Research Group of Professor Carlos Sa de Melo

Quantum Many-body Systems &
Strongly Correlated Fermion Systems

Quantum Phase Transition in Quasi-1-D Organic Superconductor
Project member: Dr. Carlos Sa de Melo, Wei Zhang

The competition or coexistence of magnetic order and superconductivity is a very important problem in condensed matter physics. There is a broad class of systems that present magnetic ordering state and superconducting state in close vicinity. One of the most important systems are the Copper Oxides, where singlet superconductivity is found next to antiferromagnetism. Although striped phases, where coexistence of antiferromagnetic order and singlet d-wave superconductivity, were observed in Copper Oxides, the locally coexisting argument is still a question under debate. Similar situations happends for Strontiun Ruthenate, and Ferromagnetic superconductors [ZrZn2 and UGe2].

For Quasi-1-dimensional organic superconductor [e.g. (TMTSF)2PF6], the same problem involves coexisting / mutually excluded antiferromagnetic and triplet superconducting states near the phase transition line on Pressure-Temperature phase diagram [Cf. Fig.1]. Due to technical difficulties, especially the high critical pressure, experiments have been done around this area only concentrate on transport properties, and without fine tuning of pressure. Spatial scanning or scattering experiments, which will be more suggestive, are still lack.

We discuss the possibility of coexistence of Antiferromagnetism (AF) and triplet superconductor (TS) in a narrow range or pressure. Within this coexisting region, material will form a non-uniform phase with alternating AF and TS stripes (or blocks).

Fig.1 Crystall structure and phase diagram of (TMTSF)2PF6

Phenomenological Approach

We perform a phenomenological approach using extended Ginzburg-Landau (GL) method. We consideri a one dimensional GL free energy including three terms: the AF term, the TS term, and the coupling energy. Due to symmetry argument, the coupling energy will only appear from the quatic term. Thus, we extend the typical GL free energy by expanding up to quatic term of order parameter and their derivatives. If the coupling energy is negative, the system will prefer as many interfaces as possible, then the coexisting region is a non-uniform phase with stripes (could be blocks if we generalize the model to 3 dimension) . Fig. 2 shows the stripes lengths and order parameter amplitudes of AF and TS phases within the coexisting region, and Fig. 3 shows the free energy.

Fig. 2

Fig. 3

Microscopic Description

We will use functional integral method to derive an effective field theory describing the interplay betwen AF and TS orders, and establish conditions for the existence of two quantum critical points in the pressure versus temperature phase diagram.

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