ANTECEDENTES INVESTIGATIVOS

4.5 K 10 K 15 K 25 K 35 K εxx(%) ∆ ρxx ( εxx ) /ρ xx (0) −1.0 −0.5 0.0 −0.3 0.0 0.3

Fig. 3.33: Elastoresistance against strain. Change in longitudinal resistiv- ity with strain at various temperatures for sample 3. Values are calculated by interpolating between separate tem- perature ramps at a series of constant strains except for 4.5 K where the strain was swept continuously.

The change in resistivity with strain at a fixed temperature is shown in figures 3.33 and 3.34. The curves in figure 3.33 are cuts through the surface plot in figure 3.32 at select temperatures whereas the measurements in figure 3.34 are from continuous strain ramps at fixed temperatures. Figure 3.34 shows both the longitudi- nal and transverse measurements as depicted in the top corners of the figure panels.

The resistivity at a given temperature peaks in the vicinity of the peak inTc before falling again rapidly at higher strains even

below its zero strain value, similar to the observed behaviour of

Tc. This is seen in both the longitudinal and transverse resistivity

measurements. Metallic behaviour is observed over the full range of strain tested. There are no signatures associated with competition from a spin density wave phase, as suggested by Liuet al. [148], where the opening of a gap is generally expected to increase the resistivity sharply.

The increase inρxxwith strain closely resembles the increase

Fig. 3.34: Longitudinal and trans- verse resistivity against strain. Strain sweeps at constant temper- atures for sample 2. A.Longitudi- nal resistivity measured in the tra- ditional geometry. B.A qualitative measure of the transverse resistiv- ity, see text for further details. This measurement geometry over exag- gerates the intrinsic anisotropy.

4.5 K 10 K

A

∆

ρ

(

ε

)

/ρ

(0)

B

ε

(%)

∆

V

(

ε

)

/V

(0)

−0.5

−0.25

0.0

0.0

0.3

0.6

0.0

0.3

0.6

80 The Physics of Sr₂RuO₄ Approaching a Van Hove Singularity

in Tc, see figure 3.35. Much as Tc is enhanced by the increasing

density of states at the Fermi level, inelastic scattering in the normal state is also expected to scale with the density of states at the Fermi level, thus resulting in a peak in resistivity at the Lifshitz transition. ρxxis increased by∼40-50 % at the peak, with a slight

variation between the two samples. The two samples have slightly different residual resistivities, sample 2 being the cleaner with a resistivity at 4.5 K of ∼0.12 µΩ cm and sample 3 _∼0.19 µΩ cm,

but both resistivities increase by approximately the same amount

∼0.07µΩ cm at the peak. Tcsample 2 Tcsample 3 ρxxsample 2 ρxxsample 3 V46/I35 sample 2 εxx Normalised change εmaxTc 0 0.0 0.5 1.0

Fig. 3.35:Comparison betweenTcand

resistivity enhancements. Normalised change with strain ofTc,ρxxat 4.5 K

and transverse resistivity at 4.5 K, e.g. (Tc(εxx)−Tc(0))/(Tc(max)−Tc(0)).

The strain scales of the two samples have been adjusted so that their peaks inTccoincide at the same strain, the

resistivity data is also adjusted accord- ingly.

The resistivity measured in a direction transverse to the di- rection of applied strain is expected to increase as a result of the geometric change but a clear peak is also apparent with applied strain. The quasiparticle scattering is therefore affected in all di- rections by the approach to the Van Hove singularity of only theγ

band at just the (0,_±π/a) point of the Brillouin zone. Intriguingly

the maximum in the transverse resistivity does not seem to coin- cide exactly with the peak inρxx, instead occurring at a slightly

higher strain. However, it is important to bear in mind what is being measured in the transverse geometry. The current is passed between two of the voltage contacts on opposite sides of the sample and the remaining two contacts, also opposite each other, are used to measure the voltage drop. This means there is always some component ofρxxin the measurement since this sets how far the

current spreads out along the sample. The meaning of transverse is to describe a current direction predominately perpendicular to the direction of applied strain but here it does not necessarily imply the current is flowing purely in the ab-plane. The extreme resistive

anisotropy in Sr2RuO4, ρ0,c/ρ0,ab ∼4000, means that any slight

vertical misalignment of the contacts on each side of the sample will lead to a smallc-axis component of the current but a significant

voltage because of the much higher out of plane resistivity. Finite element simulations show that the voltage actually measured for the transverse geometry of sample 2 at low temperature is approx- imately ten times larger than expected for when the current is fully within the ab-plane, and the measured RRR also shows this

discrepancy. A contact misalignment of only ∼5µm in opposite

directions on each side of the sample is enough to provide a ten fold increase of the simulated voltage so over a 100µm thick sample this

is entirely feasible, especially as the silver paint may be physically contacting the full height of the sample but the electrical contact resistance might be varying slightly across each contact. At room temperature where the resistive anisotropy is only∼120 the finite

element simulation and measured voltage match well, but at low temperatures a significant contribution of thec-axis resistivity is

3.4Results and discussions 81

To compare the longitudinal and transverse resistivities quantita- tively, the Fermi surfaces must in principle be considered in three dimensions. The slight warpings of the Fermi surfaces in thekz

direction mean the Van Hove singularity is actually reached over a range of strain as different parts of the Fermi surface reach the Brillouin zone boundary at slightly different strain, however, DFT calculations suggest this width is less than the discrepancy observed here [147].

At elevated temperatures the peak in the longitudinal resistivity is flattened out as one would expect when thermal population of higher energy states above the Fermi surface smooths out the dis- continuity in the density of states but a strong decrease in resistivity is still observed at strains above the suspected Lifshitz transition. The position of the peak also moves slightly with temperature, but extrapolating to find the zero temperature position still leaves a discrepancy with the strain of theTc peak.

The peak inρxxis also much narrower than that of Tc. This

is not so surprising, becauseTc can be affected by more than just

the change in density of states. If for instance the pairing strength is also modified as the Fermi surface is distorted, this could result in a variation between theρxx(εxx) andTc(εxx) curves. It is then

perhaps more likely that the peak inρxxwould coincide with the

Lifshitz transition andTcmay peak close to but be extended around

the Lifshitz transition.