Pis’ma v ZhETF, vol. 113, iss. 4, pp. 274 - 275
© 2021
February 25
Holographic model of exciton condensation in double monolayer Dirac
semimetal
A. Pikalov1)
Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
Institute for Theoretical and Experimental Physics, 117259 Moscow, Russia
Submitted 21 December 2020
Resubmitted 21 December 2020
Accepted 31
December 2020
DOI: 10.31857/S1234567821040108
We consider a holographic model of exciton conden-
the branes. We show that the distance between layers at
sation in double monolayer Dirac semimetal. Exciton is
which interlayer condensate disappears decreases with
a bound states of an electron and a hole. Being Bose
quasiparticle mass.
particles, excitons can form a Bose-Einstein conden-
The model consists of large number N of D3 branes
sate. Exciton condensation might be easier to achieve
that create AdS5 × S5 geometry with metric
in case we have electrons and holes in different layers
dρ2
(
)
of a double layer two dimensional structure. An insula-
ds2 =
+ρ2
-dt2 + dx2 + dy2 + dz2
+
ρ2
tor between the layers prevents electron and holes from
+ dψ2 + sin2 ψ dΩ22 + cos2 ψ dΩ22.
(1)
annihilation thus increasing exciton lifetime. There are
two possible types of condensates. In first case both the
Here AdS5 stands for a five-dimensional anti de Sitter
electron and the hole forming the exciton are in the same
space while S5 is a five dimensional sphere. The two lay-
layer (intralayer condensate), in the second case the elec-
ers of Dirac semimetal are modeled by two D5 branes
tron and the hole are in different layers (interlayer con-
embedded into this geometry. We treat them in probe
densate). The exciton condensation in double layer sys-
approximation that is we do not consider the D5 branes
tems in magnetic field has been extensively discussed
back-reaction on the geometry. AdS5 geometry is dual
in condensed matter literature (see, for example, [1-3]).
to the N = 4 super Yang-Mills (SYM) theory. Each
In case the electron quasiparticles can be described as
of the D5 branes supports massless Dirac fermions and
massless (gapless) Dirac fermions, exciton condensation
connected brane configuration gives the fermions mass.
is similar to the spontaneous chiral symmetry breaking
The N = 4 SYM leads to the electron interaction en-
in Quantum Chromodynamics. The condensate breaks
ergy proportional to 1/r and does not take into account
the chiral symmetry of massless fermions creating an
screening.
energy gap in the spectrum. From this point of view the
D5 branes are stretched along x, y, ρ, t directions
chiral symmetry of graphene was discussed in [4]. This
and also wrapped around of the two dimensional sphere.
analogy allows to test some basic notions of Quantum
Separation between branes and the radius of the sphere
Chromodynamics in condensed matter systems.
depends on the radial coordinate ρ. The energy of the
We study how the condensates depend on the dis-
D5 brane system is given by Dirac-Born-Infeld action.
tance between layers and the mass of the quasiparticles
There is magnetic field B perpendicular to the branes.
in presence of a strong magnetic field. The electrons and
Formation of interlayer condensate corresponds to
√
holes in the layers have quasirelativistic dispersion law
the connected configuration of branes. We compare en-
ǫ(p) ∼
m2 + p2. In order to take into account possi-
ergies of connected and disconnected branes. The low-
ble strong Coulomb interaction between electrons we use
est energy configuration corresponds to the equilibrium
holographic appoach. The holographic model consists of
state of the system. Our numerical analysis yields phase
two D5 branes embedded into anti de Sitter space. This
diagram in coordinates m - mass of the quasiparticles,
model was introduced in [5] for zero temperature and
L - layer separation. We find that for large enough sep-
mass case. Finite temperature was discussed in [6]. The
aration L > Lc interlayer condensate disappears. Criti-
condensates are described by geometric configuration of
cal layer separation decreases with mass. The results are
summarized in Fig. 1. Above the yellow line there is no
1)e-mail: arseniy.pikalov@phystech.edu
solution with interlayer condensate and above the blue
274
Письма в ЖЭТФ том 113 вып. 3 - 4
2021
