• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Thermal Hall effect and the Wiedemann-Franz law in Chern insulator

    2023-11-02 08:11:46AnxinWang王安新andTaoQin秦濤
    Chinese Physics B 2023年10期
    關(guān)鍵詞:王安

    Anxin Wang(王安新) and Tao Qin(秦濤)

    School of Physics and Optoelectronics Engineering,Anhui University,Hefei 230601,China

    Keywords: thermal Hall effect,quantum Hall effect,Chern insulator,Landauer-B¨uttike formula

    1.Introduction

    Topological properties of the quantum materials have been under extensive studies in the last decades.Thermal Hall effect is a versatile probe to investigate transport properties of quantum materials.The Wiedemann-Franz law states that in the low temperature limitκxy=L0σxyTwithL0=(π2/3)(kB/e)2the Lorentz number[1]andσxythe quantum Hall conductivity.Whether the Wiedemann-Franz law is valid in quantum materials is an interesting topic.Its validity has been verified theoretically,[2]where the key ingredient for the Wiedemann-Franz law to be valid is that there is a single non-interacting carrier for charge and thermal current,and experimentally[3]for anomalous Hall insulators.[4]Possible violations of the Wiedemann-Franz law has been explored in graphene,[5]where electrons and holes contribute differently to the quantum charge and thermal Hall transport due to special band structures of graphene in the magnetic field,and quasi-one dimensional conductor,[6]where an extra contribution of spinon to the thermal current has been identified.In high-temperature superconductors,huge thermal Hall conductivity and a violation of the Wiedemann-Franz law has been demonstrated[7]because of the contribution of chiral phonon to the thermal transport in the pseudogap phase of cuprates,[8]and opened a different avenue to rich physics.

    Recent experimental progress has made it possible to investigate transport properties of topological materials under effectively very strong magnetic fields.The Haldane model[9]and the Harper-Hofstadter(HH)model,[10,11]as two paradigmatic models of Chern insulators to introduce magnetic fluxes,have served as playgrounds for seminal ideas.However,for a long time, the interesting properties of materials in this scenario is elusive to be observed in laboratories because of the requirement of hugely strong magnetic fields.Recently,great breakthroughs have been achieved.The Haldane model is realized with the ultracold atoms in the shaken honeycomb optical lattices,[12,13]and the HH model is realized with Raman laser assisted tunneling in the optical lattice[14,15]and in the Moir′e superlattice.[16,17]These achievements afford us the possibility to investigate Chern insulators with large fluxes.

    In this work, we start with the HH model atφ=1/2,an interesting case with two Dirac cones in the first Brillouin zone, and with its generalization to introduce the complex next-nearest neighbor (NNN) hopping as the Harper-Hofstadter-Hatsugai (HHH) model.[18]For the HH model,the merging dynamics of Dirac cones resulting from uniaxial staggered potential in the first magnetic Brillouin zone (MBZ) has been investigated.[19]By combing the Bott index[20]and on-site disorders, the topological properties enhanced by onsite disorders and interactions has been detailed studied.[21,22]However,a detailed study of thermal Hall transport of the HHH model is still lacking.Using the Landauer-B¨uttiker formula,[5,23]we systematically investigate the quantum charge/thermal Hall transport in the HHH model with uniaxial staggered potentials presented,identify the validity of the Wiedemann-Franz law,and show that it is possible to characterize topological properties by the thermal Hall conductivity.Moreover, we introduce a small perturbation to the flux withφ=1/2+δφ,[19,24]equivalent to an effective magnetic field on top of the fluxφ=1/2,which brings about interesting transport physics.We need to point out that the defining property for the Chern insulator is the non-zero Chern invariant related to occupied Bloch bands, quite extensively discussed in the Haldane model,[25]and that the HHH model with a perturbation in the flux is still a Chern insulator because of non-trivial topological properties for occupied Bloch bands.Our work offers a different point of view to reveal topological properties of quantum materials.

    The remainder of the paper is organized as follows.In Section 2,we presented our model and methods.In Section 3,we show our results on the quantum charge/thermal Hall conductivity for three typical cases, and its possibility to be realized in experiments is also discussed.In Section 4, a short summary and outlook is given.Because of a pedagogical purpose,we present some technique details in the Appendix A.

    2.Model and methods

    Firstly,we introduce the HHH model with uni-axial staggered potential on a two-dimensional square lattice,

    wherem,nlabelsxandycoordinates of the sites.We consider a commensurate fluxφ=1/2.Δis the strength for the uniaxial staggered potential.Different from the usual HH model,the HHH model is featured in the NNN hopping with a complex phase.The staggered potentialΔbreaks the inversion symmetry, but keeps the reflection symmetry in thexdirection,therefore, a moderate strength ofΔshift positions of degenerate points,and strong enough one would open a gap.Whentc/=t'c, it breaks all symmetry operations in symmetry groupC4, so a non-zerotcort'cwould open a gap immediately.In this work,we focus on how to tune the topological properties with changes in parameters such astc,t'c,φ,andΔ.

    Following the method in Refs.[18,19], we briefly outline how to obtain the quantum Hall conductivity of the HHH model atφ=1/2 with the uniaxial staggered potentials.Settingn=ql+jwithlthe cell index,q=2,andj=1,2,...,q,and using the Fourier transformation

    we have

    We then have a brief review of methods to calculate the quantum Hall conductivity and thermal Hall conductivity.Following the method of Ref.[18]Appendix A1,we have shown that the quantum Hall conductivity of the electron for the halffilling case is

    with the condition thattb>0,ta/=0,tc+t'c/=0,and|Δ|<2tb.Electrons, as charge carriers, can transport energy simultaneously, and lead to the thermal Hall effect.One can show that for this model the Wiedemann-Franz law is valid at the low temperature limit.[2,26]All these derivations are based on bulk formulas.

    In this work we focus on the quantum charge and thermal Hall transport in a nano-structure based on the Landauer-B¨uttiker formula,[5,23,27,28]explore the validity of the Wiedemann-Franz law, and demonstrate that the nontrivial topological properties can be revealed by the thermal Hall conductivity.As shown in Fig.1, the nano-structure consists of a central system described by the Hamiltonian in Eq.(1)and six simple leads.The charge current flowing to the terminalncan be described by the Landauer-B¨uttiker formula as

    Fig.1.A typical set-up for quantum thermal Hall and charge Hall conductivity measurement: six-terminal nano-structure consisting of system and six leads.The central region has N+2+2L columns of lattice sites with L=5 and N=4.

    3.Results and discussion

    In this section, we presented our results for three different typical cases in the low temperatureT= 0.001.Case(i):φ= 1/2 andtc=t'c= 0.3.As shown in Fig.2, we find quantum Hall plateau for different stagger potentials in Figs.2(a) and 2(c) in the low temperature limit.The width of the plateaus is consistent with the bulk gaps in Figs.2(b)and 2(d),indicating that the charge transport is carried by the chiral edge states, which is a manifestation of the bulk-edge correspondence.[29,30]WhenΔ ≥2,the gap is closed and the plateau would disappear (Figs.2(e) and 2(f)).In Figs.2(a)and 2(b)one can determine the quantum Hall conductivity by counting how many edge states have been cut by the Fermi energy in Fig.2(b), where the band structure on a cylinder periodic in thexdirection is shown.The real-space distribution of different states in theydirection is encoded by color in Figs.2(b)and 2(d),where the color value 0,and 1 indicate two ends of the cylinder.Therefore, the edge states can be clearly identified.The numerical results for the quantum Hall conductivity is also the same as predicted by the analytical formula in Eq.(5),and the consistence benchmarked our working codes.We recall that the Harper-Hofstadter model atφ=1/2 withΔ=0 is semi-metallic.[19]It demonstrates that the topological properties of this model can be tuned by introduction of the complex next-nearest neighbor hopping.The quantum thermal Hall conductivityκxynormalized byπ2k2BT/3his nearly in coincident withσxyasκxy=L0σxy,indicating that the Wiedemann-Franz law is valid in the low temperature limit.Moreover,it means that one can reveal topological properties of a system by exploring the thermal Hall effect.

    We need to point out the a couple of issues in the numerical results.(i) It is about the numerical stability beyond the plateau in Figs.2(a), 2(c), and 2(e), where very steep lines show up.In this energy region, the bulk is metallic.The apparent imperfect agreement between the two quantities in the metallic phase results from two main factors.Firstly,it is the physics reason.We carried our calculations atT=0.001 with the NN hopping as the energy unit,and the Wiedemann-Franz law is valid in the low temperature limit.While the finite temperature effect can be forbidden by large energy gap in the Chern insulator phase, it shows up when the system is in the metallic phase.We next turn to the technical reasons.The key part of our numerical calculations is to solve inhomogeneous linear equations.Indeed, in metallic phase the numerical stability is not perfect for some parameters, as introduces relatively large deviations between charge and thermal Hall conductivities.We tried different ways to solve linear equations and the method of least squares,which we implemented in the codes, turned out to be a better one.(ii)In Fig.2(d), there is clearly discontinuity in the color of the bands aroundkx=2,and it is a reflection of the fixed boundary condition in theydirection of the cylinder.

    Fig.2.Panels (a), (c), and (e) are the quantum thermal Hall conductivity κxy (normalized by π2k2BT/3h) and charge Hall conductivity σxy (normalized by e2/h)versus the Fermi energy E for different staggered potential Δ,and their corresponding band structure with color encoded y position versus kx on a cylinder structure with periodic boundary condition in the x direction and open boundary condition in the y direction with a width of 400 in panels(b), (d), and(f).Other parameters are ta =tb =1,tc =t'c =0.3, and φ=1/2.The temperature T =0.001,which is very low compared with typical gaps around E =0.The size of the six-terminal structure in numerical calculations is N=L=80.

    We go beyond the canonical case ofφ=1/2 and introduce a small perturbation to the integer flux.[19,24]It is equivalent to a small effective magnetic fluxδφ=0.05 on top ofφ=1/2.Similar to results for case(i)in Fig.2,we find the same coincidence between the quantum Hall conductivityσxyand thermal Hall conductivityκxyin Fig.3, indicating the validity of the Wiedemann-Franz law.Furthermore, we would like to point out that the picture of chiral edge states still works for this case.

    One new feature for case (ii) is the steep change of the charge/thermal Hall conductivity around the Fermi energyE0=0 (Figs.3(a) and 3(c)).It is due to the change in the direction of the chiral edge states.We take Fig.3(b)as an example.The edge state with positive velocity (green lines) in the gap just belowE0=0,change its direction in the gap just aboveE0=0.It is this motion direction reversal which brings about the sign change in the charge/thermal Hall conductivity aroundE0=0, because carriers tansport both charge and energy.Therefore,as we have claimed,the Wiedemann-Franz is still valid for this case.Furthermore, we need to point out that one can generally characterize the topological properties of a system with thermal Hall conductivity.

    Fig.3.The physical quantities shown are the same as those in Fig.2.Different parameters are tc==0,φ =1/2+δφ,and δφ =0.05.

    For case (ii),φ=11/20, so we find there are 20 energy bands in Fig.3(b)and 3(d),where some bands are nearly flat,a reflection of the Landau level.A zoom-in shown in Figs.4(a)and 4(b), corresponding to Figs.3(b) and 3(d) respectively,preseents the fine structures of the nearly flat bands.Moreover,we show the density of states(DOS)of the bulk bands in Fig.4,where we find that peaks show up for every bulk bands.

    Case(iii):φ=1/2+δφ,δφ=0.05, andtc=t'c=0.3.In Figs.5(a) and 5(c), we find the same steep change in the charge/thermal Hall conductivity, which can be explained by the direction change in the edge states.In this case we have introduced the NNN hopping, and it indicates that this kind of steep changes in conductivity are rather universal.Even though there is anisotropy brought about by the NNN hopping,the Wiedemann-Franz law is still valid.

    We finally discuss the possible experimental realization.In a real material,the NNN hopping amplitudestc,andcan be tuned by strain[31]and laser irradiation.[32]Onsite staggered potentialΔis usually induced by substrates.The fluxφcan certainly be adjusted by strength of external magnetic fields.

    Our numerical simulation involves an extremely strong magnetic field.We have an estimate of the strength of magnetic fields required to realize the 1/2 flux byBl2=(p/q)(h/e) where the lattice constantlis approximately 1 °A andp/q=1/2.It follows thatB ≈4×104T,far beyond the reach in the laboratory, where the world record for strongest steady magnetic field is as high as approximately 45.22 T achieved on August 12 2023, in Hefei China, which cannot be directly achieved in the laboratory.However, indirectly,one can realize it with the help of the moir′e superlattice,[16,17]topolectrical circuits,[33]or Raman laser assisted tunneling of ultracold atoms in the optical lattice.[14,15]So far all the three techniques are rather sophisticated.We also need to point out that the HHH model has been realized in the metamaterial of topoelectrical circuits.[34]The possible proposal for experiment realizations in real materials will be explored in the near future.

    4.Summary and outlook

    To sum up, we have investigated the quantum charge/thermal Hall effect in the HH model and its generalization.We have numerically studied the quantum charge/thermal Hall conductivity in a six-terminal nanostructure and understood it from the point of view of the bulkedge correspondence.We demonstrate that the Wiedemann-Franz law is valid in the Chern insulator,even though there is a steep change of the Hall conductivity aroundE0=0.Our calculations show that the non-trivial topological properties can be revealed by both the charge Hall conductivity and the thermal Hall conductivity.

    Appendix A: Energy spectrum of a cylinder structure

    To make the results in this work self-contained, we present some details in this section following the methods outlined in Refs.[5,18,23].

    Appendix A1: Quantum Hall conductivity of the HHH model with staggered potential

    Following the method in Ref.[18], we presented the derivation of the quantum Hall conductivity of the HHH model atφ=1/2 with a staggered potential.We choose the first MBZ askx ∈[-π,π] andky ∈[0,π].The Hamiltonian in Eq.(4)reads

    The eigenvector for the lower band is

    where we have chosen a gauge with the componentaas real and setb= ?be-iζk.The quantum Hall conductivity for the lower band can be calculated as[18,35]

    whereΔirefers to different parts for the first MBZ.Becauseais real,

    Appendix A2: Thermal Hall conductivity calculation based on the Landauer-B¨uttiker formula

    We adopt the method in Refs.[5,23,27,28] to calculate the thermal Hall conductivity.We firstly expand respectively the charge current

    and energy currentto the first order of voltageVnand temperatureTn(n=1,2,...,6)as follows:

    where we have definedPnm=dETnm(E)?E f0,Qnm=dETnm(E)?T f0, Rnm =dEETnm(E)?E f0, and Snm =∫dEETnm(E)?T f0.For all these newly defined quantities,n/=m.We have a short comment on the integration.Since the temperature is rather low,the integral interval can be limited to a fewkBTaround the Fermi energy.To obtain the thermal Hall effect,a temperature gradient is applied across terminal 1 and 4,and we setJn=0(n=2,3,5,6)andIn=0,(n=1,2,...,6).Due to thermal current conservation,J1=-J4.Therefore,we obtain a group of linear inhomogeneous equations for unknown quantitiesTn,(n=2,3,5,6)andVn=0,(n=1,2,...,6)as follows:

    wheren=2,3,5,6,andn'=1,2,...,6.Note in Eqs.(A4)and(A5), we have redefinedP11=-∑n/=1P1n, and similarly forQ11,R11,andS11.To solve the linear equations,a method of least square solutions is important to obtain a stable solution.The thermal Hall resistance and longitudinal resistance can be calculated as ?Rxy=(J2-J6)/T1and ?Rxx=(J2-J3)/T1, respectively.Finally, the quantum thermal Hall conductivity is defined asκxy= ?Rxy/(?R2xy+ ?R2xx).

    Acknowledgements

    Project supported by the National Natural Science Foundation of China(Grant Nos.U2032164 and 12174394)and the Start-up Fund from Anhui University in China.

    猜你喜歡
    王安
    Sensitivity to external optical feedback of circular-side hexagonal resonator microcavity laser?
    元日
    王安期不鞭書生
    王安期不鞭書生
    請(qǐng)客
    曲耶?戲耶?——王安祈《紅樓夢(mèng)》京劇論
    太原理工大學(xué)學(xué)者風(fēng)采
    ——王安幫教授
    緣何抒情,怎樣寫意?——王安祈戲曲研究中傳統(tǒng)與現(xiàn)代的相互表述
    中華戲曲(2018年1期)2018-08-27 10:04:08
    做了才會(huì)知道結(jié)果
    王武龍會(huì)長(zhǎng)會(huì)見中咨公司王安總經(jīng)理一行
    伦精品一区二区三区| 亚洲 欧美一区二区三区| 免费高清在线观看视频在线观看| 欧美亚洲 丝袜 人妻 在线| 一区二区三区精品91| 这个男人来自地球电影免费观看 | 免费黄频网站在线观看国产| 久久人人爽人人片av| 欧美日韩精品网址| a级毛片黄视频| 日本欧美国产在线视频| 九色亚洲精品在线播放| 亚洲精品在线美女| 久久久精品区二区三区| 飞空精品影院首页| 国产深夜福利视频在线观看| 亚洲国产成人一精品久久久| 国产精品 欧美亚洲| 色视频在线一区二区三区| 精品少妇久久久久久888优播| 免费在线观看视频国产中文字幕亚洲 | 久久久久久人人人人人| 免费黄网站久久成人精品| 午夜福利乱码中文字幕| 久久鲁丝午夜福利片| 国产av精品麻豆| 国产极品天堂在线| 桃花免费在线播放| 中文字幕最新亚洲高清| 午夜福利视频精品| 色婷婷久久久亚洲欧美| 水蜜桃什么品种好| 香蕉精品网在线| 老女人水多毛片| 精品视频人人做人人爽| 黄色配什么色好看| 久久人妻熟女aⅴ| 国产一区二区三区av在线| av片东京热男人的天堂| 国产亚洲最大av| 卡戴珊不雅视频在线播放| 亚洲欧美精品综合一区二区三区 | 免费大片黄手机在线观看| 午夜福利网站1000一区二区三区| 欧美日韩精品成人综合77777| 大码成人一级视频| 在线观看美女被高潮喷水网站| 亚洲欧美一区二区三区久久| a 毛片基地| 欧美 日韩 精品 国产| 久久久久久久亚洲中文字幕| 一本一本久久a久久精品综合妖精 国产伦在线观看视频一区 | 日本午夜av视频| 亚洲综合色惰| 国产亚洲午夜精品一区二区久久| 黄色毛片三级朝国网站| 男人爽女人下面视频在线观看| 亚洲精品在线美女| 男女午夜视频在线观看| 1024香蕉在线观看| 欧美日本中文国产一区发布| 欧美激情高清一区二区三区 | 日韩制服骚丝袜av| 亚洲精品国产色婷婷电影| 男男h啪啪无遮挡| 丝袜脚勾引网站| 纯流量卡能插随身wifi吗| 国产日韩欧美亚洲二区| 亚洲视频免费观看视频| 成人免费观看视频高清| 亚洲一码二码三码区别大吗| 最黄视频免费看| 欧美国产精品一级二级三级| 99久久综合免费| 韩国av在线不卡| 久久精品国产鲁丝片午夜精品| 美女中出高潮动态图| 宅男免费午夜| 欧美日韩综合久久久久久| a级毛片在线看网站| 又大又黄又爽视频免费| 国产一区亚洲一区在线观看| 综合色丁香网| 国语对白做爰xxxⅹ性视频网站| 日韩一区二区三区影片| 亚洲美女搞黄在线观看| 亚洲精品久久成人aⅴ小说| 欧美激情极品国产一区二区三区| 国产av码专区亚洲av| 国产男女超爽视频在线观看| 国产成人精品无人区| 欧美日韩成人在线一区二区| 十分钟在线观看高清视频www| 亚洲情色 制服丝袜| 老司机亚洲免费影院| 晚上一个人看的免费电影| 青春草视频在线免费观看| 精品酒店卫生间| 少妇 在线观看| 精品第一国产精品| 91精品国产国语对白视频| 亚洲精品国产av成人精品| 最近2019中文字幕mv第一页| 精品亚洲成a人片在线观看| 亚洲视频免费观看视频| 肉色欧美久久久久久久蜜桃| 99热国产这里只有精品6| www.熟女人妻精品国产| 精品少妇久久久久久888优播| a级毛片黄视频| 日韩制服丝袜自拍偷拍| 久久久精品免费免费高清| 老司机影院毛片| 欧美亚洲 丝袜 人妻 在线| 精品一区二区三区四区五区乱码 | 欧美在线黄色| 日韩,欧美,国产一区二区三区| 欧美xxⅹ黑人| 欧美人与性动交α欧美精品济南到 | 亚洲av男天堂| 男男h啪啪无遮挡| 如何舔出高潮| 一个人免费看片子| 亚洲精品日本国产第一区| 亚洲一区中文字幕在线| 精品人妻一区二区三区麻豆| 久久av网站| 边亲边吃奶的免费视频| 桃花免费在线播放| 在线观看免费高清a一片| 婷婷色av中文字幕| 午夜福利乱码中文字幕| 免费女性裸体啪啪无遮挡网站| 一区在线观看完整版| 少妇的丰满在线观看| 天天躁日日躁夜夜躁夜夜| 国产精品一二三区在线看| h视频一区二区三区| 久久人妻熟女aⅴ| 亚洲欧美成人综合另类久久久| 在线观看国产h片| 亚洲欧美清纯卡通| 欧美亚洲日本最大视频资源| 美女中出高潮动态图| 精品国产露脸久久av麻豆| 观看av在线不卡| 天堂8中文在线网| 亚洲精品国产av成人精品| 自线自在国产av| 亚洲,欧美,日韩| 日韩人妻精品一区2区三区| 久久久精品国产亚洲av高清涩受| 国产精品女同一区二区软件| 久久久久网色| 丁香六月天网| 99re6热这里在线精品视频| 亚洲精品自拍成人| 日韩中文字幕视频在线看片| 91精品国产国语对白视频| 久久久久久久大尺度免费视频| 18+在线观看网站| 天天操日日干夜夜撸| 性少妇av在线| 观看美女的网站| 麻豆乱淫一区二区| 国产xxxxx性猛交| 免费高清在线观看日韩| 免费观看a级毛片全部| 欧美另类一区| 亚洲一区中文字幕在线| 男人舔女人的私密视频| 国产伦理片在线播放av一区| 国产女主播在线喷水免费视频网站| 最近最新中文字幕免费大全7| xxxhd国产人妻xxx| 国产精品免费视频内射| 美女午夜性视频免费| 最近中文字幕2019免费版| 欧美xxⅹ黑人| 色吧在线观看| 亚洲婷婷狠狠爱综合网| 三上悠亚av全集在线观看| 亚洲在久久综合| 婷婷色麻豆天堂久久| 伦理电影免费视频| 最近的中文字幕免费完整| 丝袜喷水一区| 看十八女毛片水多多多| 香蕉国产在线看| 亚洲国产av新网站| 久久青草综合色| 妹子高潮喷水视频| 久久这里有精品视频免费| 欧美日韩一区二区视频在线观看视频在线| 男人操女人黄网站| 中国国产av一级| 国产精品熟女久久久久浪| 亚洲少妇的诱惑av| 久久精品人人爽人人爽视色| 2022亚洲国产成人精品| av一本久久久久| a 毛片基地| 国产日韩欧美在线精品| 在线天堂最新版资源| 如日韩欧美国产精品一区二区三区| 一本—道久久a久久精品蜜桃钙片| 91精品国产国语对白视频| 蜜桃国产av成人99| 欧美人与善性xxx| 欧美日韩视频精品一区| 久久影院123| 女性被躁到高潮视频| 一个人免费看片子| 肉色欧美久久久久久久蜜桃| 欧美人与性动交α欧美精品济南到 | 多毛熟女@视频| 一级毛片我不卡| 99久久人妻综合| 精品国产露脸久久av麻豆| 精品久久久久久电影网| 久久ye,这里只有精品| a级毛片黄视频| 国产日韩欧美在线精品| 亚洲精品aⅴ在线观看| 大片电影免费在线观看免费| 色婷婷久久久亚洲欧美| 精品一区二区三卡| 肉色欧美久久久久久久蜜桃| 久久久久国产一级毛片高清牌| 婷婷色综合www| 精品亚洲成a人片在线观看| 欧美日韩综合久久久久久| 性少妇av在线| 天天躁日日躁夜夜躁夜夜| 新久久久久国产一级毛片| 日本免费在线观看一区| 日韩三级伦理在线观看| 高清欧美精品videossex| 日日啪夜夜爽| 午夜福利在线免费观看网站| 日韩精品有码人妻一区| 高清不卡的av网站| 亚洲欧美精品综合一区二区三区 | 免费高清在线观看视频在线观看| 可以免费在线观看a视频的电影网站 | 最黄视频免费看| 中文字幕av电影在线播放| 精品99又大又爽又粗少妇毛片| 99re6热这里在线精品视频| 欧美精品一区二区免费开放| 校园人妻丝袜中文字幕| 三级国产精品片| 日韩视频在线欧美| 一级片免费观看大全| 夫妻午夜视频| 亚洲欧美一区二区三区国产| 少妇被粗大的猛进出69影院| 亚洲国产精品一区二区三区在线| 中国三级夫妇交换| 久久国内精品自在自线图片| 精品人妻一区二区三区麻豆| 人体艺术视频欧美日本| 色婷婷av一区二区三区视频| 丝袜美足系列| 极品少妇高潮喷水抽搐| 成人亚洲欧美一区二区av| 国产成人91sexporn| 国产精品熟女久久久久浪| 国产精品香港三级国产av潘金莲 | 自线自在国产av| 熟女电影av网| 日韩,欧美,国产一区二区三区| 波野结衣二区三区在线| 国产97色在线日韩免费| 9191精品国产免费久久| 99久久人妻综合| 老司机影院毛片| 一级片'在线观看视频| 国产 精品1| 宅男免费午夜| 如日韩欧美国产精品一区二区三区| 校园人妻丝袜中文字幕| 欧美成人午夜免费资源| 成人亚洲欧美一区二区av| 久久久久国产一级毛片高清牌| 在现免费观看毛片| 久久久精品免费免费高清| av在线观看视频网站免费| 亚洲精品久久午夜乱码| 三上悠亚av全集在线观看| 叶爱在线成人免费视频播放| 国产精品亚洲av一区麻豆 | 曰老女人黄片| 成人午夜精彩视频在线观看| 亚洲av中文av极速乱| 日本av手机在线免费观看| 久久精品国产鲁丝片午夜精品| 高清黄色对白视频在线免费看| 啦啦啦在线观看免费高清www| 少妇 在线观看| 欧美日本中文国产一区发布| 日本vs欧美在线观看视频| 99九九在线精品视频| 亚洲第一av免费看| 国产精品 国内视频| 久久ye,这里只有精品| 亚洲精品在线美女| 90打野战视频偷拍视频| 国产成人免费观看mmmm| 男人爽女人下面视频在线观看| 蜜桃在线观看..| 美女主播在线视频| 国产在视频线精品| 人妻 亚洲 视频| 日本av免费视频播放| 黄色毛片三级朝国网站| 丁香六月天网| 18在线观看网站| 日本爱情动作片www.在线观看| 999久久久国产精品视频| 亚洲欧美精品自产自拍| 国产视频首页在线观看| 婷婷成人精品国产| 国产男女超爽视频在线观看| 又粗又硬又长又爽又黄的视频| 国产无遮挡羞羞视频在线观看| 色94色欧美一区二区| 久久久久视频综合| 国产黄色视频一区二区在线观看| 亚洲在久久综合| 色吧在线观看| 亚洲精品第二区| 欧美+日韩+精品| 日韩三级伦理在线观看| 久久人人爽人人片av| 亚洲中文av在线| 亚洲内射少妇av| 飞空精品影院首页| 国产有黄有色有爽视频| 国产亚洲最大av| 亚洲色图综合在线观看| 久久久久久久亚洲中文字幕| 黄片无遮挡物在线观看| 亚洲欧美清纯卡通| 欧美激情 高清一区二区三区| 精品国产乱码久久久久久小说| 我要看黄色一级片免费的| 考比视频在线观看| 99热国产这里只有精品6| 在现免费观看毛片| 亚洲,欧美精品.| 久久久精品国产亚洲av高清涩受| 日本欧美国产在线视频| 国产伦理片在线播放av一区| 日本vs欧美在线观看视频| 日韩一区二区三区影片| 成人亚洲欧美一区二区av| av一本久久久久| 国产乱人偷精品视频| 视频在线观看一区二区三区| 91精品国产国语对白视频| 成年女人在线观看亚洲视频| 国产 一区精品| 天天躁日日躁夜夜躁夜夜| 午夜福利乱码中文字幕| 国产熟女午夜一区二区三区| 最近手机中文字幕大全| 亚洲精品一二三| av免费在线看不卡| a 毛片基地| 国产精品一区二区在线观看99| 亚洲内射少妇av| 国产欧美日韩一区二区三区在线| 波野结衣二区三区在线| 国产精品一区二区在线不卡| 亚洲国产精品国产精品| 亚洲精品自拍成人| 精品卡一卡二卡四卡免费| 国产精品不卡视频一区二区| 亚洲精品乱久久久久久| 久久精品久久久久久久性| 欧美日韩一区二区视频在线观看视频在线| av天堂久久9| 亚洲三级黄色毛片| 制服诱惑二区| 亚洲精品av麻豆狂野| 午夜福利一区二区在线看| 久久精品久久久久久噜噜老黄| 国产成人aa在线观看| 波野结衣二区三区在线| 精品第一国产精品| 午夜影院在线不卡| 亚洲色图 男人天堂 中文字幕| 中文乱码字字幕精品一区二区三区| 九草在线视频观看| 亚洲内射少妇av| 免费黄网站久久成人精品| 天天躁夜夜躁狠狠久久av| videossex国产| 亚洲久久久国产精品| 免费不卡的大黄色大毛片视频在线观看| 亚洲欧美精品综合一区二区三区 | 久久久精品国产亚洲av高清涩受| 亚洲欧美精品综合一区二区三区 | 高清av免费在线| 久久人人97超碰香蕉20202| 日产精品乱码卡一卡2卡三| 老司机亚洲免费影院| 国产一区二区三区综合在线观看| 亚洲综合色网址| 亚洲美女搞黄在线观看| 男女啪啪激烈高潮av片| 日日摸夜夜添夜夜爱| kizo精华| 在线观看三级黄色| 妹子高潮喷水视频| 纵有疾风起免费观看全集完整版| 午夜福利视频精品| 黄片小视频在线播放| 中文字幕色久视频| 午夜精品国产一区二区电影| 2022亚洲国产成人精品| 亚洲国产最新在线播放| 午夜福利乱码中文字幕| 亚洲国产av新网站| 婷婷成人精品国产| 1024视频免费在线观看| 日韩欧美精品免费久久| 久久久久精品人妻al黑| 国产成人精品婷婷| 韩国精品一区二区三区| 成人手机av| 热99国产精品久久久久久7| 欧美激情极品国产一区二区三区| av天堂久久9| 精品视频人人做人人爽| 各种免费的搞黄视频| 久久人人97超碰香蕉20202| 国产黄频视频在线观看| 亚洲四区av| 久久国产精品大桥未久av| av在线播放精品| 18禁国产床啪视频网站| 一边亲一边摸免费视频| 久久久a久久爽久久v久久| 欧美bdsm另类| 妹子高潮喷水视频| 国产黄色免费在线视频| 国产精品嫩草影院av在线观看| 久久久国产精品麻豆| 我的亚洲天堂| a级片在线免费高清观看视频| 国产成人精品婷婷| 在线观看人妻少妇| 精品国产一区二区久久| 啦啦啦啦在线视频资源| 电影成人av| 国产片特级美女逼逼视频| videosex国产| 欧美日韩亚洲国产一区二区在线观看 | 大片免费播放器 马上看| a级片在线免费高清观看视频| 欧美国产精品一级二级三级| 天天躁夜夜躁狠狠躁躁| 亚洲精品,欧美精品| 又黄又粗又硬又大视频| 国产精品二区激情视频| 伦理电影免费视频| 久久精品aⅴ一区二区三区四区 | 亚洲欧美一区二区三区国产| 纵有疾风起免费观看全集完整版| 我要看黄色一级片免费的| 大陆偷拍与自拍| 色播在线永久视频| 亚洲精品一二三| 国产人伦9x9x在线观看 | 亚洲三区欧美一区| 大陆偷拍与自拍| 好男人视频免费观看在线| 国产一区二区激情短视频 | 亚洲一区中文字幕在线| 黄频高清免费视频| 日韩免费高清中文字幕av| 国产av精品麻豆| 高清不卡的av网站| 国产成人精品福利久久| 久久久久久久精品精品| 亚洲,欧美,日韩| 中国国产av一级| 日韩在线高清观看一区二区三区| 久久久国产一区二区| 欧美97在线视频| 啦啦啦在线观看免费高清www| 国产亚洲av片在线观看秒播厂| 亚洲av男天堂| 亚洲少妇的诱惑av| 精品一区二区免费观看| 伊人久久大香线蕉亚洲五| 国产精品一国产av| 国产亚洲一区二区精品| 久久99精品国语久久久| 久久人人爽人人片av| 国产黄色免费在线视频| 欧美成人午夜精品| 国产极品天堂在线| 99热全是精品| 交换朋友夫妻互换小说| 超碰成人久久| 国产成人精品久久久久久| 超碰成人久久| 黄频高清免费视频| 我要看黄色一级片免费的| 狠狠婷婷综合久久久久久88av| 最近手机中文字幕大全| av.在线天堂| 一本久久精品| 捣出白浆h1v1| av网站在线播放免费| 久久久a久久爽久久v久久| 成人国产麻豆网| 久久久久国产精品人妻一区二区| 丝袜美腿诱惑在线| 欧美 亚洲 国产 日韩一| 日本-黄色视频高清免费观看| 免费日韩欧美在线观看| 亚洲国产精品一区二区三区在线| 在现免费观看毛片| 欧美精品一区二区大全| 亚洲一区中文字幕在线| 亚洲精品aⅴ在线观看| 日韩 亚洲 欧美在线| 丝袜人妻中文字幕| 麻豆乱淫一区二区| 亚洲精品,欧美精品| 超碰97精品在线观看| 中文欧美无线码| 飞空精品影院首页| 日韩不卡一区二区三区视频在线| 九九爱精品视频在线观看| 成人国产麻豆网| 十八禁高潮呻吟视频| 中国三级夫妇交换| 国产日韩欧美在线精品| 亚洲内射少妇av| 亚洲人成网站在线观看播放| 亚洲国产精品一区三区| 国产精品二区激情视频| 亚洲 欧美一区二区三区| 成人免费观看视频高清| 国产免费一区二区三区四区乱码| 夫妻性生交免费视频一级片| 中文字幕av电影在线播放| 伦理电影大哥的女人| av国产久精品久网站免费入址| 国产高清不卡午夜福利| 9191精品国产免费久久| 最近中文字幕2019免费版| 性色avwww在线观看| 人体艺术视频欧美日本| av不卡在线播放| 国产免费福利视频在线观看| 亚洲国产精品成人久久小说| 亚洲精品aⅴ在线观看| 在线免费观看不下载黄p国产| 免费高清在线观看视频在线观看| 黄网站色视频无遮挡免费观看| 成人手机av| 免费黄网站久久成人精品| 日韩一卡2卡3卡4卡2021年| tube8黄色片| 一级片'在线观看视频| 两个人免费观看高清视频| 亚洲欧洲精品一区二区精品久久久 | 我的亚洲天堂| 国产在线视频一区二区| av卡一久久| 天堂中文最新版在线下载| 男人爽女人下面视频在线观看| 一级片免费观看大全| 99热全是精品| 制服诱惑二区| 九九爱精品视频在线观看| 国产成人免费观看mmmm| 日韩电影二区| 青春草亚洲视频在线观看| 深夜精品福利| 国产成人a∨麻豆精品| 国产男女超爽视频在线观看| 热99国产精品久久久久久7| 久久免费观看电影| 天堂俺去俺来也www色官网| 69精品国产乱码久久久| av线在线观看网站| 亚洲av福利一区| 两个人免费观看高清视频| 天堂8中文在线网| 看十八女毛片水多多多| 日韩欧美精品免费久久| 欧美精品一区二区大全| 国产乱来视频区| 欧美bdsm另类| 国产日韩欧美在线精品| 91久久精品国产一区二区三区| 不卡视频在线观看欧美| 精品卡一卡二卡四卡免费| 欧美xxⅹ黑人| 秋霞在线观看毛片| 波多野结衣一区麻豆| 免费黄网站久久成人精品| 色吧在线观看| 国产精品国产av在线观看| 免费观看性生交大片5| 国产av精品麻豆| 亚洲欧美一区二区三区国产| 一区在线观看完整版|