Dimensional reduction at a quantum critical point

Nature Materials, 2013

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. Here, we examine the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO 3 /SrTiO 3 interfaces. Through a finite-size scaling analysis, we show that it belongs to the (2 + 1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals. Moreover, by retrieving the coherence-length critical exponent ν, we show that the quantum critical behaviour can be clean or dirty according to the Harris criterion, depending on whether the phase-coherence length is smaller or larger than the size of the puddles.

Physical Review E, 2020

We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-Einstein condensates, under the action of strong confinement in one direction (z), to a 2D mean-field equation. We address this problem for the confining potential with a singular term, viz., V z (z) = 2z 2 + ζ 2 /z 2 , with constant ζ. A quantum phase transition is induced by the latter term, between the ground state (GS) of the harmonic oscillator and the 3D condensate split in two parallel non-interacting layers, which is a manifestation of the "superselection" effect. A realization of the respective physical setting is proposed, making use of resonant coupling to an optical field, with the resonance detuning modulated along z. The reduction of the full 3D Gross-Pitaevskii equation (GPE) to the 2D nonpolynomial Schrödinger equation (NPSE) is based on the factorized ansatz, with the z-dependent multiplier represented by an exact GS solution of the 1D Schrödinger equation with potential V(z). For both repulsive and attractive signs of the nonlinearity, the 2D NPSE produces GS and vortex states, that are virtually indistinguishable from the respective numerical solutions provided by full 3D GPE. In the case of the self-attraction, the threshold for the onset of the collapse, predicted by the 2D NPSE, is also virtually identical to its counterpart obtained from the 3D equation. In the same case, stability and instability of vortices with topological charge S = 1, 2, and 3 are considered in detail. Thus, the procedure of the spatial-dimension reduction, 3D → 2D, produces very accurate results, and it may be used in other settings.

Physical review letters, 2018

We study the temperature dependence of the electrical resistivity in a system composed of critical spin chains interacting with three-dimensional conduction electrons and driven to criticality via an external magnetic field. The relevant experimental system is Yb_{2}Pt_{2}Pb, a metal where itinerant electrons coexist with localized moments of Yb ions which can be described in terms of effective S=1/2 spins with a dominantly one-dimensional exchange interaction. The spin subsystem becomes critical in a relatively weak magnetic field, where it behaves like a Luttinger liquid. We theoretically examine a Kondo lattice with different effective space dimensionalities of the two interacting subsystems. We characterize the corresponding non-Fermi liquid behavior due to the spin criticality by calculating the electronic relaxation rate and the dc resistivity and establish its quasilinear temperature dependence.

The European Physical Journal B

Proximity to magnetic order as well as low dimensionality are both beneficial to superconductivity at elevated temperatures. Materials on the border of magnetism display a wide range of novel and potentially useful phenomena: high Tcs, heavy fermions, coexistence of magnetism and superconductivity and giant magnetoresistance. Low dimensionality is linked to enhanced fluctuations and, in the case of heavy fermions, has been experimentally shown to be beneficial for the fluctuations that are responsible for the rich abundance of novel emergent phases. This experimental strategy motivated us to explore 2D insulating magnets with a view to investigate phase evolution across metal-insulator and magnetic-non-magnetic boundaries. This has been a fruitful venture with totally novel results different to our expectations. We present results from 2 distinct systems. The MPS3 family are highly anisotropic in both their crystal and magnetic structures. FePS3 in particular is a model insulating honeycomb antiferromagnet. We find that the application of pressure to FePS3 induces an insulator to metal transition. The second system, Cs2CuCl4, is a highly-frustrated quantum spin liquid at low temperature. The competition of the 3 relevant exchange couplings is delicately balanced. It has been shown to become antiferromagnetic at very low temperatures (∼1 K). We have found that the application of pressure for 3 days or more followed by a return to ambient pressure stabilises a totally distinct magnetic ground state.

Physical Review B, 2007

We analyze the spin relaxation time 1/T1 for a system made of weakly coupled one dimensional ladders. This system allows to probe the dimensional crossover between a Luttinger liquid and a Bose-Einstein condensate of magnons. We obtain the temperature dependence of 1/T1 in the various dimensional regimes, and discuss the experimental consequences.

Science, 2004

Physical Review B, 2011

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase can decay into the two-particle continuum. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, this coupling becomes part of the critical theory provided that the lattice ordering wavevector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a non-trivial cubic term arises in the relevant order-parameter quantum field theory, and assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the two-particle decay of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

Physical Review Letters, 2008

We examine the superfluid and collapse instabilities of a quasi two-dimensional gas of dipolar fermions aligned by an orientable external field. It is shown that the interplay between the anisotropy of the dipole-dipole interaction, the geometry of the system, and the p-wave symmetry of the superfluid order parameter means that the effective interaction for pairing can be made very large without the system collapsing. This leads to a broad region in the phase diagram where the system forms a stable superfluid. Analyzing the superfluid transition at finite temperatures, we calculate the Berezinskii-Kosterlitz-Thouless temperature as a function of the dipole angle. PACS numbers: 03.75.Ss,03.75.Hh Trapped ultracold gases are increasingly being used to simulate solid-state systems, where clear experimental signatures of theoretical predictions are often lacking [1].

Physical Review Letters, 2011

We have studied the transition from two to three dimensions in a low temperature weakly interacting 6 Li Fermi gas. Below a critical atom number, N2D, only the lowest transverse vibrational state of a highly anisotropic oblate trapping potential is occupied and the gas is two-dimensional. Above N2D the Fermi gas enters the quasi-2D regime where shell structure associated with the filling of individual transverse oscillator states is apparent. This dimensional crossover is demonstrated through measurements of the cloud size and aspect ratio versus atom number.

We study the magnetic field driven Quantum Phase Transition (QPT) in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through finite size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting islands coupled by a two dimensional electron gas (2DEG). Depending on the 2DEG conductance tuned by the gate voltage, the QPT is single (corresponding to the long range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). By retrieving the coherence length critical exponent ν, we show that the QPT can be "clean" or "dirty" according to the Harris criteria, depending on whether the phase coherence length is smaller or larger than the island size. The overall behaviour is well described by a theoretical approach of Spivak et al., in the framework of the fermionic scenario of 2D superconducting QPT. interest . Indeed, they display very high mobilities suitable for applications , but also a rich phase diagram, with different quantum ground states such as magnetism or superconductivity[9, 10] for example. Moreover, these properties can be finely tuned using a gate voltage . Therefore, O-2DEG appear as interesting systems to study Quantum Phases Transitions (QPT) that occur between different quantum states, when a parameter in the Hamiltonian crosses over a critical value . The critical behaviour of the observables belong to universality classes which depend on general properties of the system such as its dimensionality or its symmetries, and not on the microscopic details. The associated critical exponents obey specific rules, among which the so-called "Harris criteria". The latter stipulates that the correlation length exponent ν must satisfy ν ≥ 2/d for "dirty" disordered systems and ν ≤ 2/d for "clean" ones, where d is the spatial dimensionality[14]. An important example of QPT is the transition from a superconducting to an insulating state in two dimensions, which has been a matter of debate for a long time . Numerous experiments with contrasted results have been performed, and a large variety of critical exponents have been found. The nature of the non-superconducting state and the role of the disorder are still unclear. The possibility of observing multiple QPT has been raised recently . Here we show that a perpendicular magnetic field applied on a superconducting O-2DEG drives the system towards a weakly localized metal. We evidence two QPT corresponding to the "dirty" and "clean" limits of the Harris criteria, which can be controlled by the gate voltage. More precisely, we have shown that the QPT in