Optical absorption in the soliton-lattice state of a double-quantum-well system
a r X i v :c o n d -m a t /0106091v 1 [c o n d -m a t .m e s -h a l l ] 5 J u n 2001Optical absorption in the soliton-lattice state
of a double-quantum-well system
R.C?o t′e
D′e partement de physique and Centre de Recherche sur les Propri′e t′e ′Electroniques de Mat′e riaux Avanc′e s,
Universit′e de Sherbrooke,Sherbrooke,Qu′e bec,Canada,J1K 2R1
(February 1,2008)When the separation between layers in a double-quantum-well system is su?ciently small,the ground state of the two-dimensional electron gas at ?lling factor ν=1has an in-terwell phase coherence even in the absence of tunneling.For non-zero tunneling,this coherent state goes through a commensurate-incommensurate transition as the sample is tilted with respect to the quantizing magnetic ?eld at ν=1.In this article,we compute the optical (infrared)absorption spectrum of the coherent state from the commensurate state at small tilt angle to the soliton-lattice state at larger tilt angle and comment on the possibility of observing experimentally the distinctive signature of the soliton lattice.Pacs:73.21.Fg,73.43.Lp,78.30.Fs I.INTRODUCTION At strong magnetic ?elds and for su?ciently small sep-aration between the wells,the two-dimensional electron gas (2DEG)in a double quantum well system (DQWS)can have a broken symmetry ground state with a non zero interlayer phase coherence even in the absence of tunneling.At ?lling factor ν=1,the quantum Hall e?ect is observed in such coherent state when the sep-aration between the wells does not exceed some criti-cal value d c above which the coherence is lost and the 2DEG becomes compressible.In DQWS systems,the interlayer phase coherence gives rise to a rich variety of quantum and ?nite-temperature phase transitions as well as to some exotic topological excitations such as merons and bimerons.Some of these various phases and excita-tions are reviewed in details in Refs.[1],[2],and [3].One convenient way to describe the coherent ground states of the 2DEG in a DQWS is by using a mapping to an equivalent spin-1/2system.In these states,the real spins are assumed completely frozen and,in the pseu-dospin language,an electron in the left(right)layer is equated with an up(down)pseudospin.Quantum me-chanics allows for any linear superposition of these states
and the corresponding pseudospin can point in any di-
rection in space.An interesting phase transition,?rst re-
ported by Murphy et al.[4],occurs when,at ?lling factor
ν=1,the sample is tilted with respect to the quantizing
magnetic ?eld.A study of the behavior of the activation
gap as the sample is tilted shows evidence for a phase
transition between two competing quantum Hall ground
states.Yang et al.[5]explained this change of behavior
as a transition between a commensurate and an incom-
mensurate ground states.This transition can be brie?y described in the following way.In a suitable gauge,the tunneling amplitude modi?ed by the parallel component of the magnetic ?eld acts as an e?ective magnetic ?eld for the pseudospins.This e?ective ?eld rotates in space with a wavevector given by Q =d/?2||where d is the separa-tion between the wells and ?2||= c/eB ||is the magnetic length for the parallel magnetic ?eld.For d =0,the pseudospins that are forced to ly in the plane of the wells to minimize the capacitive energy will locally align with this e?ective magnetic ?eld.This is the commensurate (C)state.As the period of the ?eld increases,however,the gain in tunneling energy obtained by aligning with the ?eld is opposed by the cost in exchange energy of having non parallel pseudospins.At a critical ?eld,the exchange energy exceeds the tunneling energy and the pseudospins cease to rotate with the e?ective ?eld,be-having almost as if t =0.But,this incommensurate (I)state is never the ground state of the system.Above some critical parallel ?eld or wavevector Q c ,the C state has defects in the form of sine-Gordon solitons where the phase of the pseudospin slips by 2π.For Q ≥Q c ,the ground state of the systems is a lattice of these kinks,a soliton-lattice state (SLS).Apart from the orignal experiment of Murphy et al.there has been no other experimental signature of the SLS.On the theoretical side,Hanna et al.[6]have dis-cussed the possibility of detecting this lattice by surface acoustic wave technique or by measuring the small contri-bution of the SLS to the parallel-?eld magnetization of the DQWS.Some possible ways of detecting the pseu-dospin phase solitons in a DQWS have also been de-scribed by Kyriakidis et al .[7]Read [8]has described in details the behavior of the energy gap near the C-I tran-sition.Some details of the absorption spectrum but in the absence of a parallel magnetic ?eld has already been worked out by Joglekar et al [9].In this work,we ex-plore another possible signature of the SLS.Building on earlier work [10]where we derived the collective excita-tions of the SLS ground state,we compute the signature of these collective modes in an absorption experiment.Our basic idea is the following.The dispersion relation of the collective mode in the SLS has many branches.The lowest-energy branch corresponds to the Goldstone mode that restores the broken translational symmetry.The higher-energy branches have non-zero frequencies at zero wavector.They (as well as the Goldstone mode)involve motion of the z component of the pseudospins,a
component that is related to changes in the charge den-sity balance between the two layers.These modes can be excited by an external electromagnetic wave.A nice fea-ture of the SLS is that simply changing the magnitude of the parallel magnetic ?eld (i.e .tilting the sample)modi-?es the period of the lattice and,consequently,the set of frequencies at zero wavevector.In principle,it could be possible to track the complete dispersion relation of the pseudospin collective modes by measuring the absorption as the parallel magnetic ?eld is changed.
This paper is organized as follow.In section II,we relate the electromagnetic absorption to the polarisation tensor of the DQWS.In section III,we derive an expres-sion for this polarisation tensor in terms of the z compo-nent of the pseudospin.Section IV gives a brief review of the commensurate-incommensurate transition.In sec-tion V and VI,we compute the absorption in the C,I and SL states and comment on the possibility of experimen-tally observing the resulting spectrum.
II.ABSORPTION OF LIGHT IN A DQWS The coherent ground states of the 2DEG in a QDWS are characterized by spatial modulations of one or several of their order parameters.If we specify a pseudospin con-?guration by the spherical-coordinate ?elds θ(x,y )which describes the di?erence in charge density between the layers,and ?(x,y ),which describes the relative phase of electrons in the right and left wells,then the SLS ground state has spatial modulations in ?(x,y )only and θ(x,y )=π/2everywhere.Other states such as a lattice of bimerons [11]in a DQWS would have spatial modula-tions in both the phase and the relative occupation of the two wells and so would the coherent charge-density-wave recently studied by Brey and Fertig [12].The approach we develop can be applied to these later two cases as well.In all these states,the reponse functions are non local in space and must be described by tensors of the form A ν,μ(r ,r ′,ω)where ν,μ=x,y,z .In this section,we derive a relation between the electromagnetic absorp-tion and the polarisation response tensor in the coherent states.
In a stationnary regime,the energy absorbed per unit time in a system is given by the Joule heating term inte-grated over all the volume,V ,of this system.This energy must also be equal to the di?erence between the incident and transmitted or di?used energy which is given by an integral of the Poynting vector over the surface S V of the sample with outward normal n :
P (t )= V
dV E (r ,t )·j (r ,t )(1)
=?c 2Re V dV E ?(r ,ω)·j (r ,ω) (2)=1V q j (q ,ω)e i q ·r ,(3)E (r ,ω)=1V q ′σ(q ,q ′,ω)·E (q ′,ω).(5)Alternatively,we can also formaly relate the current to the external ?eld by j (q ,ω)=1V 2 q ,q ′e i q ·r ?q ′·r ′σ(q ,q ′,ω).(7)With Eq.(6),the absorbed power is then P (ω)=1
ω 1
where the tensor K(q,ω)is de?ned by
K(q,ω)= q q+
1
2V2 q,q′Re[E?e(q,ω)· σ(q,q′,ω)·E e(q′,ω)],(11)
an expression that relates the absorbed power to the ex-ternal electric?eld.All local?eld corrections are in-cluded in σ.For an external electromagnetic?eld in the form of a plane wave with amplitude E0,unit polarisa-tion vectorξ,and wavevector q0,we have
P(ω)=
|E0|2
ω
σ(q,q′,ω)(13)
=Iδq,q′+4πχ(q,q′,ω),
we have
σ(q,q′,ω)=?iωχ(q,q′,ω),(14) or alternatively
σ(q,q′,ω)=?iω χ(q,q′,ω),(15) where χis the response function that takes into account all local?eld corrections.The absorption is thus related to the imaginary part of the polarisation tensor by
P(ω)=ω|E0|2
(π?2)1/4e?iXy/?2e?(x?X)2/2?2χi(z),(17)
where?2⊥= c/eB⊥de?nes the magnetic length for the
perpendicular component of the magnetic?eld andχi(z)
with i=R,L are the envelope wave functions of the
lowest-energy states centered on the right or left well.
X is the guiding center quantum number.The degen-
eracy of each Landau level is given by Nφ=S/2π?2⊥
where S is the area of the two-dimensional electron gas.
With N electrons in the DQWS,the total?lling factor
isν=N/Nφ.We de?ne another magnetic length asso-
ciated with the parallel component of the magnetic?eld
by?2
||
= c/eB||.For simplicity,we describe the DQWS
in a narrow well approximation i.e.we assume that the
width,b,of the wells is small(b< treat inter- layer hopping in a tight-binding approximation[10]. Taking the charge of the electron to be?e and measur- ing all positions with respect to the center of the DQWS, the polarisation density operator in second quantization is p(r,z)=?e j(r+z z)Ψ?j(r,z)Ψj(r,z).(18) In this expression,r is a vector in the plane of the2D gas.The Fourier transformed polarisation operator is given by p(q,q z)= d r e?i q⊥·r dze?iq z z p(r,z)(19) =?e j[ zΓ1,j(q z)n j(q)+iΓ0,j(q z)[?q n j(q)]], where the matrix elementsΓm,,j(q z)with m=0,1are given by Γm,,j(q z)= dze?iq z zχ?j(z)z mχj(z),(20) and q is now rede?ned as a vector in the plane of the 2DEG.n j(q)is the Fourier-transformed density operator for well j.For propagation of the wave along the growth axis or in the plane of the2DEG,we can assume that q z≈0.(In the later case,the period of the SLS can always be made much smaller than the wavelength of the light wave by appropriately tilting the sample i.e.by avoiding the region too close to the C-SLS transition). Then, p(q)≡p(q,q z=0)=?ed zΛ(q)?ie ?→ Θ(q), (21) where Λ(q )=n R (q )?n L (q ) [ [p (q ,t ),p (?q ′,t ′)] θ(t ?t ′)]ω,(24)where [...]ωstands for a Fourier transform in time.In terms of the operators Λand ?→Θ,we have χ(q ,q ′,ω)=e 2d 2 z z χΛ,Λ(q ,q ′,ω)+ie 2d z χΛ,Θ(q ,q ′,ω)(25)+ie 2dχΘ,Λ(q ,q ′,ω) z ?e 2χΘ,Θ(q ,q ′,ω),and we can ?nally write for the absorption in the modu-lated coherent states: P (ω)= e 2ω|E 0|22V 2 lim q →0Im ξ·χΘ,Θ(q ,q ,ω)·ξ +e 2dω|E 0|2 2V 2lim q →0Re [(ξ·χΘ,Λ(q ,q ,ω))(ξ· z )]. More speci?cally,this expression gives the absorption for an incident electromagnetic wave linearly polarised along ξand propagating in the direction Q =(q ,q z ). Exception made of the ?rst term in Eq.(26),all terms involve the scalar product of the polarization vector with a vector in the plane of the 2D gas.The calculation of the absorption for an arbitrary propagation direction of the incoming wave is complicated because of the need to solve for the response functions χΘ,Θ,χΛ,Θ,χΘ,Λ.To avoid these complications,we will consider an experimen-tal situation where the electromagnetic wave propagates in the plane of the 2D gas with its polarisation vector pointing in the z direction.This imposes severe restric-tions to an absorption experiment because of the small area that is covered by the DQWS!We believe,however,that our conclusions will not change qualitatively if the light wave makes a small angle with respect to the nor-mal to the growth axis.In fact,as we showed in Ref. [10],the pseudospin-charge coupling is extremely small in the SLS so that the neglected term are probably very small.With ξclose to z ,we have P (ω)=1N φ X e ?iq x X ?iq x q y ?2/2c ?i,X c j,X +q y ?2.(28)The diagonal elements of this operator are related to the density of electrons in the right (ρR,R (q ))or left well (ρL,L (q )).The o?-diagonal terms,ρR,L (q ),ρL,R (q )de-scribe coherence between the two wells.If the separation between the wells is smaller than some critical value,it is possible for these coherence terms to be non-zero even if the tunneling term itself is zero. In the pseudospin representation,the total density and pseudospin density operators are given by ρ(q )=ρRR (q )+ρLL (q ),(29)S z (q )=12V 2e 2ω|E 0|2d 2lim q →0Im [χS z ,S z (q ,q ,ω)],ξ z (34)where the pseudospin response functions χS z ,S z is com-puted from an analytic continuation of the ?nite temper-ature,Matsubara two-particle Green’s function ΓS z ,S z (q ,?n )=?N φ T δS z (q ,τ)δS z (?q ,0) ?n ,(35)where δS z ≡S z ? S z and ?n is a Matsubara bosonic fre-quency. https://www.wendangku.net/doc/d54719022.html,MENSURATE-INCOMMENSURATE TRANSITION IN A DQWS In the pseudospin description,the Hartree-Fock energy per particle for the2DEG in a DQWS subjected to an in-plane magnetic?eld can be written,atν=1,as E HF= d 4 qΥ(q) ρ(?q) ρ(q) + q J z(q) S z(?q) S z(q) + q J⊥(q) S⊥(?q) · S⊥(q) . All energies in this equation are in units of e2/κl⊥.The tunneling amplitude is given by t=te?d2?2/4?4||≡te?Q2?2/4.(37) In the gauge we are using,the parallel component of the magnetic?eld is responsible for the introduction of a guiding-center-dependent phase factor that depends on the X quantum number only i.e.e?iXd/?2||≡e?iQX where Q is de?ned by Q≡ d q? e?q2?2/2,(42) V b(q)= ∞0d(q′?)J0(qq′?2)e?q′2?2/2,(43) V c(q)= 1 2 .(47) The last equation indicates that S+(X) = 1 2Nφ X e?iq x X e i ?(X),(50) and so in the commensurate phase < S+(q x)>=< S x(q x)>=1 t L s (56) is the wavevector of the soliton lattice and is a function of the parallel component of the magnetic?eld. The energy of the commensurate state is E C=? t?1κ? V d(Q).(57) It increases monotonically with the magnetic?eld.In the limit of strong parallel magnetic?elds,the energy of the soliton-lattice state becomes equal to the energy of an incommensurate state described by?(X)=0i.e., ?(X)=?QX or,equivalently,< ρRL(?Q)>=1 4 e2 2 1+cos Qq y?2/2 δq,q′ 2 V a(q)?V b(q)?V c(q)cos Qq y?2/2 ,(61) b(q)=t R? 1 2 V d(Q).(63) In the limit q→0,the absorption is then proportionnal to P C(ω)～ω|E0|2d2lim q→0Im[χS z,S z (q,q,ω)]ξ z(64) ～|E0|2d2 tδ(ω?ωC(q=0))(65)where ωC(q=0)=2 2??1π2V d(Q) (66) gives the gap in the dispersion relation of the pseudospin wave in the C phase.This gap is shifted from it’s nonin-teracting value,2 t because of many-body exchange and vertex corrections.In the absence of vertex corrections (i.e.in the Hartree-Fock approximation),the SAS gap is renormalized to2t R.The vertex corrections produce a substantial reduction of the Hartree-Fock gap. From the expression of P C(ω),we see that there is no absorption in the absence of tunneling when the pseu-dospin wave mode given by Eq.(66)is gapless.The absorption is non zero,however,in the absence of the parallel magnetic?eld,if t=0and forξ z. In the I state,we have χS z,S z (q,q′,ω)= [V d(q)?V d(0)]δq,q′ (V d(0)?V d(q))(68) × and soliton-lattice states as a function of the parallel magnetic ?eld.The inset shows the dependence of the soliton-lattice wavevector on the parallel?eld. modes in the SLS for t/(e2/k?⊥)=0.01,d/?⊥=1.0and(a) Q?⊥=0.64,(b)Q?⊥=1.0,(c)Q?⊥=2.0.The full lines in (c)are given byωI(q=k+nQ s x)with n=0,±1,±2. k is a vector restricted to the?rst Brillouin de?ned of the SL.In this high-parallel?eld limit,the pseudospin modulations in the SLS results in a folding of the col-lective modes of the t=0ground state inside the?rst Brillouin zone.As the parallel?eld is decreased,the cou-pling between di?erent modes increases and gaps open up in the dispersion.As Q→Q c,the dispersion becomes increasingly di?erent fromωI(k+nQ s x). When the parallel magnetic?eld is large,the folding of the modes inside the Brillouin zone results in a set {ωn(0)}of k=0modes that correspond to the frequen-cies{ωI(nQ s x)}.As the parallel?eld decreases,these frequencies evolves into a serie of curves represented in Fig. 3.This set of curves is a distinctive feature of the SLS and would be a good signature of its existence.Un-fortunately,the absorption spectrum does not capture all of these excitations.In fact,very few branches survive in P(ω)as is clear from Fig. 4.The absorption spec-trum consists of a broad peak near the transition at Q c (at a frequency close to the renormalized tunneling en-ergy)that further spreads into a number of well-de?ned peaks as the parallel magnetic?eld is increased.Very rapidly,however,only two of the peaks(corresponding to the lowest two branches in Fig.3)survive.At larger parallel?eld,only the lowest-energy branch has signi?-cant weight in the absorption spectrum.For still larger modes branches from the commensurate to the SL state. ?elds,when the system asymptotically approaches the incommensurate state,the absorption disappears com-pletely.Below the transition to the SLS,the absorption spectrum consists of only one peak at the renormalized value of the gap energy as we have shown above.Fig.4 shows that there is a de?nite signature of the SLS in the absorption spectrum although it is not as pronounced as we might?rst have expected. From Fig.4,we also see that the large peak in the absorption spectrum occurs near the renormalized gap energy given approximately byωC(0)of Eq.(66).A large fraction of this gap comes from many-body correc-tions.For parameters appropriate to the weak-tunneling sample of Murphy et al.[4],i.e.n s=1.26×1011cm?2, d=211?A with a small tunneling energy of t=0.4 K,we have d/?=1.87and t/ e2/κ? =0.003so that ωC(0)≈0.1 e2/κ? just as for the parameters we choose in this paper.An energy of ω=0.1 e2/κ? corresponds to a frequency of approximately2.6×1011 Hz(if it were observable in the absorption,the highest-energy branch would correspond to a maximal frequency of approximately1.6×1012Hz).This places the interest-ing features in the absorption spectrum in the far-infrared region of the electromagnetic spectrum,a di?cult region to investigate with available laser sources.It is possi-ble to increaseωC(0)by a factor of5or more using a DQWS with a stronger tunneling gap or by modifying the other parameters of the sample(provided this choice soliton-lattice state for several values of the parallel magnetic ?eld. of parameters does not place the sample outside the re-gion of stability of the coherent state)but observation would still remain di?cult. VII.CONCLUSION We have computed the absorption spectrum of the 2DEG in a DQWS when the sample is gradually tilted with respect to the quantizing magnetic?eld.At?lling factorν=1,the commensurate-incommensurate transi-tion driven by the parallel?eld is re?ected in a change of behaviour of the absorption spectrum.The soliton lattice that is the ground state of the2DEG above the transition has a distinctive set of collective excitations. Some of these excitations can be seen,in principle,in the absorption spectrum in a small region above the C-I transition.Experimental observation of this behaviour, however,is expected to be di?cult. VIII.ACKNOWLEDGMENTS This research was supported by a grant from the Natu-ral Sciences and Engineering Research Council of Canada (NSERC).The author want to thank S.Charlebois and J.Beerens for helpful discussions. The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中 定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way... “tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法 不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke. 表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法 The way的用法及其含义（一） 有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析： 一、the way作先行词，后接定语从句 以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started. way 的用法 【语境展示】 1. Now I’ll show you how to do the experiment in a different way. 下面我来演示如何用一种不同的方法做这个实验。 2. The teacher had a strange way to make his classes lively and interesting. 这位老师有种奇怪的办法让他的课生动有趣。 3. Can you tell me the best way of working out this problem? 你能告诉我算出这道题的最好方法吗？ 4. I don’t know the way (that / in which) he helped her out. 我不知道他用什么方法帮助她摆脱困境的。 5. The way (that / which) he talked about to solve the problem was difficult to understand. 他所谈到的解决这个问题的方法难以理解。 6. I don’t like the way that / which is being widely used for saving water. 我不喜欢这种正在被广泛使用的节水方法。 7. They did not do it the way we do now. 他们以前的做法和我们现在不一样。 【归纳总结】 ●way作“方法，方式”讲时，如表示“以……方式”，前面常加介词in。如例1； ●way作“方法，方式”讲时，其后可接不定式to do sth.，也可接of doing sth. 作定语，表示做某事的方法。如例2，例3； t h e-w a y-的用法 The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. way的用法总结大全 way的用法你知道多少，今天给大家带来way的用法，希望能够帮助到大家，下面就和大家分享，来欣赏一下吧。 way的用法总结大全 way的意思 n. 道路,方法,方向,某方面 adv. 远远地，大大地 way用法 way可以用作名词 way的基本意思是“路,道,街,径”,一般用来指具体的“路,道路”,也可指通向某地的“方向”“路线”或做某事所采用的手段,即“方式,方法”。way还可指“习俗,作风”“距离”“附近,周围”“某方面”等。 way作“方法,方式,手段”解时,前面常加介词in。如果way前有this, that等限定词,介词可省略,但如果放在句首,介词则不可省略。 way作“方式,方法”解时,其后可接of v -ing或to- v 作定语,也可接定语从句,引导从句的关系代词或关系副词常可省略。 way用作名词的用法例句 I am on my way to the grocery store.我正在去杂货店的路上。 We lost the way in the dark.我们在黑夜中迷路了。 He asked me the way to London.他问我去伦敦的路。 way可以用作副词 way用作副词时意思是“远远地,大大地”,通常指在程度或距离上有一定的差距。 way back表示“很久以前”。 way用作副词的用法例句 It seems like Im always way too busy with work.我工作总是太忙了。 His ideas were way ahead of his time.他的思想远远超越了他那个时代。 She finished the race way ahead of the other runners.她第一个跑到终点,远远领先于其他选手。 way用法例句 t h e_w a y的用法大全 The way 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了 另外，在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms. 从那天起,其他同学是夹着书本来上课,而他们却带着"失败"的思想负担来上课. The way的用法及其含义（三） 三、the way的语义 1. the way=as（像） Please do it the way I’ve told you.请按照我告诉你的那样做。 I'm talking to you just the way I'd talk to a boy of my own.我和你说话就像和自己孩子说话一样。 Plant need water the way they need sun light. 植物需要水就像它们需要阳光一样。 2. the way=how（怎样，多么） No one can imagine the way he misses her.没人能够想象出他是多么想念她！ I want to find out the way a volcano has formed.我想弄清楚火山是怎样形成的。 He was filled with anger at the way he had been treated.他因遭受如此待遇而怒火满腔。That’s the way she speaks.她就是那样讲话的。 3. the way=according as （根据） The way you answer the questions, you must be an excellent student.从你回答问题来看，你一定是名优秀的学生。 The way most people look at you, you'd think a trash man was a monster.从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物。 The way I look at it, it’s not what you do that matters so much.依我看，重要的并不是你做什么。 I might have been his son the way he talked.根据他说话的样子，好像我是他的儿子一样。One would think these men owned the earth the way they behave.他们这样行动，人家竟会以为他们是地球的主人。 一．Way：“方式”、“方法” 1.表示用某种方法或按某种方式 Do it (in) your own way. Please do not talk (in) that way. 2.表示做某事的方式或方法 It’s the best way of studying [to study] English.。 There are different ways to do [of doing] it. 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句 正：I don’t like the way he spoke. I don’t like the way that he spoke. I don’t like the way in which he spoke.误：I don’t like the way how he spoke. 4. the way 的从句 That’s the way (=how) he spoke. I know where you are from by the way you pronounce my name. That was the way minority nationalities were treated in old China. Nobody else loves you the way(=as) I do. He did not do it the way his friend did. 二．固定搭配 1. In a/one way：In a way he was right. 2. In the way /get in one’s way I'm afraid your car is in the way， If you are not going to help，at least don't get in the way. You'll have to move－you're in my way. 3. in no way Theory can in no way be separated from practice. 4. On the way (to……) Let’s wait a few moments. He is on the way Spring is on the way. Radio forecasts said a sixth-grade wind was on the way. She has two children with another one on the way. 5. By the way By the way，do you know where Mary lives? 6. By way of Learn English by way of watching US TV series. 8. under way 1. Elbow one’s way He elbowed his way to the front of the queue. 2. shoulder one’s way 3. feel one‘s way 摸索着向前走；We couldn’t see anything in the cave, so we had to feel our way out 4. fight/force one’s way 突破。。。而前进The surrounded soldiers fought their way out. 5.. push/thrust one‘s way（在人群中）挤出一条路He pushed his way through the crowd. 6. wind one’s way 蜿蜒前进 7. lead the way 带路，领路；示范 8. lose one‘s way 迷失方向 9. clear the way 排除障碍，开路迷路 10. make one’s way 前进，行进The team slowly made their way through the jungle. 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了 另外，在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms. “the way+从句”结构的意义及用法 首先让我们来看下面这个句子： Read the following passage and talk about it with your classmates. Try to tell what you think of Tom and of the way the children treated him. 在这个句子中，the way是先行词，后面是省略了关系副词that 或in which的定语从句。 下面我们将叙述“the way+从句”结构的用法。 1．the way之后，引导定语从句的关系词是that而不是how,因此，<<现代英语惯用法词典>>中所给出的下面两个句子是错误的：This is the way how it happened. This is the way how he always treats me. 2. 在正式语体中，that可被in which所代替；在非正式语体中，that则往往省略。由此我们得到the way后接定语从句时的三种模式：1) the way +that-从句2) the way +in which-从句3) the way +从句 例如：The way(in which ,that) these comrades look at problems is wrong.这些同志看问题的方法不对。 The way(that ,in which)you’re doing it is completely crazy.你这么个干法，简直发疯。 We admired him for the way in which he faces difficulties. Wallace and Darwin greed on the way in which different forms of life had begun.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 This is the way (that) he did it. I liked the way (that) she organized the meeting. 3.the way(that)有时可以与how(作“如何”解)通用。例如： That’s the way (that) she spoke. = That’s how she spoke. I should like to know the way/how you learned to master the fundamental technique within so short a time. 4．the way的其它用法：以上我们讲的都是用作先行词的the way，下面我们将叙述它的一些用法。 定冠词the的12种用法 定冠词the 的12 种用法，全知道?快来一起学习吧。下面就和大家分享，来欣赏一下吧。 定冠词the 的12 种用法，全知道? 定冠词the用在各种名词前面，目的是对这个名词做个记号，表示它的特指属性。所以在词汇表中，定冠词the 的词义是“这个，那个，这些，那些”，可见，the 即可以放在可数名词前，也可以修饰不可数名词，the 后面的名词可以是单数，也可以是复数。 定冠词的基本用法： (1) 表示对某人、某物进行特指，所谓的特指就是“不是别的，就是那个!”如： The girl with a red cap is Susan. 戴了个红帽子的女孩是苏珊。 (2) 一旦用到the，表示谈话的俩人都知道说的谁、说的啥。如： The dog is sick. 狗狗病了。(双方都知道是哪一只狗) (3) 前面提到过的，后文又提到。如： There is a cat in the tree.Thecat is black. 树上有一只猫，猫是黑色的。 (4) 表示世界上唯一的事物。如： The Great Wall is a wonder.万里长城是个奇迹。(5) 方位名词前。如： thenorth of the Yangtze River 长江以北地区 (6) 在序数词和形容词最高级的前面。如： Who is the first?谁第一个? Sam is the tallest.山姆最高。 但是不能认为，最高级前必须加the，如： My best friend. 我最好的朋友。 (7) 在乐器前。如： play the flute 吹笛子 Way用法 A:I think you should phone Jenny and say sorry to her. B:_______. It was her fault. A. No way B. Not possible C. No chance D. Not at all 说明：正确答案是A. No way，意思是“别想！没门！决不！” 我认为你应该打电话给珍妮并向她道歉。 没门！这是她的错。 再看两个关于no way的例句： （1）Give up our tea break? NO way! 让我们放弃喝茶的休息时间？没门儿！ （2）No way will I go on working for that boss. 我决不再给那个老板干了。 way一词含义丰富，由它构成的短语用法也很灵活。为了便于同学们掌握和用好它，现结合实例将其用法归纳如下： 一、way的含义 1. 路线 He asked me the way to London. 他问我去伦敦的路。 We had to pick our way along the muddy track. 我们不得不在泥泞的小道上择路而行。 2. （沿某）方向 Look this way, please. 请往这边看。 Kindly step this way, ladies and gentlemen. 女士们、先生们，请这边走。 Look both ways before crossing the road. 过马路前向两边看一看。 Make sure that the sign is right way up. 一定要把符号的上下弄对。 3. 道、路、街，常用以构成复合词 a highway（公路），a waterway（水路），a railway（铁路），wayside（路边） way/time的特殊用法 1、当先行词是way意思为”方式.方法”的时候,引导定语从句的关系词有下列3种形式： Way在从句中做宾语 The way that / which he explained to us is quite simple. Way在从句中做状语 The way t hat /in which he explained the sentence to us is quite simple. 2、当先行词是time时,若time表示次数时,应用关系代词that引导定语从句,that可以省略; 若time表示”一段时间”讲时,应用关系副词when或介词at/during + which引导定语从句 1.Is this factory _______ we visited last year? 2.Is this the factory-------we visited last year? A. where B in which C the one D which 3. This is the last time _________ I shall give you a lesson. A. when B that C which D in which 4.I don’t like the way ________ you laugh at her. A . that B on which C which D as 5.He didn’t understand the wa y ________ I worked out the problem. A which B in which C where D what 6.I could hardly remember how many times----I’ve failed. A that B which C in which D when 7.This is the second time--------the president has visited the country. A which B where C that D in which 8.This was at a time------there were no televisions, no computers or radios. A what B when C which D thatThe way常见用法
The way的用法及其含义(二)
(完整版)the的用法
“the way+从句”结构的意义及用法
way 用法
The way的用法及其含义(一)
way 的用法
the-way-的用法讲解学习
way的用法总结大全
the_way的用法大全教案资料
the way 的用法
The way的用法及其含义(三)
way的用法
the way的用法大全
“the-way+从句”结构的意义及用法知识讲解
定冠词the的12种用法
Way的用法
way与time的特殊用法