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第二届物理学院兴诚本科生学术论坛 论文集 第二届物理学院兴诚本科生学术论坛 论文集 2015 年年 5 月月 9 日日 北京大学物理学院 北京大学物理学院 论文集目录论文集目录 高见高见 rpc 的动量无关的 EM 算法 1 刘芮杉刘芮杉 Enhanced Raman Scattering of Single Nanoparticles in a High Q Whispering Gallery Microresonator 4 袁竹君袁竹君 Observation of the Adler Bell Jackiw Chiral Anomaly in a Weyl Semimetal 11 林梦翔林梦翔 Gravitational Microlensing by Neutron Stars and Radio Pulsars Event Rates Timescale Distributions and Mass Measurements 29 林梦翔林梦翔 Oscillation driven Magnetospheric Activity in Pulsars 39 袁仁亮袁仁亮 段炼段炼 Identification and Mechanical Control of Ferroelastic Domain Structure in Rhombohedral CaMn7O12 50 袁仁亮袁仁亮 段炼段炼 胡毓文胡毓文 Soft Vibrational Mode Associated with Incommensurate Orbital Order in Multiferroic CaMn7O12 56 施骄健施骄健 In situ Studies of CH3OH Reactions on TiO2 Thin Film by Sum Frequency Generation Vibrational Spectroscopy SFG VS 63 施骄健施骄健 Methanol Adsorption on TiO2 Film Studied by Sum Frequency Generation Vibrational Spectroscopy 76 刘尚刘尚 Entropic Uncertainty Relations For Multiple Measurements 89 姚文杰姚文杰 Efficient Directional Excitation of Surface Plasmons by a Single Element Nanoantenna 95 罗州宸罗州宸 MHz level Self sustained Pulsation in Polymer Microspheres on a Chip 102 胡毓文胡毓文 Charge Density Waves and Phonon Electron Coupling in ZrTe3 109 00 2015 1 rpc s EM School of Physics Peking University Beijing 100871 China Abstract P 8P EM V P e B lb Keywords rpc EM 1 EM EM s 7 K S p v 7 p p 0 S p f x p1 p2 v x p1 p2 n p 7 x1 x2 H g p1 p2 f x1 p1 p2 f x2 p1 p2 p p 1 p 2 B p 1 EM Pc Ol c f 1 2 exp 2 2 2 v 15MeV cp r H Lrad v c H i Lrad i P s 8p B p Lrad PO 1 l P i iS H Lradb P i Hi Lrad is 2 VVV S 6 pX P p 0 P i Ol p G P p fp p H P O l p f Lrad R 0 f p Lrad fp p dp F S B 兴诚论坛 论文集 1 00 2015 1 2 F S sG4s P i Ol Q0EM B p B H p Z 7Z p p p H S P p vX P p s POl K0 7 1 2 n i P K ki 1 ki 2 ki mi P fi f i pi Lrad ki HK pn c p X P Lrad f1f2 fn HB p lnP lnf1 lnf2 lnfn n X i 1 1 2ln 2 ln i 2 i 2 2 i n X i 1 1 2ln 2 ln 15Mev icpi 1 2ln mi X j 1 Hki j Lrad ki j 2 i icpi 2 2 15Mev 2 mi P j 1 Hki j Lrad ki j n X i 1 c1 pi 1 2ln mi X j 1 Hki j Lrad ki j c2 pi 2 i mi P j 1 Hki j Lrad ki j gM B yX p s p lnP0 n X i 1 C1 1 2ln mi X j 1 Hki j Lrad ki j C2 1 mi P j 1 Hki j Lrad ki j R 0 fp p dp 1 B y 1 B C1 i s q e e s Lrad vwS I B C2 Lrad p d 6 1 2 3 1 0 s p h B v 0 Lrad LradBO p E 1 LradBO p X O pI s 6 U 0 C vB E M b B M Xi mi P j 1 Hki j Lrad ki j l B lnP0 X i 1 n lnXi 2 i Xi G XiK s HB y v y s i lnXi frac 2 iXi lnP 0 6 i y XiO pI 1 Xi 2 i X2 i 0 Xi 2 i i 1 Q0 I X 106 M 1 v 9 Lrad Xi I Near each midpoint between and X or and Y we observe a pair of open curves Fermi arcs that are terminated into two points which are the Weyl nodes These observations are in qualitatively consistent with our fi rst principles calculation shown in Fig 1e The observation of Fermi arc surface states and the agreement with the theoretical calculation provide strong evidence showing that the TaAs samples used in our transport experiments are indeed Weyl semimetals Since transport mostly probes the bulk electronic states we need to understand the electronic structure of the bulk Weyl cones In Fig 1f we show distribution of the Weyl nodes throughout the fi rst bulk Brillouin zone BZ There are in total 24 Weyl nodes and the sign of their 14 兴诚论坛 论文集 5 chiral charges are color coded in black and white Moreover these 24 Weyl nodes can be characterized into two groups Namely there are 8 Weyl nodes located on the kz plane that have the same energy and we note them as W1 The other 16 Weyl nodes which are away from the kz plane are noted as W2 After checking the electronic ground state of our TaAs samples we study their electrical transport properties Fig 1g shows the longitudinal resistivity as a function of temperature at diff erent external magnetic fi elds The current is applied along the in plane crystallo graphic direction a and b are equivalent because of the tetragonal lattice whereas the magnetic fi eld is out of plane The temperature dependent resistivity of TaAs at the zero magnetic fi eld Fig 1g shows a metallic profi le When a low magnetic fi eld 0 3 T is ap plied the resistivity changes to an insulating profi le Similar behavior has been observed in bismuth and graphite where the low fi eld eff ect was attributed to a magnetic fi eld induced excitonic insulator transition of Dirac fermions 21 In Fig 1h we show the magnetore sistance MR H 0 H H 0 as a function of the external magnetic fi eld at diff er ent temperatures At temperatures below 10 K the MR of TaAs shows extremely strong Shubnikov de Haas SdH oscillations Remarkably the MR reaches 5400 at 10 K in 9 T which is three times larger than that in the recently reported compound WTe2at 2 K in 9 T see Nature 2014 22 Moreover unlike in other semimetals where the MR has a parabolic dependence on the magnetic fi eld the titanic MR of TaAs disperses linearly as a function of the magnetic fi eld and is not saturated at the highest applied fi eld of 56 T Fig 1j In order to understand the electronic states that contribute to our transport signals we study the SdH oscillation Figure 2a shows the Hall resistance yx at diff erent temperatures It can be seen that the yx shows a positive magnetic fi eld response at temperatures above 100 K which reveals that the majority carriers are hole like at these higher temperatures By contrast the fi eld response becomes clearly negative below 75 K which shows the dominance of electron like carriers in the Hall measurements at low temperatures In order to obtain the carrier density n and the mobility for the electron and hole carriers we fi t the Hall conductivity tensor using a two band model see Supplementary Information SI for details As shown in Fig 2b the carrier density for both carriers are on the order of 1017cm 3 which is consistent with the semimetallic nature of TaAs At temperatures above 100 K the transport data can be fi tted by considering only the hole like band However as one 兴诚论坛 论文集 15 6 decreases the temperature below 100 K the electron band sets in and its mobility increases dramatically We note that the mobility of the electron band is as high as e 5 105cm2 V s at T 2 K which is comparable to that in Cd3As2 23 In order to obtain the critically important electronic band structure parameters we an alyze the SdH quantum oscillation data at T 2 K We note that since at T 2 K the SdH oscillation is dominated by the electron carriers the obtained band parameters will correspond to the electron like band We use the following expression to analyze the SdH oscillation data xxat T 2 K for a 3D system xx 0 1 A B T cos2 F B 24 where 0is the non oscillatory part of the resistivity A B T is the amplitude of the SdH oscillations B is the magnetic fi eld is the Onsager phase and F 2 eAF is the frequency of the oscillations Here AFis the extremal cross sectional area of the Fermi surface FS associated with the Landau level index e is the electron charge and is the Planck s constant We obtain a Fermi surface area ofAF 7 07 10 4 A 2 and a Fermi wave vector kFis pA F 0 015 A 1 We note that since the magnetic fi eld is parallel to the c crystallographic axis the obtained Fermi surface area corresponds to the 2D cross section of the 3D Fermi pocket that is perpendicular to the kzdirection Then the Landau level index 1 0 H is plotted as a function of the inverse of the magnetic fi eld strength in Fig 2d from which one can see that for all four samples the linear interpolation of the curve intersects with the x axis at 0 This suggests that the electron carriers arise from a linearly dispersive band with a non trivial Berry s phase 24 which is likely the Weyl cone In order to obtain the Fermi vector the Fermi velocity the energy position of the chemical potential and other important band parameters we apply the Lifshitz Kosevich formula for a 3D system see the SI This enable us a cyclotron mass mcycof 0 15me From the cyclotron mass we obtain the Fermi wave vector kFis pA F 0 015 A 1 and the fermi velocity vFis kF mcyc 1 16 105m s By assuming a linear dispersion of this electron pocket we obtain the chemical potential relative to the energy of the Weyl node to be EF mcycv2 F 11 48 meV We further study the anisotropy of the electron like pocket by tilting the magnetic fi eld away from the c direction Our data Fig 2e shows that the Fermi surface area along the a axis is about 5 times larger that of along the c axis Therefore we fi nd that the electron like Fermi pocket is an ellipsoid that is elongated along the c axis We now systematically check if the obtained band parameters make sense and if the electron like band indeed corresponds to the Weyl cone In order to do so we place the 16 兴诚论坛 论文集 7 chemical potential at 11 48 meV above the Weyl nodes W1 in our fi rst principles calculations and try to compare the calculated band parameters to those of obtained from transport We have found an excellent agreement between calculation and transport 1 As shown in Figs 2f and 2g if the chemical potential is placed at 11 48 meV above W1 calculation shows that electron like purple pockets and hole like yellow pockets indeed coexist at the Fermi level which is consistent with our Hall measurements shown in Fig 2a 2 Our calculation shows that the electron like pocket is indeed the Weyl cones Fig 2g This agrees with our Landau fan diagram analysis Fig 2d which suggests a linear band dispersion with a nontrivial Berry s phase 3 The calculated carrier density of the electron pockets is 5 07 1017cm 3 which also agrees well with our experimentally measured value in Fig 2d 4 Finally the anisotropy of the Fermi surface area is found to be 4 9 which is also in line with the experimentally determined value of 5 All these agreements taken collectively provide compelling evidence that the electron like bands that dominate the SdH oscillations are indeed the Weyl cones W1 and that the chemical potential is 11 5 meV above the energy of the Weyl nodes W1 We note that according to our band calculations the energy position of the Weyl nodes W2 is 13 meV higher than that of W1 Therefore based on our systematic measurements and our careful comparison with calculations we obtain a band diagram presented in Fig 2f The chemical potential lies 11 5 meV above W1 but it is extremely close to W2 This means that although the contribution of Weyl cones W2 to the SdH oscillation Fig 2a H i where i is the direction of the current is not signifi cant due to its extremely small size of Fermi surface the Weyl cones W2 will play the most essential role in the chiral anomaly the positive magnetoconductance at H k i because the chemical potential is extremely close to the Weyl nodes of W2 Keeping the experimentally determined band diagram Fig 2f in mind we now turn to the measurements of the chiral anomaly We fi rst discuss how the chiral anomaly manifests itself in a magnetoconductance measurement in the presence of parallel electrical and magnetic fi elds H k i In the semiclassical regime in which our measurements are performed the Weyl nodes act as sources of Berry fl ux in the BZ This Berry fl ux alters the semiclassical equation of motion for the momentum k of an electronic wave packet by an additional term E B k 25 26 where E and B are the applied electric and magnetic fi elds and kis the momentum dependent Berry fi eld strength Close to the Weyl node which we assume to be isotropic for simplicity k has the monopole confi guration k kv3 F 2 EF 3 E 2 F 兴诚论坛 论文集 17 8 where the sign is the chirality of the Weyl node Since the Weyl nodes are separated in momentum space the scattering of electrons between them is suppressed and the extra contribution to the equations of motion alters the transport properties of the Weyl semimetal at nonzero applied E and B fi eld as long as E B 6 0 For small magnetic fi elds parallel to E the contribution to the conductivity from an isotropic Weyl node is at low temperatures given by 26 27 chiral 0 2e2 2 F 3 2 B2 1 where 0is the conductivity originating from inter node scattering and F is the Berry fi eld strength at the Fermi energy Because the Fermi energy of the Weyl nodes W1 is about 7 times larger than that of W2 the contribution of W1 to chiralis suppressed by a factor of 50 as compared to the contribution from W2 We can thus assume that the chiral anomaly in TaAs is dominated by the Weyl node W2 On the basis of these considerations we expect chiralto show the following behavior 1 It has a weak temperature dependence for temperatures small compared to the EF and is reduced for temperatures much larger than EF 2 It is largest for E k B and zero for E B 3 It scales E 2 F for suffi ciently small EF 26 We will now show that our data is consistent with each of these points In the following we present the magnetoconductivity instead of the magnetoresistance for two reasons i The conductivity is a sum of contributions from the chiral anomaly an conventional transport which makes it easier to disentangle the two contributions ii The resistivity at zero fi eld is dominated by the conventional contribution and it is therefore unnatural to normalize the contribution from the chiral anomaly that we want to single out by this nonuniversal value The magnetoconductivity shown in Fig 3 was measured in a confi guration where the applied electric and magnetic fi elds are parallel Figure 4 shows the change in the magne toconductivity as the angle between the applied electric and magnetic fi elds is varied The measurements were performed with two samples S1 and S2 that diff er in the location of their Fermi energy Relative to the Weyl node W2 S1 has EF 1 1 5 meV and S2 has EF 2 3 0 meV see Fig 3d For both samples the magnetoconductivity in Fig 3c shows two peaks as a function of magnetic fi eld strength one at zero and one at fi nite magnetic fi eld We identify these as a classical magnetoconductivity of conventional carriers and the chiral anomaly of the Weyl points respectively To support this we fi tted the experimentally 18 兴诚论坛 论文集 9 obtained conductivity with the functional form proposed in 28 H 0 a H 1 CWH2 1 AH2 1 A H2 2 where the fi rst term is associated with the Weyl nodes and includes a weak anti localization correction with coeffi cient a 0 are conventional contributions to the magneto conductivity that we attribute to the other Fermi pockets Using Eq 2 we obtain excellent fi ts to the data at all temperatures and angles as presented in Fig 3a and Fig 4a respec tively We found that no satisfactory fi t can be obtained if only one of the conventional contributions is included As a function of temperature the chiral anomaly contribution 0CW shown in Fig 3b for S1 is indeed nearly constant for small temperatures It rapidly decreases for temperatures around 20 K which is comparable to the Fermi energy EF 1 1 5meV of the sample This confi rms point 1 from the above As a function of the angle between electric and magnetic fi eld the chiral anomaly contribution 0CW shown in Fig 4b for S2 is found to be sharply peaked for E k B and falls off to nearly zero for relative angles as small as 5 This is in qualitative agreement with point 2 from the above Finally with the two samples studied we have observed the chiral anomaly contribution to the conductivity for two diff erent Fermi energies EF 1 1 5 meV and EF 2 3 0 meV We can use the two chiral anomaly contributions to the magnetoconductivity 0 1CW 1and 0 2CW 2obtained for S1 and S2 to test the scaling form chiral E 2 F quantitatively Indeed 0 1CW 1 0 2CW 2 5 0 each taken at T 2K compares well with E2 F 2 E 2 F 1 4 0 thus confi rming point 3 from the above These systematic experimental results corroborated by our ARPES results and our the oretical calculations suggest the existence of Weyl fermion related chiral anomaly in TaAs analogous to anomalies in quantum fi eld theory Our results not only provide the fi rst trans port signature for the Weyl fermions in TaAs but also paves the way for realizing new device platforms for the next generation quantum technology frontier 1 Bertlmann R A Anomalies in Quantum Field Theory International Series of Monographs on Physics 2011 兴诚论坛 论文集 19 10 2 Adler S Axial Vector Vertex in Spinor Electrodynamics Physical Review 177 2426 2438 1969 3 Bell J S daishi 2CSIRO Astronomy and Space Science Australia Telescope National Facility Box 76 Epping NSW 1710 Australia 3Shanghai Astronomical Observatory Chinese Academy of Sciences Shanghai 200030 China msmith 4National Astronomical Observatories Chinese Academy of Sciences Beijing 100012 China 5Kavli Institute for Astronomy and Astrophysics Peking University Beijing 100871 China Received 2014 December 4 accepted 2015 February 8 published 2015 April 1 ABSTRACT We investigate properties of Galactic microlensing events in which a stellar object is lensed by a neutron star For an all sky photometric microlensing survey we determine the number of lensing events caused by 105potentially observable radio pulsars to be 0 2 yr 1 for 1010background stellar sources We expect a few detectable events per year for the same number of background sources from an astrometric microlensing survey We show that such a study could lead to precise measurements of radio pulsar masses For instance if a pulsar distance could be constrained through radio observations then its mass would be determined with a precision of 10 We also investigate the timescale distributions for neutron star events fi nding that they are much shorter than had been previously thought For photometric events toward the Galactic center that last 15 days around 7 will have a neutron star lens This fraction drops rapidly for longer timescales Away from the bulge region we fi nd that neutron stars will contribute 40 of the events that last less than 10 days These results are in contrast to earlier work which found that the maximum fraction of neutron star events would occur on timescales of hundreds of days Key words gravitational lensing micro pulsars general stars neutron 1 INTRODU