Apparent Fermi Liquid (AFL)

During the systematic search of boosting thermoelectric efficiency used to convert heat into electric energy some delafossites In 1873 Friedel named the commonly found mineral CuFeO2 after his colleague Gabriel Delafosse. Nearly a century later it was shown that in the same structure several compounds crystallize, allowing a systematic study of the group which was therefore called the delafossites. In this group, copper could even be replaced by platinum, palladium or silver, leading to rarely known crystalline oxides of noble metals, but which are not so important for thermoelectric applications.
More important in this sense is the semi-conductor class. Additionally, it shows a rich variety of physical systems due to an underlying low dimensional structure. This range reaches from band insulators, like CuRhO2 over multiferroica, like doped CuFeO2, to Mott-insulators, like CuCrO2, where an AFL behavior has been observed for doped systems too. The physics of these materials are governed by the substituent of iron. The observed effects of strong correlation is due to the close oxygen atoms, mediating a superexchange coupling between these atoms. Moreover, the oxygen atoms are octrahedraly coordinated around these atoms. This means that the five d-orbitals will split into the two-fold degenerate eg and the three-fold degenerate t2g states. Thus the different shifts in energy of these states arising from the crystal field explains the semi-conductor gap.
These octahedrons form layers which are separated by the copper atoms, like in the perovskite structure. However, in contrast to this structure the layers are closer since neighboring octahedrons not only share two, but three oxygen atoms. Therefore the layers form a hexagonal lattice.

and manganites The structure of these materials is similar to Perovskite and the high-temperature superconductors. However, in those materials the charge carriers are highly localized and therefore have a very low carrier mobility. Thus the materials are not suitable for thermoelectric devices. However, in the manganites like CaMnO3 a substitution of the Calcium by some lanthanides will trigger a semiconductor-metal transition and therefore delocalize the charge carriers. showed an extraordinary effect above room temperature: The Seebeck coefficient S It is the ratio of the generated voltage and the applied temperature gradient if no current is flowing. determining this efficiency as well as other physical quantities resemble at those high temperatures the ones at very low temperature, known as the ones of a Fermi liquid It is the standard theory of metals at low temperatures and is deduced from the assumption that the excitations in those materials behave as the ones of free electrons, but with renormalised parameters. e.g. the effective mass. . However, the low temperature parameters are quite different from the ones determined at the considered temperatures. Furthermore, additional offsets in the extrapolated physical quantities challenges the interpretation as a Fermi liquid behavior. Instead this behavior is called the one of an apparent Fermi liquid (AFL).
To explain this region new methods, like the temperature independent correlation ratio (TICR) or the approximation of the polylogarithm difference (APLD) are developed, which focus at an intermediate temperature regime where the AFL behavior is expected to be observed. Furthermore its relation to a Quantum Phase Transition The concept of QPTs was introduce 1976 by J. Hertz. In contrast to classical phase transitions they only occur at zero temperature. This is the reason why the fluctuation of the order parameter would not follow the classical theory. Instead the quantum statistic is necessary to describe the behaviour.
Systems, in which QPT occur, posses multiple kind of ground states with different physical properties. The transition point between the two phases corresponding to the two ground states is called the quantum critical point (QCP) similar to the classical critical point. Near the QCP the two ground states can quantum mechanical overlap (blue region in the phase diagram) leading to additional, new phases which can be present even at higher temperatures. Therefore, these make it difficult to identify the QCP. Usually cross-over temperatures are obtained (green line in the phase diagram) where some few properties are pointing towards a phase transition, but all the other do not exhibit unusual behaviour.

is studied.
• S. Kremer, R. Frésard, Annalen der Physik 524, 21 (2012)
• E. Guilmeau, M. Poienar, S. Kremer, S. Marinel, S. Hébert, R. Frésard, A. Maignan, Solid State Communications 151, 1798 (2011)
• S. Kremer, PhD thesis urn:nbn:de:swb:90-241252 (2011)
• A. Maignan, V. Eyert, C. Martin, S. Kremer, R. Frésard, D. Pelloquin, Physical Review B 80, 115103 (2009)

• A. M. Oleś, Expert Opinion on the AFL concept by Kremer and Frésard, Annalen der Physik 524, A33 (2012)

Mesoscopic Ring Structures

If metallic atoms are assembled in a ring geometry like in Benzene, which consists of six Carbon atoms forming a ring a simple magnetic field will induce a current flowing through the ring. For an ideal system those currents will not meet any resistance and thus will flow indefinitely. However, if the ring is cut or a strong interaction This transition is extensively studied as a Kosterlitz-Thouless transition. A repulsive interaction at half filling will lead to occupancy of every second site (Charge Density Wave) and therefore localized electrons which cannot contribute to a current. between the electrons is present the persistent current will stop. Nevertheless, small interaction strengths or a single change in the coupling strength to one atom with an additional interaction this model is known as the Interacting Resonant Level Model will not affect the persistent current.
These effects can be experimentally investigated and can be easily studied using the Density-Matrix Renormalization Group method

The DMRG combines exact diagonalisation and the renormalisation group approach by Wilson However it even enhances the last method: In each step the model is separated into a system and a environment block where inbetween new sites will be added in one cycle. The decision which states the method will keep can now be enhanced by the density-matrix of statistical physics. Their item gives the probability of the states of the system described by the system block when it is surrounded by different excited systems described by the environment block. Only the most probable are being kept for the later calculation.


The enlarging of the system can be stopped at a certain size. Then even better convergence can be obtained by additional asymmetric sweeping throughout the system, which means increasing the system block while decreasing the environment block and switching their roles at to small / large blocks. For this goal the data collected for small block at the construction of the system can be reused. Therefore the DMRG can investigated much larger systems as the exact diagonalisation, but since only certain energy levels are calculated the evaluation of thermodynamic properties is still part of ongoing research.
an improvement of exact diagonalisation In exact diagonalisation a Hamiltonian, the matrix modelisation of a system, is directly diagonalised to get the energies as diagonal elements (eigenvalues) and wave functions as eigenvectors. However, since the calculation capacity is limit only very small systems can be investigated by this method. and the renormalisation group approach by Wilson The renormalisation group by Wilson can solve infinitely large systems. This is done by stepwise increasing the size of the system and renormalise the system parameter (e.g. coupling constants) at the same time. There the renormalisation is done by neglecting the degree of freedoms of the highly excited system. Since they are not explicitly calculated the memory need to perform the calculation remains finite. The calculation is repeated until convergence is achieved, so to say when the calculated values are not changing any more. .
• S. Kremer, PhD thesis urn:nbn:de:swb:90-241252 (2011)

Fluxphases in high-temperature superconductors

Some experiments conducting on high-temperature superconductors

The structure of these materials is similar to Perovskite (left structure). Therein copperoxyd planes are separated by transition ions which only contribute to the doping in the layers. As seen by experiments these planes dominate the physical properties. The unit cell of the plane consists of two oxygen and one copper atom which might explain the unusual properties of these materials since this feature might enable fluxphases.
are pointing towards a Quantum Phase Transition The concept of QPTs was introduce 1976 by J. Hertz. In contrast to classical phase transitions they only occur at zero temperature. This is the reason why the fluctuation of the order parameter would not follow the classical theory. Instead the quantum statistic is necessary to describe the behaviour.
Systems, in which QPT occur, posses multiple kind of ground states with different physical properties. The transition point between the two phases corresponding to the two ground states is called the quantum critical point (QCP) similar to the classical critical point. Near the QCP the two ground states can quantum mechanical overlap (blue region in the phase diagram) leading to additional, new phases which can be present even at higher temperatures. Therefore, these make it difficult to identify the QCP. Usually cross-over temperatures are obtained (green line in the phase diagram) where some few properties are pointing towards a phase transition, but all the other do not exhibit unusual behaviour.
. While for large doping the material can very well be described by Fermi liquid theory, the second phase of the Quantum Phase Transition remains unknown For very small doping antiferromagnetismus is observed. However since this phase does not overlap with the superconducting phase, this gives rise to another quantum critical point. .
Varma showed 2006 by a mean field calculation, that fluxphases, if they exist, posses a lower energy as the ground state of the Fermi liquid theory. Such phases exhibit circulating electrical currents between the different atoms in the unit cell. Since these are three atoms circulating currents are possible which would not break the translational invariance, which was the reason of other theory consisting of fluxphases to fail.
Fauqué could experimental support this theory by measuring a translational invariant magnetic order within the unit cell, which could result from such a current pattern.
However, while a closer theoretical investigation rebut the idea of currents with in such a unit cell enlarging the unit cell by the attached oxygen atoms outside the copperoxyd plane seem to stabilise such phases.
• S. Kremer, diploma thesis (2007)

• R. Thomale, M. Greiter, Verification of the result by Kremer using exact diagonalisation, Physical Review B 77, 094511 (2008)
• C. M. Varma, Original mean-field theory, Physical Review B 73, 155113 (2006)