Time Reversal Symmetry Breaking & Charge Ordering in Pseudogap Phase of HTSC

Time Reversal Symmetry Breaking & Charge Ordering in Pseudogap Phase of HTSC
Aharon Khapitulnik, Stanford University

Good morning everybody, the second talk of the morning is by Aharon on time reversal symmetry breaking and charge ordering in the pseudo gap phase of HTSC.

Aharon starts with an intro on Time reversal symmetry, T = i \sigma^y K (K is complex conjugation)

Magneto-optics and T, Kerr effect.

By axial symmetry, the index of refraction for left and right light is related by:

\epsilon_{r,l} = 1 + 4 pi i \sigma_{r,l} \omega^-1

To measure the Faraday effect, they use a Sagnac loop with 2 quarter waveplates to select the circular polarization.

The new feature is the use of interferometry to detect broken rotational symmetry.

Pseudogap Phase in HTSC:

Theory 1. T* represents a cross-over into a state with pre-formed pairs and a d-wave symmetry.

Theory 2. T* marks a true phase transition into a phase with broken symmetry that ends at a QCP, usually within the SC dome.

Recent neutron scattering, Kerr effect and ARPES all show a broken symmetry phase at T*, and the possibilities include a structural phase, electronic nematic, smectic, stripe phase, DDW, etc.

Kerr effect measurement data on YBCO (detwinned):

1. First they cool in high field 5T, and then measure Kerr while warming up at ZF.
2. Kerr effect is seen above T_c, and disappears completely at T_s.
3. The response below T_c is due to trapped vortices, and cooling in ZF eliminates the vortices.
4. Note that the Kerr effect seen below T_c, within the SC phase as well!

Additional experiments on YBCO also signatures of TRSB, including neutron scattering measurements to detect signatures of the Varma loop current state; and resonant ultrasound spectroscopy that measure compression and shear modes, and they see a transition at 280 K and 200 K, which correspond to neutron scattering and Kerr respectively.

Resonant soft X-ray scattering shows 2D charge fluctuations with incommensurate periodicity, and high energy X-ray shows a co-exiting CDW and SC phase in YBCO. This indicates that there is a structural-type transition at a higher temperature with evidence of a short-range CDW state, and then TRSB at a lower temperature T*.

TRSB Data in LSCO:

There is a 1st order transition from LTO to LTT phase measured using birefringence, and when Aharon measures the Kerr effect, he finds a large signal at the LTT phase transition, which peaks at the spin-orbit temperature, and then levels off below T_c, and remains broken in the SC state!

Moreover, there is no training effect for the Kerr, meaning it does not change sign even when we flip the B field. One possibility is that there is TRSB  even at high temperatures, but Aharon will discuss another possibility later.

The zero-field Nernst effect also shows TRSB at the charge-ordering temp, T_co = 54 K, and the Nernst effect is seen also in the SC state, i.e. TRSB in SC state! Ong's group tried to change the sign by heating up to 290 K and then cooling in an opposite B field, but the sign of the Nernst signal remains the same!

ARPES data in Bi2201 also shows evidence of TRSB at T*. The energy position of k_F is the measure at which the pseudogap becomes nonzero below T*, and this agrees with the T-dependent data from Kerr effect.

Aharon has also measured the Kerr effect in HgBa2CuO4, and TRSB is also seen in this system.

Aharon predicts that below T*, a weak charge ordering will be found!

Key Observations:
1. The Kerr effect occurs at the charge-order transition T_co.

2. Possibility of TRSB is being broken at higher temperatures, due to a pre-existing magnetic phase that changes its coupling to the off-diagonal conductivity at T*, and changes due to cystal symmetry changing at T*.

3. Another possibility is that HTSC are magnetoelectric below T*, and below T_co, symmetry is further lowered to acquire AHE effect, and this allows for a finite Nernst effect and Kerr signal.

Free energy, F_{ME} = \alpha_{ij} E_i H_j

4. Comments on Varma Loop-Current state with net moment = 0 in unit cell.

Type 1 Varma state: In-plane loops that breaks T and I(Inversion), but not TI.

Type II Loop current state: Breaks T and C(Chirality), and gives rise to AHE.

Mixed State: Breaks T and Chirality (AHE).

Aharon suggests a Possible Scenario:

At higher T*, there is a Varma loop state, and at T_co a Type II state occurs, giving rise to a mixed state below T_co and thus gives rise to a finite Kerr effect.

Another Scenario: Start with Type I at T*, and at T_co there is canting of the moments that gives rise to a Kerr effect.

Consequence of the magnetoelectric state: This means that there should be no sign of Kerr effect alignment with perpendicular B field, which is what is seen and also in the Nernst effect measurement. Furthermore, there should be the same sign on opposite side of sample, which is also seen in Kerr effect.

Qn: Pierls transition can be measured using derivative of resistance, d \rho/ dT. Was this measured?

Ans:  In Bi2201, yes this was measured and found at the same T* as Kerr effect.

Qn: Is there a possibiltity of a QCP within SC dome?

Ans: Yes, there is a Kerr effect below the SC dome and also evidence from resonant ultrasound sepctroscopy, indicating that this should terminate at a QCP.

Qn: What is the wavelength used in the Kerr effect, and do they have data for different wavelengths?

Ans: Wavelength is 1.55 microns, and they have a new system at 830 nm. But they do not have wavelength-dependent measurements.

Qn: Does the community have a consensus that fluctutations due to TRSB and current loops are the cause of linear-T resistivity?

Ans; No consensus in community on this point yet.

We thank the speaker for a very interesting talk!