Interlayer transverse magnetoresistance in the presence of an anisotropic pseudogap
M. F. Smith* and Ross H. McKenzie
Department of Physics, University of Queensland, Brisbane, Queensland 4072, Australia
Received 9 July 2009; revised manuscript received 29 September 2009; published 23 December 2009
The interlayer magnetoresistance of a quasi-two-dimensional layered metal with a d-wave pseudogap is
calculated semiclassically. An expression for the interlayer resistivity as a function of the strength and direction
of the magnetic field, the magnitude of the pseudogap, temperature, and scattering rate is obtained. We find that
the pseudogap, by introducing low-energy nodal quasiparticle contours, smooths the dependence on field
direction in a manner characteristic of its anisotropy. We thus propose that interlayer resistance measurements
under a strong field of variable orientation can be used to fully characterize an anisotropic pseudogap. The
general result is applied to the case of a magnetic field parallel to the conducting layers using a model band
structure appropriate for overdoped T2201.
DOI: 10.1103/PhysRevB.80.214528 PACS numbers: 74.25.Fy, 74.72.-h, 72.15.Gd
I. INTRODUCTION
High-temperature superconducting cuprates, organic
charge-transfer salts, some heavy fermion materials, and a
host of other intriguing electronic systems, are layered met-
als in which electrons are approximately confined to a given
atomic layer. Much of the interesting behavior of these ma-
terials arises because of strong electronic correlations within
a single layer. Surprisingly, it turns out that one of the most
effective means of accessing in-layer properties, particularly
those properties that are highly anisotropic within a layer, is
to measure interlayer electronic-transport coefficients in a
strong magnetic field.
1–11
The interlayer electrical resistivity
zz
depends on the di-
rection of the magnetic field in a manner that is highly sen-
sitive to the anisotropy of the quasi-two-dimensional quasi-
2D band structure. High-resolution maps of the Fermi
surface and other band-structure properties have already
been obtained by fitting
zz
data to calculations based on
semiclassical magnetotransport theory. This technique has
been applied to a wide variety of layered materials including
overdoped cuprates,
1–4
ruthenates,
5,6
and organic charge-
transfer salts.
7,8
The
zz
data also contains information about
in-plane scattering and can be used to study the directional
dependence of elastic- and inelastic-scattering rates.
12–18
No-
tably, it has been used to reveal a T-linear, anisotropic scat-
tering contribution in overdoped cuprate superconductors
that appears to be tied to superconductivity itself.
2,19,20
It is
important to press further, to ask what other anisotropic
properties of the metallic layers can be detected and charac-
terized via interlayer transport in high magnetic fields.
In this paper we ask what field-angle-dependent inter-
plane transport data can tell us about an anisotropic
pseudogap
k
in quasi-2D metals. Since an anisotropic gap
in the density of states will affect the field-direction depen-
dence of
zz
, we expect that interlayer magnetoresistance can
be used to map out
k
as well. A natural application of this
technique would be to slightly overdoped cuprates. For these
materials, a model of a 2D metal with a small d-wave
pseudogap that is starting to emerge with reduced doping is
a plausible description of the metallic state at fields above
H
C2
and semiclassical calculations of
zz
may adequately
capture transport properties. If the magnitude of the gap is
small then it will not appreciably reduce the density of states
or be observable in angle averaged transport
measurements
21
but, as revealed below, can still have a sig-
nificant effect on the field-angle dependence of the interlayer
resistivity. To extract from
zz
information about the doping,
temperature, and field dependence of
k
would be of great
value toward understanding the relationship between the
pseudogap and superconductivity.
22,23
The effects of a non-
zero
k
may already be present in existing interlayer resis-
tance data on slightly overdoped cuprates, convoluted with
the effects of anisotropic scattering.
24
If so, a reinterpretation
of these data using models that incorporate a pseudogap
could be fruitful.
We study a model with well-defined electronic quasipar-
ticles existing in the presence of a d-wave pseudogap in the
density of states. The manner in which the opening of the
pseudogap will change the interlayer resistivity is predicted
and the following main results obtained: i an expression for
the interlayer resistance
zz
in the semiclassical limit in a
strong magnetic field of arbitrary strength and direction. ii
For the simple case of a field parallel to the layer with arbi-
trary intralayer orientation
B
, the quantitative effect of a
pseudogap on
zz
B
is calculated using a realistic model
band structure. The average magnitude of
zz
B
varies non-
monotonically with the size of the pseudogap while its
B
dependence is modified in a manner distinctive of the
pseudogap symmetry. A strongly anisotropic normal state
zz
is smoothed by the pseudogap through the introduc-
tion of new low-energy current contributions associated with
d-wave nodes.
Considering our results in light of the success of the
angle-dependent magnetoresistance oscillations AMRO
technique in extracting band structure and scattering param-
eters of cuprates, we propose that this technique should also
prove to be a viable means of obtaining a T-, B-, and doping-
dependent parametrization of the d-wave pseudogap. The
characterization of the pseudogap at high fields and low tem-
peratures, following this approach, would be complementary
to the array of other experimental probes of the anisotropic
pseudogap and would likely provide unique insight. The an-
isotropic interlayer resistance technique is a bulk probe, can
be carried out under high magnetic fields thereby accessing
PHYSICAL REVIEW B 80, 214528 2009
1098-0121/2009/8021/2145288 ©2009 The American Physical Society 214528-1