Poisson's ratio is, for specified directions, the ratio of a lateral contraction to the longitudinal extension during the stretching of a material. Although a negative Poisson's ratio (that is, a lateral extension in response to stretching) is not forbidden by thermodynamics, this property is generally believed to be rare in crystalline solids 1 . In contrast to this belief, 69% of the cubic elemental metals have a negative Poisson's ratio when stretched along the [110] direction. For these metals, we find that correlations exist between the work function and the extremal values of Poisson's ratio for this stretch direction, which we explain using a simple electron-gas model. Moreover, these negative Poisson's ratios permit the existence, in the orthogonal lateral direction, of positive Poisson's ratios up to the stability limit of 2 for cubic crystals. Such metals having negative Poisson's ratios may find application as electrodes that amplify the response of piezoelectric sensors.There is considerable fundamental and practical interest in materials with negative Poisson's ratios 1-14 , which Evans 4 called auxetic. We refer to auxetic crystals as axially auxetic or non-axially auxetic, depending upon whether or not a negative Poisson's ratio arises for a crystal-axis direction. The calculation of Poisson's ratio is complicated for directions oblique to the crystal axes, because the elastic constant tensor for general orientations involves as many as 21 interrelated components for even a cubic phase 15 . This complication probably explains why the common existence of non-axial auxetic behaviour has largely remained unrecognized. However, the important early work of Milstein and Huang 16 established the occurrence of non-axial auxetic behaviour for cubic metals and rare gases. The origin of this behaviour must differ from that of other known types of auxetic materials and structures: foams, honeycombs and hypothetical carbon phases having re-entrant or hinged structures [2][3][4][5]8,13 ; microporous organic polymers 4 ; polymer laminates 11,14 ; polymer/fibre composites 12 ; and crystals such as ␣-cristobalite 1,6 .We simplify the search for auxetic materials by deriving a general criterion for the existence of auxetic behaviour. This 'auxetic criterion', expressed in elastic compliances (S ij ) for the axial directions, is that S 11 þ S 33 þ 2S 13 Ϫ S 44 Ͼ 0. Satisfying this inequality is a necessary and sufficient condition for auxetic behaviour for a hexagonal or cubic phase when the Poisson's ratios for axial directions are all positive. This general criterion is derived from equations for the Poisson's ratio for an arbitrary direction for cubic 15 and hexagonal 17 phases. Using these equations, the Poisson's ratios that usually have extremal values for cubic phases are:11 C 44 þ ðC 11 Ϫ C 12 ÞðC 11 þ 2C 12 ÞÞ ð1Þ nð110; 001Þ ¼ 4C 12 C 44 =ð2C 11 C 44 þ ðC 11 Ϫ C 12 ÞðC 11 þ 2C 12 ÞÞ ð2Þ These are the Poisson's ratios for a [110] stretch, measured for [110] and [001] lateral directions, respectively. Such Po...

A transient four-wave-mixing signal is shown to arise from an excitation induced shift. In semiconductors, this signal can be comparable to or stronger than signals arising from saturation, local fields, or excitation induced dephasing. Calculations using modified optical Bloch equations show that multiple peaks in the transient four-wave-mixing spectrum are a signature of an excitation induced shift contributing to the signal. We observe this experimentally from a semiconductor multiple quantum well and confirm the presence of a shift directly using spectrally resolved differential transmission.The interaction between light and semiconductors provides fundamental insight into the dynamics of the optically created excitations. This is particularly true when techniques that are sensitive to coherence are employed. Coherent spectroscopy is well understood for a dilute vapor, where only isolated atoms or molecules need to be considered. 1 In dense materials, such as semiconductors or a dense atomic vapor, many-body interactions lead to dramatic differences from the dilute limit. 2 These effects can completely alter the interpretation of spectroscopic measurements and the performance of optoelectronic devices.Substantial progress has been made in understanding how interactions among elementary optical excitations ͑excitons or unbound electron-hole pairs͒ influence the coherent optical response of semiconductors, which is typically observed using transient four-wave mixing ͑TFWM͒. Early work 3-5 was interpreted based on the optical Bloch equations ͑OBE's͒, 6 which are appropriate in the dilute limit. Subsequently, it was realized that in addition to the signals arising from saturation, which are described by the OBE's, there were additional signals due to the interactions. The appearance of a signal for ''negative'' delay in a two-pulse TFWM experiment and a delay in the emission as a function of real time 7,8 are the most dramatic signatures. These effects can be calculated using a full many-body treatment. 9,10 In addition, they can be described phenomenologically in a few-level approach as arising from local fields, 11,12 excitation induced dephasing ͑EID͒, 13-15 and biexcitonic effects. 16,17 The phenomenological approach yields corrections to the OBE's, which can produce very good agreement with experiment 18 including complex polarization selection rules. 19 While the full many-body treatment is clearly based on a stronger theoretical foundation, the phenomenological description is usually easier to understand in terms of the underlying physics. The foundation provided by the full many-body treatment has been used to develop a microscopic basis for the phenomenological few level approach. 20 We show that an excitation induced shift ͑EIS͒ can result in a TFWM signal similar to that produced by the other mechanisms listed above. EIS is a manifestation of fundamental many-body interactions that result in a modification of the excitonic frequency in the presence of an excited carrier population. While the presence o...

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By two-color pulse shaping, we simultaneously create virtual and real amplitudes for excitons in GaAs quantum wells, and monitor population and amplitude by pump-probe and four-wave mixing spectroscopies. Excited-state probability amplitude can be induced by the off-resonant, virtual excitations as well as by the resonant, real excitations. Population modulation in time-domain results from the interference between the virtual and real amplitudes, and the modulation depth reveals the relative contributions of these two amplitudes. The fact that virtual and real amplitudes have a phase difference of 90 degrees is demonstrated directly in time-domain.

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Quantum interference between real and virtual polarizations is demonstrated in the time domain. Using a novel technique we can visualize the excited state quantum amplitude and its phase under off-resonant excitation.