Pis’ma v ZhETF, vol. 110, iss. 3, pp. 163 - 164
© 2019 August 10
Layered superconductor in a magnetic field: breakdown of the effective
masses model
A. G. Lebed1)
Department of Physics, University of Arizona, 1118 E. 4-th Street, AZ 85721 Tucson, USA
L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 117334 Moscow, Russia
Submitted 14 June 2019
Resubmitted 14 June 2019
Accepted 15
June 2019
DOI: 10.1134/S0370274X19150049
The upper critical magnetic field, Hc2(T ), is known
H∥c2(0) ≈ 0.75 |dH∥c2/dT|Tc Tc,
(1)
to be one of the most important properties of the type-
for a parallel magnetic field. We recall that, for a perpen-
II superconductors. It destroys superconductivity due
dicular magnetic field the corresponding solution is ex-
to the orbital Meissner currents in case, where we can
ponential one and gives much smaller coefficient - 0.59,
disregard the Pauli spin-splitting paramagnetic effects.
as shown by different method in [7]:
The Ginzburg-Landau (GL) theory gave tools to calcu-
late a slope of the Hc2(T ) [1] in the vicinity of super-
H⊥c2(0) ≈ 0.59 |dH⊥c2/dT|Tc Tc.
(2)
conducting transition temperature, (Tc-T)/Tc ≪ 1. On
the other hand, at zero temperature, the upper critical
Note that Eqs. (1) and (2) directly break the effective
magnetic field was calculated for an isotropic 3D super-
mass model, since the corresponding coefficients, 0.75
conductor in [2]. Temperature dependence of Hc2(T) in
and 0.59 are not close to each other.
a whole temperature region in an isotropic 3D super-
In the Letter, we consider a layered superconductor
conductor was calculated later in [3]. Important gen-
with the following realistic Q2D electron spectrum:
eralization of the GL theory to the case of anisotropic
1
superconductors was obtained in [4], where the so-called
ǫ(p) =
(p2x + p2y) - 2t⊥ cos(pz c∗),
2m
effective mass model was implicitly introduced. The ef-
(3)
fective mass model, partially based on the results ob-
m
= mvF2,
tained in [4] in the GL region, states more: ratios of the
where m - the electron in-plane mass, t⊥ - the integral
upper critical magnetic fields measured along fixed dif-
of overlapping of electron wave functions in a perpen-
ferent directions do not much depend on temperature.
dicular to the conducting planes direction; ǫF , pF , and
Recently observed experimental temperature dependen-
vF are the Fermi energy, Fermi momentum, and Fermi
cies of anisotropy of the upper critical fields in layered
velocity, correspondingly; ℏ ≡ 1. In a parallel to the
compound MB2 [5] and other materials are prescribed
conducting planes magnetic field,
exclusively to many-band effects (see introductory part
of review [6]).
H = (0,H,0) , A = (0,0,-Hx),
(4)
The goal of our Letter is to consider the orbital ef-
fect in a parallel magnetic field in a Q2D conductor
we make use of the so-called Peierls substitution
at zero temperature, where we explicitly take into ac-
method:
count a Q2D anisotropy of the electron spectrum. In
(
)
(
)
∂
∂
contrast to [1-4,6], we demonstrate that, in a Q2D case
px → -i
, py → -i
,
∂x
∂y
in a parallel magnetic field, the solution of the so-called
(
)
)
gap equation can not be expressed as some exponential
∂
(ωc
evF c∗H
c∗pz → -ic∗
-
x, ωc(H) =
(5)
function. Moreover, we show that the above mentioned
∂z
vF
c
solution even changes a sign with changing space coor-
Under such conditions the electron orbital Hamiltonian
dinate. This leads to unusual value of the corresponding
in a magnetic field can be written in the following way:
coefficient, 0.75, in the equation,
)
(
)
1
(∂2
∂2
∂
H
-2t⊥ cos -ic∗
-
ωc x . (6)
1)e-mail: lebed@email.arizona.edu
= -2m ∂x2 +
∂y2
∂z
vF
Письма в ЖЭТФ том 110 вып. 3 - 4
2019
163
2∗
