Magnetic Field Dependence of Laser Emission inPb1−XSnXSeDiodes

Abstract

unpublished). 6 This formalism for the natural-mode E e field parallels that given by Stix in the approximate theory [Ref.The temperature dependence of laser emission in Pb^^Sn^Se diodes in the composition range 0 ^x ^0.3 has recently been reported 1 and the magnetic field dependence of laser emission and spontaneous luminescence has been measured for PbS, PbSe, and PbTe 2 and for low-SnTe-content Pb^^Sn^Te diodes. 3 We report here the results of measurements made on a number of Pbi-^Sn^Se diode lasers in the above composition range at magnetic fields up to 145 kG. The results support the model previously proposed 4 in which the valence-and conduction-band states in Pb^^Sn^Se alloys approach each other, invert, and move apart as SnSe is added to PbSe. At low temperatures this inversion occurs at about x = 0.15. For the alloys on the SnSe-rich side of the inversion point the lowest energy transition between magnetic levels of the conduction and valence bands has an energy which decreases with increasing magnetic field. To our knowledge this is the first such observation in any material. In addition the results give a direct indication of the effect that the higher lying energy bands have on the conduction and valenceband-edge masses and ^factors in these materials. 4, Sec. 5-4, in which T = kpJ i (vp)K 1 '(kp)-ppJ 1 '(vp)K 1 (kp)]. 7For the magnetic-field measurements the diodes were near liquid-He temperature and oriented with the diode current parallel to the magnetic field in a (100) crystallographic direction. The laser radiation was emitted perpendicular to this direction. The photon energy of the laser emission as a function of magnetic field is shown in Fig. 1 for diodes of Pb^^Sn^Se with x = 0, 0.05, and 0.10 and in Fig. 2 for # = 0.19, 0.22, and 0.28. The Landau levels shown schematically in the insets identify the transitions observed. At low magnetic fields one generally observes the line T 2 . As the field is increased the emission switches to T v If the diode current is increased the T 2 emission persists up to higher magnetic field values and in some cases a third line T 3 is observed. For all of the alloys studied with #<0.15 (including PbSe) the T\ line is found to have a positive slope, in most cases about 10 ~7 eV/G. For alloys with x > 0.15 the slope of this line is negative but has about the same magnitude. The zero-field energy gap as a function of alloy composition is shown in Fig. 3. The mole fraction of SnSe (x) was measured using an electron microprobe, and the energy-gap values were obtained from extrapolations of the magnet- MAGNETIC FIELD DEPENDENCE OF LASER EMISSION IN Pb x ^Sn^Se DIODES*The magnetic field dependence of long-wavelength infared laser emission has been studied in Pb^^Sn^Se diodes for compositions in the range 0 ^x ^0.3. For x >0.15 the energy of the lowest transition decreases with increasing magnetic field whereas for x <0.15 this energy increases. This unique observation is consistent with a theory of magnetic energy levels proposed by Baraff and also strongly supports...

Michel Besson's stay at Harvard

“…Finally, in the pressure studies at least, the total intensity of radiative emission decreased to quite low values as the pressure was increased. All of these results are consistent with the suggestion (not definitely proven to my knowledge) that their cause lies in the onset of energy absorption by optical phonons or plasmons [22][23][24]. As a relevant calculation, a concentration of 1 Â 10 18 carriers=cm 3 , having an effective mass of 0.023 m 0 , and an optical dielectric constant of 35 (appropriate parameters here) has a plasmon energy of about 40 meV.…”

Magnetooptical determination of a topological index

“…1b). 28,29,[41][42][43] The bulk Fermi surface of Pb 1-x Sn x Se and Pb 1-x Sn x Te is shown in Fig. 1b.…”

Negative Longitudinal Magnetoresistance from the Anomalous N=0 Landau Level in Topological Materials

“…[23] shown, that the energy of the lowest (N=0) conduction (valence) Landau level in topological insulators decreases (increases) as a function of increasing magnetic field, opposite to what usually happens in a topologically trivial system ( Fig.1(a,b)). This behavior is anomalous and leads to a field-induced closure of the energy gap in a TI [21] (Fig.1(b)), whereas in a trivial material, the energy gap usually opens with increasing magnetic field ( Fig.1(a)). This anomaly is a hallmark of the inverted band structure of topological materials.…”