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Crystal twinning plane — superconducting “two-dimensional metal”
Physica 108B (1981) 1259-1260 North-Holland Publishing Company
SF 24
CRYSTAL TWINNING PLANE - SUPERCONDUCTING
"TWO-DIMENSIONAL
METAL"
M. S. Khalkin and I. N. Khlustlkov
Institute for Physical Problems Acad. Sci. USSR, Moscow
The superconductivity effect of a tin crystal twinning plane (301) is discovered. The effect takes place at a temperature T < T < T + 0,15 K and in a magnetic field c c H < 50e. To explain the effect we introduce an idea of "two-dimensional metal '~ consisting of: a twinning plane crystal lattice; a two-dimensional group of electrons moving parallel to the twinning plane; two-dimensional twinning plane phonons. Electronic properties of a thin "two-dimensional metal" layer differs from electronic properties of a bulk mother crystal twins.
In paper [i] an effect of a deformed tin crystal superconductivity was studied by an apparatus containing SQUID [2]. Now we have ascertained the fact that the superconductivity [i] is connected with twinning planes but not with di~locations [3]. A very demonstrative experiment was carried out in the following way: a long tin crystal having no diamagnetic moment M D was bent in its middle part which was then recrystallized. So we got a sample consisting of three monocrystals which orientations difference at the first boundary corresponded to a twinning plane but at the second boundary it was i0 + 12 ° apart and formed a layer of dislocations. Measurements discovered ~ at the first boundary only. Another sample produced by mechanical twinning gave the same M D. Figure la shows the record of the M n of a sample containing a twinning plane ( 3 0 1 ) . ~ For comparison fig. ib shows the record of superconducting phase fluctuations moment M F in a crystal of the same volume. The jump M M at the field ~ takes place because of a small sample part - thin layer containing a twinning plane-transition from metastable normal state to a superconductivity. Figure 2 shows the function MM(T) samples [i]: = M C exp[-(T-Tc)/T]
for some
,
where M_ = 3.10 -6 Gauss. cm and T = 0.01 K. Values c of ~ are reduced to 1 cm 2 of a twinning plane area. So far as the moment M M is determined by the magnetic susceptibility of a layer containing a twinning plane, let us define an "equivalent" thickness W of the layer taking its diamagnetic susceptibility X_ = - 1/4 ~. The scale for W given in fig~ 2 shows that: max W(T) ~ W(T c) = ~o where ~0 is the coherence
' length.
way. The function HM(T) measured in experiment is linear [i]. By the extrapolation of this function to the point ~.(T ) = 0 we get the f~ o value of T . Then after extrapolation of fig. 2 diagrams°up to the temperature T (crosses on o fig. 2) we get: min W(T) = W(T o) = I0 a
,
where a is a tim lattice spacing. Similar experiments show the existence of the effect in twins of indium also. The origin of the effect and the related hypothesis are to be discussed. A twinning plane (x,y,0) is at the same time a mirror symmetry plane of a bi-crystal in which twins occupy two half-spaces: +z and -z. Now let us consider the energy spectrum of electrons moving close by and parallel (or almost parallel) to the twinning plane. This spectrum may be represented by a narrow Fermi surface belt symmetrical with respect to the llne of its intersection by the plane (Px' p ' 0). Some of such belts may exist at intersections of twin Fermi surfaces parts by the plane (p , p , 0). In each twin many electrons are mo~ingYclose enough to twinning plane (x,y,0) to feel another twin, because electrons have very long free paths and accordingly widely extended wave bunches. So a separated two-dimensional extremal group of electrons appears in a bicrystal close by a twinning plane in a layer of thickness of the order of t0. (Such group of electrons does not exist in a monocrystal.) At the same time a new branch of two-dimensional phonons of twinning plane oscillations appears in a phonon spectrum of a bicrystal. (Such phonons do not exist in a monocrystal also.) These two phenomena create a layer of a "twodimensional metal" fastened to a twinning plane. The "two-dimensional metal" has its own electrons and phonons, interaction of which does not remove them out of this system. And this interaction may give rise to the superconductivity discovered in our experiments.
Now let us estimate a mln W(T) in the following 0378-4363/81/0000-0000/$02.50
© North-Holland PublishingCompany
125 9
1260
It should be mentioned that in the examined case some other effects may be also of importance. They are for example magnetic surface levels [4] and Tamm levels. Energy levels and effects arising because of electron interaction with a metal surface are analysed theoretically by E. Stern [5]. We have to emphasize one more point clearly shown by this work. A well ~nown increase of T c as a result of a metal deformation usually is connected with dislocations. Now we may say that not dislocations but twinning planes play the main part in the effect.
m 4 -- -- --
O~
•
M " ~
$
2
Figure i : (a) Record of a magnetic moment of the Sn bicrystal, having a twinning plane (301); (b) magnetic moment of superconducting phase fluctuations in the Sn monocrystal. Magnetic moment of normal state is excluded by compensation in the apparatus [1,2].
Figure 2 : Graphs of values of M M taken from records like fig. I and the equivalent thickness W of a superconducting layer for various specimens. REFERENCES: i.
2. In conclusion we have to remark that the "twodimensional metal" phenomenon arising in a twinning plane is to take place in twin crystals of many metals, superconducting and not superconducting, and shows itself besides superconductivity in other effects. These considerations open wide possibilities for various investigations of a "two-dimensional metal" as a new physical object.
3.
4. 4.
Khlustikov, I. N., and Khaikin, M. S., Dislocation superconductivity at above-critical temperatures in tin, Soy. Phys. JETP 48 (3) (Sept. 1978) 583-588. Khlustikov, I. N., and Khaikin, M. S., Quantum magnetometer with superconducting transformer, Prib. Tekn. Eksp. N 4 (1980) 184-187. Khaikin, M. S., and Khlustikov, I. N., Twinning plane of a metal crystal--two-dimensional superconductor, Pisma JETP 33 (1981) 167-170. Khaikin, M. S., Magnetic surface levels, Adv. in Phys. 18 (1969) 1-40. Stern, E. A., Electron states near boundaries, Phys. Rev. 162 (1967) 565.
SF 24
CRYSTAL TWINNING PLANE - SUPERCONDUCTING
"TWO-DIMENSIONAL
METAL"
M. S. Khalkin and I. N. Khlustlkov
Institute for Physical Problems Acad. Sci. USSR, Moscow
The superconductivity effect of a tin crystal twinning plane (301) is discovered. The effect takes place at a temperature T < T < T + 0,15 K and in a magnetic field c c H < 50e. To explain the effect we introduce an idea of "two-dimensional metal '~ consisting of: a twinning plane crystal lattice; a two-dimensional group of electrons moving parallel to the twinning plane; two-dimensional twinning plane phonons. Electronic properties of a thin "two-dimensional metal" layer differs from electronic properties of a bulk mother crystal twins.
In paper [i] an effect of a deformed tin crystal superconductivity was studied by an apparatus containing SQUID [2]. Now we have ascertained the fact that the superconductivity [i] is connected with twinning planes but not with di~locations [3]. A very demonstrative experiment was carried out in the following way: a long tin crystal having no diamagnetic moment M D was bent in its middle part which was then recrystallized. So we got a sample consisting of three monocrystals which orientations difference at the first boundary corresponded to a twinning plane but at the second boundary it was i0 + 12 ° apart and formed a layer of dislocations. Measurements discovered ~ at the first boundary only. Another sample produced by mechanical twinning gave the same M D. Figure la shows the record of the M n of a sample containing a twinning plane ( 3 0 1 ) . ~ For comparison fig. ib shows the record of superconducting phase fluctuations moment M F in a crystal of the same volume. The jump M M at the field ~ takes place because of a small sample part - thin layer containing a twinning plane-transition from metastable normal state to a superconductivity. Figure 2 shows the function MM(T) samples [i]: = M C exp[-(T-Tc)/T]
for some
,
where M_ = 3.10 -6 Gauss. cm and T = 0.01 K. Values c of ~ are reduced to 1 cm 2 of a twinning plane area. So far as the moment M M is determined by the magnetic susceptibility of a layer containing a twinning plane, let us define an "equivalent" thickness W of the layer taking its diamagnetic susceptibility X_ = - 1/4 ~. The scale for W given in fig~ 2 shows that: max W(T) ~ W(T c) = ~o where ~0 is the coherence
' length.
way. The function HM(T) measured in experiment is linear [i]. By the extrapolation of this function to the point ~.(T ) = 0 we get the f~ o value of T . Then after extrapolation of fig. 2 diagrams°up to the temperature T (crosses on o fig. 2) we get: min W(T) = W(T o) = I0 a
,
where a is a tim lattice spacing. Similar experiments show the existence of the effect in twins of indium also. The origin of the effect and the related hypothesis are to be discussed. A twinning plane (x,y,0) is at the same time a mirror symmetry plane of a bi-crystal in which twins occupy two half-spaces: +z and -z. Now let us consider the energy spectrum of electrons moving close by and parallel (or almost parallel) to the twinning plane. This spectrum may be represented by a narrow Fermi surface belt symmetrical with respect to the llne of its intersection by the plane (Px' p ' 0). Some of such belts may exist at intersections of twin Fermi surfaces parts by the plane (p , p , 0). In each twin many electrons are mo~ingYclose enough to twinning plane (x,y,0) to feel another twin, because electrons have very long free paths and accordingly widely extended wave bunches. So a separated two-dimensional extremal group of electrons appears in a bicrystal close by a twinning plane in a layer of thickness of the order of t0. (Such group of electrons does not exist in a monocrystal.) At the same time a new branch of two-dimensional phonons of twinning plane oscillations appears in a phonon spectrum of a bicrystal. (Such phonons do not exist in a monocrystal also.) These two phenomena create a layer of a "twodimensional metal" fastened to a twinning plane. The "two-dimensional metal" has its own electrons and phonons, interaction of which does not remove them out of this system. And this interaction may give rise to the superconductivity discovered in our experiments.
Now let us estimate a mln W(T) in the following 0378-4363/81/0000-0000/$02.50
© North-Holland PublishingCompany
125 9
1260
It should be mentioned that in the examined case some other effects may be also of importance. They are for example magnetic surface levels [4] and Tamm levels. Energy levels and effects arising because of electron interaction with a metal surface are analysed theoretically by E. Stern [5]. We have to emphasize one more point clearly shown by this work. A well ~nown increase of T c as a result of a metal deformation usually is connected with dislocations. Now we may say that not dislocations but twinning planes play the main part in the effect.
m 4 -- -- --
O~
•
M " ~
$
2
Figure i : (a) Record of a magnetic moment of the Sn bicrystal, having a twinning plane (301); (b) magnetic moment of superconducting phase fluctuations in the Sn monocrystal. Magnetic moment of normal state is excluded by compensation in the apparatus [1,2].
Figure 2 : Graphs of values of M M taken from records like fig. I and the equivalent thickness W of a superconducting layer for various specimens. REFERENCES: i.
2. In conclusion we have to remark that the "twodimensional metal" phenomenon arising in a twinning plane is to take place in twin crystals of many metals, superconducting and not superconducting, and shows itself besides superconductivity in other effects. These considerations open wide possibilities for various investigations of a "two-dimensional metal" as a new physical object.
3.
4. 4.
Khlustikov, I. N., and Khaikin, M. S., Dislocation superconductivity at above-critical temperatures in tin, Soy. Phys. JETP 48 (3) (Sept. 1978) 583-588. Khlustikov, I. N., and Khaikin, M. S., Quantum magnetometer with superconducting transformer, Prib. Tekn. Eksp. N 4 (1980) 184-187. Khaikin, M. S., and Khlustikov, I. N., Twinning plane of a metal crystal--two-dimensional superconductor, Pisma JETP 33 (1981) 167-170. Khaikin, M. S., Magnetic surface levels, Adv. in Phys. 18 (1969) 1-40. Stern, E. A., Electron states near boundaries, Phys. Rev. 162 (1967) 565.