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We report the first observation of the de Haas–van Alphen (dHvA) effect in the novel spin-triplet superconductor UTe2 using high quality single crystals with a high residual resistivity ratio (RRR) over 200. The dHvA frequencies, named α and β, are detected for the field directions between c- and a-axes. The frequency of branch β increases rapidly with the field angle tilted from c- to a-axis, while branch α splits, owing to the maximal and minimal cross-sectional areas from the same Fermi surface. Both dHvA branches, α and β reveal two kinds of cylindrical Fermi surfaces with a strong corrugation at least for branch α. The angular dependence of the dHvA frequencies is in very good agreement with that calculated by the generalized gradient approximation (GGA) method taking into account the on-site Coulomb repulsion of U = 2 eV. It indicates that the main Fermi surfaces are experimentally detected. The observed cyclotron effective masses are large in the range from 32 to 57 m0. They are approximately 10–20 times lager than the corresponding band masses, consistent with the mass enhancement obtained from the Sommerfeld coefficient, γ and the calculated density of states at the Fermi level. The local density approximation (LDA) calculations of ThTe2 assuming U4+ with the 5f2 localized model are in less agreement with our experimental results, in spite of the prediction for two cylindrical Fermi surfaces, suggesting a mixed valence states of U4+ and U3+ in UTe2.
UTe2 attracts much attention because of the unusual superconducting properties due to the spin-triplet state.1–3) UTe2 is a heavy fermion paramagnet with a Sommerfeld coefficient
It was first pointed out1) that UTe2 is located at the verge of the ferromagnetic order and resembles ferromagnetic superconductors.13,14) However, no ferromagnetic fluctuations are experimentally established; instead antiferromagnetic fluctuations with an incommensurate wave vector are detected in inelastic neutron scattering experiments.15,16) Furthermore, above
The electronic structure of UTe2 has been investigated by angle-resolved photoemission spectroscopy (ARPES) at 20 K. The results obtained from the soft X-ray19) and the vacuum ultraviolet synchrotron radiation20) are contradicting, probably related to the different inelastic mean free path of the photoelectrons. The fine structure near the Fermi level was unresolved in the soft X-ray experiments. On the other hand, the high resolution ARPES experiments revealed two light quasi-one dimensional bands and one heavy band at the Fermi level, which is, however, inconsistent with the soft X-ray ARPES experiments. Thus, no clear conclusion on the electronic structure emerges up to now. The determination of the Fermi surface topology at low temperatures through the direct observation of quantum oscillations is highly desired, which will be a key experiment to investigate the topological superconducting phenomena as well.
In order to clarify the electronic structure, we performed de Haas–van Alphen (dHvA) experiments on new high quality single crystals. Clear dHvA oscillations were successfully detected, and the angular dependence of the dHvA frequencies reveals two kinds of cylindrical Fermi surfaces. The results are well explained by the generalized gradient approximation (GGA) calculation with the on-site Coulomb repulsion,
High quality single crystals of UTe2 were grown at Oarai (sample #1) and Tokai (sample #2). The details of single crystal growth will be published elsewhere.21) The dHvA experiments were performed at low temperatures down to 60 mK and at high fields up to 147 kOe, as well as resistivity, specific heat and AC susceptibility measurements.22) The band calculations were done by the GGA+U method in UTe223,24) and the local density approximation (LDA) method in ThTe2 as a reference.25)
First we present the superconducting properties of our high quality single crystals. Figure 1(a) shows the temperature dependence of the resistivity for the current along the a-axis. The superconducting transition at
Figure 1. (Color online) (a) Temperature dependence of the resistivity for the current along a-axis in UTe2 (sample #1). The residual resistivity ratio (RRR) is 220. The dotted line is the results of fitting. (b) Temperature dependence of the electronic specific heat in the form of
Figure 1(b) shows the temperature dependence of the electronic specific heat in the form of
Figure 2 shows the anisotropy of
Figure 2. (Color online) Anisotropy of
Next we show in Fig. 3 the dHvA oscillations at different field angles tilted from c- to a-axis. The clear dHvA signals were observed at the field angles between 11.8 and 56.8 deg above
Figure 3. (Color online) dHvA oscillations at 70 mK at different field angles with the 4.5 deg step tilted from c- to a-axis in UTe2 (sample #2). Small up-arrows indicate
Figure 4 shows the typical dHvA oscillations and the corresponding FFT spectrum at the field angle of 26 deg tilted from c- to a-axis. Four dHvA frequencies, named
Figure 4. (Color online) Typical dHvA oscillations and the FFT spectrum in the field range between 110 and 147 kOe at the field direction tilted by 26 deg from c- to a-axis in UTe2 (sample #1).
Figure 5(a) shows the angular dependence of the dHvA frequencies from c- to a-axis. The results are obtained using two different samples, #1 and #2. The sample #1 was rotated from
Figure 5. (Color online) (a) Angular dependence of the dHvA frequency in UTe2. Two samples, #1 (square) and #2 (circle) were used for
In order to determine the cyclotron effective masses, the dHvA oscillations were measured at different temperatures.28) The results are summarized in Table I. The detected effective masses are very large in the range from 32 to
|
The Dingle temperature,
The angular dependence of the dHvA frequencies are compared to those obtained from the calculations. Figures 5(b) and 5(c) are the results from the GGA+U (
The results of the LDA calculations in ThTe2, which corresponds to U4+ with the localized
Assuming the two kinds of cylindrical Fermi surfaces, which occupy approximately 20% of volume for each in the Brillouin zone with the carrier compensation, one can roughly calculate the γ-value derived from each Fermi surface, from the following equation,
The effective masses can be compared to the band masses from GGA+U (
In the LDA calculations for ThTe2 without the electron correlation, the band masses are much smaller. For instance,
A question is whether the anisotropy of the resistivity for
It should be noted that we cannot exclude the existence of small pocket Fermi surfaces with heavy masses, which may induce a Lifshitz transition under magnetic field as proposed in thermopower experiments.35) This may also compromise with possible topological superconductivity.
In summary, the dHvA oscillations were detected for the first time in UTe2. The angular dependence of the dHvA frequencies from
Acknowledgements
We thank Y. Ōnuki, S.-i. Fujimori, V. Mineev, Y. Tokunaga, M. Kimata, K. Ishida, K. Izawa, A. Miyake, J. P. Brison, D. Braithwaite, A. Pourret, I. Sheikin, and S. Fujimoto for fruitful discussion. This work was supported by KAKENHI (JP19H00646, JP20K20889, JP20H00130, JP20KK0061, JP22H04933), GIMRT (20H0406), ICC-IMR, and ANR (FRESCO).
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