Universal thermal and electrical transport near the superconductor-metal quantum phase transition in nanowires

Abstract

We describe the thermal (κ) and electrical (σ) conductivities of quasi-one dimensional wires, across a quantum phase transition from a superconductor to a metal induced by pairbreaking perturbations. Fluctuation corrections to BCS theory motivate a field theory for quantum criticality. We describe deviations in the Wiedemann-Franz ratio κ/σT (where T is the temperature) from the Lorenz number (π 2 /3)(kB/e) 2 , which can act as sensitive tests of the theory. We also describe the crossovers out of the quantum critical region into the metallic and superconducting phases.The Wiedemann-Franz law relates the low temperature (T ) limit of the ratio W ≡ κ/(σT ) of the thermal (κ) and electrical (σ) conductivities of metals to the universal Lorenz number L 0 = (π 2 /3)(k B /e) 2 . This remarkable relationship is independent of the strength of the interactions between the electrons, relates macroscopic transport properties to fundamental constants of nature, and depends only upon the Fermi statistics and charge of the elementary quasiparticle excitations of the metal. It has been experimentally verified to high precision in a wide range of metals [1], and realizes a sensitive macroscopic test of the quantum statistics of the charge carriers.It is interesting to note the value of the WiedemannFranz ratio in some other important strongly interacting quantum systems. In superconductors, which have low energy bosonic quasiparticle excitations, σ is infinite for a range of T > 0, while κ is finite in the presence of impurities [2], and so W = 0. At quantum phase transitions described by relativistic field theories, such as the superfluid-insulator transition in the Bose Hubbard model, the low energy excitations are strongly coupled and quasiparticles are not well defined; in such theories the conservation of the relativistic stress-energy tensor implies that κ is infinite, and so W = ∞ [3]. Li and Orignac [4] computed W in disordered Luttinger liquids, and found deviations from L 0 , and found a non-zero universal value for W at the metal-insulator transition for spinless fermions.The present paper will focus on the quantum phase transition between a superconductor and a metal (a SMT). We will consider quasi-one dimensional nanowires with a large number of transverse channels (so that the electronic localization length is much larger than the mean free path (ℓ)) which can model numerous recent experiments [5,6,7,8,9,10,11,12,13]. We will describe universal deviations in the value of W from L 0 , which can serve as sensitive tests of the theory in future experiments.The mean-field theory for the SMT goes back to the early work [14] of Abrikosov and Gorkov (AG): in one of the earliest discussions of a quantum phase transition, they showed that a large enough concentration of magnetic impurities could induce a SMT at T = 0. It has since been shown that such a theory applies in a large variety of situations with 'pair-breaking' perturbations: anisotropic superconductors with non-magnetic impurities [15], lower-dimensional superco...

Infinite-randomness quantum critical points induced by dissipation

“…30 It can be described by a one-dimensional O(2) LGW theory with Ohmic dissipation. 31,32,33 There is experimental evidence that the pair breaking in this systems is caused by surface magnetic impurities which necessarily also introduce quenched disorder.…”

“…It is worth noting that Del Maestro et al 33 very recently studied the large-N action (3) in one dimension by numerically solving the saddle-point equations. All their results are in beautiful agreement with our predictions, i.e., they confirmed that the quantum critical point is of infinite-randomness type and in the universality class of the random transverse-field Ising model.…”

“…30 The clean version of this transition was studied by means of a one-dimensional LGW theory (1) with a complex order parameter (equivalent to N = 2) and Ohmic dissipation. 31,32 However, there is experimental evidence for the pair breaking in this system being caused by magnetic impurities at the surface of the nanowire. This inevitably introduces quenched disorder due to the random positions of the magnetic impurities.…”

Dynamics of superconducting nanowires shunted with an external resistor

“…Advances in fabricating ultra-narrow superconducting nanowires has greatly boosted the interest in studying phase slippage in quasi-one-dimensional superconductors 2 . There has been an intense activity to establish the existence of quantum phase slips (QPS) related to macroscopic quantum tunneling (MQT) [3][4][5][6][7][8][9][10][11] and to study quantum phase transitions between possibly superconducting, metallic and insulating phases in nanowires 4,[12][13][14][15][16][17] . A dissipation-controlled quantum phase transition [18][19][20][21][22][23][24][25] has been predicted in junctions of superconducting nanowires.…”

Theory of the pairbreaking superconductor–metal transition in nanowires

“…(43)), and find exact agreement. After a rather lengthy calculation it was confirmed that perfect correspondence is also found for the thermal conductivity in this limit (61). The concurrence between the two theoretical approaches in this limit is a result of an approximation made in the diagrammatic calculation involving an infinite sum over a class of ladder diagrams which turns out to be equivalent to the large-N limit taken here.…”