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Physica C 282-287

New type of superconducting

(1997) 2497-2498

field-effect

transistor

A.V.Okomel’kova =Institute GSP-105,

for Physics of Microstructures, Russian Nizhny Novgorod, 603600, Russia

Academy

of Sciences,

A theoretical vortices barriers

model is proposed to describe the effect of a nonuniform electric field on the pinning of magnetic in superconducting films. The model shows that a nonuniform electric field can create additional energy in the superconductors, which are pinning potentials for magnetic vortices.

Our basic idea is that a spatially nonuniform electric field should play the role of an additional pinning potential. We now consider a field effect transistor which has a gate in form of a number of strips. The gate strips are extended along the direction of the transport current in the superconducting film (i.e., perpendicular to the direction of motion of the vortices).The strip structure of the gate creates a quasi-one-dimensional potential relief for vortices in the superconducting film in the direction of their motion. Following Ref. [l], we next discuss the difference in free energies of two states-with and without a vortex-in a film with electric field. In this way we determine the value of the energy barrier for a vortex. Without including anisotropy of coherence length 6, the Ginzburg-Landau free energy has the form [l]

G

(B -H)’ 8?r

= -

+12+

PIAl 2

temperature at E = 0), pairing constant, no is the carrier density at E = 0, and 6n = bn(E) is the change in carrier density in the near-surface layer due to the presence of the electric field. We will assume that the electric field is directed along the z axis (see Fig.l), and that the characteristic (where

T, is the critical

g is the superconducting

++(V-?+I

11T, d3

b, Vortex

(1)

where A is the order parameter, B and H are the magnetic induction and external magnetic field vectors respectively, and v is density of states. Let us assume that the electric field is perpendicular to the plane of the film and is directed along the z axis, while the coordinate axes for x and y lie in the plane of the film. In Eq.(l), the presence of the electric field can be taken into account in the linear approximation [1,2] by renormalizing the value of (Y : LY= r+6n/gno, here we have set 7 = (T,-‘7)/T, 0921-4534/97/$17.00 0 Elsevier Science B.V. All rights reserved PII SO921-4534(97)01348-g

Figure 1. Structure of the electric field E created by the gate; 10 is the scale of Thomas-Fermi screening. The electric field vector E is paral1e.lto the magnetic induction vector in the film B (the field in the vortices).

scale of variation of the field in the xy plane can be larger than the characteristic scales [, lo, so that E - E, = Ez(z, y, z). In t.he Thomas-Fermi approximation we have

A. V Okomel’kou/Ph)~sica

2498

h/no

= (E/E*)

exp(-z/lo),

where E’ = 4relono/c. By analogy with Refs. [I] tute (4) into Eq.(l) and find Ginzburg-Landau functional. in E we obtain the following potential barrier for a vortex

(2) and [3], we substithe variation of the Then to first order expression for the in the electric filed:

AG=

-u/s

Y)I’- lA0(4~), Jd3+#lAo(~,

where Ao(z, y) is the order paramet.er in the presence of a vortex for E = 0, and Ao(co) is order parameter in the uniform state of the superconductor, AO(CXJ)~ = r/2p. We will assume that E(z, y, z) fr’Eexp(-z/lo), i.e., E can be approximately taken outside the integration sign with respect to 2: and y. Finally one can easily obtain the following estimate for the change in free energy for a vortex in a n electric field:

!zr,p~,

AG-Pg N

Equation (3) gives an estimate of magnitude of the modulation of the pinning potential by the electric field to first order in the field E. Let us estimate the value of the characteristic field for a high-T, superconductor: Ee

=

4relono -.

c

(4)

Here 10 is the characteristic scale for screening the electric field (see [l]), lo - { - 10 &X 10m7cm 710 G nF = p3,/(37r2ti3) x 1 5 ’ 102* cmW3 is the carrier concentration (elect;ons at the Fermi surface), and 6 M 20-30 is the dielectric constant. Then, according to Eq.(4), E* 21 lo7 B/cm. Equation (3) can be written in the form

C 282-287

From this model of the effect of an electric field on a superconducting film, it is clear that the largest change in the resistive state of the film can be achieved by modulating its superconducting properties in the direction of motion of the magnetic vortices (i.e., perpendicular to the direction of current flow). To do this, we can use a gate made, e.g., in the form of the number of strips. It is of great interest to calculate a current- voltage characteristic of the transistor-like structure. A simple estimation of this one can see in Ref. [4]. In the simple estimation the current-voltage characteristic exponentially depends on t,he electric field amplitude on the gat,e. In describing the mechanism proposed here for the action of an electric field on a superconduct,or, we have demonstrated that. a nonuniform electric field creates an additional pinning potential for magnetic vortices. It is clear that in this case the films should be rather thin. In fact, the length of a vortex in the film is the same order as it.s thickness, and the largest effect should occur when the electric fields acts over a large portion of the vortex. In the opposite case, if the film is thick and the electric field is concentrated near the surface, the electric field will bring about only surface pinning, and the vortex pinning will be determined by structural nonuniformities in the volume of the film. In order to experimentally reveal this mechanism, it appears to us that a spatially nonuniform gate configuration must be used, in a geometry similar to that of a field-effect transistor. This will correspond to an artificially created pinning potential profile, whose strength can be controlled by an applied voltage. REFERENCES 1.

Let us assume that 2?r/g - 1; then AG v(~)A&~~E/E* M lOK.E/E*. In magnetic flux creep, all quantities (for instance, the resistivity) are proportional to exp(-G/T), where G is the pinning potential; then for AG/G < 1 the relative change is - (lOK/T)(E/E*); which,e.g., in fields E - E* at T - 80K gives - 10%.

(1997) 2497-2498

2. 3. 4.

L.Burlachkov, I.B.Khalfin, and B.Ya.Shapiro, Phys. Rev. B 48, 1156 (1993). V.M.Nabutovsky and B.Ya.Shapiro, Zh. Eksp. Teor. Fiz. 75, 948 (1978). V.V.Geshkenbein, Zh.Eksp.Teor.Fiz.94,(10), 368 (1988). A.V.Okomel’kov, Zh.Eksp.Teor.Fiz. 110, 61 l-623 (1996).

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