetic monopole g2 1Department of Physics, Stanford University, Stanford, CA are at (0, 0, −d). The red solid lines 94305–4045, USA. 2Department of Physics, Fudan Uni- represent the electric field lines, and blue versity, Shanghai, 200433, China. solid lines represent magnetic field lines. *To whom correspondence should be addressed. E-mail: (Inset) Top-down view showing the in-plane component of the electric field at the surface (red arrows) [email protected] and the circulating surface current (black circles).

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We propose a manifestation of the TME ef- (0, 0, −d); the magnetic field is given by an image by the in-plane component of the electric field fect. When a charged particle is brought close to magnetic monopole g2 at (0, 0, −d). The above and is perpendicular to this component. This the surface of a topological insulator, a magnetic ansatz satisfies the Maxwell equations on each current is nothing but the quantized Hall current monopole charge is induced as a mirror image of side of the boundary. At the boundary z =0,the mentioned earlier. For the problem under consider- the electric charge. The full set of electromag- solution is then matched according to the standard ation, the surface current density is calculated as netic field equations can be obtained from the boundary condition, giving e2 q r q q ^ functional variation of the action S0 + Sq (14), and 1 2 j P3 2 2 3 eϕ 5 ¼ ¼ h 1 a P 2 2 2 ð Þ they can be presented as conventional Maxwell’s 1 e − e 1=m 1=m − 4a2P2 3 r d 1 2 1 2 3 q þ ð þ Þ equations but with the modified constituent equa- ð Þð þ Þ 2 2 which is circulating around the origin (inset of ¼ e1 e1 e2 1=m1 1=m2 4a P3 tions describing the TME effect (3) ð þ Þð þ Þþ Fig. 1) (here, r is the radial distance and ^eϕ is the g1 −g2 tangental unit vector). Physically, this surface D E 4pP − 2aP3B ¼ ¼ þ 2 4aP3 current is the source that induces the magnetic H B − 4pM 2aP3E ð Þ − q ¼ þ 2 2 field. On each side of the surface, the magnetic ¼ e1 e2 1=m1 1=m2 4a P3 where P (x)=q(x)/2p is the magneto-electric ð þ Þð þ Þþ field induced by the surface current can be viewed 3 3 polarization (3), D is the electric displacement, P ð Þ as the field induced by an image magnetic mono- is the electric polarization, H is the magnetic We will first take e1 = e2 = m1 = m2 =1below pole on the opposite side. field, and M is the magnetization. It takes the and then recover the e1,2, m1,2 when discussing According to the above calculation, the image value of P3 =0invacuumorconventional the experimental proposals later. The solution magnetic monopole field indeed has the correct insulators and P3 = T1/2 in topological insulators, shows that, for an electric charge near the surface magnetic field dependence expected from a with the sign determined by the direction of the of a topological insulator, both an image mag- monopole, and it can be controlled completely surface magnetization. netic monopole and an image electric charge will through the position of the electric charge. As we Now consider the geometry as shown in Fig. 1. be induced, as compared with conventional elec- started with the Maxwell’s equation, which The lower-half space (z <0)isoccupiedbya tromagnetic media where only an electric image includes ∇⋅B 0, the magnetic flux integrated ¼ topological insulator with a dielectric constant e2 charge will be induced. It is notable that the over a closed surface must vanish. We can check and a magnetic permeability m2,whereasthe magnitudes of the image magnetic monopole and that this is the case by considering a closed upper-half space (z > 0) is occupied by a image electric charge satisfy the relation q 1,2 = surface— for example, a sphere with radius a— conventional insulator with a dielectric constant T(aP3)g1,2.Thisisjusttherelationq =(q/2p)g for that encloses a topological insulator. The detailed on January 4, 2010 e1 and a magnetic permeability m1.Apointelec- the electric and magnetic charges of a dyon inside calculation is presented in the supporting online tric charge q is located at (0, 0, d)withd >0.The the q vacuum (16), with q/2p = TP3 here. material (17). Inside the closed surface, there is Maxwell equations, along with the modified The physical origin of the image magnetic not only a image magnetic monopole charge, but constituent equations and the standard boundary monopole is understood by rewriting part of also a line of magnetic charge density whose conditions, constitute a complete boundary value the Maxwell equations as integral exactly cancels the point image magnetic problem. To solve this problem, the method of monopole. However, when the separation be- ∇ B 2aP3d z ^n E 4 images (15)canbeused.Weassumethat,inthe Â ¼ ð Þ Â ð Þ tween the electric charge and the surface (d)is lower-half space, the electric field is given by an with P3 = T1/2 the value for the topological in- much smaller than the spherical radius (a), the effective point charge q /e1 and an image charge sulator [in the above equation, ∇ is the derivative magnetic field is completely dominated by the www.sciencemag.org q 1 at (0, 0, d), whereas the magnetic field is given vector, ^n is the normal vector of the surface, and image magnetic monopole, and the contribution by an image magnetic monopole g1 at (0, 0, d). d(z)istheDiracd function]. The right-hand side due to the line of magnetic charge density is In the upper-half space, the electric field is giv- of the above equation corresponds to a surface vanishingly small. Therefore, we propose here to en by q /e1 at (0, 0, d)andanimagechargeq 2 at current density j sxy ^n E ,whichisinduced experimentally observe the magnetic monopole ¼ ð Â Þ in the same sense that we can experimentally observe other fractionalization, or de-confinement, Fig. 2. Illustration of the experi- phenomena in condensed matter physics. In any mental setup to measure the image closed electronic system, the total charge must Downloaded from monopole. A magnetic layer is be quantized to be an integer. However, one deposited on the surface of the can separate fractionally charged elementary topological insulator, as indicated by the layer with blue arrows. (The same layer is drawn in Figs. 3 and 4.) A scanning MFM tip carries a magnetic flux f and a charge q.A charged impurity is confined on the surface with charge Q and distance D out of the surface. By scanning over the voltage V and the distance r to the impurity, the effect of the image monopole magnetic field can be measured (see text).

Fig. 3. Illustration of the fractional statistics induced by image monopole effect. Each electron forms a dyon with its image monopole. When two electrons are exchanged, an AB phase factor is obtained (which is determined by half of the image monopole flux) and leads to statistical transmutation.

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excitations arbitrarily far from each other, so that netic layer can have defects such as domains model has been studied in the fractional quantum fractional charge can have well-defined meaning and steps that induce an inhomogeneous fringe Hall context (24).] According to Eq. 3, the locally. A similar situation occurs in spin-charge magnetic field acting on the MFM tip. However, statistical angle of an electron-induced dyon is 2 separation. Whereas the total charge and the total all surface roughness effects can only induce 2a P3 spin of a closed system must be linked to each magnetic field of dipolar or higher order. Con- ϕ 2 2 7 ¼ e1 e2 1=m 1=m 4a P ð Þ other, spin and charge can occur as separated sequently, the contribution of surface roughness ð þ Þð 1 þ 2Þþ 3 local excitations. In our case, as long as d is much decays faster than 1/r3 so that the monopole which is of order a2 and can generally be smaller than the radius of curvature of a topo- contribution proportional to 1/r3 still dominates irrational (25). It should be noticed that the image logical surface a,thelocalmagneticfieldis the long-range behavior. Further detail on the charge beneath the electron does not contribute completely determined by a single image mag- calculations is presented in the supporting online additional AB phase because its motion cor- netic monopole. material (17). responds to a displacement current. For P3 = Such an image monopole can be observed Because the position of the image monopole 1/2 and e1, m1, m2 ~1,e2 ~100,weobtainϕ ≅ experimentally by a magnetic force microscope is determined by that of the charge above the a2/200 ≅ 2.6 ×10−7 rad. Though the statistical (MFM). Consider the surface of the topological surface, the pure monopole is not an elementary angle is quite small, it is physically observable. insulator with a localized charged impurity (Fig. excitation of the system, and this is different from With the geometry of Fig. 4, a quasi-1D super- 2). A scanning MFM tip can be applied to detect the monopole proposed in some spin ice models conducting ring and a metallic island surrounded the magnetic field distribution of the image (19). However, if we consider the electrons mov- by the ring are deposited on top of the topological monopole. However, the charge of the impurity ing on the topological surface as part of the insulator surface (which has already been gapped also generates an electric force to the tip. The system, the bound state of an electron and its by a magnetic layer). By tuning the gate voltage contribution of the image monopole can be dis- image monopole does become a dynamical of the central island, the number of electrons N on tinguished from other trivial contributions by scan- object with nontrivial properties. Such a bound the island can be tuned. Because of the statistical ning both the tip position r and the tip voltage V. state of charge and monopole is known in high- angle ϕ given by Eq. 7, each electron in the For a given position r, fmin(r)definesthemini- energy physics as a “dyon” (16)”:acomposite central island induces a flux of ϕ seen by the mal force applied to the tip when scanning the particle with both electric and magnetic charges. electrons in the ring. Consequently, the net flux voltage, and D is the distance of the charged Besides contributing a monopole-monopole through the ring is Nϕ in unit of the flux quanta, impurity to the surface. In the limit of r >> D,the Coulomb interaction, the image monopole also which generates a supercurrent in the super- 6 conventional charge interaction leads to a 1/r induces a statistical interaction between two conducting ring as in a standard superconducting on January 4, 2010 dependence of fmin(r). The image monopole mag- dyons. When two dyons are exchanged, each of quantum interference device. For a typical netic field leads to more dominant contribution them will obtain an Aharonov-Bohm (AB) phase electron density of n =1011/cm2 and island size due to the magnetic field of the other one. The net R =1mm, the net magnetic flux is n ϕpR2ℏc=e ≃ 4aP3 Qf −4 fmin r ≃ AB phase obtained by the two-particle system 2:6 10 hc=2e, and the corresponding mag- 2 2 3 Â −3 ð Þ 1 e2=e1 1=m1 1=m2 − 4a P3 r during an exchange process is independent of the netic field is B n ϕℏc=e ≃ 1:7 10 G, which ð þ Þð þ Þ ¼ Â 6 path of the particles on the 2D plane, which thus is observable. It is possible to have some other ð Þ can be interpreted as a statistical angle of the topological insulator material with a smaller in which Q is the impurity charge and f is the net dyon (Fig. 3). Therefore, this setup provides a dielectric constant e2,inwhichthestatistical

flux of the magnetic tip. For the estimated condensed matter realization of the anyon angle of the dyon can be larger. www.sciencemag.org parameters e2 ≅ 100 for the Bi1−xSbx alloy (18), concept (20, 21)intheabsenceofanyexternal We have shown theoretically that the topo- e1 =1,m1 ≅ m2 ≅ 1, f ≅ 2.5hc/e,andatypical magnetic field. Anyons have unusual quantum logical surface states of a 3D topological insu- distance r =50nm,theforceisfmin(r) ≅ 0.3 pN/mm, statistics; interchanging a pair of them gives rise lator can act as a mirror that images an electron as which is observable in the present experiments. to a complex phase factor different from zero (as amagneticmonopole.Suchatransmutationbe- In a real experimental system, the surface mag- in the case of bosons) or p (as in the case of tween electric field and magnetic field is a direct fermions). This effect also provides a mechanism manifestation of the TME effect (3). Because of of statistical transmutation in (3+1) dimensions this effect, a 2D electron gas in the neighborhood (22, 23). If each dyon has charge q and monopole of the surface will become a dyon gas with Downloaded from flux g,thenthestatisticalangleisgivenby fractional statistics. We have presented realistic ϕ gq .Forexample,thebindingofanelec- experimental setups to observe the field of the ¼ 2ℏc tron withÀÁ charge e and a monopole with flux hc/e image magnetic monopole and the statistical leads to ϕ = p,inwhichcasethedyonisaboson. angle of the dyon. However, there is a difference between the dyon studied here and that in high-energy physics. In References and Notes 1. L. D. Landau, E. M. Lifshitz, Electrodynamics of high-energy physics, the charged particle and Continuous Media (Pergamon, Oxford, 1984). monopole are point-like particles moving in three 2. E. Witten, Sel. Math. New Ser. 1, 383 (1995). dimensions. Consequently, the monopole flux 3. X.-L. Qi, T. L. Hughes, S.-C. Zhang, Phys. Rev. B 78, must be quantized in unit of hc/e,andcorre- 195424 (2008). 4. L. Fu, C. L. Kane, Phys. Rev. B 74, 195312 (2006). spondingly, the statistical angle ϕ can only be 0 5. J. E. Moore, L. Balents, Phys. Rev. B 75, 121306 (2007). or p modular 2p.Thisisconsistentwiththefact 6. R. Roy, preprint available at http://arxiv.org/abs/ that there are no anyonic statistics in (3+1) cond-mat/0604211. dimensions. Our dyon can only be defined if an 7. C. L. Kane, E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005). Fig. 4. Illustration of the experimental propos- electron is moving close to the surface of a 8. B. A. Bernevig, S.-C. Zhang, Phys. Rev. Lett. 96, 106802 al measuring the fractional statistics of the topological insulator. Consequently, the dyon is (2006). dyons. When a gate voltage is applied to the always confined to a 2D surface. In this case, 9. B. A. Bernevig, T. L. Hughes, S.-C. Zhang, Science 314, central metallic island, the number of electrons ∇⋅B 0issatisfiedeverywhereandthefluxof 1757 (2006). ¼ 10. M. König et al., Science 318, 766 (2007); published in the central island can be tuned, which in turn the image monopole does not have to be online 19 September 2007 (10.1126/science.1148047). changes the net flux threaded in the super- quantized. Correspondingly, the dyon can have 11. A. M. Essin, J. E. Moore, D. Vanderbilt, preprint availble conducting ring and leads to a supercurrent. anyonic statistics. [A possibly related anyon at http://arxiv.org/abs/0810.2998.

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12. D. Hsieh et al., Nature 452, 970 (2008). 19. C. Castelnovo, R. Moessner, S. L. Sondhi, Nature 451,42 supported by the U.S. Department of Energy, 13. S.-C. Zhang, T. H. Hansson, S. Kivelson, Phys. Rev. Lett. (2008). Office of Basic Energy Sciences under contract 62, 82 (1989). 20. J. Leinaas, J. Myrheim, Nuovo Cim. B 37, 1 (1977). DE-AC03-76SF00515. 14. F. Wilczek, Phys. Rev. Lett. 58, 1799 (1987). 21. F. Wilczek, Phys. Rev. Lett. 49, 957 (1982). 15. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 22. R. Jackiw, C. Rebbi, Phys. Rev. Lett. 36, 1116 (1976). Supporting Online Material www.sciencemag.org/cgi/content/full/1167747/DC1 1999). 23. P. Hasenfratz, G. ’t Hooft, Phys. Rev. Lett. 36, 1119 SOM Text 16. E. Witten, Phys. Lett. B 86, 283 (1979). (1976). Figs. S1 to S5 17. See supporting material on Science Online. 24. E. Fradkin, S. Kivelson, Nucl. Phys. B 474, 543 References 18. O. Madelung, U. Rössler, M. Schulz, in (1996). Landolt-Börnstein, Substance/Property Index, 25. C. Chamon et al., Phys. Rev. Lett. 100, 110405 27 October 2008; accepted 16 January 2009 Semiconductors, Non-Tetrahedrally Bonded Elements (2008). Published online 29 January 2009; and Binary Compounds I, Subvolume III/17E-17F-41C 26. We thank O. M. Auslaender, T. L. Hughes, S. Kivelson, 10.1126/science.1167747 (Springer, Berlin, 1998), pp. 1–11. and L. Luan for insightful discussions. This work is Include this information when citing this paper.

carbonate ion concentration that occurred during Global Cooling During the the E-O climate transition. Indeed, shallow-water Mg/Ca–based temperatures, from exceptionally well-preserved foraminifera deposited above the Eocene-Oligocene Climate Transition CCD, indicate ~2.5°C of cooling in the tropics Zhonghui Liu,1,2* Mark Pagani,1* David Zinniker,1 Robert DeConto,3 Matthew Huber,4 (14, 15)andcastfurthersuspicionondeep-water Henk Brinkhuis,5 Sunita R. Shah,6 R. Mark Leckie,3 Ann Pearson6 Mg/Ca–based temperatures across this major CCD deepening event. About 34 million years ago, Earth’s climate shifted from a relatively ice-free world to one Here, we report E-O sea surface temperature ’ (SST) changes, which were determined with with glacial conditions on Antarctica characterized by substantial ice sheets. How Earth s K′ temperature changed during this climate transition remains poorly understood, and evidence alkenone unsaturation index (U 37)andtetrather for Northern Hemisphere polar ice is controversial. Here, we report proxy records of sea surface index (TEX86)(16, 17), from 11 globally dis- temperatures from multiple ocean localities and show that the high-latitude temperature persed ocean localities. These localities include decrease was substantial and heterogeneous. High-latitude (45 degrees to 70 degrees in both Ocean Drilling Program/Deep Sea Drilling Project on January 4, 2010 hemispheres) temperatures before the climate transition were ~20°C and cooled an average of (ODP/DSDP) sites 277, 336, 511, 913, and 1090, ~5°C. Our results, combined with ocean and ice-sheet model simulations and benthic oxygen with paleolatitudes between ~45° and 70° in both isotope records, indicate that Northern Hemisphere glaciation was not required to accommodate hemispheres (18), and sites 628, 803, 925, 929, the magnitude of continental ice growth during this time. 998, and 1218 in the tropics (Fig. 1 and table S1) (19). Chronologies for these sites were previously established or refined and/or determined in this he abrupt shift to glacial conditions near that must be accommodated by Northern Hemi- study (table S2 and fig. S1). TEX86 indices were the Eocene-Oligocene (E-O) boundary sphere glaciation (2, 9, 12). This conclusion is converted to SST by use of a modified temper-

T~33.7 million years ago (Ma) is character- nearly untenable given scant physical evidence ature calibration based on all published ocean www.sciencemag.org ized by a ~+1.5 per mil (‰ )changeinoxygen for Northern Hemisphere ice sheets before the surface sediment data (fig. S2) (20). Nonetheless, isotopic (d18O) values of benthic foraminifera latest Miocene (7, 12–15). Deep-water forami- older calibrations would yield qualitatively similar (1–3)in~300,000years,whichisindicativeof niferal Mg/Ca ratios could be affected by factors results over the temperature ranges observed. K′ continential ice accumulation and high-latitude other than temperature (9, 11), including a deepen- Both U 37 and TEX86 SSTs show substantial cooling, and an ~1-km deepening of the global ing of the CCD (2)andchangesindeep-water high-latitude cooling between ~34 and 33 Ma (Fig. calcite compensation depth (CCD) (2). Proposed causes for this fundamental change in Earth’s climate state include changes in ocean circulation Downloaded from due to the opening of Southern Ocean gateways (4), a decrease in atmospheric CO2 (5–8), and a 913 minimum in solar insolation (2). 336 How Earth’stemperaturechangedduringice expansion is poorly defined, largely because benthic d18Orecordsdonotdistinguishbetweenice 628 volume and temperature. Deep-sea temperature 998 929 925 records based on foraminiferal Mg/Ca ratios show 1218 little change during ice expansion (9–11). As a re- 803 sult, benthic d18OrecordsimplyE-Oicevolumes

1Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA. 2Department of Earth Sciences, Univer- 1090 511 sity of Hong Kong, Hong Kong, People’sRepublicofChina. 277 3Department of Geosciences, University of Massachusetts- Amherst, Amherst, MA 01003, USA. 4Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907, USA. 5Laboratory of Palaeobotany and Palynology, Utrecht University, Budapestlaan 4, 3584 CD Utrecht, Nether- lands. 6Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA. *To whom correspondence should be addressed. E-mail: Fig. 1. Paleolocations of DSDP and ODP sites used in this study, superimposed on a map of [email protected] (Z.L.); [email protected] (M.P.) reconstructed E-O bathymetry and geography (18).