Heavy fermion materials
1 ,1 ,2 ,3 ,1 ,4 ,5 ,1 ,6 ,1 ,7 ,1 ,8 and 9,
1Max-Planck-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany 2University of California, Irvine, California 92697, USA 3HH Wills Laboratory, University of Bristol, Bristol BS8 1TH, UK 4Center for Correlated Matter, Zhejiang University, Hangzhou, Zhejiang 310058, China 5Institute of Physics, Goethe-Universität Frankfurt, 60438 Frankfurt/Main, Germany 6Dept. of Condensed Matter Physics, Weizmann Institute of Science, 76100 Rehovot, Israel 7Dept. of Physics and Astronomy, Rice University, Houston, TX 77005, USA 8Los Alamos National Laboratory, Los Alamos, NM 87545, USA 9Institut für Mathematische Physik, TU Braunschweig, 38106 Braunschweig, Germany
Electronic correlations give rise to a plethora of interesting phenomena and phases. For example, hybridization between 4f and conduction electrons in heavy fermion metals may result in the generation of low-energy scales that can induce quantum criticality and unconventional superconductivity (see Special Issue, Ref. 1). These complex interactions often operate, and compete, on different lengths scales. One of the most important techniques that helped shaping our understanding of nonlocal correlations, both magnetic and superconducting, has been scanning tunneling spectroscopy (STS) with its unique ability to give local, microscopic information that directly relates to the one-particle Green’s function. We complement these local measurements with global probes, most importantly magnetotransport (see review on Hall effect, Ref. 2), magnetization and x-ray diffraction measurements, in order to unambiguously assign the local, surface-sensitive findings by STS to bulk properties of the single crystals under scrutiny.
As a pivotal prerequisite for a possible disentanglement of the involved interactions, to rule out inadvertent influences of impurities as well as to successfully relate local with global properties, samples of highest possible quality need to be investigated. Here, the so-called 115 family of compounds (CeMIn5 with M = Co, Ir, Rh) exhibiting superconductivity, magnetism and Fermi surface changes, are a clear-cut example for which we could identify nanometer-scale defects, Wirth et al. 2014 . A substitution series of these compounds was recently instrumental in identifying the Ce 4f wave function as a significant parameter for the realization of either a superconducting or an antiferromagnetic ground state, Willers et al. 2015 . For CeCoIn5 a field-induced quantum critical point (QCP) of spin-density-wave (SDW) type is extrapolated to exist inside the superconducting phase. Single crystals of 115 compounds were provided through our long-term collaboration with groups led by Dr. Zachary Fisk (UC Irvine, USA) and Dr. Joe D. Thompson (Los Alamos National Laboratory, USA). Similarly, in CeCu2Si2 a SDW type of QCP was established in the vicinity of which superconductivity was demonstrated to be mediated by spin fluctuations, Steglich et al. 2013 .
Very strong correlation effects can be realized through the above-mentioned hybridization between 4f and conduction electrons via the Kondo effect. In case of the prototypical heavy fermion metal YbRh2Si2 this can result in quasiparticle masses beyond a thousand times the free electron mass. Our low-temperature electronic transport measurements at high magnetic field (μ0H ≤ 15 T) in concert with thermal transport measurements (conducted in the group Novel states of matter on the border of magnetism) and renormalized band structure calculations by Prof. Gertrud Zwicknagl indicate that the de-renormalization of the quasiparticles, i.e. the destruction of the local Kondo singlets, occurs smoothly and likely requires magnetic fields of the order of 30 T to complete, Naren et al. 2013 , Pfau et al. 2013 . On the other hand, the spin splitting of the very flat, hybridized bands results in three successive Lifshitz transitions which are confined to relatively narrow magnetic field intervals and clearly visible in magnetotransport  (see Fig. 1, lower panel) and thermopower measurement .
The renormalized band structure calculations indicate a neck-forming Lifshitz transitions in the hybridized band 37 at around 3 T (from region I to II) along the Γ→X direction, a neck disruption in band 37 as well as the formation of a single surface in the f-derived band 35 at around 9 T, and finally the disappearance of a pocket along X→P→u in band 37 around 11 T (from region III to VI). As can be seen, the calculations are in excellent agreement with our measurements. Neither our measurements, nor the renormalized band structure calculations provided any hint of a metamagnetic transition, Friedemann et al. 2013 . Again, all these measurements require high-quality single crystalline YbRh2Si2 which are provided by the Materials design and synthesis group.
Numerous electronic transport and thermodynamic measurements indicate an unconventional nature of the QCP in YbRh2Si2 related to the break-up of the quasiparticles right at the QCP, Steglich et al. 2014 . However, the corresponding large and small Fermi surfaces are sharply separated at zero temperature, only. At finite temperature, the quantum critical fluctuations broaden this cross-over.
In consequence, the single-particle spectral function at T ≳ 0.5 K and zero magnetic field has significant weight at both the small and large Fermi surfaces, Paschen et al. 2015 . Therefore, for unambiguous measurements of the Fermi surface volume sufficiently low temperatures are required.
YbRh2Si2 single crystals were studied by low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). The topography on samples cleaved in situ at low temperature and perpendicular to the crystallographic c-direction confirms the excellent quality of the latest generation of samples, see Fig. 2. Two types of defects can be distinguished, which are likely caused by site exchange: The single protrusions may originates from a larger Rh ion occupying a Si site at the surface while the dumbbell-shaped dents result from a smaller Si occupying a Rh site within the second-to-topmost layer and affecting the two adjacent Si in the topmost layer. Our studies support two conclusions (see Wirth et al. 2012 ): i) The exact stoichiometry of the single crystals can be determined down to an atomic level. ii) More importantly, such surfaces provide a first indication that they are Si terminated. This assignment is could be supported further by the first-ever observation of crystalline electric field (CEF) excitations by STS. Moreover, our STS spectra are dominated by a gap-like feature around zero-bias resulting from the hybridization of conduction and 4f electrons. Clearly, the local Kondo entanglement modifies the local density of states (DOS) govern the measured tunneling spectra g(V,T). The temperature dependence of the reduction in g(V,T) can nicely be reproduced by calculations within the non-crossing approximation (NCA) whereas renormalized band structure calculation (which are restricted to zero temperature) capture 4f-derived intersite correlations. An additional hump in our tunneling spectra at around V = -6 mV strongly evolves at low temperatures and is likely caused by a lattice Kondo resonance.
The interpretation of the results of our studies requires in many cases profound theoretical support. Here we rely primarily on collaborations in house and with Dr. Qimiao Si (Rice University, USA).
 Special Issue: “Quantum Criticality and Novel Phases”, edited by S. Kirchner, O. Stockert and S. Wirth, Phys. Stat. Sol. 250(3), pp. 417-659 (2013) http://onlinelibrary.wiley.com/doi/10.1002/pssb.v250.3/issuetoc.
 S. Nair, S. Wirth, S. Friedemann, F. Steglich, Q. Si and A. J. Schofield Hall effect in heavy fermion metals. Adv. Phys. 61, 583-664 (2012) http://dx.doi.org/10.1080/00018732.2012.730223.
 S. Wirth, Y. Prots, M. Wedel, S. Ernst, S. Kirchner, Z. Fisk, J. D. Thompson, F. Steglich and Y. Grin Structural investigations of CeIrIn5 and CeCoIn5 on macroscopic and atomic length scales. J. Phys. Soc. Jpn. 83, 061009 (2014) http://dx.doi.org/10.7566/JPSJ.83.061009.
 T. Willers, F. Strigari, Z. Hu, V. Sessi, N. B. Brookes, E. D. Bauer, J. L. Sarrao, J. D. Thompson, A. Tanaka, S. Wirth, L. H. Tjeng and A. Severing Correlation between ground state and orbital anisotropy in heavy fermion materials. Proc. Natl. Acad. Sci. USA 112, (2015) http://dx.doi.org/10.1073/pnas.1415657112.
 F. Steglich, O. Stockert, S. Wirth, C. Geibel, H. Q. Yuan, S. Kirchner and Q. Si Routes to heavy-fermion superconductivity. J. Phys.: Conf. Series 449, 012028 (2013) http://iopscience.iop.org/article/10.1088/1742-6596/449/1/012028.
 H. R. Naren, S. Friedemann, G. Zwicknagl, C. Krellner, C. Geibel, F. Steglich and S. Wirth Lifshitz transitions and quasiparticle de-renormalization in YbRh2Si2. New J. Phys. 15, 093032 (2013). http://dx.doi.org/10.1088/1367-2630/15/9/093032.
 H. Pfau, R. Daou, S. Lausberg, H. R. Naren, M. Brando, S. Friedemann, S. Wirth, T. Westerkamp, U. Stockert, P. Gegenwart, C. Krellner, C. Geibel, G. Zwicknagl and F. Steglich Interplay between Kondo suppression and Lifshitz transitions in YbRh2Si2 at high magnetic fields. Phys. Rev. Lett. 110, 256403 (2013) http://dx.doi.org/10.1103/PhysRevLett.110.256403.
 S. Friedemann, S. Paschen, C. Geibel, S. Wirth, F. Steglich, S. Kirchner, E. Abrahams and Q. Si Comment on “Zeeman-Driven Lifshitz Transition: A Model for the Experimentally Observed Fermi-Surface Reconstruction in YbRh2Si2”. Phys. Rev. Lett. 111, 139701 (2013) http://dx.doi.org/10.1103/PhysRevLett.111.139701.
 F. Steglich, H. Pfau, S. Lausberg, Peijie Sun, U. Stockert, M. Brando, S. Friedemann, C. Krellner, C. Geibel, S. Wirth, S. Kirchner, E. Abrahams and Qimiao Si Evidence of a Kondo destroying quantum critical point in YbRh2Si2. J. Phys. Soc. Jpn. 83, 061001 (2014) http://dx.doi.org/10.7566/JPSJ.83.061001.
 S. Paschen, S. Friedemann, S. Wirth, F. Steglich, S. Kirchner and Q. Si Kondo destruction in heavy fermion quantum criticality and the photoemission spectrum of YbRh2Si2. J. Magn. Magn. Mater. (2015) accepted http://dx.doi.org/10.1016/j.jmmm.2015.09.008.
 S. Wirth, S. Ernst, R. Cardoso-Gil, H. Borrmann, S. Seiro, C. Krellner, C. Geibel, S. Kirchner, U. Burkhardt, Y. Grin and F. Steglich Structural investigations on YbRh2Si2: from the atomic to the macroscopic length scale. J. Phys.: Condens. Matter 24 294203 (2013) http://dx.doi.org/10.1088/0953-8984/24/29/294203.